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9RBL PRFSFNTBT ONSContents
Overview of the meeting…1

Schedule of the meeting…2

Sep 7 Wed…3

Sep 8 Thu…6

Sep 9 Fri

…9

Posters…12

Traffic…15

Campus map & Lunch…16

General Information…18

Presentation…19

Plenary Session and Award Lecture…20

Plenary Session Abstract…21

Award Lecture Abstract…23

Mini-Symposia

Mini-Symposia Abstract…26

Oral Session

Oral Session Abstract…150

Poster Session

Poster Session Abstract

…205

Index

Participant List

…264

The 2016 (26th) annual meeting of
The Japanese Society for Mathematical Biology
September 7(Wed.) - 9(Fri.), 2016
Shiiki Hall, Ito campus, Kyushu University

Message from Organizing Committee of JSBM2016
Welcome to the 25th annual meeting of Japanese Society for Mathematical
Biology (JSMB2016) at Ito campus, Kyushu University. With over 200
participants, both domestic and overseas, we look forward to plenary lectures,
many symposia, oral and poster sessions.
School of Science, Kyushu University has a long history of research andeducation activities in mathematical biology since early 1970's. Last autumn, we
moved to Ito-campus, located in the west part of Fukuoka city. JSMB2016 is a very
good opportunity to show this new campus to the participants.
We also hope that you enjoy your stay in Fukuoka -- rich with heritage,surrounded by picturesque countryside. Fukuoka is also a modern lively city withmany tourist attractions.
We would like to thank JSMB and Japan Society for the Promotion of Science
for their financial support.
Yoh Iwasa and Shingo Iwami
Co-chairs of the local organizing committee
Organizing Committee

Chairs: Yoh Iwasa, Shingo Iwami(Department of Biology, Faculty of Sciences, Kyushu University)
HP of the Meeting:

http://bio-math10.biology.kyushu-u.ac.jp/jsmb2016/home.html
E-mail:hello.jsmb2016@gmail.com-1-

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JSMB2016 Fukuoka

Graduate School of Medicine, The University ofTokyo
Department of Electrical Engineering andBioscience, Waseda University
University of Tokyo

RIKEN

Advanced Industrial Science and Technology

NIRS, QST

Nagoya University

The Graduate University for Advanced Studies

Department of Evolutionary Studies of Biosystems,
SOKENDAI
Department of Electrical Engineering andBioscience , Waseda University
Dept of Biosci Bioinfor, Kyushu Inst of Tech

Kyoto University

Kyushu University

Department of Electrical Engineering andBioscience, Waseda University
Math. Sci. group, AIMR, Tohoku Univ.

Graduate School of Arts and Sciences, The
University of Tokyo
Graduate School of Information Science Nagoya
University
Department of Evolutionary Studies of Biosystems,
SOKENDAI (The Graduate University for Advanced
Studies)
Kyoto University

Naoki Nakada

Shinji Nakaoka

Seiya Nishikawa

Takayuki Hiraoka

Kentaro Inoue

Masashi Kamo

Isao Kawaguchi

Masahiko Higashi

Mariko Ito

Mitsuhiro Nakamura

Junpei Okuno

Chikoo Oosawa

Hemma Philamore

Motohide Seki

Shohei Utsunomiya

Fumiko Ogushi

Shota Shibasaki

Masanori Tsuchiya

Yu Uchiumi

TakahiroYamagishi

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

11232 265

Department of Electrical Engineering andInformation Systems, The University of Tokyo
Aoyama gakuin university

40

Kazumasa Kaneko

6265- 12 -

Joint Evolution of cytoplasmic male sterility and selfing rate in plant

An agent-based evolutionary model for diversification of phenotypic plasticity andpersonality in resource partitioning
Evolution of vertical transmission of symbionts by reducing the rate of cell division

The evolutionary game in sexual reproduction of the social amoeba

Optimality and evolutionary stability of life histories with stages for culturaltransmission of information
Diversity of behavioral preference on cooperative transport in ants reduces obstacle
passing time
A mean-field analysis of the simple model of evolving open systems

Trophallaxis for Swarms of Energy-Scavenging Artificial Organisms.

Gathering animals by escaping

Foraging strategy using multi-tentacles in plasmodial slime moldLearning processes and matching behavior in domestic chicks foraging

A Coevolution Model of Individual and Social Learning in a Rugged Fitness
LandscapeEmergence of opinion leaders in reference networks

Mathematical model approach to understand abscopal effect with radiotherapy.

Explanation of non-additive effects in mixtures of similar mode of action chemicals

Mathematical model for NF-kB signal transduction system

Computational modeling of three-dimensional cell migration

Fate after ‘cell competition’ depending on initial states in tumor-suppressor system

Mathematical modeling and analysis of cancer immunotherapy: exploring the effectof cytokine mediated communication among T and NK cells
Development of a computational grammar for immune cell processes

Modeling and inferring dynamics of T cell population in thymus.2 30 61 769 08 780905

JSMB2016 Fukuoka

Kyushu University

University of Hokkaido

The Graduate University for Advanced Studies(Sokendai)
Nara Women's University

Nara Women's University

Ryukyu Sankei Co., Ltd.

The University of Tokyo

School of Human Science andEnvironment,University of Hyogo
National Institute for Environmental Studies

Hokkaido University

Hiroshima University

Tokyo University of Marine Science andTechnology
Department of Electrical Engineering andBioscience,Waseda University
National Institute of Informatics

Nara Women's University

Yusuke Ito

Nao Yamamoto

Kenta Yashima

Shiori Abe

Miki Hamada

Ikegawa Yusuke

Takahiro Irie

Nariyuki Nakagiri

Kenta Suzuki

Takenori Takada

Takahiro Hiraga

Shigehide Iwata

Kodai Sato

Takuya Sekiguchi

Mayumi Seto

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

11232 265

Aoyama University

40

Nobuyuki Ishizuka

6

265- 13 -

How population clusters predict the
population growth in Japan
Cost-benefit analysis of food safety management: The case of radioactive
contaminantzone planning for emergency evacuation using Physarum algorithm

The catch control by the allocation of number of boat

Mathematical study of the rising movement and its support from the chair

Population statistics of random matrices

Resilience of hydrothermal vent communities: a metacommunity framework

Effects of spatial and temporal homogeneity of releases of sterile insects on controlof pests with limited dispersal ability
A hierarchical Bayesian estimation of wild population size from the neutral genetic
information
Nest plate model for spacial effects and simulation of honey bees

Spatial SIS model as a point pattern dynamics

How Does Correlation between Condom Use and Partner Type Influence theTransmission Dynamics of STI?
Network centrality measure based on sensitivity analysis of the basic reproductive
ratio
Population viability analysis of the Japanese rock ptarmigan

Estimating the number of HIV-1 to infect target cells in nonrandom co-infection

Analysis of Lymph tissues network model of HIV infection dynamics.2 30 61 769 08 780905

JSMB2016 Fukuoka

RIKEN (Nishina Center / iTHES)

Kyushu University

Kyoto Prefectural University of Medicine

The univ. of Tokyo

Botanical Gardens, Graduate School of Science,
The University of Tokyo
Theoretical Biology Laboratory, RIKEN

Noriaki Ogawa

Naoto Shingu

Hiroto Shoji

Suguru Yaginuma

Takaaki Yonekura

Yoshinori Hayakawa

Kazuya Horibe

Osamu Iizuka

-

-

-

-

-

-

-

-

-

RIKEN QBiC

Theoretical Biology Laboratory, RIKEN

Department of Developmental Biology, Shimane
University Faculty of Medicine
Kyushu University

Kyushu University

Kyushu University

Kyushu University

Tokyo University of Science

Doshisha Univ.

Institute of Industrial Science, The University ofTokyo
Institute of Industrial Science, The University ofTokyo
Kyushu University

Sang-Woo Lee

Fumito Mori

Shigeru Moriyama

Yuto Naroda

Toshiki Oguma

Daiki Sasaki

Hisako Takigawa-Imamura

Emiko Ishiwata

Kohkichi Kawasaki

Yohei Saito

Yuki Sughiyama

Kousaku Kitagawa

-

-

-

-

-

-

-

-

-

-

-

-

Osaka University Graduate School of Information
Science and Technology
Kyushu University

Doshisha Univ.

Masatomo Matsushima-

11232 265

National Institute for Basic Biology

40

Hironori Fujita

6

265- 14 -

Multiscale model of HCV infection and its reduction to ODE

Steady State Thermodynamics in Population Dynamics

Exact traveling wave solution with minimum speed for nonlinear reaction-diffusion
equation and its properties
Discreteness-induced transition in multi-body reaction systems

Emergence of hierarchical structure of lung: a model and observation of cellularresponse to FGF
Effect of time delay for an ultra-discretized logistic equation

The effect of cell dynamics on Delta-Notch pattern formation during retinal
angiogenesis
Mathematical Modeling for Meshwork Formation of Endothelial Cells in Fibrin Gel

Mathematical representation and analysis of the number of cells in the intestinal
epithelium of mouse embryos
Mathematical analysis of fractality of skull sutures

Origin of cell diversity: Analysis of fixed points in Boolean networks

Neutral cell competition and tissue growth efficiency

Mechanism of Scaling law formation in developing retina vasculature

Mathematical study of gene expression and morphogenesis coupling that realizes
flat leaf formation
Curvature-driven splitting of a planar traveling wave

Analysis of orixate phyllotactic pattern with expanded Douady and Couder's model

Searching for 'ROP reaction system' which realizes Turing Pattern

Mathematical analysis for aging effects of endothelial cells on their self-organizedpattern size.
Physical Analysis of Branching Patterns of Sinusoidal Networks in Hepatic Lobule

Dynamical Pattern Selection of Growing Cellular Mosaic in Fish Retina

Classifying of synchronization pattern in oscillator circuits with optical signal

Pattern density control in Turing systems.2 30 61 769 08 780905

JSMB2016 Fukuoka

- 15 -

HakataShiiki Hall (Ito Campus, Kyushu Univ.)

Walk

Kyudai BigOrange mae (Bus Stop)

Showa bus going to "Kyudai-sougou ground"

JR Kyudaigakkentoshi Station

JR Chikuhi Line (Transfer or Through)Nishitetsu Express Bus
going to"Kyudai-sougou ground"

Tenjin Kita
(Bus Stop)

TenjinJR Hakata Station(Bus Stop)

Fukuoka City Subway & JR
Meinohama Station

Fukuoka City Subway
Tenjin Station

Fukuoka City Subway
Hakata Station

Fukuoka City Subway Kuko Line

Fukuoka City Subway
Fukuoka Airport Station

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JSMB2016 Fukuoka

Stairsm- 16 -

Galleria

Stairs

1st floor
South lobbyWC

1st floor
North lobby

WC

WC

WC

2F

WC

WC

WC

Break room is open while
1st floor
Sep 7 (Wed) 13:00 – 18:00
South lobby
Sep 8WC(Thu) 13:00 – 18:00
Sep 9 (Fri) 09:00 – 15:00

Break room

WC

WC

Galleria

Stairs

1st floor
North lobby

Stairs

1st floor

1F

StairsStairsReception desk

2nd floor
South lobby

StairsStairs2nd floor
North lobby Stairs

Outdoor stairs

2nd floor

A

E

Shiiki Hall

WC

WC

B

D

C

3rd floor

WC

WC

C

Plenary talkAward lecture
Board meeting
General meeting

D(304)A(301), C(303)

B

D

Oral session

A

E

B(302), D(304), E(305)

StairsStairsMini-symposia

2nd floor
East lobby

Poster exhibit area

3F

JSMB2016 Fukuoka

- 17 -

Restaurant andConvenience store

Big Dora

Parking

E-cafe (rest space)

West Zone

Bus stop
Kyudai Kougakubu mae
20 minutes walk from the hall

Academic Lantern(Coop restaurant)&

Parking

Library

Convenience store

To Kyudai Gakken-Toshi
Station5 minutes walk from the hall

Big SandBus stop (get it on only)
Kyudai Center Zone iriguchi

Restaurant (Coop) and convenience store

Center Zone

Bus stop
Kyudai Big Orange mae

Restaurant, Mos Burger, Tully’s coffee
and Convenience store
10 minutes walk from the hall

Big Leaf

15 minutes walk from the hall

Chinese Restaurant
Ten-TenShiiki Hall

JSMB2016 Fukuoka

JSMB2016 Fukuoka

General Information
Rooms

There are five rooms in Shiiki Hall:
A (301), B (302), C (303), D (304), E (305)lSymposiums take place in room B, D and E.

lOral Sessions take place in room A and C.

l

Poster Sessions take place in room during launch time; 12:15 ‒ 14:00 on
Wednesday 7th and Thursday 8th September.

ID

Mini-symposia and oral sessions:
7

A

1

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Presentation
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1Your order in thesessionPosters: P-(number)
BanquetDate: Thursday, September 8
Venue: 博多百年蔵 (Hakata Hyakunenngura)
博多百年蔵 Website (in Japanese): http://www.ishikura-shuzou.co.jp/
Introduction of the venue

博多百年蔵 (Hakata Hyakunenngura) is a great Japanese sake brewery built
in 1870, the only one in Hakata city. It is a familiar place to Hakata residents, due
to its traditional style of brewing Japanese sake, as well as the building of historicalvalue. We hope that participants will join us for a delicious dinner and wonderfultime at 博多百年蔵 (Hakata Hyakunenngura).
For vegitarians

We plan to prepare a vegetarian menu.

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JSMB2016 Fukuoka

Presentation
Symposium

1.

All talks in symposia will be delivered in English.

2.

Organizers should manage their symposium at their own responsibility.

3.

PC for presentations is not prepared. Please bring your own PC.

4.

Display connecters of projectors are VGA. If the output of your PC is not
VGA, please bring an appropriate display adapter.

Oral Presentation

1.

In order to encourage attendance of non-Japanese researchers, presentationles must be prepared in English. We also strongly recommend speakers to talkin English.

2.

Each talk must be delivered within 20 min, including questions andcomments.

3.

PC for presentations is not prepared. Please bring your own PC.

4.

Display connecters of projectors are VGA. If the output of your PC is not
VGA, please bring an appropriate display adapter.

5.

Please test your projection before your session starts.

Poster Presentation

1.

Posters must be prepared in English. We also strongly recommend presenters
to explain in English.

2.

Posters are numbered. Core times of odd and even numbered posters are
12:15 ‒ 14:00 on Sep 7 and 8, respectively.

3.

Please display before lunch time on Sep 7. To examine posters for prize, keep
your poster displayed until 17:15 on Sep 8, then remove your poster before
14:00 on Sep 9.

4.

Please keep in mind that posters left at the place will be discard by theorganizing committee.

Poster Award

Prizes will be awarded for the best posters.

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JSMB2016 Fukuoka

Special session
Plenary Talk
Award Lecture- 20 -

Plenary Talk
Sep 7 Wed
JSMB2016 Fukuoka
Mark Rees
Sheffield University
e-mail: m.rees@sheffield.ac.uk

Evolutionary Demography an Integral Projection Approach
Integral projection models (IPMs) project a continuously structured population, where say individuals
are characterized by their size, in discrete time. An overview of the application of IPMs to field populations
will be given covering 1) model parameterization in both constant and stochastic environments, 2)
populations where multiple traits influence an individual’s fate (e.g. size and age), and 3) density
dependence. The use IPMs to understand the evolution of traits in natural populations will then be explored.
In these IPMs individuals are characterized by traits that vary over the organism’s life, such as size and age,
and invariant traits, such as genotype or breeding value. Methods of approximating the dynamics of boththe mean and variance of the genotype/breeding value distribution will be presented. Methods forembedding quantitative genetics models into IPMs will be presented and used to explore the timing of
reproduction in two plant populations. These models will be used to explore the maintenance of genetic
variability in natural populations.

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Plenary Talk
Sep 7 Wed
JSMB2016 Fukuoka
Miles Davenport
Centre for Vascular Research, University of New South Wales, Sydney, Australia.
e-mail: m.davenport@unsw.edu.au

Modeling “latent” Infection
When we think of infection, we usually think of active replication of a virus or parasite, causing illness.
However, some infections can lie sleeping (latent) for many years before they re-activate to cause a newactive infection. Understanding how infections become latent, and how they reactivate from latency, is
important to controlling infection. Because it is not easy to measure the latent (sleeping) infection, modelingis needed to study how infection reactivates. This talk will discuss modeling applied to experimental datafrom patient and animal studies to better understand the dynamics of latency in HIV infection.
REFERENCES[1] Pinkevych M, Cromer D, Tolstrup M, Grimm AJ, Cooper DA, Lewin SR, Søgaard OS, Rasmussen TA, Kent SJ,
Kelleher AD, Davenport MP.HIV Reactivation from Latency after Treatment Interruption Occurs on Average Every
5-8 Days--Implications for HIV Remission.PLoS Pathog. 2015 Jul 2;11(7):e1005000.
[2] Reece J, Petravic J, Balamurali M, Loh L, Gooneratne S, De Rose R, Kent SJ, Davenport MP.An "escape clock"for estimating the turnover of SIV DNA in resting CD4⁺ T cells.PLoS Pathog. 2012;8(4):e1002615.

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Award Lecture
Sep 8 Thu
JSMB2016 Fukuoka
Takeshi Kano
Research Institute of Electrical Communicatione-mail: tkano@riec.tohoku.ac.jp

Toward Understanding of the Decentralized Control Mechanism
Underlying Adaptive Locomotion of Animals
In this presentation, I talk about my research activities up to now, mainly focusing on the decentralized
control mechanism underlying animal locomotion.
Animals exhibit adaptive, versatile, and resilient locomotion under unpredictable and unstructured realworld constraints. They achieve such movements by successfully coordinating many points along theirbodies, each of which has some degrees of freedom, even though their computational resources are limited.
A key mechanism for the coordination of many body points is an autonomous decentralized control,
whereby the non-trivial macroscopic behavior or functionality of an entire system emerges through thecoordination of simple individual components. In fact, several biological findings indicate that animal
locomotion depends on autonomous decentralized control mechanisms such as biochemical oscillators intrue slime molds [1] and central pattern generators (CPGs) found in many animals [2].
We are trying to understand the decentralized control mechanism of various animals by using a synthetic
approach: we propose a mathematical model based on the observation of real animals, and then we
implement the propose mechanism in a robot to reproduce the locomotion of real animals. I introduce ourrecent results based on this approach, particularly focusing on the locomotion of snakes and ophiuroids[3,4].
REFERENCES[1] Takamatsu, A., Tanaka, R., Yamada, H., Nakagaki, T., Fujii, T., and Endo, I., 2001. Spatio-temporal Symmetry inRings of Coupled Biological Oscillators of Physarum Plasmodium, Phys. Rev. Lett., 87: 078102.
[2] Ijspeert, A.J., 2008. Central Pattern Generators for Locomotion Control in Animals and Robots: A Review, Neural
Networks, 21: 642–653.
[3] Kano, T., Sato, T., Kobayashi, R., and Ishiguro, A., 2012. Local Reflexive Mechanisms Essential for Snakes'
Scaffold-based Locomotion, Bioinsp. Biomim., 7: 046008.
[4] Kano, T., Sato, E., Aonuma, H., Matsuzaka, Y., and Ishiguro, A., 2014. Mathematical Model of Inter-arm
Coordination Mechanism of Ophiuroids, JSMB/SMB 2014.

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Award Lecture
Sep 8 Thu
JSMB2016 Fukuoka
Yukihiko Nakata
Department of Mathematics, Shimane University
e-mail: ynakata@riko.shimane-u.ac.jp

Analysis and applications of delay equations in mathematical epidemiology
Mathematical description of disease transmission dynamics often yields a nonlinear infinitedimensional dynamical system ([1]). Many important mathematical theories for infectious diseases
dynamics have been developed [2]. However, the waning immunity is a major challenge for mathematicalmodeling and analysis. We present our recent studies for epidemiological models with waning immunity[3]. Here we also discuss delay equation formulation in the spirit of Lotka’s renewal equation. We thenintroduce an application of delay differential equations for modeling periodical outbreak of a childhood
disease [4].
REFERENCES[1] W.O. Kermack, A.G. McKendrick, A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond.
B Biol. Sci. 115 (1927) 700-721[2] O. Diekmann, H. Heesterbeek, and T. Britton, Mathematical tools for understanding infectious disease dynamics.
Princeton University Press, (2012)[3] Y. Nakata, Y. Enatsu, H. Inaba, T. Kuniya, Y. Muroya, Y. Takeuchi, Stability of epidemic models with waning
immunity. SUT J. Math. Vol. 50, No. 2 (2014), 205–245[4] R. Omori, Y. Nakata, H. L. Tessmer, S. Suzuki, K. Shibayama, The determinant of periodicity in Mycoplasma
pneumoniae incidence: an insight from mathematical modelling. Scientific Reports 5, 14473 (2015)- 24 -

Award Lecture
Sep 8 Thu
JSMB2016 Fukuoka
Takeshi Miki
Institute of Oceanography, National Taiwan University
Research Center for Environmental Changes, Academia Sinica
tksmiki@ntu.edu.tw

Multiple modeling approaches for better understanding the roles of microbial
diversity in community and ecosystem dynamics.
Microbial diversity in natural environments had been not observable for long time but microbial
ecology and environmental microbiology have identified microbial diversity in the last two decades.
General ecology also has just started investigating in-situ roles of microbial diversity, not only for using
microbial community as model system. Major research interests include the roles of microbial communityand diversity as the determinant of fitness of other organisms and their diversity through interactions, e.g,
those between microbes and plants, their impacts on ecosystem functions (i.e. biogeochemical processes
such as carbon and nutrient cycling), and community and ecoststem stability. In this presentation, after
briefly summarizing my past studies on the roles of microbial community (bacteria and fungi) in plant-soil
feedback in terrestrial ecosystems, I’m going to talk on recent achievements and developing ideas for better
understanding the roles of bacterial diversity in ecosystem functions and their stability.
With a series of mathematical models, we have investigated the roles of microbes in the plant-soil
feedback system where plant community alters soil abiotic and biotic environment that in turn affects plant
growth, competition, and thus community and ecosystem dynamics. A model of two plant-two microbe
species coupled with nutrient cycling demonstrated the roles of microbial diversity in buffering speciesspecific plant control on soil environments, and thus maintaining plant coexistence [1]. The buffering effectwas later supported by the microcosm experiment. A model of the stage-structured plant population coupledwith two distinct microbial functional groups (parasitic and mutualistic ones) demonstrated that different
plant traits are the key determinants of plant fitness under the dominance of parasitic or mutualistic
microbes, which could also explain the empirical pattern [2]. We have also reviewed the past achievementin the field of plant-soil feedback from the point of mathematical modeling [3].
For better understanding the roles of bacterial diversity in the maintenance of ecosystem functioning
in aquatic ecosystems, we are developing an integrated framework that combines comparative genomic
analysis, microcosm experiments, and model simulations [4]. The key index to predict the decline of
ecosystem functionality due to species loss is called ‘functional redundancy’, i.e., how many functions areshared by coexisting species within a community. Our new approach succeeded in evaluating the functional
redundancy through species loss simulation using whole genome information of bacteria, which canquantitatively explain the results from microcosm experiments. On-going study extends this framework fordeveloping new indices to predict functional stability of ecosystem, as well as the magnitude of ecosystem
functions. Finally, I will briefly address the importance of developing new statistical methods to quantify
microbial functions, which will be the main topic in my presentation at the mini symposium “Mathematicaland statistical modeling to bridge the gap between empirical and theoretical research in ecology” on Sep.
9.
REFERENCES[1] T. Miki*, Masayuki Ushio, Shin Fukui, Michio Kondoh. (2010) Functional diversity of microbial decomposers facilitates plant
coexistence in a plant-microbe-soil feedback model. Proceedings of the National Academy of Sciences, USA 107:14251-14256[2] Po-Ju Ke, Takeshi Miki*, Tzung-Su Ding (2015) The soil microbial community predicts the importance of plant traits in plantsoil feedback. New Phytologist DOI: 10.1111/nph.13215[3] Po-Ju Ke*, Takeshi Miki (2015) Incorporating the soil environment and microbial community into plant competition theory.
frontiers in Microbiology http://dx.doi.org/10.3389/fmicb.2015.01066[4] Takeshi Miki, Taichi Yokokawa, Kazuaki Matsui* (2014) Biodiversity and multifunctionality in a microbial community: a novel
theoretical approach to quantify functional redundancy. Proceedings of The Royal Society B vol.281 no.1776 20132498- 25 -

JSMB2016 Fukuoka

Mini-Symposium Abstract- 26 -

7B1-S1 (Special)
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka

Special Symposium
Sep 7, 9:00 – 10:30, Room B
Complexity and coexistence of population in simple ecological systems
Organizer(s):Malay Banerjee
Associate professor of IIT Kanpur, Editorial Advisory board member of EcologicalComplexity, Department of Mathematics and Statistics, Kanpur - 208016, INDIA
e-mail: malayb@iitk.ac.in
Yasuhiro TAKEUCHI
Aoyama Gakuin University, College of Science and Engineering, Department of
Physics and Mathematics, Fuchinobe, ChuoKu, Sagamihara-shi, Kanagawa, 2525258, Japane-mail: takeuchi@gem.aoyama.ac.jp

Lotka-Volterra (LV) model is fundamental in population dynamics. The two-species LV model admits
no isolated periodic orbits. It is known the three-species LV model can exhibit periodic and even chaotic
dynamics (2 prey, one-predator case and prey-predator with intra-guild predation by the top predator). If
we modify two-species LV type prey-predator by adopting Holling type II functional response, the model
can have a periodic solution but the appearance of large amplitude limit cycles leads to the paradox ofenrichment. Recently several interesting bifurcation scenarios have been found when the logistic growthfor prey is substituted with growth including Allee effect. The purpose of the symposium is to summarize
the complex dynamics known in simple population models and how the modification of functional responseor the growth with Allee effect or inclusion of maturation delay can change the bifurcation scenario. Also
we discuss on the effect given by these modifications on the stable coexistence and persistence of
population.
Time

Title & Presenter

09:00 – 09:30

Coexistence of predators in simple ecological systems of intra-guild predation
Toshiyuki Namba (Department of Biological Science, Graduate School of Science,
Osaka Prefecture University)

09:30 – 10:00

Maturation delay for the predators can enhance stable coexistence in preypredator model with Allee effectYasuhiro Takeuchi (Department of Physics & Mathematics, College of Science &Engineering, Aoyama Gakuin University)

10:00 – 10:30

Maturation delay can stabilize the prey-predator dynamics
Malay Banerjee (Department of Mathematics & Statistics, IIT Kanpur)- 27 -

7B1-S1-1
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Toshiyuki Namba
Department of Biological Science, Graduate School of Science, Osaka Prefecture University, Sakai, 5998531 JAPANe-mail: tnamba@b.s.osakafu-u.ac.jp

Coexistence of predators in simple ecological systems of intra-guild predation
Prey-predator interactions are the basic building block of food-webs and food-chains. In a simple
three-species module of intraguild predation, one of the two predators sharing common resources feeds
on the other and three predator-prey interactions are included. Therefore, types of the functional
responses and strengths of the interactions have significant effects on stability and persistence of thesystem.
In ecology, there is a controversial issue in a system of intraguild predation; Classical theory
predicts that the intraguild prey goes to extinction at high productivity, but empirical observations do notsupport the prediction. In this talk, I will propose two hypotheses which can resolve the contradiction,using models with the functional responses of type II or type III. Importance of the relative profitability of
two types of prey for the intraguild predator and the complex oscillations appearing through nonlinearityof the interactions will be emphasized.
REFERENCES[1] Holt, R.D., and Polis, G.A., 1997. A theoretical framework for intraguild predation. American Naturalist,
149:745–764.
[2] Tanabe, K., and Namba, T., 2005. Omivory creates chaos in simple food web models. Ecology, 86: 3411–3414.
[3] Namba, T., Tanabe, K., and Maeda, N., 2008. Omnivory and stability of food webs. Ecological Complexity, 5: 7385.

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7B1-S1-2
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Yasuhiro Takeuchi
Department of Physics & Mathematics, College of Science & Engineering, Ayoama Guykin University,
Kanagawa, JAPAN
Malay Banerjee
Department of Mathematics & Statistics, IIT Kanpur, Kanpur, INDIA
e-mail: malayb@iitk.ac.in

Maturation delay for the predators can enhance stable coexistence in preypredator model with Allee effectWe consider a prey-predator model with Allee effects in prey growth and Michaelis-Menten typefunctional response to describe the grazing pattern. We obtain the conditions for stable and oscillatory
coexistence of prey and their specialist predator in case of strong and weak Allee effect in prey growth.
Main objective of the present work is to show the stabilizing role of maturation delay in the presence ofAllee effect in prey growth. We construct the delayed model by incorporating maturation delay parameterand juvenile predators death rate into the growth equation of predators. Apart from the analytical results
for the non-delayed and delayed models, we perform extensive numerical simulations to construct therelevant bifurcation diagrams. We provide the biological implications of the current investigation in detailat the conclusion section.
REFERENCES[1] Banerjee, M. and Takeuchi, Y., 2016. Maturation delay for the predators can enhance stable coexistence in preypredator model with Allee effect. (under review).

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7B1-S1-3
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Malay Banerjee
Department of Mathematics & Statistics, IIT Kanpur, Kanpur, INDIA
e-mail: malayb@iitk.ac.in
Yasuhiro Takeuchi
Department of Physics & Mathematics, College of Science & Engineering, Ayoama Guykin University,
Kanagawa, JAPANMaturation delay can stabilize the prey-predator dynamics
Prey-predator type interaction model is the basic building block for several types of food-webs andfood-chains. Two component prey-predator models are capable to exhibit a wide variety of complex
dynamics which have relevance with the ecological phenomena we observe in real world ecosystems. There
are several types of modeling approaches to construct the relevant models and analyze them to understandthe system dynamics. It is well-known that delay differential equation models with such type of interactions
are capable to produce oscillatory dynamics due to the introduction of delay in ordinary differential
equation models. As a result it is common to believe that the delay is responsible for the destabilization of
the system dynamics. This talk is intended to describe the construction of delayed prey-predator model withmaturation delay and analysis of the complete model reveals that the delay can also stabilize the system
dynamics. Furthermore, we emphasize that the construction of delayed model with appropriate ecologicalassumptions cannot always predict the destabilization although the incorporation of delay is ecologicallyjustified. Conclusions are drawn based upon the analysis of two prey-predator model with Allee effect, onewith prey-dependent functional response and another with ratio-dependent functional response.
REFERENCES[1] Banerjee, M. and Takeuchi, Y., 2016. Maturation delay for the predators can enhance stable coexistence in preypredator model with Allee effect. (under review).
[2] Sen, M., Banerjee, M. and Morozov, A., 2014. Stage-structured ratio-dependent predator-prey models revisited:
When should the maturation lag results in systems' destabilization? Ecological Complexity, 19: 23–34.

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7D1-S2
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 7, 9:00 – 10:30, Room D
Structure-based control of complex network systems
Organizer(s):Atsushi Mochizuki
Theoretical Biology Laboratory, RIKEN, 2-1 Hirosawa, Wako 351-0198, JAPANe-mail: mochi@riken.jp

Controlling complex biological systems is one of the most important missions in basic biology andmedical science. Especially in regenerative medicine, it is strongly required to establish non-empiricalmethods to regenerate cells or tissues artificially. Experimental methods have provided large information
on interactions between bio-molecules. However, such network information is not sufficient to specify
detail of the dynamics of systems. Recently, different theoretical methods were proposed independently,
by which rational criteria to choose key nodes for controlling whole systems are given from structure of
networks alone. In this symposium, we invite advanced researchers studying theoretical methods to control
complex network systems. We discuss mathematical and practical aspects of these methods, and consider
possible improvement and collaborations between different methods.
Time

Title & Presenter

09:00 – 09:20

Minimum Dominating Set-Based Approaches for Controlling and Analyzing
Biological Networks
Tatsuya Akutsu (Kyoto University, Japan)

09:20 – 09:40

Tipping point in networked dynamical systems: control, recovery, and early
warnings
Ying-Cheng Lai (Arizona State University, USA)

09:40 – 10:00

Cell fate reprogramming by control of intracellular network dynamics
Jorge Gómez Tejeda Zañudo (Pennsylvania State University, USA)

10:00 – 10:20

Controlling regulatory networks by feedback vertex sets
Atsushi Mochizuki (RIKEN, Japan)- 31 -

7D1-S2-1
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Tatsuya Akutsu
Bioinformatics Center, Institute for Chemical Research, Kyoto University
e-mail: takutsu@kuicr.kyoto-u.ac.jp

Minimum Dominating Set-Based Approaches for Controlling and Analyzing
Biological Networks
Extensive studies have recently been done on structural controllability of complex networks. Different
from the well-studied approach based on bipartite matching, we have been studying an approach based on
the minimum dominating set (MDS), where MDS is a well-known concept in graph theory and has been
applied to analysis and control of engineering systems. We showed that if nodes in MDS are selected ascontrol nodes and each of these nodes can control its connecting edges independently, the system isstructurally controllable [1]. We also showed via theoretical analysis and computer simulation that the moreheterogeneous a network degree distribution is, the easier it is to control the entire system [1]. Since thenwe have been extending this MDS-based approach as follows [2].
(1) Since many networks have bipartite network structure such as drug-disease networks and ncRNAprotein networks, we extended the MDS-based approach to bipartite networks in which controls are given
for nodes in only one side.
(2) Jia et al. introduced the concepts of critical and redundant nodes in the maximum matching-based
approach to controllability of complex networks. We applied these concepts to the MDS-based approachin both unipartite and bipartite networks.
(3) We introduced the robust MDS using which a network remains structurally controllable against
arbitrary failures of up to a constant number of communication links (i.e., edges).
MDS has also been applied to analysis of various kinds of biological networks by us and by several
other research groups, which include protein-protein interaction networks, drug-target protein network,
non-coding RNA-protein network, and cancer metabolic network [2]. In this talk, we overview these
extensions and applications of the MDS-based approach. This talk is based on joint work with Jose Nacher
in Toho University.
REFERENCES[1] Nacher, J.C. and Akutsu, T., 2012. Dominating scale-free networks with variable scaling exponent:
heterogeneous networks are not difficult to control. New Journal of Physics, 14:073005.
[2] Nacher, J.C. and Akutsu, T., 2016. Minimum dominating set-based methods for analyzing biologicalnetworks. Methods, 102:57-63.

- 32 -

7D1-S2-2
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Ying-Cheng Lai
Arizona State University, USAe-mail: Ying-Cheng.Lai@asu.edu

Tipping point in networked dynamical systems: control, recovery, and early
warnings
A variety of complex dynamical systems, ranging from ecosystems and the climate toeconomic, social, and infrastructure systems, can exhibit a tipping point at which an
abrupt transition to a catastrophic state occurs. To understand the dynamical propertiesof the system near a tipping point, to predict the tendency for the system to drift toward
it, to issue early warnings, and finally to apply control to reverse or slow down the trend,
are outstanding and extremely challenging problems. We consider two empirical bipartite
mutualistic networks of pollinators and plants from the real world and investigate theissues of control, recovery, and early warning indicators. In particular, both networks
exhibit a tipping point as a parameter characterizing the population decay changes
continuously, at which the system collapses suddenly to zero abundance for all the species.
We articulate two control strategies: (a) maintaining the abundance of a single influential
pollinator and (b) eliminating the factors contributing to the decay of the pollinator. In
both cases, we find that control can turn the sudden collapse into a more gradual process
in the sense that extinction of the species occurs sequentially with variation of theparameter, indicating that control can effectively delay the occurrence of global extinction.
We then investigate population revival as the bifurcation parameter varies in the opposite
direction away from the tipping point. Without control, there is a hysteresis loop whichindicates that, in order to revive the species abundance to the original level, the parameter
needs to be further away from the tipping point, i.e., the environment needs to be fitter
than before the collapse. However, with control the hysteresis behavior diminishes,suggesting the positive role of control in facilitating species revival. The issue of early
warnings is also addressed. To develop effective control strategies to prevent the systemfrom drifting towards a tipping point is an unsolved problem at the present, and we hope
our work can shed light on the challenging and significant problem of understanding andcontrolling tipping point dynamics in nonlinear and complex systems.
This is a joint work with Mr. Junjie Jiang (PhD student at Arizona State University), Prof.
Zigang Huang (Lanzhou University), Prof. Wei Lin (Fudan University), Prof. Tom
Seager (Arizona State University), and Prof. Celso Grebogi (University of Aberdeen).

- 33 -

7D1-S2-3
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Jorge G. T. Zañudo
The Pennsylvania State University. Department of Physics. University Park, Pennsylvania, USA.
Dana-Farber Cancer Institute. Boston, Massachusetts, USA
Broad Institute of MIT and Harvard. Cambridge, Massachusetts, USA.
e-mail: jgtz@phys.psu.edu
Réka Albert
The Pennsylvania State University. Department of Physics. University Park, Pennsylvania, USA.
The Pennsylvania State University. Department of Biology. University Park, Pennsylvania, USA.

Cell fate reprogramming by control of intracellular network dynamics
Practical applications in modern molecular and systems biology, such as the search for new therapeutictargets for diseases and stem cell reprogramming, have generated a great interest in the cell fate
reprogramming, i.e., controlling the internal state of a cell so that it is driven from an initial state to a final
target state. Although the topic of controlling the dynamics of a system, of which cell fate reprogramming
can be considered a subset, has a long history in control and systems theory [1, 2], most of this work is notdirectly applicable to intracellular networks. Among the main reasons for this are the nonlinear nature of
intracellular dynamics and the lack of consideration of biologically admissible states [3]. Furthermore, mostcontrol methods rely solely on the structural or the functional information available for a system, and thus,
do not take advantage of the full range of biological information available for intracellular networks.
Here we present a network control method that integrates the structural and functional information available
for intracellular networks to predict control targets [4]. Formulated in a logical dynamic scheme [5, 6], ourcontrol method takes advantage of certain function-dependent network components, referred to as stablemotifs [7], and their relation to steady states, in order to identify targets whose manipulation (upregulationor downregulation) ensures the convergence of the system towards or away from a steady state of interest.
Among the noteworthy properties of our approach are that it drives any initial state to the target state with
100% effectiveness and needs to be applied only transiently for the network to reach and stay in the desired
state [4]. We illustrate our method's potential to find intervention targets for cancer treatment and celldifferentiation by applying it to a leukemia signaling network [8] and to the network underlying theepithelial-to-mesenchymal transition in liver cancer [9]. We show that stabilizing the expression or activityof a few select components in these models can drive the cell towards a desired fate or away from anundesired fate. Moreover, we confirm the validity of the predicted control targets in a differential equation
version of the tested models and also find the predicted interventions are supported by experimental work,
thus suggesting our control targets are effective in a broad dynamic sense. Overall, our approach provides
new insights into how to control the dynamics of intracellular networks.
REFERENCES[1] Luenberger DG (1979) Introduction to Dynamic Systems: Theory, Models, and Applications. Wiley.
[2] Slotine JJ, Li W (1991) Applied Nonlinear Control. Prentice-Hall.
[3] Müller FJ and Schuppert A (2011) Few inputs can reprogram biological networks. Nature 478, E4.
[4] Zañudo JGT, Albert R (2015) Cell Fate Reprogramming by Control of Intracellular Network Dynamics. PLoS
Comput Biol 11(4): e1004193.
[5] Morris MK, Saez-Rodriguez J, Sorger PK, and Lauffenburger DA (2010). Logic-based models for the analysis ofcell signaling networks. Biochemistry 49, 3216–24.
[6] Wang RS, Saadatpour A, and Albert R (2012). Boolean modeling in systems biology: an overview ofmethodology and applications. Physical Biology 9, 055001.
[7] Zañudo JGT and Albert R (2013) An effective network reduction approach to find the dynamical repertoire of
discrete dynamic networks. Chaos 23 (2), 025111. Focus Issue: Quantitative Approaches to Genetic Networks.
[8] Zhang R, Shah MV, Yang J, et al. (2008) Network Model of Survival Signaling in LGL Leukemia. PNAS 105,
16308–16313.
[9] Steinway SN, Zañudo JGT, Ding W, et al. (2014) Network Modeling of TGFβ Signaling in Hepatocellular
Carcinoma Epithelial-to-Mesenchymal Transition Reveals Joint Sonic Hedgehog and Wnt Pathway Activation.
Cancer Research 74 (21), 5963–77.

- 34 -

7D1-S2-4
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Atsushi Mochizuki
Theoretical Biology Laboratory, RIKEN, Japan
CREST, JST, Japane-mail: mochi@riken.jp
Bernold Fiedler
Department of Mathematics, Free University of Berlin, Germany
Yutaka Satou
Graduate School of Science, Kyoto University, Japan
Kazuki Maeda
School of Science and Technology, Kwansei Gakuin University, Japan

Controlling regulatory networks by feedback vertex sets
Modern biology provides many networks describing regulations between a large number of speciesof bio-molecules. It is widely believed that the dynamics of molecular activities based on such regulatory
networks are the origin of biological functions. In this study we present a mathematical theory to provide
an important aspect of dynamics from information of regulatory linkages alone. We also present anapplication of our theory to a real biological network, and experimental results to verify our prediction.
In theoretical part, we show that the "feedback vertex set" (FVS) of a regulatory network is a set of"determining nodes" of the dynamics. It assures that i) any long-term dynamical behavior of the wholesystem, such as steady states, periodic oscillations or quasi-periodic oscillations, can be identified bymeasurements of a subset of molecules in the network, and that ii) the subset is determined from theregulatory linkage alone. The theory also claims that iii) dynamical behavior of the whole system can beswitched from one attractor to others just by controlling the dynamics of the FVS.
In experimental application, we analyzed a gene regulatory network including 90 genes, which is
responsible for cell differentiation in early development of ascidian. We identified five genes in minimum
FVS of the network. We conducted a series of experiments to control activities of these five genes to verify
our prediction. The exhaustive artificial activation/inhibition of five genes showed that the system of cellfate determination could be controlled totally just by controlling activities of five genes in FVS.
REFERENCES[1] Mochizuki, A., Fiedler, B., Kurosawa, G. and Saito, D., 2013. Dynamics and control at feedback vertex sets. II: A
faithful monitor to determine the diversity of molecular activities in regulatory networks. J. Theor. Biol., 335, 130146.
[2] Kobayashi, K., Maeda, K., Tokuoka, M., Mochizuki, A. and Satou, Y. In Preparation.

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7E1-S3
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 7, 9:00 – 10:30, Room E
Biological oscillations at diverse spatiotemporal scales
Organizer(s):Takayuki Ohara
Graduate School of Environmental Science, Hokkaido University, N10W5, Kita-ku,
Sapporo 060-0810, Japane-mail: t.ohara.63920@ees.hokudai.ac.jp
Akiko Satake
Department of Biology, Faculty of Science, Kyushu University, 744, Motooka, Nishiku, Fukuoka 819-0395, Japane-mail: akiko.satake@kyudai.jp

Periodic or chaotic oscillations are observed in diverse biological phenomena at different
spatiotemporal scales ranging from gene expression to mass flowering of forests.
These rhythmic phenomena are directly connected with the fitness of organisms, e.g. rhythmic
patterns of plant starch metabolism to avoid carbon starvation.
In this session, recent findings about biological oscillations at different scales including cellularcircadian rhythms of plants and mammals, growth patterns of plant tissue, and synchronization of plant
reproduction will be presented.
The purpose of the session is (i) to provide the audiences with diverse topics of biological rhythms,and (ii) to develop our understanding of the oscillation phenomena by sharing different viewpoints obtained
from the studies of distinct spatiotemporal scales.
Time

Title & Presenter

09:00 – 09:25

The plant circadian clock as a multi-oscillator system
Tomoaki Muranaka (Nagoya University)

09:25 – 09:45

Phase response of circadian clocks optimizes the growth of Arabidopsis thaliana
Takayuki Ohara (Hokkaido University)

09:45 – 10:10

GABA-mediated phasesuprachiasmatic nucleus
Sungho Hong (OIST)

10:10 – 10:30

Parameterization and validation of a resource budget model for masting using
spatiotemporal flowering data of individual trees
Akiko Satake (Kyushu University)

couplings- 36 -

andseasonaltime

codinginthe7E1-S3-1
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Tomoaki Muranaka
Graduate School of Science, Nagoya University
e-mail: muranaka.tomoaki@c.mbox.nagoya-u.ac.jp
Tokitaka Oyama
Graduate School of Science, Kyoto University

The plant circadian clock as a multi-oscillator system
The circadian clock is the endogenous timing system based on self-sustained oscillations. In
eukaryotes, the circadian clock is implemented in individual cells as a gene regulatory oscillator. Thus, thecircadian system of multicellular organisms should be understood as a multi-oscillator system. For thispurpose, the observation of circadian rhythms at a cellular level is essential. Recent bioluminescenceimaging techniques using mammalian cells revealed noisy and heterogeneous circadian rhythms in isolated
cells and tight coupling between neurons in the suprachiasmatic nucleus, the master clock organ.
In plants, a tendency of independence in behaviors of cellular clocks has been demonstrated. Previous
studies reporting the intra-tissue desynchronization of circadian rhythms indicated the heterogeneous traitsof cellular clocks and the weakness of cell-to-cell coupling. However, fundamental properties of the cellular
clock, such as instability, heterogeneity, and the manner of cell-to-cell interaction, remain unclear becauseof the difficulty of monitoring the circadian gene expression in individual cells.
To address this problem, we developed a single-cell bioluminescence imaging system using
duckweeds [1]. In this system, a circadian reporter, AtCCA1::LUC, was introduced into cells located nearupper surface of a plant body by particle bombardment. Then the luminescence from transfected cells that
dispersed on the same frond (leaf-like structure) was monitored by a high-sensitive CCD camera. The tiny
and flat body of duckweeds was remarkable advantages for a long-term imaging of the entire body.
Using this system, we monitored cellular circadian rhythms under various light conditions for morethan a week [2]. Under constant light conditions, each cellular rhythm was maintained but
desynchronization between cells in the same frond was observed. Quantitative analysis of theseasynchronous rhythms uncovered the heterogeneity and instability of cellular clocks and partial
synchronization between neighboring cells. The extents of heterogeneity and instability of plant cellular
clocks were comparable to those of cultured fibroblast cells of mouse. Then we exposed the plants at an
asynchronous state to the external light-dark cycles. Cellular rhythms at any phase were synchronized tolight-dark cycles within a couple of days. Interestingly, the luminescence traces in the first dark period wasdepended on their onset phases, suggesting that cellular clocks in the same tissue individually responded tothe dark signal. Furthermore, we found that cellular clocks in the plant body under light-dark cycles showeda centrifugal phase pattern. Because there was no such spatial pattern in free-running periods of them, thelocked phase of each cellular clock depended on its position rather than its free-running period.
Collectively, our studies revealed that cellular circadian clocks in intact plants work individually asheterogeneous oscillators under constant conditions and that the heterogeneity is corrected under light-darkcycles to coordinate the daily rhythms of the plant body. These findings provide a novel perspective on
spatiotemporal architectures in the plant circadian system.
REFERENCES[1] Muranaka, T., Kubota, S. and Oyama, T., 2013. A single-cell bioluminescence imaging system for monitoring
cellular gene expression in a plant body. Plant Cell Physiology, 54: 2085-2093[2] Muranaka, T. and Oyama, T., 2016. Heterogeneity of cellular circadian clocks in intact plants and its correction
under light-dark cycles. Science Advances, 2: e1600500- 37 -

7E1-S3-2
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Takayuki Ohara
Graduate School of Environmental Science, Hokkaido University, Sapporo, Japane-mail: t.ohara.63920@ees.hokudai.ac.jp
Akiko Satake
Department of Biology, Faculty of Science, Kyusyu University, Fukuoka, Japan

Phase response of circadian clocks optimizes the growth of Arabidopsis thaliana
Circadian clocks are internal pacemakers of living organisms that coordinate their physiology andmetabolism to periodically changing environment. In higher plants, diverse biological processes such as
flowering and gene expression are under the control of the circadian clocks [1]. Recent experimental studies
have showed that growth rates of leaves and roots of Arabidopsis thaliana diurnally oscillate [2,3], whichsuggest the circadian regulation of the plant growth. One of the important characteristics of the circadianclocks is the regulation of their phase by external stimuli such as light and sugar [4]. In our previous study,
we have showed that the phase response of plant circadian clocks to sugar signals reduces the variations of
sucrose concentration [5]. This means that plants can avoid the situation where the amount of sucrose
extremely decreases, i.e. starvation of sucrose occurs. In pgm mutants, which are not able to accumulate
starch, sucrose largely fluctuates throughout a day, and depletes at night [6]. Moreover, the growth of pgm
mutants is severely impaired compared with wild type plants [7]. These observations suggest that sucrose
starvation causes the reduction of the plant growth. Taken together, there is a possibility that the phase
response to sugar signals leads to the stable growth of plants.
In this study, we investigate the effect of the phase response of circadian clocks on the plant growth.
We first construct the mathematical model describing the sugar dynamics in source leaves and sink tissues.
In source leaves, sugar is produced by photosynthesis and is exported to growing sink tissues. In sink tissues
such as root or young leaves, sugar is supplied from sources and is spent for growth. Carbon metabolism
in the source region is regulated by the circadian clocks. In addition, based on the pressure flow hypothesis,
we model the sucrose translocation between the source and the sink on the basis of the Hagen-Poiseuillelaw. Regarding the plant growth, we assume that the growth of sink tissues is proportional to the amountof sucrose existing in each sink and the growth is inhibited when the amount of sucrose falls below thethreshold level of sucrose. We then simulate the long-term growth patterns of wild type plants and mutants,
which are insensitive to sugar signals, in the presence of annual changes of day lengths. Based on thecomparison of the growth patterns, we discuss whether the phase response of circadian clocks is effectivein the achievement of the stable growth in the natural environment.
REFERENCES[1] Harmer, S.L., 2009. The circadian system in higher plants. Annu. Rev. Plant Biol., 60: 357–377.
[2] Wiese, A., Christ, M.M., Virnich, O., Schurr, U. and Walter, A., 2007. Spatio-temporal leaf growth patterns ofArabidopsis thaliana and evidence for sugar control of the diel leaf growth cycle. New Phytologist, 174: 752–761.
[3] Yazdanbakhsh, N., Sulpice, R., Graf, A., Stitt, M. and Fisahn, J., 2011. Circadian control of root elongation and C
partitioning in Arabidopsis thaliana. Plant Cell Environ., 34: 877–894.
[4] Haydon, M.J., Mielczarek, O., Robertson, F.C., Hubbard, K.E. and Webb, A.A.R., 2013. Photosynthetic
entrainment of the Arabidopsis thaliana circadian clock. Nature, 502: 689–692.
[5] Seki, M., Ohara, T., Hearn, T.J., Frank, A., da Silva, V.H., Caldana, C., Webb, A.A.R. and Satake, A., in
preparation.
[6] Gibon, Y., Bläsing, O.E., Palacios-Rojas, N., Pankovic, D., Hendriks, J.H.M., Fisahn, J., Höhne, M., Günther, M.
and Stitt, M., 2004. Adjustment of diurnal starch turnover to short days: depletion of sugar during the night leads to atemporary inhibition of carbohydrate utilization, accumulation of sugars and post-translational activation of ADPglucose pyrophosphorylase in the following light period. Plant J., 39: 847–862.
[7] Caspar, T., Huber, S.C. and Somerville, C., 1985. Alterations in growth, photosynthesis, and respiration in a
starchless mutant of Arabidopsis thaliana (L.) deficient in chloroplast phosphoglucomutase activity. Plant Physiol.,79: 11–17.

- 38 -

7E1-S3-3
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Sungho Hong
Computational Neuroscience Unit, Okinawa Institute of Science and Technology
e-mail: shhong@oist.jp
Jihwan MyungLaboratory for Mental Biology, RIKEN Brain Science Institute

GABA-mediated phase couplings and seasonal time coding in the suprachiasmatic
nucleus
The fundamental processes underlying the function and behavior of most life forms on Earth, such as
plants and animals, are locked in a circadian rhythm that is synchronized with the 24-hour cycle of lightand darkness. Furthermore, organisms can adapt the rhythm to changes in this cycle, such as seasonalvariation in day length, which is crucial for survival.
I will present our recent findings [1] that can explain how the suprachiasmatic nucleus (SCN), a masterclock for the circadian rhythm in the brain [2], can memorize and encode information about daylength. We
have found that GABA-mediated signaling, which is dominant in the SCN neural circuit, organizes 24hour rhythmic activity of gene expression networks within individual neurons into an oscillator network.
Crucially, the network structure has asymmetrically distributed phase repulsive (desynchronizing) andattractive (synchronizing) couplings, and this leads to a unique computational property that can explain
various features of the SCN dynamics and circadian behavior. Furthermore, the daylength-dependent shift
in the balance between two different couplings, which can explain seasonal changes in the SCN oscillators
and animal’s circadian behavior, comes from the changes in GABAergic signaling due to plasticity incellular mechanisms regulating intracellular chloride.
We suggest that these results show that the SCN is a memory for circadian information in the brain,governed by the tunable balance between excitation and inhibition in its neural circuit that regulates thebalance between repulsive and attractive phase couplings within the network of gene expression oscillators.
REFERENCES[1] Myung J, Hong S, DeWoskin D, De Schutter E, Forger DB, Takumi T. 2015. GABA-mediated repulsive coupling
between circadian clock neurons in the SCN encodes seasonal time. Proc Natl Acad Sci USA 112:E3290-9.
[2] Welsh DK, Takahashi JS, Kay SA. 2010. Suprachiasmatic Nucleus: Cell Autonomy and Network Properties.
Annu Rev Physiol 72: 551–577.

- 39 -

7E1-S3-4
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Akiko Satake
Department of Biology, Faculty of Science, Kyusyu University, Fukuoka, Japane-mail: akiko.satake@kyudai.jp
Tomoyuki Abe
Hirokazu Kon
Akiko Nagasaka
Kensuke Onodera
Kazuhiro Minamino
Hokkaido Research Organization, Forestry Research Institute, Higashiyama, Koshunai, Bibai 079-0198,
Japan.
Yuuya Tachiki
Department of Biology, Faculty of Science, Kyusyu University, Fukuoka, Japan
Qingmin Han
Department of Plant Ecology, Forestry and Forest Products Research Institute, Tsukuba 305-8687,
Japan.

Parameterization and validation of a resource budget model for masting using
spatiotemporal flowering data of individual trees
Synchronized and fluctuating reproduction by plant populations, called masting, is widespread indiverse taxonomic groups. Proximally, many studies have suggested significant links between masting andclimatic variables, such as temperature, the temperature difference in the two previous seasons and rainfall.
Conversely, effects of internal factors such as carbon and nitrogen have been demonstrated to play animportant role in the regulation of masting. These ecological findings for proximate factors of masting are,at least for the flowering process, consistent with recent findings from the molecular genetic studies offlowering time that indicate that requirements from both climatic cues and resource availability must be
satisfied for a plant to switch from vegetative growth to flowering. Although the way climate factors
influence seed production is not well understood, the interplay between climatic factors and resource
dynamics could be found in the process of seed ripening that determines the quantity of mature seedproduction because seasonal precipitation and temperature influence plant nitrogen and carbon availability.
Therefore, we need to study coupled effects of climatic factor and internal resource dynamics on masting[1].
A family of resource budget models would be an ideal tool to evaluate the coupled effect of climatic
factors and resource availability on masting [2]. Here, we propose a new method to explore the proximate
mechanism of masting by combining spatiotemporal flowering data, biochemical analysis of resource
allocation, and the resource budget model [3]. Flowering data of 170 trees over 13 years showed theemergence of clustering with trees in a given cluster mutually synchronized in reproduction, which was
successfully explained by resource budget models that consider dynamic allocation of carbon or nitrogen
resources for reproduction [4]. Analysis of resources invested in the development of reproductive organs
showed that parametric values used in the model are significantly different between nitrogen and carbon.
Using a fully parameterized model, we showed that the observed flowering pattern is explained only when
the interplay between nitrogen dynamics and climatic cues was considered. This result indicates that ourapproach successfully identified resource type-specific roles on masting and that the method is suitable fora wide range of plant species.
REFERENCES[1] Monks, A., Monks, J.M. & Tanentzap, A.J. 2016. Resource limitation underlying multiple masting models makes
mast seeding sensitive to future climate change. New Phytologist, 210, 419-430.
[2] Crone, E.E. & Rapp, J.M. 2014. Resource depletion, pollen coupling, and the ecology of mast seeding. Ann. N.Y.
Acad. Sci., 1322, 21-34.
[3] Satake, A. & Iwasa, Y. 2000. Pollen coupling of forest trees: forming synchronized and periodic reproduction outof chaos. J. Theor. Biol., 203, 63-84.
[4] Abe, T, Tachiki, Y., Kon, H., Nagasaka, A., Onodera, K., Minamino, K., Han, Q., Satake, A. 2016. Parameterizationand validation of a resource budget model for masting using spatiotemporal flowering data of individual trees. Ecology
Letter DOI: 10.1111/ele.12651.

- 40 -

7B2-S4
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 7, 10:45 – 12:15, Room B
Cancer Modeling
Organizer(s):Hiroshi Haeno
Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japane-mail: haeno@kyushu-u.org

In the field of cancer research, the demand of mathematical and theoretical analysis has recently been
increasing. Based on tons of genomic data and tumor growth data with/without drugs, lots of mathematicaland statistical models have been investigated for revealing the theory of cancer dynamics and evolution. In
this symposium, we will present the up-to-date mathematical models of cancer based on experimental andclinical data and spread the opportunities that theoretical researchers study cancer.
Time

Title & Presenter

10:45 – 11:08

The evolution of tumor metastasis during clonal expansion with alterations inmetastasis driver genes
Hiroshi Haeno (Kyushu University)

11:08 – 11:30

Cancer risk of Japanese Atomic bomb survivors: challenge in radiation
epidemiology to investigate radiation carcinogenesis
Munechika Misumi (Radiation Effects Research Foundation)

11:30 – 11:53

A unified framework to model induced stem cell - a case study of generalized
multi-type branching process and beyond
Lin L. Liu (Harvard University)

11:53 – 12:15

Computational Modeling of Individualized Management in Pancreatic
Adenocarcinoma
Kimiyo N. Yamamoto (Kyushu University)- 41 -

7B2-S4-1
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Hiroshi Haeno
Department of Biology, Kyushu University
e-mail: haeno@kyushu-u.org

The evolution of tumor metastasis during clonal expansion with alterations inmetastasis driver genes
Metastasis is a leading cause of cancer-related deaths. Carcinoma generally initiates at a specific organ
as a primary tumor, but eventually metastasizes and forms tumor sites in other organs. In this report, wedeveloped a mathematical model of cancer progression with alterations in metastasis-related genes. In cases
in which tumor cells acquire metastatic ability through two steps of genetic alterations, we derive formulas
for the probability, the expected number, and the distribution of the number of metastases. Moreover, weinvestigate practical pancreatic cancer disease progression in cases in which both one and two steps ofgenetic alterations are responsible for metastatic formation. Importantly, we derive a mathematical formulafor the survival outcome validated using clinical data as well as direct simulations. Our model provides
theoretical insights into how invisible metastases distribute upon diagnosis with respect to growth rates,(epi)genetic alteration rates, metastatic rate, and detection size. Prediction of survival outcome using theformula is of clinical importance in terms of determining therapeutic strategies.

- 42 -

7B2-S4-2
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Munechika Misumi
Department of Statistics, Radiation Effects Research Foundatione-mail: misumi@rerf.or.jp

Cancer risk of Japanese Atomic bomb survivors: challenge in radiation
epidemiology to investigate radiation carcinogenesis
The Life Span Study (LSS) of the Radiation Effects Research Foundation (RERF) has long been a
primary resource for evaluation of health risks associated with exposure to ionizing radiation. Radiation
risks are usually described by a parametric regression model in the LSS [1]. However, there are issues withimposing a parametric assumption on the dose-response, such as unrealistic uncertainty estimates due tothe parametric constraint. If we are uncertain of the exact shape of the dose-response, a linear function
passing through the origin provides unrealistically narrow confidence intervals especially in low dose range.
Also, the risk estimate based on a simple linear dose-response function is strongly influenced by cases withhigh dose, which are actually very few in the LSS cohort due to the highly skewed distribution of radiation
dose. In estimating the uncertainty based on a non-parametric function, such messages reflecting the realityof the data were revealed [2]. In addition to the radiation dose-response, the variables that modify theradiation risk have also traditionally been modeled with parametric functions which are used to describe
risk. With regard to this conventional parametric modeling, there was a concern about risk estimates near
the limits of ranges of the data. We recently applied a multi-dimensional smoothing for the radiation excess
relative risk (ERR), simultaneously smoothing with respect to the dose and the modifiers of the radiation
effect, such as age at exposure, to loosen the parametric constraints on the age trends of ERR with theresults graphically described [3]. That method enabled us to have better insights about the risks of low dose
exposure at young ages, which are of general public concern. However, in investigating and understanding
radiation carcinogenesis, we are facing a big challenge with statistical limitations related to small effectsize in the low radiation dose range.
REFERENCES[1] Preston D, Ron E, Tokuoka S, Funamoto S, Nishi N, Soda M, Mabuchi K, Kodama K. Solid cancer
incidence in atomic bomb survivors: 1958-1998. Radiat Res 2007; 168: 1-64.
[2] Furukawa K, Misumi M, Cologne JB, Cullings HM, A Bayesian Semiparametric Model for Radiation
Dose-Response Estimation., Risk Analysis, 2016 Jun;36(6):1211-23.
[3] Misumi M, Furukawa K, Multi-dimensional smoothing for age trends of radiation effects on the cancer
risk of Japanese Atomic bomb survivors, unpublished.

- 43 -

7B2-S4-3
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Lin L Liu
Department of Biostatistics, Harvard University
e-mail: lliu.hsph@gmail.com

A unified framework to model induced stem cell - a case study of generalized
multi-type branching process and beyond
Reprogramming of somatic cells to induced pluripotent stem cells (iPSCs) is a promising tool for
novel therapeutic strategies in cancer research. A fundamental question that biologists working on iPSCs
often ask is whether the reprogramming process is deterministic or stochastic. A variety of physical models
have been employed to study such process as attempts to answer such question, albeit none of the previous
works were analyzed altogether in a unified and interpretable mathematical framework. With such goal inmind, we modeled the system using generalized multi-type branching processes that can help us dissect thevariability observed in the experiments into process-intrinsic noise (stochasticity in random
proliferation/apoptosis/cell fate transition) and process-extrinsic noise (such as variability among cells or
measurement noise). We found that reprogramming driven by the Yamanaka factors alone is aheterogeneous process due to cell-specific reprogramming rates, which can be homogenized by the additionof additional factors. We also validated our approach using all publicly available induced reprogrammingtime-series data with different types of information recorded, such as the distribution of some vague formof first passage time, direct cell counts and etc., and thus demonstrated the general utility and predictive
power of our methodology for investigating reprogramming and other cell fate change systems. If time
permits, I will also briefly talk about some other ongoing projects related to therapeutic optimization incancer and models on antibody stimulation in cancer vaccine and germinal center reaction based on
knowledge gained very recently on the newly discovered follicle regulatory T cells in the germinal center.

- 44 -

7B2-S4-4
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Kimiyo N. Yamamoto
Department of Biology, Kyushu University
e-mail: kyamamoto@kyushu-u.org

Computational Modeling of Individualized Management in Pancreatic
Adenocarcinoma
Pancreatic ductal adenocarcinoma (PDAC) is one of the leading causes of cancer-related mortality.
To treat patients with this malignancy most effectively, we propose individualizing management based ona mathematical framework validated by clinical data from two independent institutes. The computationalmodel considers alterations in specific genes – KRAS, CDKN2A, TP53, and SMAD4. The model well
represents the dynamics of PDAC regarding metastatic patterns, response to medical interventions, and thegenetic evolution. Importantly, we succeed in identifying a potential predictive factor indicating a subgroupof patients with low metastatic efficiency. The marker is universally applicable throughout the range of
detected sizes of tumors. From computational clinical trials with the predictive factor, we reveal that the
selected subgroup obtains its best benefits from (i) complete resection, (ii) adjuvant chemoradiation therapy,and (iii) salvage treatment for isolated recurrence. Our computational approach provides insights into
clinical decision making in PDAC.

- 45 -

7D2-S5
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 7, 10:45 – 12:15, Room D
Network and Timeline: Recent Topics in Complex Networks
Organizer(s):Takaaki Aoki
Faculty of Education, Kagawa University
e-mail: aoki@ed.kagawa-u.ac.jp
Satoru Morita
Department of Mathematical and Systems Engineering, Shizuoka University
e-mail: morita.satoru@shizuoka.ac.jp

The purpose of this symposium is to bring together some new topics in network science, which are
expected to be associated with mathematical biology. We will discuss possibility of new models of temporal
networks, adaptive networks and epidemics on networks．
Time

Title & Presenter

10:45 – 11:05

Burst behavior and scale-free network emerging in adaptive temporal Networks
Takaaki Aoki (Kagawa University)

11:05 – 11:25

Controlling the emergence of event cascades in inhomogeneous networks
Tomokatsu Onaga (Kyoto University)

11:25 – 11:45

On uncertainty of epidemic spreading in complex networks
Taro Takaguchi (National Institute of Information and Communications Technology)

11:45 – 12:05

Comparison among several types SIS epidemic models on networks
Satoru Morita (Shizuoka University)

12:05 – 12:15

Discussion- 46 -

7D2-S5-1
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Takaaki Aoki
Kagawa University
e-mail :aoki@ed.kagawa-u.ac.jp

Burst behavior and scale-free network emerging in adaptive temporal Networks
The spread of information in society depends on communication networks between people. These
networks are characterized by both structure, i.e. who is connected to whom, and by temporal patterns, i.e.
the times when communication actually occurs. The increasing availability of large high-resolution data on
human behavior revealed that these networks follow non-trivial structural and temporal patterns, such
Bursting behavior of social contact patterns and the scale-free structure of social networks.
To study these patterns on human communication, previous research has treated structure and timings
as different phenomena, even though they both originate from communication. From the physics
perspective, we address a fundamental question that is to find a unified process able to reproduce both
structural temporal patterns, telling us more on the nature of human dynamics. We propose a model basedon a feedback between communication of information and adaptive network behavior that explains the
emergence of structural and temporal patterns as observed in real-life.
In statistical physics, particles interact with each other and exchange energy. Our intuitive model,
motivated by kinetic theory, considers that many interacting individuals exchange hypothetical resourcesthat in turn regulate their own activation rate. We show that this model exhibits distinct behavior,reminiscent of real-life communication, by simply varying a control parameter, similarly to changes oftemperature in kinetic theory.
This relatively simple and theoretically tractable physics model of stochastic processes opens up
several opportunities to better understand human communication by using methods of statistical physics.
REFERENCES[1] Takaaki Aoki, Luis E. C. Rocha, and Thilo Gross, 2016. Temporal and structural heterogeneities emerging in
adaptive temporal networks. Physical Review E Rapid Communication, 93, 040301(R) .

- 47 -

7D2-S5-2
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Tomokatsu Onaga
Department of Physics, Kyoto University, Kyoto 606-8502, Japane-mail: onaga@scphys.kyoto-u.ac.jp
Shigeru Shinomoto
Department of Physics, Kyoto University, Kyoto 606-8502, Japan

Controlling the emergence of event cascades in inhomogeneous networks.
There is a commonality among contagious diseases, tweets, and neuronal firings that past events
facilitate the future occurrence of events. A key quantity representing the interaction in these various
phenomena is the basic reproduction ratio, which is defined as the average number of additional events
induced by a single event. The spread of events has been extensively studied such that the systems exhibit
catastrophic chain reactions if the interaction represented by the ratio of reproduction exceeds the epidemic
threshold [1]. In epidemics, a disease becomes a pandemic if the reproduction ratio is greater than theepidemic threshold, as in a nuclear chain reaction, and vanishes otherwise. Nevertheless, the eventoccurrence does not cease if individuals are stimulated in external communities or exhibit spontaneous
activity. In such situations, the system may still exhibit cascades of event-occurrences intermittently, even
if the reproduction ratio is smaller than the epidemic threshold, as in tweets and neuronal firings in vivo.
Here, we report that these systems are possessed by nonstationary cascades of event-occurrences
already in the subthreshold regime [2]. Event cascades can be a nuisance in some contexts, such as when
the peak-demand causes vaccine shortages or heavy traffic on communication lines, but may be beneficial
in other contexts; for example, spontaneous activity in neural networks may be used to generate motion orstore memory [3]. Thus it is important to comprehend the mechanism by which such cascades appear, andconsider controlling a system to tame or facilitate fluctuations in the event-occurrences. We use epidemic
Markov process and Hawkes process to analyze event cascades and derive the condition in which eventcascades emerge. The critical interaction for the emergence of cascades depends greatly on the network
structure in which individuals are connected. We demonstrate that we can predict whether cascades may
emerge, given information about the interactions between individuals. Furthermore, we suggest asystematic method for controlling systems to oppress or promote the event cascades. Accordingly we foundthat reciprocal connections and clustering tends to facilitate event cascades.
REFERENCES[1] Pastor-Satorras, R., Castellano, C., Van Mieghem, P. and Vespignani, V., 2015. Epidemic processes in complex
networks. Rev. Mod. Phys., 87: 925.
[2] Onaga, T. and Shinomoto, S., 2014. Bursting transition in a linear self-exciting process. Phys. Rev. E, 89:
042817.
[3] Sussillo, D., Abbott, L. F., 2009. Generating coherent patterns of activity from chaotic neural networks. Neuron,63(4): 544-557.

- 48 -

7D2-S5-3
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Taro Takaguchi
National Institute of Information and Communications Technology
Global Research Center for Big Data Mathematics, National Institute of Informatics
JST, ERATO, Kawarabayashi Large Graph Projecte-mail: taro.takaguchi@nict.go.jp

On uncertainty of epidemic spreading in complex networks
Threat of epidemic spreading in societies partly stems from the uncertain nature of its behavior. The
uncertainty has been taken into account in mathematical modeling of spreading process by means of
stochastic processes [1]. On the other hand, recent theoretical studies proved that a characteristic measureof epidemics converges to a deterministic function in a long-term limit [2]. We investigated this transition
from stochastic to deterministic behavior on the basis of numerical simulations. The main results presented
in this talk are based on the collaboration work [3] with Petter Holme (Sungkyunkwan University, Korea).
In addition, we will discuss a future direction on predicting epidemics beyond model simulations by using
additional information sources.
REFERENCES[1] Romualdo Pastor-Satorras, Claudio Castellano, Piet Van Mieghem, and Alessandro Vespignani, 2015. Epidemic
processes in complex networks. Review of Modern Physics, 87: 925.
[2] Svante Janson, Malwina Luczak, and Peter Windridge, 2014. Law of large numbers for the SIR epidemic on arandom graph with given degrees. Random Structures & Algorithms, 45: 724-761.
[3] Petter Holme and Taro Takaguchi, 2015. Time evolution of predictability of epidemics on networks. PhysicalReview E 91: 042811.

- 49 -

7D2-S5-4
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Satoru Morita
Shizuoka University
e-mail: morita.satoru@shizuoka.ac.jp

Comparison among several types SIS epidemic models on networks
Spreading phenomena are ubiquitous in nature and society. For example, disease and information
spread over underlying social and information networks. Recently, spreading processes on scale-free
networks have been intensively studied. In scale-free networks the distribution of degree obeys a powerlaw, and high degree nodes are called hubs. It has been well known that the hubs can lead to the absence ofan outbreak threshold. In the previous work [1], I introduced six types of SIS models on scale-free networks,
where the links represent potential connections. It is assumed that a node is activated at random. Then, theactivated node can contact its nearest neighbors on the network. Two possibilities for transmission are
considered: an activated node is (a) the sender or (b) the receiver. I also consider the hybrid case (c): an
active node plays both roles. In the previous work, I considered the two cases: (1) all neighbors or (2) only
one neighbor is contacted at the same time. Thus, by combining the transmitting and contacting types, sixmodels are constructed.
Here, I extend the models in the previous work and consider the case that activated individual contacts
only one neighbor, but the rate of activation depends on the degree. Thus, the power exponent of the degree
distribution can be different from that of the distribution of the contact number. I explore the equilibrium
solution and calculate the outbreak threshold by using degree-based mean-field theory. I confirm that thefeatures of prevalence depends on the details of contact and propagation mechanism.
REFERENCES[1] Satoru Morita, Six Susceptible-Infected-Susceptible Models on Scale-free Networks. Scientific Report 6, 22506(2016).

- 50 -

7B3-S6
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 7, 16:15 – 17:45, Room B
Cancer evolution
Organizer(s):Kimiyo N. Yamamoto
Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japane-mail: kyamamoto[at]kyushu-u.org

Cancer progression can be considered as the consequences of evolution. Recently, lots of genomic
data have been acquired due to the advancement of sequencing technologies, and research of theevolutionary process of cancer by genomic analysis and mathematical modeling is in attention. In this
symposium, we will present the up-to-date mathematical and statistical analysis with experimental andclinical data and spread the opportunities that theoretical researchers study cancer.
Time

Title & Presenter

16:15 – 16:45

TBA
Subhajyoti De (Rutgers University)

16:45 – 17:15

Tumor and immune cell dynamics explain the PSA bounce after prostate cancer
brachytherapy
Yoichiro Yamamoto (Shinshu University)

17:15 – 17:45

Identification of neutral tumor evolution across cancer types
Benjamin Werner (Cancer Research UK)- 51 -

7B3-S6-1
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka- 52 -

7B3-S6-2
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Yoichiro Yamamoto
Department of Pathology, Shinshu University School of Medicine
e-mail: yoichiro@shinshu-u.ac.jp

Tumour and immune cell dynamics explain the PSA bounce after prostate cancer
brachytherapy
Background: Interstitial brachytherapy for localised prostate cancer may be followed by transient increases inprostate-specific antigen (PSA) that resolve without therapy. Such PSA bounces may be associated with an improved
outcome but often cause alarm in the patient and physician, and have defied explanation.
Methods: We developed a mathematical model to capture the interactions between the tumour, radiation and antitumour immune response. The model was fitted to data from a large cohort of patients treated exclusively withinterstitial brachytherapy. Immunohistological analysis for T-cell infiltration within the same tumours was also
performed.
Results: Our minimal model captures well the dynamics of the tumour after therapy, and suggests that a strong antitumour immune response coupled with the therapeutic effect of radiation on the tumour is responsible for the PSA
bounce. Patients who experience a PSA bounce had a higher density of CD3 and CD8 cells within the tumour thatlikely contribute to the PSA bounce and the overall better outcomes observed.
Conclusions: Our observations provide a novel and unifying explanation for the PSA bounce in patients with early
prostate cancer and also have implications for the use of immune-based therapies in such patients to improveoutcomes.

- 53 -

7B3-S6-3
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Benjamin WernerCancer Research UK
e-mail: werner@evolbio.mpg.de

Identification of neutral tumor evolution across cancer types
Despite extraordinary efforts to profile cancer genomes, interpreting the vast amount of genomic
data in the light of cancer evolution remains challenging. Here we demonstrate that neutral tumor
evolution results in a power-law distribution of the mutant allele frequencies reported by next-generation
sequencing of tumor bulk samples. We find that the neutral power law fits with high precision 323 of 904
cancers from4 types and from different cohorts. In malignancies identified as evolving neutrally, allclonal selection seemingly occurred before the onset of cancer growth and not in later-arising subclones,
resulting in numerous passenger mutations thatare responsible for intratumoral heterogeneity.
Reanalyzing cancer sequencing data within the neutral framework allowed the measurement, in eachpatient, of both the in vivo mutation rate and the order and timing of mutations. This result provides a
new way to interpret existing cancer genomic data and to discriminate between functional and nonfunctional intratumoral heterogeneity.

- 54 -

7D3-S7
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 7, 16:15 – 17:45, Room D
Ecosystem Dynamics and Management
Organizer(s):Yoh Iwasa
Department of Biology, Faculty of Science, Kyushu University, 744 Motooka, Nishiku, Fukuoka 819-0395, Japane-mail: yohiwasa@kyudai.jp
Joung-Hun Lee
Center for Decision Sciences, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka
819-0395, Japane-mail: clinamen2013@gmail.com

Many ecosystems on earth have been formed under strong human activity. For the sustainable
management of natural resources to be successful, we need to understand the coupling between social
economic aspects and ecological and resource sciences. This is particularly important given the demandsof increasing global population, environmental change and rising living standards (which lead to increased
demand for resources). Mathematical and computational modeling has a great potential to improve ourunderstanding of many aspects that are difficult to predict otherwise. In this symposium, we introduce
several examples of coupled socio-economic and resource models, we discuss their common features anddifferences, and the future of this increasingly important section of mathematical biology.
Time

Title & Presenter

16:15 – 16:17

Introduction

16:17 – 16:39

Coupled social and ecological models for ecosystem management
Yoh Iwasa (Kyushu University, Japan)

16:39 – 17:01

Assessment of Communities Responding to Natural and Anthropogenic
Variability in Aquatic Ecosystems
Tae-Soo Chon (Pusan National University, Korea)

17:01 – 17:23

Optimisation and statistics used in an Australian weed eradication program
Cindy Hauser (University of Melbourne, Australia)

17:23 – 17:45

Optimal management of tropical forests with high risk of illegal logging: role ofagroforestry and profit sharing
Joung-Hun Lee (Kyushu University, Japan)- 55 -

7D3-S7-1
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Yoh Iwasa
Department of Biology, Kyushu University
e-mail: yohiwasa@kyudai.jp

Coupled social and ecological models for ecosystem management.
Many ecosystems on earth have been formed under strong human activity. For the sustainable
management of natural resources to be successful, we need to understand the coupling between social
economic aspects and ecological and resource sciences. This is particularly important given the demandsof increasing global population, environmental change and rising living standards (which lead to increased
demand for resources). Mathematical and computational modeling have a great potential to improve ourunderstanding of many aspects that are difficult to predict otherwise. In this symposium, we introduce
several examples of coupled socio-economic and resource models, we discuss their common features anddifferences, and the future of this increasingly important section of mathematical biology.
For successful ecosystem management and biodiversity conservation, in addition to ecological andevolutionary processes, we need to consider social and economic influences on the management target. In
this symposium, four speakers will talk on different systems in which socio-economic consideration is very
important in ecosystem management.
After briefly explaining the structure of symposium "Ecosystem Dynamics and Management” (ogs.
Y. Iwasa and J-H. Lee), Yoh Iwasa introduces two theoretical models.
The first model analyzes coupled socio-economical and ecological dynamics for lake water pollution.
Players choose between cooperative (but costly) option and economical option, and their decision isaffected by the fraction of cooperators in the community and by the importance of water pollution problem.
When an opportunity for choice arrives, players take the option with the higher utility [5].
Results are: Oscillation of large amplitude is generated if social change occurs faster than ecosystem
responses. The model can show "paradox of nutrient removal" [4]. If phosphorus is removed more
effectively either from the inflow or from the lake water, the pollution level may increase (rather thandecrease) due to the decline in people's willingness to cooperate.
The second model analyzes punishment as a mechanism to maintain cooperative behavior in a socialgroup [3]. We discuss the efficiency of a graduated punishment system, in which the severity of thepunishment applied to deviators increases with the amount of harm caused by the selfish action, which fieldresearch has shown to be essential for successful resource management.
We conclude that graduated punishment is the most efficient way to ensure cooperation whenevaluation errors are unavoidable and when the social group is heterogeneous with respect to the sensitivityof its members to utility difference [3].
REFERENCES[1] Lee, J-H., Kakinuma, K., Okuro, T. and Iwasa, Y. 2015. Coupled social and ecological dynamics for herders in therangeland. Ecological Economics, 114: 208-217.
[2] Iwasa, Y. and Lee, J-H. 2013. Graduated punishment is efficient in resource management if people areheterogeneous. Journal of Theoretical Biology, 333:117-125.
[3] Lee, J-H. and Y. Iwasa. 2011. Tourists and traditional divers in a common fishing ground. Ecological Economics
70:2350-2360.
[4] Iwasa, Y., Suzuki-Ohno, Y. and Yokomizo, H. 2010. Paradox of nutrient removal in coupled socio-economic andecological dynamics for lake water pollution. Theoretical Ecology, 3:113-122.
[5] Iwasa, Y., Uchida, T. and Yokomizo, H. 2007. Nonlinear behavior of the socio-economic dynamics for lake waterpollution control. Ecological Economics 63: 219-229.
[6] Satake, A., Levin, S.A. and Iwasa, Y. 2008. Comparison between perfect information and passive-adaptive social
learning models of forest harvesting. Theoretical Ecology, 1: 189-197.
[7] Satake, A., Leslie, H.M., Iwasa, Y. and Levin, S.A. 2007. Coupled ecological-social dynamics in a forested landscape:spatial interactions and information flow. Journal of Theoretical Biology, 246: 695-707.

- 56 -

7D3-S7-2
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Tae-Soo Chon
Ecology and Future Research Association (EnFRA), Busan, Republic of Korea
Prof. (Emer.), Pusan National University, Busan, Republic of Korea
e-mail: tschon.chon@gmail.com, tschon@pusan.ac.kr
Dong-Hwan Kim
National Institute of Ecology, Republic of Korea
Woon-Seok Cho, Muyoung Heo
Pusan National University, Republic of Korea

Assessment of Communities Responding to Natural and Anthropogenic Variability
in Aquatic Ecosystems
Two aspects should be linked effectively in achieving sustainable ecosystem management, social-economic
management and ecological/resource sciences. Considering that numerous biological and environmental
factors are involved in a complex manner, objective ecological assessment of ecosystems is a steppingstone for better human understanding of ecological systems for decision making in social-economic
management. In this presentation, by taking aquatic communities as examples, objective assessment of
ecological integrity is presented utilizing a series of informatics and computational methods. After
collecting field data and establishment of data matrix, various aspects of community data are addressed in
responding to natural (e.g., flooding) and anthropogenic (e.g., pollution) variability, including community
patterns, responses to environmental impacts, prediction, determining indicators for water quality
evaluation, and characterizing community structure properties. Initially self-organizing map (SOM) wasused to outline community patterns and visualize relationships with environmental factors. SOM wasfurther utilized to screen metrics of community data to indicate water quality according to discriminative
power, redundancy, and responsiveness to disturbing factors pertaining to the community data in thesurveyed area. Temporal prediction of communities was further performed using temporal neural networks.
Subsequently community structure was analyzed based on species abundance distribution (SAD) models
including log-normal distribution and geometric series. SADs and related parameters were feasible inindicating community response to natural and anthropogenic variability from the structure aspect. Hidden
Markov model was additionally used to define the state of communities in relation with the observable
events in field conditions including water quality and seasonal effect. Computational methods would be an
efficient means of expressing ecological integrity that could serve as an objective reference system forapplying socio-economic models for ecosystem management.

REFERENCES[1] Kim D.-H., Cho, W.-S., and Chon, T.-S., 2013. Self-organizing map and species abundance
distribution of stream benthic macroinvertebrates in revealing community patterns in different seasons.
Ecological Informatics 17: 14–29.
[2] Kim D.-H., Song, M.-Y., and Chon, T.-S., 2016. Inferring pollution states based on community
structure of benthic macroinvertebrates in streams. Ann. Limnol. - Int. J. Lim. 52: 91–108.
[3] Kim D.-H., Van Nguyen, T., Heo, M., and Chon, T.-S., 2015. Subsequent application of selforganizing map and hidden Markov models infer community states of stream benthic macroinvertebrates
J. Ecol. Environ. 38: 1-13.

- 57 -

7D3-S7-3
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Cindy Hauser
University of Melbourne, Australia
e-mail: chauser@unimelb.edu.au
Katherine Giljohann, Inka Veltheim, Beth Crase, Gurutzeta Guillera-Arroita, Michael McCarthy
University of Melbourne, Australia
Joslin Moore
Monash University, Australia

Optimisation and statistics used in an Australian weed eradication program
Three species of hawkweed (Hieracium spp.) have invaded Australia’s Alpine National Park. The
first incursion was discovered by students of the University of Melbourne and since then, University
researchers have had a strong collaborative role in hawkweed management.
Hawkweeds have a high capacity to outcompete other plant species, and are capable of long distancedisturbance via wind and other vectors. They are an immediate threat to biodiversity within the National
Park and, if they are left unmanaged, are also expected to reduce grazing productivity. Therefore state
government agencies have funded an eradication program to remove hawkweed populations.
Finding and removing hawkweeds can be difficult in the vast and varied terrain of the Alpine National
Park. We have used field observations, statistics, modelling and optimisation techniques to assist managers
in the effective use of their resources.
First, modelling is used to predict where hawkweed seeds are likely to disperse by wind from the
known infestations. Habitat information is used to identify which locations are most suitable for seedestablishment. Together, these models predict where mature hawkweeds are most likely to occur in thelandscape.
Second, hawkweeds cannot be found by searchers with 100% confidence, because they look similar
to other plants and can also be hidden by shrubs and other vegetation. We have conducted observational
experiments to assess the conditions under which human searchers and trained scent dogs can successfully
detect hawkweeds. We use statistics to predict the probability of hawkweed detection in different scenarios.
Third, we bring together the above occurrence modelling and detection statistics in an optimisation.
Here we seek to minimise the negative impacts of hawkweeds in the National Park by deploying limited
search effort across the landscape.
This program demonstrates how managers and researchers can work together to develop efficient
strategies for conservation work.
REFERENCES[1] Williams, N.S.G. and Holland K.D, 2007. The ecology and invasion history of hawkweeds (Hieracium species) in
Australia. Plant Protection Quarterly, 22: 76-80.
[2] Williams, N.S.G., Hahs, A.K. and Morgan, J.W., 2008. A dispersal-constrained habitat suitability model for
predicting invasion of alpine vegetation. Ecological Applications, 18: 347-359.
[3] Moore, J.L., Hauser, C.E., Bear, J.L., Williams, N.S.G. and McCarthy, M.A., 2011. Estimating detection-effort
curves for plants using search experiments. Ecological Applications, 21: 601-607.
[4] Hauser, C.E. and McCarthy, M.A., 2009. Streamlining ‘search and destroy’: cost-effective surveillance forinvasive species management. Ecology Letters 12: 683-692.
[5] Hauser, C.E., Giljohann, K.M., Rigby, M., Herbert, K., Curran, I., Pascoe, C., Williams, N.S.G., Cousens, R.D.
and Moore, J.L., 2016. Practicable methods for delimiting a plant invasion. Diversity and Distributions 22: 136-147.

- 58 -

7D3-S7-4
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Joung-Hun Lee
Kyushu University
e-mail: clinamen2013@gmail.com
Y. Kubo, T. Fujiwara, Y. Iwasa
Kyushu University

Optimal management of tropical forests with high risk of illegal logging: role ofagroforestry and profit sharing
Illegal logging is a serious threat for plantation management in tropics. Here we study the role ofprofit-sharing and agroforestry as management strategies. The owner chooses the age of trees to cut, andthe workers choose their monitoring effort to prevent illegal logging.
Assumptions are: After the trees were removed, either by cutting, physical disturbances, or illegal
logging, the owner hires workers to replant young trees. While trees are young, the land is also used as
agriculture. In addition, the owner may share a fraction of profit obtained by selling logs with the workers.
Illegal logging may be prevented by hiring forest guards or by monitoring effort of the workers. We derived
recursive formulas for the values of a site with trees of age t, and solved it by iteration.
Results are: (1) Under the presence of illegal logging pressure, the owner may find it profitable toshare the income with the workers to solicit their monitoring efforts. We discuss policy implications ofthese results. (2) As the fixed cost of harvesting increases, the owner should delay the tree harvesting age.
It decreases mutual surveillance effort, and profit-sharing rate increases. Increased agricultural income has
similar effect.

REFERENCES[1] Lauren Persha, Arun Agrawal, Ashwini Chhatre, 2011. Social and ecological synergy: Local rulemaking, forest
livelihoods, and biodiversity conservation. Science, 311:1606–1608[2] Ashwini Chhatre and Arun Agrawal, 2009. Trade-offs and synergies between carbon storage and livelihood
benefits from forest commons. PNAS, 106:17667–17670.
[3] Joung-Hun Lee, Kaoru Kakinuma, Toshiya Okuro and Yoh Iwasa, 2015. Coupled social and ecological dynamics
of herders in Mongolian rangelands. Ecol Econ, 114:208–217- 59 -

7E3-S8
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 7, 16:15 – 17:45, Room E
Infectious diseases in structured populations
Organizer(s):Yukihiko Nakata
Department of Mathematics, Shimane University
e-mail: yunayuna.na@gmail.com
Ryosuke Omori
Research Center for Zoonosis Control, Hokkaido University
e-mail: omori@czc.hokudai.ac.jp

When describing the complex dynamics of infectious diseases in the real world, heterogeneity, suchas spatial heterogeneity and individual heterogeneity, is always an issue. Tons of structured population
models have been proposed so far, we need to know what kind of model can reveal what. In this symposium
five speakers will talk about the state-of-art analyses of the dynamics of infectious diseases at different
scales from within-host to between host communities using the different model descriptions.
Time

Title & Presenter

16:15 – 16:32

Metapopulation epidemic models with heterogeneous patches
Gouhei Tanaka (The University of Tokyo)

16:33 – 16:50

Evolution of global and local viral infection in the structured SIS model
Koichi Saeki (SOKENDAI)

16:51 – 17:08

Challenges in control strategies of spatially explicit epidemic models
Diána Knipl (Department of Mathematics, University College London)

17:09 – 17:26

Discretization approach for the global stability analysis of structured epidemic
modelsToshikazu Kuniya (Graduate School of System Informatics, Kobe University)

17:27 – 17:45

Outbreaks in the SIR epidemics with multiple seeds - a statistical physics
approach
Takehisa Hasegawa (Department of Mathematics and Informatics, Ibaraki
University)- 60 -

7E3-S8-1
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Gouhei Tanaka
The University of Tokyoe-mail: gouhei@sat.t.u-tokyo.ac.jp

Metapopulation epidemic models with heterogeneous patches
Metapopulation models have been widely used to describe the spreading of epidemics on a networkof spatially separated patches. The epidemic events such as infection and recovery of individuals in eachpatch follow a standard compartment epidemic model. Therefore, if a patch is isolated, the basic
reproductive number computed from the model determines whether an epidemic outbreak occurs or not in
the patch. However, when the patches are connected via complex migration pathways and individuals canmove from one patch to another, it is not obvious whether a local epidemic outbreak grows and leads to a
global outbreak in the entire network or not. One of the major concerns in the studies on metapopulation
models with complex network topology is the derivation of the global invasion threshold [1, 2].
In many studies on metapopulation epidemic models, the patches have been assumed to be identicalfor simplicity. However, the environments of the patches, related to epidemics, are not necessarily
homogeneous. Namely, the local basic reproductive number in patches can be different. We haveincorporated patch heterogeneity into the metapopulation epidemic models [3]. Assuming that there exist
high-risk patches with local basic reproductive number larger than 1 and low-risk patches with local basic
reproductive number smaller than 1, we have analytically derived the critical fraction of low-risk patches,
above which the global epidemic spreading is controlled. In this presentation, the recent developments inthe metapopulation epidemic models with heterogeneous patches are introduced.
REFERENCES[1] V. Colizza, R. Pastor-Satorras, and A. Vespignani. 2007. Reaction-diffusion processes and metapopulation
models in heterogeneous networks. Nature Physics, 3: 276–282.
[2] V. Colizza, and A. Vespignani. 2008. Epidemic modeling in metapopulation systems with heterogeneous
coupling pattern: Theory and simulations. Journal of Theoretical Biology, 251: 450–467.
[3] G. Tanaka, C. Urabe, and K. Aihara. 2014. Random and targeted interventions for epidemic control in
metapopulation models. Scientific Reports, 4: 5522.

- 61 -

7E3-S8-2
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Koichi Saeki
SOKENDAI (The Graduate University for Advanced Studies), Kanagawa, Japan.
e-mail: saeki_koichi@soken.ac.jp
Akira Sasaki
SOKENDAI (The Graduate University for Advanced Studies), Kanagawa, Japan.

Evolution of global and local viral infection in the structured SIS model
There are two types of viral infections in a host, one is global and the other is local.
Global infection means that an infected cell produce viral particles that travel tosusceptible cells somewhere. In contrast, local infection occurs via physical contact
between an infected cell and a susceptible cell. The emergence of mutant virus that has ahigh ability of local infection is observed in vitro[1] and suggested in vivo[2], and thosemutants are considered to have a relationship with a severe disease caused by virus
infection[2]. In the previous study, the evolution of global versus local infection has beenmodeled, and it suggested that the spatial structure have an important effect to theevolution[3]. However, the emerged structure in that model is only a part of possible spatial
structures, and the spatial structure has not been parameterized.
Here we attempt to reveal what is the evolutionarily stable proportion of global andlocal infection, and how it depends on the spatial parameters. We consider a lattice spacein which each site is occupied by either a target or a non-target cell for virus, and assume
that whether a site is occupied by a target cell or a non-target cell will never change. Then,
how target and non-target cells are distributed over the lattice space is parameterized by
the frequency of target cells and the pair frequency of target cells.
At first, the infection dynamics are modeled by pair approximation and the endemic
condition for a virus with a certain proportion of global infection is calculated. Next, theevolutionarily stable strategy is obtained by an invasibility analysis using pairapproximated dynamics. The results show that higher proportion of local infection is
selected as target cells become clustered. We also observe the parameter region that even
if global infection is more efficient than local one, using local infection at a certain rate
becomes the optimal due to spatial clustering of target cells.

REFERENCES[1] Shirogane Y., Watanabe S., Yanagi Y., 2012. Cooperation between different RNA virus genomes
produces a new phenotype. Nat.Commun.
[2] Watanabe S., Shirogane Y., Suzuki SO., Ikegame S., Koga R., Yanagi Y., 2013. Mutant fusion proteins
with enhanced fusion activity promote measles virus spread in human neuronal cells and brains ofsuckling hamsters. J.Virol. 87(5): 2648-59.
[3] Kamo M., Boots M., 2006. The evolution of parasite dispersal, transmission, and virulence in spatial
host populations. Evol. Ecol. Res. 8: 1333-1347.

- 62 -

7E3-S8-3
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Diána Knipl,
Department of Mathematics, University College London
e-mail: d.knipl@ucl.ac.uk

Challenges in control strategies of spatially explicit epidemic models
Mathematical epidemiology is an important branch of mathematical biology, concerned with the
propagation of infectious diseases in human populations. Through mathematical modeling we gain valuable
insight into the spatio-temporal spread of infectious diseases, and by better understanding their dynamics
we become capable of designing their intervention strategies, like vaccination and social distancing. In thistalk we present some simple models for disease spread when individuals travel between different cities,
and describe by mathematical analysis their control measures including travel restrictions.

- 63 -

7E3-S8-4
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Toshikazu Kuniya
Graduate School of System Informatics, Kobe University
e-mail: tkuniya@port.kobe-u.ac.jp

Discretization approach for the global stability analysis of structured epidemic
modelsIn this talk, we focus on structured epidemic models with heterogeneity (age, sex, position etc.) written
as partial differential equations. By discretization, they can be rewritten to multi-group models as ordinary
differential equations. For multi-group epidemic models, a celebrated graph theoretic approach has recently
been developed by Guo et al. (2006). By using the approach, in a relatively formal way, we can construct
suitable Lyapunov functions for the global stability analysis of the discretized multi-group epidemic models.
From the form of these Lyapunov functions, we can expect the form of corresponding Lyapunov functions
for the original structured models as partial differential equations.
Specifically, in this talk, we focus on two SIR epidemic models with age-structure and space-structure,
respectively. By constructing the Lyapunov functions, we prove that the global asymptotic stability of eachequilibrium is completely determined by the size of the basic reproduction number Ro. That is, the infected
population converges to zero as time goes to infinity if Ro < 1, and it converges to a positive distribution
as time goes to infinity if Ro > 1. This is a joint work with Dr. Jinliang Wang (Heilongjiang University)and Prof. Hisashi Inaba (University of Tokyo).
REFERENCES[1] Kuniya, T., 2011. Global stability analysis with a discretization approach for an age-structured multigroup SIR
epidemic model. Nonlinear Anal. RWA, 12: 2640–2655.
[2] Kuniya, T., Wang J., 2016. Lyapunov functions and global stability for a spatially diffusive SIR epidemic model.
Appl. Anal., 13:15 DOI: 10.1080/00036811.2016.1199796.
[3] Kuniya T., Wang J., Inaba H., A multi-group SIR epidemic model with age structure. Disc. Cont. Dyn. Syst.
Series B, under revision.

- 64 -

7E3-S8-5
Sep 7, Wed (mini-symposia)
JSMB2016 Fukuoka
Takehisa Hasegawa
Department of Mathematics and Informatics, Ibaraki University
e-mail: takehisa.hasegawa.sci@vc.ibaraki.ac.jp
Koji Nemoto
Department of Physics, Hokkaido University

Outbreaks in the SIR epidemics with multiple seeds- a statistical physics approach
The threat of infectious disease is conspicuous for modern society, wherein there is a large amount ofinternational travel all over the world. Understanding how infectious diseases spread in our society is
crucial to the development of strategies for disease control. In recent years, many studies have been devoted
to epidemic models, e.g., the susceptible-infected-removed (SIR) model and the susceptible-infectedsusceptible model, with a network structure of individuals [1]. Diseases spread over the networks ofphysical contacts between individuals, and the structure of real networks has crucial effects on this spread.
Many analytical approaches for epidemic models with network structures, such as the edge-based
compartment model, the effective degree approach, and the pair approximation, have been proposed andhave succeeded in describing epidemic dynamics. Numerical simulations have also revealed how epidemics
spread in more realistic situations.
Most previous studies using the SIR-type epidemic models have assumed that the fraction of initialinfection seeds is infinitesimally small. In contrast, there have been few studies on epidemic models withfinite fractions of seeds. What we discuss here is a fundamental, but almost overlooked problem: How doepidemic models with finite fractions of seeds undergo phase transitions? In this talk, we consider the SIR
model with finite fractions of seeds on the six-regular random graph [2]. In this case, the SIR model exhibitsa kind of percolation transition. We regard the epidemic clusters generated from seeds as supernodes andstudy the percolation problem of these supernodes. We analytically and numerically obtain the percolationtransition point of supernodes, λc1, to show a gap between this critical infection rate and so-called epidemic
threshold, indicating that the percolation of epidemic clusters occurs before a single seed can induce a
global outbreak (Fig.1). Our result also shows the sensitivity of the seed fraction on percolation transition
point, i.e., that a small seed fraction drastically reduces the critical infection rate for the emergence of theinfinite epidemic cluster.

R-dominant phasecoexisting phase
S-dominant phase

Phase diagram of the SIR model in the (ρ, λ)-space.
Here ρ is the fraction of initial seeds and λ is theinfection rate (the recovery rate is set to 1). In the Sdominant phase, there is no infinite epidemic cluster(no global outbreak occurs). In the coexisting and Rdominant phases, an infinite epidemic cluster appears(global outbreak occurs). In the latter, almost all nodes
are removed so that residual components are
disintegrated. Solid-red and dashed-blue lines
represent the analytical estimates of the critical
infection rates, λc1 between the S-dominant andcoexisting phases, and λc2 between the R-dominantand coexisting phases, respectively.

Figure 1
REFERENCES[1] R. Pastor-Satorras, C. Castellano, P. Van Mieghem, and A. Vespignani, 2015. Epidemic processes in complex
networks. Reviews of Modern Physics, 87 925.
[2] T. Hasegawa, and K. Nemoto, 2016. Outbreaks in susceptible-infected-removed epidemics with multiple seeds.
Physical Review E, 193: 032324.

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8B1-S9
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 8, 9:00 – 10:30, Room B
Towards data-driven mathematical biology
Organizer(s):Joung-Hun LEE
Mathematical Biology Laboratory, Department of Biology, Kyushu University, 744
Motooka, Nishi-ku, Fukuoka 819-0395, Japane-mail: clinamen2013@gmail.com
Marko JUSUP
Center of Mathematics for Social Creativity, Hokkaido University, N12W7, Kita Ward,
Sapporo, 060-0811 Japane-mail: mjusup@gmail.com

Mathematical biology is often driven by purely theoretical considerations. Although theoreticalcontributions in themselves are extremely valuable, there is a huge potential for mathematical biology to
add value to existing and new empirical data. To realize this potential it is necessary to open up a continuous
dialogue between experimentally and theoretically oriented researchers from various disciplines who sharethe interest in biology. The proposed mini-symposium is intended to establish such a dialogue by
illustrating several interesting case studies which greatly benefited, or could benefit, from mathematicalmodeling. Challenging questions are posed for future developments.
Time

Title & Presenter

09:00 – 09:01

Foreword
Joung-Hun Lee (Kyushu University)

09:01 – 09:21

Different bees, different needs – nest site selection in honeybees
Madeleine Beekman (The University of Sydney)

09:21 – 09:41

Life-history adaptations and the latitudinal diversity gradient in medaka fishes
Kazunori Yamahira (Tropical Biosphere Research Center, University of the
Ryukyus)09:41 – 10:01

Electronic tagging applications and migration of Pacific bluefin tuna, Thunnus
orientalis
Takashi Kitagawa (The University of Tokyo)

10:01 – 10:21

Change in energy intake and cost of skipjack tuna (Katsuwonus pelamis) withnorthward migration in the western North Pacific
Yoshinori Aoki (The University of Tokyo)

10:21 – 10:30

Discussion & comments
Cindy Hauser (University of Melbourne) & Marko Jusup (Hokkaido University)- 66 -

8B1-S9-1
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Madeleine Beekman
Behaviour and Genetics of Social Insects Lab, School of Life and Environmental Sciences, The University
of Sydneye-mail: madeleine.beekman@sydney.edu.au

Different bees, different needs – nest site selection in honeybees
During reproductive swarming and seasonal migration, a honeybee swarm needs to locate and moveto a new nest site. Our current knowledge of swarming and nest site selection in honeybees is based
primarily on studies of just one species, Apis mellifera. Natural colonies of A. mellifera live in tree cavities.
The quality of the cavity is often critical to the survival of a swarm. The scouts must search thousands oftrees to ensure that they do not settle for a poor cavity when a better one is available. More recently anotherspecies of honeybee has been included in studies of nest site selection: the open-nesting dwarf honeybee
Apis florea. A. florea builds a small nest comprised of a single comb suspended from a twig of a shrub ortree in the open. For a cavity-nesting species like A. mellifera there is only a limited number of potential
nest sites that can be located by a swarm, simply because suitable nest sites are scarce. In contrast, for an
open-nesting species like A. florea it seems that there is an abundance of shaded twigs that would be equallysuitable for building a nest. Here I pull together recent research that shows that the nest site selection
processes of A. florea and A. mellifera have been shaped by each species’ nest site requirements. I argue
that both species use the same behavioural algorithm, tuned to allow each species to solve their speciesspecific problem.

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8B1-S9-2
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Kazunori Yamahira
Tropical Biosphere Research Center, University of the Ryukyus
e-mail: yamahira@lab.u-ryukyu.ac.jp

Life-history adaptations and the latitudinal diversity gradient in medaka fishes
Explaining the latitudinal diversity gradient has long been one of the central subjects in ecology andevolutionary biology [1,2]. In many taxa, species are more abundant in the tropics than in the temperatezone. Such a latitudinal pattern can be seen also in the family Adrianichthyidae, a freshwater fish groupcalled “medaka” in Japan; many medaka species are distributed in the tropical regions of Southeast Asia,
whereas only two species in the Japanese Archipelago. In this study, I focus on life-history adaptations
along latitudes, which might result in the latitudinal gradient in population extinction rates.
In ectotherms such as fishes, lower temperatures in high-latitude environments would theoreticallyreduce the annual growth and reproduction rates of individuals. If smaller body size and lower fecundity
reduce fitness, individuals in higher latitudes may evolve compensatory responses. Two alternative models
of such latitudinal compensation are possible: adaptation-to-temperature model: thermal reaction norms for
growth and reproduction rates of high-latitude individuals may be horizontally shifted to a lower range oftemperatures, or adaptation-to-seasonality model: reaction norms may be vertically shifted so that highlatitude individuals can grow and reproduce faster across all temperatures. Common-environment
experiments revealed that average thermal reaction norms for growth and reproduction rates of the Japanese
medaka (Oryzias latipes species complex) differed primarily in elevation among latitudinal populations ina manner consistent with adaptation-to-seasonality model, suggesting that natural selection in high latitudes
prefers individuals that grow and reproduce faster even within a shorter growing and reproductive season
to individuals that have longer growing and reproductive seasons by growing and reproducing at lower
temperatures. However, intrapopulation variation in reaction norms was also vertical: some full-sib families
grew faster than others across all temperatures examined. This tendency in intrapopulation genetic variation
for thermal reaction norms may have genetically constrained the evolution of latitudinal compensation,
irrespective of the underlying selection pressure.
Comparative population ecological surveys in the wild revealed that latitudinal populations differ in
population demography. As predicted from the adaptation-to-seasonality model, in high-latitude
populations, reproduction concentrated during a shorter favorable period of a year, and young-of-the-year(YOY) individuals grew faster within a shorter period before long winter. In contrast, both reproduction
and growth were slower but continued for a longer period in low-latitude populations. It was found that
overwinter mortality of YOYs is size-dependent in the high-latitude populations; smaller individuals suffer
cold death and starvation more frequently. Therefore, YOYs produced later in a season or YOYs growing
slower are expected to suffer higher mortality, which is considered to be the main selection pressure on theadaptations to seasonality. As a result of the temporal synchronization of reproduction and growth withina shorter period of a year, high-latitude populations exhibited larger seasonal fluctuation in population size
than low-latitude populations.
Theories predict that larger fluctuation in population size causes higher risk of stochastic extinctionof the population [3,4]. The life-history adaptations to seasonality at high latitudes, therefore, willsecondarily cause higher population extinction rates, which may reduce the number of species coexistingin high-latitude environments. Adaptation to temperature and resultant ability to reproduce and grow at
lower temperatures would lessen the magnitude of population fluctuation, but the evolution of adaptation
to temperature is genetically constrained as demonstrated above, resulting in inevitable high extinction risk
in high-latitude populations.
REFERENCES[1] Gaston, K. J., 2000. Global patterns in biodiversity. Nature, 405: 220–227.
[2] Hillebrand, H., 2004. On the generality of the latitudinal diversity gradient. American Naturalist, 163: 192–211.
[3] May, R. M. 1973. Stability in randomly fluctuating versus deterministic environments. American Naturalist, 107:
621–650.
[4] Lande, R. 1993. Risks of population extinction from demographic and environmental stochasticity and random
catastrophes. American Naturalist, 142: 911–927.

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8B1-S9-3
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Takashi Kitagawa
Atmosphere and Ocean Research Institute, The University of Tokyo, Chiba 277-8564, Japane-mail: takashik@aori.u-tokyo.ac.jp
Ko Fujioka
National Research Institute of Far Seas Fisheries, Japan Fisheries Research and Education Agency,
Shizuoka 428-8633, Japan
Yoshinori Aoki
Atmosphere and Ocean Research Institute, The University of Tokyo, Chiba 277-8564, Japan

Electronic tagging applications and migration of Pacific bluefin tuna, Thunnus
orientalis
Investigations of the migration and distribution of Pacific bluefin tuna (PBT) in the Pacific Ocean
have used fisheries data analysis and/or conventional tagging experiments mainly in the 20th century, butthese previous studies could not follow the detailed behavior of individuals at a higher resolution.
The electronic tags that were developed and applied to fish species at the end of the last century
allowed the measurement of environmental and physiological variables by recording raw or processed datain their memory. The tags used for PBT research provide an estimation of fish geolocation using a lightsensor and algorithms based on astronomy. To date, more than 800 PBT tuna tagged with the electronictags have been released in the western Pacific Ocean (WPO). These fish range in size from 18 to 158 cm.
Analyses of the retrieved tag data have showed that the vertical distributions and movements of immature
PBT are affected by spatial and seasonal changes in the vertical temperature structure. PBT often makebrief dives to depths below the thermocline for foraging and maintaining body temperature. Track durations
ranged from 1 to 1285 days, and the location data indicate PBT in the WPO aggregate in the KuroshioOyashio transition region where they spent more time at the surface feeding than in the other areas in the
WPO. Archival tags have revealed the timing of trans-Pacific migrations from the transition region to theEastern Pacific appears to depend on their specific wintering areas in the WPO. We also suggest directionsof future research for investigating PBT migratory characteristics in the WPO.
REFERENCES[1] Kitagawa, T., and Kimura, S. eds., 2015. Biology and ecology of bluefin tuna. CRC Press, pp 433.
[2] Kitagawa, T., 2013. Behavioral Ecology and thermal physiology of immature Pacific bluefin tuna (Thunnus
orientalis). In Ueda, H., and Tsukamoto, K. eds.: Physiology and ecology of fish migration. CRC press, 152–178.
[3] Kitagawa, T., Boustany, A.M., Farwell, C.J., Williams, T.D., Castleton M., and Block, B.A., 2007. Horizontal
and vertical movements of juvenile bluefin tuna (Thunnus orientalis) in relation to seasons and oceanographic
conditions in the eastern Pacific Ocean. Fisheries Oceanography, 16: 409–421.
[4] Kitagawa, T., Kimura, S., Nakata, H., and Yamada, H., 2004. Diving behavior of immature Pacific bluefin tuna(Thunnus thynnus orientalis) for feeding in relation to seasons and areas: the East China Sea and the KuroshioOyashio transition region. Fisheries Oceanography 13: 161–180.
[5] Kitagawa, T., Nakata, H., Kimura, S., Itoh, T., Tsuji, S., and Nitta, A., 2000. Effect of ambient temperature on thevertical distribution and movement of Pacific bluefin tuna (Thunnus thynnus orientalis). Marine Ecology
Progress Series, 206: 251–260.

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8B1-S9-4
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Yoshinori, Aoki
Atmosphere and Ocean Research Institute, The University of Tokyo, Chiba 277-8564, Japane-mail: aokiyoshinori@aori.u-tokyo.ac.jp
Takashi, Kitagawa
Atmosphere and Ocean Research Institute, The University of Tokyo, Chiba 277-8564, Japan
Hidetada, Kiyofuji
National Research Institute of Far Seas Fisheries, Japan Fisheries Research and Education Agency,
Shizuoka 428-8633, Japan
Suguru Okamoto
Hokkaido National Research Institute, Japan Fisheries Research Agency and Education Agency,
Hokkaido 085-0802, Japan
Tomohiko Kawamura
Atmosphere and Ocean Research Institute, The University of Tokyo, Chiba 277-8564, Japan

Change in energy intake and cost of skipjack tuna (Katsuwonus pelamis) withnorthward migration in the western North PacificSkipjack tuna, Katsuwonus pelamis, are a highly migratory pelagic species distributed throughout
tropical to temperate waters worldwide. In the western North Pacific, after hatching in subtropical ocean,juveniles travel long distances and extend their distribution through subtropical to temperate waters near
Japan (northward migration) with their body composition changing especially in lipid content. In this study,
we investigated their migration paths and behavior during the migration in terms of energy budgets
measured with archival tags, which can record swimming depth, water and body temperatures, and lightintensity, focusing on lipid composition changes between habitats. The tags were inserted into the stomach
and 465 individuals with tag were released in total recording their migration from subtropical to temperatearea. The tags were recaptured by fishermen and the data were retrieved from 16 individuals and used foranalysis. The estimation of energy intake was based on the heat increment of feeding. As an indicator ofuse of the consumed energy, horizontal and vertical daily movement distances were also calculated. It was
found that the daily energy intake increased with the northward movements, whereas the daily verticaldistance was decreased, although the horizontal distances were not changed among habitats. This result
suggests that skipjack spend less energy in acquiring prey in temperate than in subtropical waters since
prey are available in higher densities, thereby providing excess energy for growth or lipid reserves.

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8D1-S10
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 8, 9:00 – 10:30, Room D
Mathematical modeling for viral infections within host
Organizer(s):Yusuke Kakizoe
Systems Life Sciences, Graduate school of Kyushu University, 744 Motooka Nishi-ku
Fukuoka, 819-0395, Japan,
e-mail: yusuke.purple5@gmail.com

Mathematical model of viral infections has a very important role in our quantitative understanding ofviral dynamics. For instance, we can estimate the pathogenesis of viruses, evaluating the efficacy of anti
viral drugs, predicting the viral dynamics, etc. In this symposium, we will present recent advances ofmathematical modeling for viral infections.
Time

Title & Presenter

09:00 – 09:20

Modeling to quantify HIV-1 entry
Yusuke Kakizoe (Graduate School of Systems Life Sciences, Kyushu University)

09:20 – 09:40

Epitope-specific CD8+ T cell kinetics rather than viral variability determines thetiming of immune escape in SIV infection
Alexey Martyushev (Department of Biology, Faculty of Sciences, Kyushu University)

09:50 – 10:10

The impact of influenza A defective interfering particles on plaque assays
Laura Liao (Department of Physics, Ryerson University)

10:10 – 10:30

Something is wrong with the respiratory syncytial virus
Catherine Beauchemin (Department of Physics, Ryerson University)- 71 -

8D1-S10-1
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Yusuke Kakizoe
Systems Life Sciences, Graduate School of Kyushu University, Japane-mail: yusuke.purple5@gmail.com
Shingo Iwami
Faculty of Science, Kyushu University, Japan

Modeling to quantify HIV-1 entry
The entry of HIV-1 into a target cell is the first step of HIV-1 replication process, so entry inhibitor
has advantages over the inhibition of steps in the viral life cycle after infection. Although we havemaraviroc, one of the few entry inhibitor of HIV-1, the efficacy of the drug varies depending on CCR5 or
CXCR4 co-receptor toropism, and patients need to take it twice a day contrary to other drugs once a day.
More potent HIV-1 entry inhibitor is needed. So far, many researchers revealed HIV-1 entry processes
qualitatively.
The entry of HIV-1 into a target cell is established between envelope glycoprotein (Env) on the surface
of a virus and CD4 receptors on a target cell. The Env is a trimer composed of three gp120 and three gp41
envelope proteins, and it mediates virus entry by fusion. The entry of HIV-1 into target cells starts frombinding of CD4 to gp120 protein. This binding induces conformational changes of Env that allows
interactions with a coreceptor such as CCR5 or CXCR4. These interactions in turn trigger additional
conformational changes in Env, which expose gp41 protein, and inserts into the membrane of host cell.
Finally, the viral and target cell membranes are fusion.
In this way, we already know HIV-1 entry process qualitatively in detail. However, in order to develop
a new entry inhibitor, we should quantitatively understand HIV-1 entry process. For example, Magnus etal. investigated the HIV-1 entry process using mathematical model, and estimated the number of gp120
trimmers on HIV-1 surface for the virus entry [1,2]. In this study, we focused on an interaction between
HIV gp120 and CCR5 molecules during entry step and investigated how many number of CCR5 molecules
are associated with HIV-1 entry. We made a mathematical model describing HIV entry and analyzed
infectivity assay data using our model.
REFERENCES[1] Carsten Magnus, Roland R. Rogoes: Estimating the Stoichiometry of HIV neutralization. PLoS Comput Biol
2010, 6(3): e1000713.
[2] Carsten Magnus, Roland R. Rogoes: Analysis of the Subunit Stoichiometry in Viral Entry. PLoS ONE 2012,
7(3):e33441.

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8D1-S10-2
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Dr. Alexey Martyushev
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japane-mail: martyushev.alexey.745@m.kyushu-u.ac.jp

Epitope-specific CD8+ T cell kinetics rather than viral variability determines thetiming of immune escape in SIV infection
Untreated human immunodeficiency virus (HIV) infection causes Acquired Immune Deficiency
Syndrome (AIDS) that ultimately leads to death. Previous studies of HIV and its analogue in monkeys –Simian Immunodeficiency Virus (SIV) showed that CD8+ T cell responses are important for the control of
infection [1, 2]. Virus-specific CD8 T-cells can detect and suppress HIV-infected cells, but they achieve
only a temporary success. As soon as the virus mutates, viral variants can escape the established immune
response. The strength of the CD8+ T cell response, as well as mutation rates, patterns of particular aminoacids undergoing escape and growth rates of escape mutants may affect the time when escape occurs.
However, this study demonstrates that the appearance of CD8 T-cell response, rather than viral variability,
plays the dominant role in determining the time of immune escape.
This study is based on the analysis of epitope-specific CD8+ T cell response in 25 SIV-infected pigtail
macaques at three SIV epitopes. Mathematical modeling and statistical analysis were applied in order tointerpret and analyze the complex results of experiments. The rate of appearance of new mutants was firstly
introduced in this research project and is defined by the following formula:m’(ti, ti+1) = [m(ti+1) – m(ti)]/(ti+1 – ti),(1)
where m(ti) is the number of mutants at a frequency above 1% in the sequence data at the time point ti. The
increase in mutants m’ is discrete and takes values within time intervals defined by start and end time points,
ti and ti+1, respectively, i.e. mutants with fraction less than 1% in the sequence were not taken into accountin the values of m(ti) and m(ti+1). For example, if the number of variants at >1% went from two to five inthree days, this would be an average increase in variants of (5 mutants – 2 mutants) / 3 days = 1 mutant perday.
Two of the studied epitopes showed a variable escape pattern and one had a highly monomorphic
escape pattern. Despite very different patterns, immune escape occurs with a similar delay of on average
18 days after the epitope-specific CD8+ T cells reach 0.5% of total CD8+ T cells. Moreover, the mostdelayed escape occurs in one of the highly variable epitopes, and that this is associated with a delay in theepitope-specific CD8+ T cells responding to this epitope. The kinetics of immune escape (see Eq. 1)
demonstrated that multiple escape mutants emerge simultaneously during the escape, implying that adiverse population of potential escape mutants is present during immune selection. The similar effect has
been previously observed in a HIV-1 study, however it was not deep investigated [3].
The results demonstrate that timing of escape is largely determined by the kinetics of epitope-specificCD8+ T cells. This discovery highlights a need of vaccines inducing immune response to conserved regionsof HIV genome. In contrast, since vaccination aims to drive an earlier and stronger CD8+ T cell response,
it seems possible that this would simply drive earlier immune escape at variable HIV genome regions.
REFERENCES[1] Koup, R. A., Safrit, J. T., Cao, Y., Andrews, C. A., McLeod, G., Borkowsky, W., Farthing, C. and Ho, D. D.,
1994. Temporal association of cellular immune responses with the initial control of viremia in primary humanimmunodeficiency virus type 1 syndrome. J Virol, 68(7): 4650–4655.
[2] Jin, X., Bauer, D. E., Tuttleton, S. E., Lewin, S., Gettie, A., Blanchard, J., Irwin, C. E., Safrit, J. T., Mittler, J.,
Weinberger, L., Kostrikis, L. G., Zhang, L., Perelson, A. S. and Ho, D. D., 1999. Dramatic rise in plasma viremia
after CD8(+) T cell depletion in simian immunodeficiency virus-infected macaques. J Exp Med, 189(6): 991–998.
[3] Goonetilleke, N., Liu, J. F. Salazar-Gonzalez, G. Ferrari, E. Giorgi, V. V. Ganusov, B. F. Keele, G. H. Learn, E.
L. Turnbull, M. G. Salazar, K. J. Weinhold, S. Moore, CHAVI Clinical Core B, N. Letvin, B. F. Haynes, M. S.
Cohen, P. Hraber, T. Bhattacharya, P. Borrow, A. S. Perelson, B. H. Hahn, G. M. Shaw, B. T. Korber, andMcMichael, A. J, 2009. The first T cell response to transmitted/founder virus contributes to the control of acuteviremia in HIV-1 infection, J Exp Med, 206: 1253–1272.

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8D1-S10-3
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Laura Liao
Department of Physics, Ryerson University
e-mail: laura.liao@ryerson.ca
Catherine Beauchemin
Department of Physics, Ryerson University
The impact of influenza A defective interfering particles on plaque assays
Working stocks of influenza A virus are propagated in cell culture either from virus samples orexisting virus stocks [1]. During propagation, unwanted defective interfering particles (DIP) –particles
which competitively inhibit virus replication-- might be amplified from the initial inoculum itself, orspontaneously generated during infection [2]. To minimize the presence of DIPs, virus stocks can bepassaged using a very dilute initial inoculum, in order to reduce instances of co-infection (i.e., when a cell
receives both virus and DIP) which foster more DIPs. Despite this DIP depletion step, the virus stock
obtained will still contain low levels of DIPs [3]. Furthermore, it is notoriously difficult to physicallyseparate DIPs from virus, since they mainly differ in genomic content which is less than 0.8% of the total
mass [2]. Hence, influenza virus stocks inevitably contain DIPs.
Since virus stocks contain DIPs, we are interested in how DIPs might impact the quantification ofvirus in the stock, specifically by plaque assay. In a plaque assay, virus stock dilutions are used to infectcell monolayers that are overlaid with agar. The agar restricts the diffusion of virus progeny to an infected
cell's nearest neighbours. Hence, a single infected cell will infect its neighbours, and so on, and the infected
patch of cells will spread radially outward. When the cells die, a circular void or “plaque” remains.
Quantifying the number of plaques allows us to calculate the infectious virus concentration in the stock
which is represented by the number of plaque-forming units per millilitre (PFU/mL).
As DIPs can alter the number of visible plaques through the arrest of early plaque growth [4], thisresearch will use an agent-based model to investigate the degree of systematic error which leads tounderestimation of stock virus concentration.
REFERENCES[1] Szretter, K.J., Balish, A.L., and Katz, J.M., 2006. Influenza: propagation, quantification, and storage. Curr.
Protoc. Microbiol., Chapter 15:Unit 15 G.1.
[2] Nayak, D.P., Chambers, T.M., and Akkina, R. K., 1985. Defective-interfering (DI) RNAs of influenza viruses:
origin, structure, expression, and interference. Curr. Top. Microbiol. Immunol., 114:103–151.
[3] Marcus, P.I., Ngunjiri, J.M., and Sekellick, M.J., 2009. Dynamics of biologically active subpopulations of influenza
virus: Plaque-forming, noninfectious cell-killing, and defective interfering particles. J. Virol., 83(16):8122–8130.
[4] Janda, J.M., Davis, A.R., Nayak, D.P. and De, B.K., 1979. Diversity and generation of defective interfering
influenza virus particles. Virology. 95(1):48–58.

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8D1-S10-4
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Catherine Beauchemin
Department of Physics, Ryerson University, Canada
iTHES, RIKEN, Japane-mail: cbeau@ryerson.ca
Something is wrong with the respiratory syncytial virus
Mathematical models of virus infection within a host or cell culture make assumptions about theproperties of the virus. These assumptions are rarely validated when a model for one virus is applied to
study another. Similarly, virology aims to rapidly develop vaccines and antiviral therapies by often learning
only as much about the virus as is required to do so. In this haste, important characteristics are missed withsometimes devastating consequences, as was the case with the failed respiratory syncytial virus (RSV)
vaccine. In this talk I will discuss the particularities of RSV and what we uncovered through mathematicalanalysis of available experimental data.

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8E1-S11
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 8, 9:00 – 10:30, Room E
Plant phenotyping with morphometrics
Organizer(s):Koji Noshita
Graduate School of Agriculture and Life Science, The University of Tokyo, 1-1-1 Yayoi,
Bunkyo, Tokyo, Japane-mail: noshita@morphometrics.jp

With recent advancements in genotyping, phenotyping is now a bottleneck in development of several
research fields in plant science (e.g. agricultural science, developmental and evolutionary biology).
Particularly, morphological properties are the most important information but hardest to treat in plant
phenotyping. Morphometrics is one of the candidates to relieve the bottleneck by providing quantifying,visualizing, analyzing and summarizing techniques. In this minisymposium, we focus on how to understandand interpret the morphological data of plants with genomic, developmental, and physiological information.
Time

Title & Presenter

09:00 – 09:05

Introduction
Koji Noshita (The University of Tokyo)

09:05 – 09:30

Leaf surface reconstruction from “noisy” point cloud data for geometric analysis
Koji Noshita (The University of Tokyo)

09:30 – 10:00

Morphometric analysis of leaves
Dan Chitwood (Donald Danforth Plant Science Center)

10:00 – 10:30

Low cost field based plant phenotyping with cameras and image analytics
Wei Guo (Institute for Sustainable Agro-ecosystem Services, The University of Tokyo)- 76 -

8E1-S11-1
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Koji Noshita
The University of Tokyo, Japane-mail: noshita@morphometrics.jp
Wei Guo
Institute for Sustainable Agro-ecosystem Services, The University of Tokyo, Japan
Bangyou Zheng
CSIRO Agriculture, Australia
Tao Duan
CSIRO Agriculture, Australia
Scott Chapman
CSIRO Agriculture, Australia
Hiroyoshi Iwata
The University of Tokyo, Japan

Leaf surface reconstruction from “noisy” point cloud data for geometric analysis
In recent years, 3D scanners, Depth cameras, LiDAR and etc. have become more widely available,
and they have been used to acquire morphological and color information for target objects. A pipeline using
Structure from Motion (SfM) and Multi-View Stereo (MVS) is a promising technique to reconstruct asurface as point cloud data from a set of 2D images. High-resolution point cloud data now can be acquired
easily and cost-effectively because the pipeline has been implemented as several libraries and software
products.
For estimating and evaluating biological traits (e.g. leaf area, leaf shape, curvature), not only point
clouds but also 3D surfaces themselves need to be reconstructed. In this study, we propose a method toreconstruct 3D surfaces of leaves from “noisy” point clouds. In the proposed method, a leaf is modeled asa 2D closed surface embedded in the Euclidean space ℝ" . Firstly, point cloud is parameterized by using
isomap [1], which is one of the non-linear dimension reduction methods. Secondly, we fit a penalized Bspline surface to the point cloud based on the parameterized point cloud data. Finally, several biologicaltraits can be estimated from the reconstructed surface. In this talk, we will show both computational andempirical researches on several crop species.
REFERENCES[1] Tenenbaum, J.B., de Silva, V., Langford, J.C., 2000. A global geometric framework for nonlinear dimensionality
reduction. Science, 290: 2319–2323.

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8E1-S11-2
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Dan Chitwood
Donald Danforth Plant Science Center, St. Louis, MO USA
e-mail: dchitwood@danforthcenter.org

Morphometric analysis of leaves
Natural variation in leaf shape is spectacularly diverse. Leaf shape is genetically specified within
a complex developmental and environmental context. Leaf shape varies between species, changes
between successive nodes on the same shoot, is altered between seasons in response to climate in long
lived perennials, and even correlates with the paleoclimate in the fossil record. In this seminar I will talkabout applying a variety of morphometric techniques—from Procrustes-adjusted landmarks to Elliptical
Fourier Descriptors—to the genetic, developmental, and environmental analysis of leaf shape. I will end
with a discussion of the caveats of each of these approaches and the application of a promising newtechnique, Persistent Homology, to more universally characterize the plant form.

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8E1-S11-3
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Wei Guo
Institute for Sustainable Agro-ecosystem Services, The University of Tokyo, Japane-mail: email@address
Seishi Ninomiya
Institute for Sustainable Agro-ecosystem Services, The University of Tokyo, Japan

Low cost field based plant phenotyping with cameras and image analytics
Nowadays, field based plant phenotyping (investigates how a plant's genome, interacting with theenvironment, affects the observable traits of a plant) is becoming new bottleneck for plant breeding research.
The measurements by image analytics allow the recording and monitoring of relevant phenotypes
noninvasively, with higher precision, accuracy and throughput than manual measurement and at
considerable reduced cost and human labors. In this talk, we will present some of the on-going field
phenotyping researches using image analytics techniques. The image data collecting solutions which areintegrating digital cameras into variance field sensing platforms such as field-server, ground moving
vehicles and drones, image analyzing algorithms that aimed to measure the phenotypic traits of crops will
be introduced. Then the futuristic challenges of field based phenotyping will also be discussed.

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8B2-S12
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 8, 10:45 – 12:15, Room B
Horizon of mutualism studies
Organizer(s):Hisashi Ohtsuki
SOKENDAI (The Graduate University for Advanced Studies), Shonan Village,
Hayama, Kanagawa 240-0193, Japane-mail: ohtsuki_hisashi@soken.ac.jp

Evolution of mutualism and its ecological consequences have recently been drawing a wider attention.
For example, it is not obvious how mutualism is initially established between different species withdifferent interests, how the evolutionary transition from parasitism to mutualism occurs, and how
mutualism is stably maintained despite the possibility of exploitation by cheaters. In community ecology,
it has been theoretically shown that mutualism destabilizes the community. This symposium aims toprovide recent theoretical findings in mutualism studies and discuss future direction in this field.
Time

Title & Presenter

10:45 – 10:50

Introduction
Hisashi Ohtsuki (SOKENDAI)

10:50 – 11:10

The ecology of the microbiome: Networks, competition & cooperation, andstability
Jonas Schluter (Memorial Sloan Kettering Cancer Center)

11:10 – 11:30

Coevolutionary dynamics of one-to-many mutualisms
Hideo Ezoe (Osaka Prefecture University)

11:30 – 11:50

Resampling after discrimination destabilizes mutualism
Yu Uchiumi (SOKENDAI)

11:50 – 12:10

Joint evolution of interspecific mutualism and developmental stability under
directional selection in trait space
Atsushi Yamauchi (Center for Ecological Research, Kyoto University)

12:10 – 12:15

General Discussion- 80 -

8B2-S12-1
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Jonas Schluter *+Memorial Sloan Kettering Cancer Centere-mail: jonas.schluter+sokendai@gmail.com
Katharine Z. Coyte*
Memorial Sloan Kettering Cancer Center
Kevin R. Foster+
University of Oxford*These author contributed equally to this work
+Corresponding authors

The ecology of the microbiome: Networks, competition & cooperation, andstability [1]The human gut harbors a large and complex community of beneficial microbes that remain stable overlong periods. This stability is considered critical for good health but is poorly understood. Here we develop
a body of ecological theory to help us understand microbiome stability.
Although cooperating networks of microbes can be efficient, we find that they are often unstable.
Counterintuitively, this finding indicates that hosts can benefit from microbial competition when thiscompetition dampens cooperative networks and increases stability. More generally, stability is promoted
by limiting positive feedbacks and weakening ecological interactions.
We have analyzed host mechanisms for maintaining stability—including immune suppression, spatial
structuring, and feeding of community members—and support our key predictions with recent data.
REFERENCES[1] Coyte KZ*, Schluter J *+, Foster, KR+, 2016 The ecology of the microbiome: Networks, competition, andstability. Science, 350: 6261, p663-666.

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8B2-S12-2
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Hideo Ezoe
Osaka Prefecture University, Sakai, Japane-mail: hezoe@b.s.osakafu-u.ac.jp

Coevolutionary dynamics of one-to-many mutualisms
One-to-many mutualisms—interspecific cooperations in which each host individual can potentiallyinteract with multiple symbiont individuals while each symbiont individual can only one hostindividual—are ubiquitously found in nature and include well-known mutualistic systems such as fig–fig
wasp, legume–rhizobium etc., although their evolutionary stability has not been explored. It has been
often thought that partner choice by hosts can stabilize multi-player mutualisms [1][2]. However, in oneto-many mutualisms, partner choice is inevitably asymmetric between hosts and symbionts, which mightdestabilize the system.
In this study, I develop a simple mathematical model to describe the (co)evolutionary dynamics
between host and symbiont populations in a one-to-many mutualism. I assume that each host chooses a
constant number of symbionts from a potential symbiont population, a fraction of which are chosen
through preferential choice on the basis of the cooperativeness of the symbionts and the rest are chosenrandomly. After the associations between hosts and symbionts are established, the host offers a constantamount of resource to each associating symbiont. The symbiont spends a part of the resource to increase
the fitness of the host in proportion to its cooperativeness, and the rest for its own reproduction.
First I fix the fraction and strength of the preferential symbiont choice of the host and concentrate on
the evolutionary dynamics of cooperativeness of the symbiont. I show that the pure mutualist population
is evolutionarily stable when the fraction of preferential choice c is large and the strength of preferential
choice k is small, otherwise mutualists and cheaters receiving benefits from their host without a returncoexist in the symbiont population. In the coexistence state the frequency of mutualists increases with c.
In contrast, it decreases with k, while the cooperativeness of mutualists increases. The two factors offset
against each other, so that the fitness gain of the host remains constant.
Next I examine coevolutionary dynamics of the traits of both hosts and symbionts, assuming that thepreferential choice by the host incurs a cost. Using numerical calculations, I find that mutualism ismaintained when the preferential choice by the host is not very costly and the mutation rate of thesymbiont is sufficiently large. However, mutualist symbionts coexist with cheaters in the symbiont
population when the cost of increasing the fraction of preferential choice is high. Moreover, hosts that do
not engage in preferential partner choice (indiscriminator hosts) coexist with discriminator hosts when thecost of increasing the strength of preferential choice is high. As a result, the parameter domain of puremutualism, i.e. the state free from cheater symbionts and indiscriminator hosts, can be much narrower
than the whole domain where the mutualism can persist.
REFERENCES[1] Bull, J. J. and Rice W. R., 1991. Distinguishing mechanisms for the evolution of co-operation. J Theor Biol 149:
63–74.
[2] Noë, R. and Hammerstein, P. 1995. Biological Markets. Trends Ecol Evol 10: 336–339.

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8B2-S12-3
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Yu Uchiumi
Department of Evolutionary Studies of Biosystems, SOKENDAI (The Graduate University for Advanced
Studies), Hayama, Kanagawa, Japane-mail: uchiumi_yu@soken.ac.jp
Hisashi Ohtsuki
Department of Evolutionary Studies of Biosystems, SOKENDAI (The Graduate University for Advanced
Studies), Hayama, Kanagawa, Japan
Akira Sasaki
Department of Evolutionary Studies of Biosystems, SOKENDAI (The Graduate University for Advanced
Studies), Hayama, Kanagawa, Japan

Resampling after discrimination destabilizes mutualism
Mutualism based on the reciprocal exchange of costly services must avoid exploitation by free-riders,which exploit their partners without helping. Accordingly, hosts discriminate against free-riding symbionts
in many mutualistic relationships. For example, it was experimentally shown by Kiers et al.[1] that soybeans(Glycine max) penalized non-N-fixing rhizobia (Bradyrhizobium japonicum) by halting oxygen supply tothem. Such a mechanism is not limited to legumes. In fact, similar mechanisms have been reported inflowering plants in obligate pollination mutualism, ant plants with ants, and land plants with arbuscular
mycorrhizal fungi (reviewed by Frederickson[2]). These mechanisms have been called “sanctioning”,“partner choice”, and/or “selective abortion”. Here we call these phenomena “discrimination”, regardlessof their finer details. Because the selective advantage of discriminators comes from the presence of the freeriders that they eliminate, previous studies[3,4] have argued that free-riders must be frequently supplied bymutation or immigration to maintain such discrimination mechanisms in the population.
However, by rethinking the classification of discrimination, we found that the recurrent supply of freeriders is not always essential to maintaining discrimination. We classified discrimination into two types
and analyzed the corresponding coevolutionary dynamics between host discrimination and symbiont
cooperation. In the first type of discrimination, which we call “resampling” discrimination, a hostterminates the symbiotic interaction with symbionts that it judges to be free-riders, and then resamples fromthe environment the same number of new symbionts as the ones that it rejected. In the second type of
discrimination, called “one-shot” discrimination, a host terminates the symbiosis with free-riding
symbionts, but does not resample new symbionts from the environment. We then asked whether mutational
supply of free-riders must be frequent enough to evolutionarily maintain the discrimination, by comparing
the differences in their coevolutionary outcomes.
Our comparison of the two discrimination types revealed two novel findings: (i) one-shotdiscriminators invade the resident populations consisting of free-riding symbionts and non-discriminating
hosts, whereas resampling discriminators do not; (ii) one-shot discriminators are stably maintained
regardless of the rate of mutation generating free-riders, whereas resampling discriminators are maintained
only if the mutation rate is moderately high. Although previous studies[3-5] have emphasized the necessityof a recurrent supply of free-riders to maintain discrimination, our results strongly suggest that the type of
actual discrimination mechanism should be focused on more than how the variability in a symbiont
population is maintained.
REFERENCES[1] Kiers, E.T., Rousseau, R.A., West, S.A. & Denison, R.F., 2003. Host sanctions and the legume-rhizobium
mutualism. Nature 425: 78–81.
[2] Frederickson, M.E., 2013. Rethinking mutualism stability: cheaters and the evolution of sanctions. Q. Rev. Biol.
88: 269–295.
[3] Foster, K.R. & Kokko, H., 2006. Cheating can stabilize cooperation in mutualisms. Proc. R. Soc. B Biol. Sci. 273:
2233–9.
[4] McNamara, J.M., Barta, Z., Fromhage, L. & Houston, A.I., 2008. The coevolution of choosiness and cooperation.
Nature 451: 189–92.
[5] Heath, K.D. & Stinchcombe, J.R., 2014. Explaining mutualism variation: a new evolutionary paradox? Evolution
68: 309–17.

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8B2-S12-4
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Atsushi Yamauchi
Center for Ecological Research, Kyoto University
Hirano 2-509-3, Otsu 520-2113, Japane-mail: a-yama@ecology.kyoto-u.ac.jp

Joint evolution of interspecific mutualism and developmental stability under
directional selection in trait space
The present study theoretically examines the process by which interspecific mutualism is established withtrait matching. The mathematical model for this process includes joint evolution of the mutualistic
relationship between two species and developmental instabilities of relevant traits in one-dimensional trait
space, assuming abiotic directional selection on the traits. The model indicates that the mutualism canevolve when (1) the scaled difference in directional selections on each species is small, (2) the scaled benefitof mutualism is large, and (3) the ratios of the cost coefficients of developmental stability to the benefits ofmutualism are small. It also shows that the evolution of developmental stability can promote the evolutionof mutualism with trait matching when the costs of stable development (which is a decreasing function of
instability) have minimum thresholds at high instability that restrict unlimited increments in instability. In
plant–pollinator interactions, it has recently been proposed that evolutionary surges of developmental
stability in mutualistic relationships might promote species diversification. The present results partly
support this theory with respect to the evolutionary relationship between mutualism and developmental
instability.

- 84 -

8D2-S13
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 8, 10:45 – 12:15, Room D
Patterns and Dynamics in Partial Differential Equations appearing in
Mathematical Biology
Organizer(s):Toshiyuki Ogawa
Meiji University, 4-21-1 Nakano, Nakano, 164-8525, Japane-mail: togw@meiji.ac.jp

Recent developments of the analysis for the PDE model relating to mathematical biology are discussed
in this mini-symposia. Four speakers introduce reaction-diffusion approximation for non-local effects,
amoeba behaviour, 2-dimensional traveling wave composed of convex curves and drift bifurcation of
traveling waves.
Time

Title & Presenter

10:45 – 11:05

Pattern formation through non-local interactions
Hirokazu Ninomiya (Meiji University)

11:05 – 11:25

Differentiation of behavioral type induced by environmental variationsin an amoeba
Keiichi Ueda (University of Toyama)

11:25 – 11:45

Convex traveling wave solutions to an interface equation
Harunori Monobe (Tokyo Institute of Technology)

11:45 – 12:05

Bifurcation of traveling wave in Competition-Diffusion equations
Toshiyuki Ogawa (Meiji University)- 85 -

8D2-S13-1
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
H. Ninomiya
Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japane-mail: hirokazu.ninomiya[at]gmal.com
Y. Tanaka
Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo, Hokkaido, 060-0810, Japan
H. Yamamoto
Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan

Pattern formation through non-local interactions
Recent years have seen the introduction of non-local interactions in various fields. A typical example
of a non-local interaction is where the convolution kernel incorporates short-range activation and longrange inhibition. This paper presents the relationship between non-local interactions and reaction-diffusion
systems in the following sense:(a) the relationship between the instability induced by non-local interaction and diffusion-driven
instability;(b) the realization of non-local interactions by reaction-diffusion systems.
To study these issues, we consider the following non-local evolution equation:
ut = du uxx + g(u, Ju(x, 0) = u0 (x),u),

in [ L, L] {t > 0},
on [ L, L],

under suitable assumptions for the nonlinear function g where du is a positive constant, J is a kernel. To
approximate this non-local evolution equation, we introduce the following reaction-diffusion system:M
ut = du uxx + g u, j=0 j vj ,1
vj,t =(dj vj,xx + u vj ) , (j = 0, · · · , M ).
Using this reaction-diffusion system, we show that the non-local interaction of a Mexican-hat kernel
destabilizes the stable homogeneous state and that this instability is related to diffusion-driven instability.
Furthermore, a reaction-diffusion system that approximates the non-local interaction system with any evenconvolution kernel is shown to exist.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]

S. Amari, 1977, Dynamics of Pattern Formation in Lateral-Inhibition Type Neural Fields, Biol. Cybernetics,
27, 77-87
J. Furter, M. Grinfeld, 1989, Local vs. non-local interactions in population dynamics, J. Math. Biol. 27, 65-80
V. Huston, S. Martinez, K. Mischaikow, G.T. Vickers, 2003, The evolution of dispersal, J. Math. Biol. 47,
483-517
M. Iida, M. Mimura, H. Ninomiya, 2006, Diffusion, cross-diffusion and competitive interaction, J. Math. Biol.
53 617-641
C. R. Laing, W. Troy, 2003, PDE methods for nonlocal models, SIAM J. APPLIED DYNAMICALSYSTEMS, 2, 487-516
H. Ninomiya, Y. Tanaka, H. Yamamoto, Reaction, diffusion and non-local interaction, submitted to J. Math.
Biol.
A.M. Turing, 1952, The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B, 237, 37-72- 86 -

8D2-S13-2
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Itsuki Kunita
Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan
Keiichi Ueda
Graduate School of Science and Engineering, University of Toyama, Toyama, Japane-mail: kueda@sci.u-toyama.ac.jp
Dai Akita
Graduate School of Life Science, Hokkaido University, Sapporo, Japan
Shigeru Kuroda
Hokkaido University, Sapporo, Japan
Toshiyuki Nakagaki
Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan

Differentiation of behavioral type induced by environmental variationsin an amoeba
We experimentally found that statistical distribution of passage time across the quinine zone
switched from unimodal to bimodal (two groups of crossing faster and not crossing at all) when the
periodic perturbation of light stimulation is applied homogeneously in space in addition to the quinineinduced differentiation. Here, we develop a continuum mathematical model of the cell dynamics ofamoeboid movement. Our model incorporates the dynamics of the mass flow of the protoplasmic sol, in
relation to the generation of pressure based on the autocatalytic kinetics of pseudopod formation andretraction (mainly, sol-gel conversion accompanying actin-myosin dynamics). Based on the mathematicalmodel, we succeeded to reproduce the stimulation-induced differentiation observed in the experiment. A
possible mechanism originates from a saddle structure around a canard solution.

- 87 -

8D2-S13-3
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Harunori Monobe
Tokyo Institute of Technology
e-mail: monobe.h.aa@m.titech.ac.jp
Hirokazu Ninomiya
Meiji University

Convex traveling wave solutions to an interface equation
The curve shortening flow (CSF) is an interface equation and a geometric flow of hypersurfaces in
two-dimensional spaces. CSF was originally proposed by Mullins [3] to analyze the motion of grainboundaries, and there are a lot of analysis results related to the flow. For instance, Grayson [2] showed that
any Jordan curve (simple and closed curve) will be convex in a finite time. Moreover Gage-Hamilton[1]confirmed that any convex Jordan curves shrink to a single point at a finite time. From these two results,
any Jordan curve will become to a convex shape and shrink to a single point in a finite time. We remarkthat there exists a traveling wave called Grim Reaper defined in the whole space.
In recent years, CSF with driving force F also appear in various physical and biological problems.
The most simple one is that F is a positive constant, called Eikonal-curvature flow. This equation isrelated to a ray optics. Ninomiya and Taniguchi [4] showed that there exists a traveling wave, called Vshaped traveling front, defined in the whole space. Also this flow appears as a singular limit problem ofsome reaction-diffusion equations and systems, e.g., Allen-Cahn equation, FitzHugh-Nagumo equation anda kinematic model of excitable media. In addition, CSF with driving force is related to not only interface
equations but also free boundary problems related to cell motility.
In this talk, we consider the existence of a traveling wave composed of a Jordan curve for CSF withdriving force F. More precisely, we investigate the condition of driving force F such that CSF has travelingwave composed of Jordan curve. As a result, we obtain that
(1) If F is a Lipschitz function, all traveling waves are convex.
(2) In addition, when F is a positive, there exists a unique traveling wave.
(3) Assume that there exist traveling waves for CSF with a driving force F . Then there is at most one
traveling wave.
REFERENCES[1] M. E. Gage and R. S. Hamilton, 1986. The heat equation shrinking convex plane curves, J. Differential Geom.,
23: 69–96.
[2] M. A. Grayson, 1987. The heat equation shrinks embedded plane curves to round points, J. Differential Geom.,
26: 285–314.
[3] W. Mullins, 1963. Solid surface morphologies governed by capillarity, Metal Surface: Structure, Energetics andKinetics. Am. Soc. Metals., 17–66.
[4] H. Ninomiya and M. Taniguchi, 2005. Existence and global stability of traveling curve fronts in the Allen-Cahn
equations, J. Differential Equations, 213: 204–233.

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8D2-S13-4
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Toshiyuki Ogawa
Meiji University, Nakano campus, 4-21-1 Nakano, Nakano-ku, Tokyo, Japane-mail: togw@meiji.ac.jp
Shin-Ichiro Ei
Hokkaido University, Kita 8, Nishi 5, Kita-ku, Sapporo, Japane-mail: Eichiro@math.sci.hokudai.ac.jp
Hideo Ikeda
Toyama University, Gofuku Campus, 3190 Gofuku, Toyama, Japane-mail: ikeda@sci.u-toyama.ac.jp
Masayasu Mimura
Meiji University, Nakano campus, 4-21-1 Nakano, Nakano-ku, Tokyo, Japane-mail: mimura.masayasu@gmail.com

Bifurcation of traveling wave in Competition-Diffusion equations
There have been a lot of studies on the traveling wave solutions to a reaction-diffusion system with 2
competing species. Let us consider, here, the situation where we have third competing species adding tothe original two competing species. Since this system has a trivial traveling solution which consists of thetraveling wave solution of 2 species, the question is the stability of this solution in the full 3 component
system. It turns out there is one critical point by taking the birth rate of the third species as a bifurcation
parameter and we study the bifurcation structure around this critical point.
REFERENCES[1] H. Berestycki, O.Diekmann, C.Nagelkerke and P.A.Zegeling, Can a species keep pace with a shifting climate?,
Bull. Math. Biol., 71, 399-429, 2009.
[2] S.Ei, The motion of weakly interecting pulses in RD sysytems, J. Dyn.Diff. Eqs. 14(1), 2002.
[3] Y.Kan-on, Parameter dependence of propagation speed of traveling waves for competition-diffusion equations,
SIAM J. Math. Anal., 26, 340-363, 1995.

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8E2-S14
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 8, 10:45 – 12:15, Room E
Extraordinary forms - exploring the limits of cell shape modeling
Organizer(s):Shigeo Hayashi
Laboratory for Morphogenetic Signaling, RIKEN Center for Developmental Biology,22-3 Minatojima-Minamimachi, Chuo-ku, Kobe, Japan, 650-0047
e-mail: shayashi@cdb.riken.jp
Takashi Miura
Department of Anatomy and Cell Biology, Kyushu University Graduate School of
Medicine, 3-1-1 Maidashi Higashi-ku Fukuoka 812-0054 JAPANe-mail: miura_t@anat1.med.kyushu-u.ac.jp
Co-presented by Spontaneous pattern formation ex vivo, JST CREST

Cells have been extensively studied as a building block of living organisms in cell biology andmathematical biology. As a result, morphogenesis of standard cells like epithelia, fibroblasts or neurons aregradually understood. However, cells exhibit much diverse shape in the real world. In this symposium, we
present several strange cell shapes which we cannot imagine from textbook knowledge together withcurrent theoretical models that has been used to model cell form. By combining these biological examples
and theoretical models, we try to clarify the possibility and limit of cell shape modeling in mathematicalbiology.
Time

Title & Presenter

10:45 – 11:03

Mechanism of jigsaw-puzzle pattern formation in plant leaf epidermal cell:
modeling single cell shape by interface equation and convolution kernel
Takashi Miura (Kyushu University Graduate School of Medical Sciences)

11:03 – 11:21

Form and Function of Pollen Grains
Hideki Takahashi (The University Museum, Hokkaido University)

11:21 – 11:39

Recreating human podocytes in the kidney
Ryuichi Nishinakamura (Institute of Molecular Embryology and Genetics,
Kumamoto University)

11:39 – 11:57

Cellular Tessellation in Sensory Epithelia
Hideru Togashi (Kobe University Graduate School of Medicine)

11:57 – 12:15

Simulating the Onset and Development of Polycystic Kidney Disease using
Virtual Tissues
James Glazier (Department of Intelligent Systems Engineering and Biocomplexity
Institute, Indiana University)- 90 -

8E2-S14-1
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Takashi Miura
Kyushu University Graduate School of Medical Sciencese-mail: miura_t@anat1.med.kyusu-u.ac.jp
Takumi Higaki
Department of Integrated Biosciences, The University of Tokyo
Natsumaro Kutsuna
LPixel Inc. & Department of Integrated Biosciences, The University of Tokyo
Kae Akita
Department of Integrated Biosciences, The University of Tokyo
Hisako Takigawa-Imamura
Kyushu University Graduate School of Medical Sciences
Kenji Yoshimura
Department of Neurology, Osaka City General Hospital

Mechanism of jigsaw-puzzle pattern formation in plant leaf epidermal cell:
modeling single cell shape by interface equation and convolution kernel
Plant leaf epidermal cell shows beautiful jigsaw-puzzle like pattern. Various molecules are known to
be involved in this process. For example, two small rho GTPase ROP2 and ROP6, are involved in
production and degradation of cell wall under the control of auxin [1]. However, how the interaction ofthese molecules results in pattern formation remain to be elucidated.
In the present study, we model this phenomenon using interface equation and convolution kernel [2].
We consider the movement of the boundary between cytoplasm and cell wall. At first we define the speedof growth normal to the interface as 𝑉. Next we define the effect of short-range signaling molecule (𝑣)which is released from cytoplasm as convolution kernel k. Effect of surface tension is defined as 𝜎𝜅, inwhich 𝜅 represents local curvature and 𝜎 represents strength of surface tension. The governing equationis𝑉 = 𝑓(𝑣) − 𝜎𝜅𝑣 = 𝑘 ⊗ 𝑢.
We use Heaviside function for kernel 𝑘 and numerically calculate the equation using Phase field
method. We reproduced the formation of cell wall interdigitation by this model, and analytically obtain thefastest growing wavenumber. We also reproduced the dynamics of three-way junction of cell wall and cellwall thickening by degradation of cellulose.
REFERENCES[1][2]

T. Xu, M. Wen, S. Nagawa, Y. Fu, J.-G. Chen, M.-J. Wu, C. Perrot-Rechenmann, J. Friml, A. M. Jones, andZ. Yang, “Cell Surface- and Rho GTPase-Based Auxin Signaling Controls Cellular Interdigitation in
Arabidopsis,” Cell, vol. 143, no. 1, pp. 99–110, Oct. 2010.
T. Higaki, N. Kutsuna, K. Akita, H. Takigawa-Imamura, K. Yoshimura, and T. Miura, “A Theoretical
Model of Jigsaw-Puzzle Pattern Formation by Plant Leaf Epidermal Cells.,” PLoS Comput Biol, vol. 12, no.
4, p. e1004833, Apr. 2016.

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8E2-S14-2
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Hideki Takahashi
The University Museum, Hokkaido University, Sapporo, 060-0810, JAPANe-mail: hide@museum.hokudai.ac.jp

Form and Function of Pollen Grains
Pollen grain is one of the most important cells in the plant life cycle. Genetic content of pollen grain
is united with that of the female embryo sac, through the double-fertilization the next generation, the seedis formed. Thus if pollen grains could not reach the stigma of the pistils and they could not germinate thepollen tube, the next generation does not made.
Form and function of the pollen grains have been studied by Wodehouse (1935), Erdtman (1952), andFaegri et al. (1989) in light microscopic level (LM). They show many relationships between pollen
morphology and plant taxonomic system and/or plant phylogeny and evolution. But mainly since 1970’s,
transmission electron microscope (TEM), and a little later scanning electron microscope (SEM) haveworked as the useful tools for clarifying the fine pollen morphology. Especially TEM have worked wellin clarifying the developmental processes of the exine (pollen wall) and aperture (lacking place of exine).
Four cells derived from one mother cell is enclosed in the callose special wall, and the primexine works as
template for making the exine.
We can divide the pollen morphology into several factors; size and shape of pollen grains, the number
and position and structure of the pollen apertures, and structure and sculpture of pollen wall. Pollen grain
is usually a single cell-size unit, but sometimes they unite into tetrad, polyad, or pollen mass (pollinia) insome special taxonomic groups.
In the spores (ancient pollen grains) of the mosses, ferns and fern allies, the single aperture is situatedat the proximal pole on evely four cells that derived from one mother cell through the meiosis. In the firststage of the seed plant, i.e., Gymnospers, single aperture is changed to the distal pole. In the next
evolutional stage, many angiospermous families show the three longitudinal, equatorially arranged colpi
on the grain. This sudden change from one to three in the number of apertures is a very interesting
problem in the plant evolution. And the pollen grains that have many apertures globally on the surface ofthe grains appeared in some special plant taxa.
Aperture shape is usually pore or colpus (slit-like). And in the next evolutional stage, colpus in theouter wall and pore in the inner wall are combined and form the ‘colporate’ apertures. Aperture is a thinwall area on the pollen surface and important in the pollen tube germination on the stigma, but during thepollen dispersal time, pollen grains have to maintain their own humidity, so shrinking shape by the intrusionof apertures work well in preserving the cell content. Structure of pollen wall and aperture is important inchanging the cell shape both in dry and wet conditions. This function is called as ‘hermomegathy’.
Structure and sculpture of the pollen wall works as the sticking method on the body of visiting insects.
A layered structure of the pollen wall also work as the deposition space for some sticky materials for thepollinators and some efficient materials in incompatibility systems. Sculpture of the wall and shape and/or
size of the pollen grain itself may include an important meaning in anemophily vs. entomophily.
REFERENCES[1] Miyoshi, N., Fujiki, T. & Kimura, H. 2016. Pollen Flora of Japan (in Japanese), enlarged and 2nd ed. Hokkaido
Univ. Press,[2] Faegri, K., Kaland, P.E. and Krzywinski, K. 1989. Textbook of Pollen Analysis, 4th ed. John Wiley & Sons,
Chichester.
[3] Erdtman, G. 1952. Pollen Morphology and Plant Taxonomy, Angiosperms. Almqvist & Wiksell, Stockholm.
[4] Wodehouse, R.P., 1935. Pollen Grains. McGraw-Hill Book Co., Inc., New York.

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8E2-S14-3
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Hideru Togashi
Kobe University Graduate School of Medicine
e-mail: htogashi@med.kobe-u.ac.jp

Cellular Tessellation in Sensory Epithelia
Animal tissues are composed of multiple cell types arranged in complex and elaborate patterns. In
sensory epithelia, including the auditory epithelium and olfactory epithelium, different types of cells arearranged in unique mosaic patterns. These mosaic patterns are evolutionarily conserved, and are thought tobe important for hearing and olfaction. The complex patterns of cells in tissues often arise through selforganization of cells. Differential adhesion has been proposed to promote selective aggregation or
rearrangement of cells, and these mechanisms could drive self-organized cell movements in the sensory
epithelia. Recent progress has provided accumulating evidence that the cellular pattern formation in sensory
epithelia involves cell rearrangements, movements, and shape changes. These morphogenetic processes arelargely mediated by intercellular adhesion systems. Many different types of cells in tissues express various
types of cell adhesion molecules. Although cooperative mechanisms between multiple adhesive systems
are likely to contribute to the production of complex cell shapes and patterns, our current understanding is
insufficient to entirely explain the complex mechanisms. Recent studies have revealed that nectins, incooperation with cadherins, are crucial for the mosaic cellular patterning in sensory organs. The nectin andcadherin systems are physically and functionally associated with one another, and these associations
provide cells with differential adhesive affinities for complex cellular pattern formations in sensory
epithelia. In this symposium, I will introduce and discuss recent progress of our studies on cellularpatterning and unique morphology of the cells in sensory organs.
REFERENCES[1] Katsunuma, S., Honda, H., Shinoda, T., Ishimoto, Y., Miyata, T., Kiyonari, H., Abe, T., Nibu, K., Takai, Y., andTogashi, H. 2016. Synergistic action of nectins and cadherins generates the mosaic cellular pattern of the olfactory
epithelium. J. Cell Biol., 212: 561–575.
[2] Fukuda, T., Kominami, K., Wang, S., Togashi, H., Hirata, K., Mizoguchi, A., Rikitake, Y., and Takai, Y. 2014.
Aberrant cochlear hair cell attachments caused by Nectin-3 deficiency result in hair bundle abnormalities.
Development, 141: 399-409.
[3] Togashi, H., Kominami, K., Waseda, M., Komura, H., Miyoshi, J., Takeichi, M., and Takai, Y. 2011. Nectins
Establish a Checkerboard-like Cellular Pattern in the Auditory Epithelium. Science, 333: 1144–1147.

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8E2-S14-4
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Ryuichi Nishinakamura
Institute of Molecular Embryology and Genetics, Kumamoto University
e-mail: ryuichi@kumamoto-u.ac.jp

Recreating human podocytes in the kidney
Recapitulating three-dimensional structures of the kidney in vitro is a major challenge for developmental
biology and regenerative medicine. The kidney develops by the reciprocal interaction between themetanephric mesenchyme and the ureteric bud, the former of which contains nephron progenitors. We
found that nephron progenitors are derived from posteriorly located T-positive population at the postgastrulation stage, and succeeded in generating the three-dimensional nephrons in vitro from pluripotent
stem cells both in mice and humans.
Nephrons consist of glomeruli and renal tubules, the former of which contribute to the filtration processof the kidney. Glomerular podocytes possess numerous cellular protrusions, and between these footprocesses, the slit diaphragms are formed and prevent protein leakage into the urine. The podocytes
induced from human iPS cells in vitro exhibit many of these features, suggesting that the basic
morphology of the podocytes is generated cell-autonomously. However, the foot process become more
complicated when glomeruli are vascularized upon transplantation, indicating that the interactions
between the vascular endothelial cells and podocytes may be required for further maturation. Thesefindings will be useful for dissecting human glomerular development and diseases.
Although many proteins, including nephrin and podocin, are involved in the formation of slit diaphragms,
little is known how morphology of podocytes is regulated. I will update the podocyte biology to discuss
whether the unique feature of the podocytes is a good target of mathematical biology.
REFERENCES[1] Tanigawa S et al. Selective in vitro propagation of nephron progenitors from embryos and pluripotent stem cells.
Cell Rep 15: 801-813, 2016[2] Sharmin S et al. Human induced pluripotent stem cell-derived podocytes mature into vascularized glomeruli upon
experimental transplantation. J. Am. Soc. Nephrol. 27: 1778-1791, 2016[3] Taguchi A et al. Redefining the in vivo origin of metanephric nephron progenitors enables generation of complex
kidney structures from pluripotent stem cells. Cell Stem Cell 14: 53-67, 2014

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8E2-S14-5
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
James A. Glazier
Department of Intelligent Systems Engineering and Biocomplexity Institute.
Indiana University
Bloomington, Indiana, USAe-mail: jaglazier@gmail.com

Simulating the Onset and Development of Polycystic Kidney Disease using Virtual
TissuesIn polycystic kidney disease (ADPKD), the normal structural organization of the kidney breaks down
as cysts appear, grow and progressively impair kidney function. Mutations in PKD1 and PKD2 genes
appear to cause ADPKD, but we do not know how mutations in these genes change cell behaviors to
produce ADPKD pathogenesis. A clue to the mechanism of kidney disorganization is that human ADPKD
cysts frequently express cadherin-8 (an adhesion molecule found in normal juvenile kidney but absent fromnormal adult kidney), and that ectopic expression of cadherin-8 in vitro initiates cystogenesis. To explore
the possible roles of cadherin-8 in cyst initiation, we developed a virtual-tissue computer simulation using
the open-source CompuCell3D modeling environment [1]. Our simulations showed that cadherin-8induced reduction of either cell-cell adhesion or contact inhibition of proliferation could initiate cyst
formation [2]. However, the dynamics and morphologies of the cysts differ between these two mechanisms,with reduced adhesion replicating the morphologies of in vitro cadherin-8-induced cysts. Decreased contact
inhibition results in a disctinct morphology of “Saccular” cysts which have also been observed in somehuman patients, suggesting that cysts may form through multiple mechanisms in humans. We confirmed
our simulation findings using in vitro experiments to show that ectopic cadherin-8 expression did, in fact,
reduce cell-cell adhesion. Since adhesion loss due to cadherin type switching in ADPKD suffices to drive
cystogenesis, control of cadherin type switching could provide an effective therapy for ADPKD.
REFERENCES[1] http://www.compucell3d.org/[2] Belmonte, J.M., Clendenon, S.G., Oliveira, G.M., Swat, M.H., Greene, E.V., Jeyaraman, S., Glazier,
J.A., Bacallao, R.L., 2016. Virtual-Tissue Computer Simulations Define the Roles of Cell Adhesion andProliferation in the Onset of Kidney Cystic Disease. Molecular Biology of the Cell, (2016), doi:
10.1091/mbc.E16-01-0059- 95 -

8B3-S15
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 8, 15:45 – 17:15, Room B
Biological Relevances of Mathematical Models
Organizer(s):Kunimochi Sakamoto
Hiroshima University, 1-3-1 Kagamiyama, HigashiHiroshima, 739-8526, Japane-mail: kuni@math.sci.hiroshima-u.ac.jp

The purpose of the symposium is to investigate, by three talks, whether or not dynamical systemmodels for biological phenomena are really relevant to, or capture certain aspects of, the biological systems
which the differential equations are originally intended to model. It is not intended to assert that our views
are the definite ones. Through our talks, we attempt to set a stage for open discussion.
Time

Title & Presenter

15:45 – 16:15

Bulk reaction versus Boundary flux in diffusive systems
Kunimochi Sakamoto (Hiroshima University)

16:15 – 16:45

A mathematical approach to the economy of atomic power generation
Fumio Nakajima (Iwate University)

16:45 – 17:15

Diffusion driven destabilization of a spatially homogeneous limit cycle in reactiondiffusion systems
Masataka Kuwamura (Kobe University)- 96 -

8B3-S15-1
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Kunimochi Sakamoto
Hiroshima University, Higashi-Hiroshima, Japane-mail: kuni@math.sci.hiroshima-u.ac.jp

Bulk reaction versus Boundary flux in diffusive systems
In dealing with the polarity and rhythmicity of a cell, several researchers have proposed reactiondiffusion systems with natural boundary conditions [2,3]. In addition, the proposed systems have anotherfeature that they have a mass-conserving property. It should be emphasized that in these systems reaction
takes place in the bulk (i.e., in the interior of domain).
On the other hand, the authors of [1] proposed a diffusive system with nonlinear boundary flux conditions,in order to account for rhythmic activities of cells. Although the system proposed in [1] contains bulk
decay and growth, its essential innovation lies in the introduction of nonlinear boundary flux conditions
into the modeling of cell activities. Following the same line of research area as in [1], a Turing typemechanism is extended for diffusive systems with boundary flux conditions by [4,5].
It is our interest to compare the behavior of solutions of two types of models:(1) Diffusive systems with bulk reaction and the natural boundary conditions;and(2) Diffusive systems with flux boundary conditions.
It seems that the boundary flux in (2) has an effect similar to the bulk reaction in (1).
On one hand, systems of type (1) have solutions monotonic in one direction (or, traveling wave typesolutions) and solutions with a single peak (so-called, a spike). On the other hand, the steady statesolutions of systems of type (2) automatically have the characteristic of polarity. Therefore, stability
property of steady states, studied in[4,5], is relevant in systems of type (2).
Exhibiting these features of solutions, the talk will propose that boundary flux conditions in diffusive
systems may play an alternative modeling role of bulk reaction. Between bulk reaction and boundary flux,
which mechanism is more relevant to biology depends on the phenomena one wish to understand. It isalso natural that both of these effects, bulk reaction and boundary flux, should be appropriately combinedin order to better describe processes taking place in cells. This is a challenge to both mathematics andbiology.
REFERENCES[1] Levine, H. and Rappel, W-J., 2005, Membrane-bound Turing patterns, Physical Review E 72: 061912.
[2] Ishihara, S., Otsuji, M. and Mochizuki, A., 2007, Transient and steady state of mass-conserver
reaction diffusion systems, Physical Review E 75: 356--368.
[3] Mori, Y., Jilkine, A. and Edelshtein-Keshet, L., 2008, Polarity from a Bistable Reaction-Diffusion
Systems, Biophysical Journal 94: 3648--3697.
[4] Anma, A. and Sakamoto, K., 2013, Turing type mechanisms for linear diffusion systems under nondiagonal Robin boundary conditions, SIAM Journal of Math. Anal. 45: 3611--3628.
[5] Sakamoto, K., 2016, Destabilization threshold curves for diffusion systems with equal diffusivity
under non-diagomal flux boundary conditions, Discrete and Continuous Dynamical Systems, Series B 21:
641--654.

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8B3-S15-2
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Fumio Nakajima
Iwate University, Morioka, Japane-mail: fnaka@iwate-u.ac.jp

A mathematical approach to the economy of atomic power generation
In 1970's Dr. Schumacher appealed that the atomic power generation should be immediately abolishedbecause of the various poisonous influence due to radiation [1]. Even at the present day, we have not found
any safe disposal of the radio-active waste. The purpose of this paper is to innovate a mathematical modelof the economy of the atomic power generation in our society, and then to conduct Schumacher's appeal asa theorem.
Now, setting x(t) to be the population of the society at time t, and y(t) and z(t) to be the total power ofthe non-atomic power generation and atomic power generation demand by this society, respectively, we
shall consider the system (1), (2) and (3) as follows.
(1)
(2)
(3)

x'=a(1-x)x+y+zy'=θx-byz'=(1-θ)x -cz -d ∫ z(s) ds,

where the integral in s is between s=0 and s=t, while a, b, c, d and θ are positive constant with 0<θ<1.
This system has the following meaning. First of all, (1) is the logistic equation when y and z are absent,and (1) implies that x(t) increases by the addition of y(t) and z(t) to the society. In (2) and (3), the term θxand (1-θ)x are the incomes for the non-atomic power generation and the atomic power generation from thesociety, respectively, where the units of the power generation and the incomes are appropriately chosen,
and terms by and cz are their immediate costs, respectively, for example the cost of the fossil fuel and thecost of the uranium, respectively. Finally the integral term in the right hand side of (3) is the cost for thetreatment of the radio-active waste, which is a feature of the atomic power generation, where the lower
limit of the integral, t=0, is the initial time for the atomic power generation to start, and hence our initialcondition is as follows.
(4)x(0)>0,y(0)≥0,z(0)=0.

Clearly (1) (2) (3) are meaningful in the case where x(0)>0, y(0)≥0, z(0)≥0, and in fact by the conditionsin (4),we have x(t)>0,y(t)>0 and z(t)>0 for small t >0. Therefore there exists the maximal number ω>0such that x(t)>0, y(t)>0 and z(t)>0 for 0<t<ω, where ω could be infinity.Our main result is the following.
Theorem 1(i) If ω is finite, then x(t), y(t) and z(t) are defined for t=ω, and z(ω)=0, which x(ω)>0 and y(ω)>0.
(ii) If ω=∞, then the following hold as t goes to ∞: z(t) converges to 0; x(t) converges to (θ/ab) +1;

 y(t) converges to (θ/b)((θ/ab) +1);

 the integral of z(t) on the non-negative half line [0,∞) is equal to (1-θ)((θ/ab) +1)/d.
RemarkThe conclusion of Theorem 1, that is either z(ω)=0 or z(ω)=0, claims that the atomic power
generation should be abolished sooner or later.
REFERENCES[1] E. F. Schumacher, Small is beautiful: A study of economics as if people matterd,
Blond and Briggs Ltd, London (1973).

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8B3-S15-3
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Masataka KUWAMURA
Kobe University, Kobe, Japane-mail: kuwamura@main.h.kobe-u.ac.jp
Hirofumi IZUHARA
University of Miyazaki, Miyazaki, Japane-mail: izuhara@cc.miyazaki-u.ac.jp

Diffusion driven destabilization of a spatially homogeneous limit cycle
in reaction-diffusion systems
In this talk, we study the diffusion driven destabilization of a spatially homogeneous limit cycle in 2component reaction-diffusion systems defined on a finite size interval under the periodic boundary
condition.
It is shown that a spatially homogeneous limit cycle becomes unstable and changes to a stable spatiallynonhomogeneous limit cycle for appropriate diffusion coefficients.
This is analogous to the diffusion driven destabilization (Turing instability) of a spatially homogeneous
equilibrium.
Our approach is based on a reaction-diffusion system with mass conservation and its perturbed system
which is considered as an infinite dimensional fast-slow system.
It should be emphasized that the spatially nonhomogeneous limit cycle cannot be captured in the frameworkof the perturbation theory as seen in the previous works by Maginu [1] and Kuramoto [2].
Our approach would provide an useful and alternative viewpoint for studying the diffusion driven
destabilization (Turing instability) of a spatially homogeneous limit cycle.
This is a first step for extending the scope of application of Turing's theory from stationary states tononstationary states including limit cycles.

REFERENCES[1] K. Maginu, Stability of spatially homogeneous periodic solutions of reaction-diffusion equations, J. Diff. Eqns. 31(1979) 130-138.
[2] Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer-Verlag, Berlin Heidelberg, 1984.
[3] M. Kuwamura, Y. Morita, Perturbations and dynamics of reaction-diffusion systems with mass conservation,
Phys. Rev. E 92 (2015), 012908.
[4] S.-I. Ei, H. Izuhara, M. Mimura, Infinite dimensional relaxation oscillation in aggregation-growth systems,
DCDS series B, 17 (2012) 1859-1887.
[5] H. Izuhara, M. Kuwamura, submitted.

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8D3-S16 (Special)
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka

Special Symposium
Sep 8, 15:45 – 17:15, Room E
Pattern formation in heterogeneous environments
Organizer(s):Izumi Takagi
Institute of Liberal Arts and Sciences, Tohoku University, 980-8576 Kawauchi 41,
Aoba-ku, Sendai
e-mail: takagi@m.tohoku.ac.jp
Fang Li
Center for PDE, East China Normal University, No 500 Dongchuan Road, Center for
PDE, Administration Building 12th floor, Minhang Campus, East China Normal
University, Shanghai, 200241, Chinae-mail: fli@cpde.ecnu.edu.cn

Turing used the principle of diffusion-driven instability (DDI, for short) to explain how a spatiallyhomogeneous state can develop spontaneously a spatially nontrivial structure, i.e., pattern. However, actual
biological phenomena take place in more or less non-uniform environments. In some cases organisms
themselves create non-uniformity of the environment. Therefore, it is very important to understandquantitatively the effect of spatial heterogeneity on resulting patterns.
The purpose of this symposium is to explore the frontiers of mathematical researches on models of
pattern formation that utilize partial differential equations, laying emphasis on how spatial heterogeneity
influences patterns. Moreover, this mini-symposium is co-organized by Japanese and Chinesemathematicians in the hope of promoting collaboration not only between biologists and mathematicians,
but also collaboration among young scientists in Eastern Asia.
Time

Title & Presenter

15:45 – 15:50

OpeningIzumi Takagi (Institute of Liberal Arts and Sciences, Tohoku University)

15:50 – 16:10

Pattern formation in homogeneous media vs in heterogeneous media: cutting andgrafting experiments on hydra
Izumi Takagi (Institute of Liberal Arts and Sciences, Tohoku University)

16:10 – 16:30

Spiky steady states for a chemotaxis system with singular sensitivity
Huicong Li (Center for PDE, East China Normal University)

16:30 – 16:50

Self-organization of bacterial communities against environmental pH variation
Sohei Tasaki (Frontier Research Institute for Interdisciplinary Sciences, Tohoku
University)

16:50 – 17:10

Non-local effects in an integro-PDE model from population genetics
Fang Li (Center for PDE, East China Normal University)

17:10 – 17:15

ClosingFang Li (Center for PDE, East China Normal University)- 100 -

8D3-S16-1
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Izumi Takagi
Institute of Liberal Arts and Sciences
Tohoku University
41 Kawauchi, Aoba-ku, Sendai 980-8576, JAPANe-mail: takagi@morphos.jp

Pattern formation in homogeneous media vs in heterogeneous media:
cutting and grafting experiments on hydra
In their seminal paper [1] Gierer and Meinhardt derived their model equations by assuming that theinteraction takes place in a spatially uniform environment. Once they obtained the equations, they
proceeded to taking spatial heterogeneity into account. They wrote: “A shallow gradient of source
distribution can lead to a striking pattern of activator concentration, with a maximum at the terminal of highsource density, … . Thus the source density distribution determines the polarity of the pattern.” (p.34 of[1]). They applied their theory to transplantation experiments on hydra. Their computer simulations madeuse of the activator-inhibitor system with a fairly steep gradient of source density distribution, whichsuggests that to form a second head, strong heterogeneity in source distribution is needed.
Based on decades of mathematical studies on reaction-diffusion systems, we know that in spatially
uniform environments, steady-state patterns are determined by the geometry of domain, while in spatially
non-uniform environments, they are determined as a result of competition between the domain geometry
and the spatial heterogeneity of the system. Hence, much more attention is required in modeling aphenomenon which involves the control of patterns by way of spatial heterogeneity. In this talk we present
a modification of the activator-inhibitor system by Gierer and Meinhardt to explain hydra grafting
experiments. Also, we compare our modification with receptor-based models by [5] and by MarciniakCzochra [3, 4].
REFERENCES[1] Gierer, A. and Meinhardt, H., 1972. A theory of biological pattern formation, Kybernetik (Berlin) 26: 30–39.
[2] Maini, P.K., Takagi, I. and Yamamoto, H. (in preparation)[3] Marciniak-Czochra, A. 2003. Receptor-based model with diffusion-driven instability for pattern formation in
hydra. J. Biol. Syst. 11, 293—324.
[4] Marciniak-Czochra, A. 2006. Receptor-based models with hysteresis for pattern formation in hydra.
Mathematical Biosciences 199, 97—119.
[5] Sherratt, J.A., Maini, P.K., Jäger, W. and Müller, W, 1995. A receptor-based model for pattern formation in
hydra. Forma 10, 77—95.

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8D3-S16-2
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Huicong Li
Center for PDE, East China Normal University, Shanghai, Chinae-mail: hli7@tulane.edu

Spiky steady states of a chemotaxis system with singular sensitivity
This project is concerned with the steady state problem of a chemotaxis model with singular sensitivity
function in a one dimensional spatial domain. Using the chemotactic coefficient 𝜒 as the bifurcation
parameter, we perform local and global bifurcation analysis for the system. It is shown that positive
monotone steady states exist as long as 𝜒 is larger than the first bifurcation value. Then we use Helly’s
compactness theorem and Sturm’s oscillation theorem to obtain basic and refined asymptotic profiles ofthese steady states, as 𝜒 becomes large. In particular, our results show that the cell density function formsa spike, which models the important physical phenomenon of cell aggregation.

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8D3-S16-3
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Sohei Tasaki
Frontier Research Institute for Interdisciplinary Sciences (FRIS), Tohoku University, Sendai, Japan
Graduate School of Science, Tohoku University, Sendai, Japane-mail: tasaki@tohoku.ac.jp
Madoka Nakayama
Sendai National College of Technology, Natori, Japan
Wataru Shoji
Frontier Research Institute for Interdisciplinary Sciences (FRIS), Tohoku University, Sendai, Japan
Institute of Development, Aging and Cancer (IDAC), Tohoku University, Sendai, Japan

Self-organization of bacterial communities against environmental pH variation
As with many living organisms, bacteria often live on the surface of solids, such as foods, organisms,
buildings and soil. Compared with dispersive behavior in liquid, bacteria on surface environment exhibit
significantly restricted mobility. They have access to only limited resources and cannot be liberated fromthe changing environment. Accordingly, appropriate collective strategies are necessarily required for longterm growth and survival. However, in spite of our deepening knowledge of the structure and characteristics
of individual cells, strategic self-organizing dynamics of their community is poorly understood andtherefore not yet predictable. Here, we report self-organizing processes of Bacillus subtilis communities
highly depending upon environmental pH, and present mathematical models for the spatio-temporal
dynamics.
B. subtilis, one of the most well-studied bacteria, exhibits diverse colony patterns on the surface ofnutrient agar media, which selectively develop in response to environmental conditions [1-3]. Amongothers, nutrition (e.g. peptone concentration) and surface moisture (inversely correlated with agar
concentration) are known as principal environmental factors for the pattern selection. In the early 1990’s,
a phase diagram was described for B. subtilis strain OG-01, in which five distinct patterns were conditioned
by nutrition and agar parameters [3]. However, little has been known if other environmental factors affectcolony morphology. B. subtilis is also widely known to form thick biofilms in which cells are held together
by a self-produced extracellular matrix. The wild-type strain OG-01 also creates thick biofilms on hard agar
media, while swarming of motile cells results in rapid expansion of thin (almost one cell layer thick)colonies on soft media. We first focus on the thick biofilms of the same strain on hard plates (containing
1% agar), and report novel pH sensitive colony morphology. Self-generated directional motility depending
upon pH underlies the morphological alteration, and our simulation model, based on the pH-dependentdose-response diagram, successfully explained the self-organizing dynamics of environment-sensitive
biofilm morphology. Further, recent findings indicate that high pH sensitivity arises in a broad range ofself-organizing processes such as cell migration, collective swarming and more detailed cell type
heterogeneity, causing macroscopically morphologically diverse colonies in which sophisticatedly
regulated collective behaviors maintain and rearrange the population structure for growth and survival inchanging environment.
REFERENCES[1] Ohgiwari, M., Matsushita, M. and Matsuyama, T., 1992. Morphological changes in growth phenomena ofbacterial colony patterns. J. Phys. Soc. Jpn., 61: 816–822.
[2] Ben-Jacob, E., Schochet, O., Tenenbaum, A., Cohen, I., Czirók, A. and Vicsek T., 1994. Generic modeling ofcooperative growth patterns in bacterial colonies. Nature, 368: 46-49.
[3] Wakita, J., Komatsu, K., Nakahara, A., Matsuyama, T. and Matsushita, M., 1994. Experimental investigation on
the validity of population dynamics approach to bacterial colony formation. J. Phys. Soc. Jpn., 63: 1205-1211.

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8D3-S16-4
Sep 8, Thu (mini-symposia)
JSMB2016 Fukuoka
Fang Li
Center for PDE, East China Normal University, Shanghai, Chinae-mail: fangli0214@gmail.com

Non-local effects in an integro-PDE model from population genetics
In this talk, we discuss qualitative properties of a genetic model with partial panmixia. This model
was proposed by T. Nagylaki in 2012 to describe the evolution of two alleles under the joint action of
selection, migration and partial panmixia for the complete dominance case.
First, properties for general non-local problems are studied. Then, existence of non-trivial
steady states, in terms of the diffusion coefficient d and the partial panmixia rate b, is obtained under
different signs of the integration of g(x), which denotes the heterogeneous environment. Furthermore,stability andinstability properties for non-trivial steady states, as well as the trivial steady states u = 0 and u = 1 areinvestigated. Our results illustrate how the non-local term – namely, the partial panmixia- helps the
migration in this model.

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9B1-S17
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 9, 9:00 – 10:30, Room B
Hans Meinhardt; The Loss of the Meister of Developmental Pattern Formationand Unachieved Discussions
Organizer(s):Akiko Nakamasu
Kyushu University, Japane-mail: nakamasu@anat1.med.kyushu-u.ac.jp
Co-presented by 3D morphologic, Scientific Research on Innovative Areas, JSPS

Hans Meinhardt was a giant and pioneer of mathematical biology in the field of developmental biology.
He set up various mathematical models based on reaction-diffusion systems and was the first person who
made systematic use of computer simulations in explanations of developmental phenomena. He hadbrought about positive impacts on this field; however we lost him last February. So, in this symposium
scientists who have been working on subjects closely related to him get together and continue unachieved
discussions with him. We will hope to deepen our understanding of current topics in the study of patternformation and reaction-diffusion systems.
Time

Title & Presenter

09:00 – 09:05

Opening
Akiko Nakamasu (Kyushu University)

09:05 – 09:25

Mathematical beauty of the activator-inhibitor system
Izumi Takagi (Tohoku University)

09:25 – 09:45

Simpler modelling of the biological pattern formation
Shigeru Kondo (Osaka University)

09:45 – 10:05

Notion of diffusion-induced instability
Masayasu Mimura (Meiji University)

10:05 – 10:25

Pattern formation in chemotaxis cells and body axis formation
Tatsuo Shibata (QBiC RIKEN)

10:25 – 10:30

Closing
Akiko Nakamasu (Kyushu University)- 105 -

9B1-S17-1
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Izumi Takagi
Institute of Liberal Arts and Sciences
Tohoku University
41 Kawauchi, Aoba-ku, Sendai 980-8576, JAPANe-mail: takagi@morphos.jp

Mathematical beauty of the activator-inhibitor system
In order to illustrate his idea that “Diffusion-Driven Instability” triggers spontaneous formation ofpatterns in a chemical system, Turing made use of a digital computer [7]. To do numerical simulation, he
needed a system of equations and devised a hypothetical chemical reaction. Indeed, to find a real chemical
reaction system which exhibits patterning was the most important step in his research project after theseminal paper [7], which was never done due to his death.
Twenty years later, Gierer and Meinhardt [1] found that interaction between a slowly diffusing
activator and a rapidly diffusing inhibitor produces a pattern. They derived a two-species model system
under the assumptions(i) the interactions are described as a ratio of the power of the concentration of one species to thatof the other,(ii)
the system has a uniform steady state which is stable under spatially uniform disturbances,and(iii) one species is auto-catalytic.
They showed that these local requirements are sufficient to determine the nonlinearity. Here, “local” refers
to a neighborhood of the uniform steady-state.
It is to be emphasized that they derived the activator-inhibitor system by purely mathematicalarguments. (As a matter of fact, they found a family of reaction-diffusion systems, which has threesubclasses [4].) This may account for the beautiful mathematical structures their model systems have.
There has been a sizable amount of literature on mathematical analysis of the activator-inhibitor model(e.g., boundedness of nonstationary solutions [6], a monograph on stationary solutions [8]). In this talk we
review some results of mathematical analysis of the activator-inhibitor systems including(a) classification of kinetic behavior ([4]);(b) ultimate simplification of the system: right vs. wrong directions ([5, 2]).
As Turing did, Gierer and Meinhardt wrote down a few groups of partial differential equations which
can generate patterns in order to do computer simulations ([1, 3]). What they wanted to say was the generalstatement “short-range activator and long-range inhibitor make patterns”. Therefore, it is a mathematicalchallenge to justify their claim by identifying a class of nonlinearities which includes the activator-inhibitor
system Gierer and Meinhardt proposed.
REFERENCES[1] Gierer, A. and Meinhardt, H., 1972. A theory of biological pattern formation, Kybernetik (Berlin), 26: 30–39.
[2] Karch, G., Suzuki, K. and Zienkiewicz, J., 2016. Finite-time blowup of solutions to some activator-inhibitor
systems. Discrete and Continuous Dynamical Systems 36, 4997--5010.
[3] Meinhardt, H., 1982. Models of Biological Pattern Formation. Academic Press, London/New York.
[4] Ni, W.-M., Suzuki, K. and Takagi, I., 2006. The dynamics of a kinetic of activator-inhibitor system. J.
Differential Equaitons 229, 426--465.
[5] Ni, W.-M., Takagi, I. and Yanagida, E., 2001. Stability of least energy patterns of the shadow system for an
activator-inhibitor model. Japan J. Indust. Appl. Math. 18, 259--272.
[6] Suzuki, K. and Takagi, I., 2010. On the role of basic production terms in an activator-inhibitor system modelingbiological pattern formation. Funkcial. Ekvac. 54, 237--274.
[7] Turing, A.M., 1952. The chemical basis of biological pattern formation. Phylos. Trans. Roy. Soc. London Ser. B
237, 37--72.
[8] Wei, J. and Winter, M., 2014. Mathematical Aspects of Pattern Formation in Biological Systems. Springer- 106 -

9B1-S17-2
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Shigeru Kondo
Osaka University,Osaka,Japane-mail: shigerukondo@gmail.com

Simpler modelling of the biological pattern formation
In 1952, Turing presented the reaction-diffusion model that explains how the spatial patterns inorganisms form autonomously. About 20 years later, Gierer and Meinhardt published their first paper about
the pattern formation. Although the concept of their models was very similar, the models of Meinhardt
assumed realistic cellular interactions that attracted many of experimental biologists. I (Kondo) am oneof them. Another significant contribution of them are summarized the necessary conditions for the stable
pattern formation in a short phrase, “local activation and long range inhibition (LALI)”. This is importantbecause this “condition” does not need any specific cellular or molecular event. There are many variety ofmathematical models those based on different cellular events. However, all of them share the same LALI
condition. Owing to this simple formulation, we can recognize the variety of models as the brothers in theTuring model family. In short, Meinhardt made the reaction-diffusion model understandable for biologists,and established the basement for the wide acceptance of the model.
I think the task of the people following him is to proceed the way more. In my talk, I present an attempt tomodify the reaction diffusion model.

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9B1-S17-3
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Masayasu Mimura
Meiji Institute for Advanced Study of Mathematical Sciences
Meiji University
4-21-1 Nakano, Nakanoku, Tokyo 164-8525, Japane-mail: mimura.masayasu@gmail.com

Notion of diffusion-induced instability
From the understanding of pattern formation arising in biological, we know that there are two typesof instability. One is diffusion-induced instability which is stated by Turing and independently by Gierer
and Meinhardt. The instability is generated as the interaction of diffusion and suitable reaction. The otheris cross-diffusion- induced instability which is observed in Shigesada-Kawasaki-Teramoto (SKT) model,
for instance. It is generated as the interaction of diffusion and cross-diffusion. The mechanism of the two
types of instabilities seems to be different. In this talk, we show that the singular limit analysis reveals
the relation between these instabilities, that is, both of them possess the same mechanism to generateinstability.
REFERENCES[1] Turing, A. (1952). The basis of morphogenesis, Phil. Trans. R. Soc. Lond B 327: 37-72–909.
[2] Gierer, A. and Meinhardt, H. (1972). A theory of biological pattern formation. Kybernetik 12, 30-39.
[3] Shigesada, N., Kawasaki K. and Teramoto, E. (19979) Spatial segregation of interating species, J. Theor, Biol.
79, 83-99[4] Iida, M., Mimura M. and Ninomiya M. Cross-diffusion and competitive interaction, J. Math. Biol. (2006), 53,
617-641- 108 -

9B1-S17-4
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Tatsuo Shibata
RIKEN Quantitative Biology Center & Center for Developmental Biology
e-mail: tatsuo.shibata@riken.jp

Pattern formation in chemotaxis cells and body axis formation
Meinhardt proposed numerous mathematical models on many processes from bacteria to development.
I was in contact with him through models of single cell chemotaxis and body axis formation [1-2]. His last
paper was on BMP-Chordin network published in June 2015 [2].. In my talk, I will introduce his
contribution on both topics, together with the recent works in the fields.
REFERENCES[1] Meinhardt, H., 1999. Orientation of chemotactic cells and growth cones: models and mechanisms. Journal of Cell
Science, 112, pp.2867–2874.
[2] Meinhardt, H., 2015. Dorsoventral patterning by the Chordin-BMP pathway: a unified model from a patternformation perspective for Drosophila, vertebrates, sea urchins and Nematostella. Developmental Biology, 405(1),pp.137–148.

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9D1-S18 (Special)
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka

Special Symposium
Sep 9, 9:00 – 10:30, Room D
Unifying epidemiological and genomic approaches to infectious diseases
joint hosting symposium of the Japan Science and Technology Agency (JST)CREST big data application project “Detecting premonitory signs and real-time
forecasting of pandemic using big biological data”
Organizer(s):Yusuke Asai
Hokkaido University
e-mail: yusuke.asai@yahoo.de
Hiroshi Nishiura
Hokkaido University, Kita 15 Jo Nishi 7 Chome, Kita-ku, Sapporo-shi, Hokkaido 0608638, Japane-mail: nishiurah@med.hokudai.ac.jp

Our special symposium highlights the halfway achievements of abovementioned
project that excels into prediction and premonitory sign detection of pandemic, unifying
epidemiological, genetic and other diverse datasets, supported by Japan Science andTechnology Agency. The symposium aims to share a mixture of different mathematicalmodeling approaches to infectious diseases and enhance cutting edge collaborations
among researchers who share common interest in handling infectious disease data.
Especially, the organizers are pleased to have invited Dr Cornelia Pokalyuk from
Germany to share important insights of population genetic modeling to evolutionary
dynamics of viruses.
Time

Title & Presenter

09:00 – 09:30

The role of reinfection in a viral population subject to balancing selection
Cornelia Pokalyuk (Universität Magdeburg)

09:30 – 09:50

Mathematical modeling of MERS using epidemiological and genomic data
Hiroshi Nishiura (Hokkaido University)

09:50 – 10:10

Identifying the location of virus source by the effective distance approach
Yusuke Asai (Hokkaido University)

10:10 – 10:30

Estimating the population dynamics of influenza viruses from genomic data
Kiyeon Kim (Research Center for Zoonosis Control, Hokkaido University)- 110 -

9D1-S18-1
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Cornelia Pokalyuk
Institut für Mathematische Stochastik, Otto-von-Guericke-Universität Magdeburg
e-mail: cornelia.pokalyuk@ovgu.de

The role of reinfection in a viral population subject to balancing selection
The importance of balancing selection in evolution is still under discussion. However, there is
general agreement that immunity genes, like the HLA locus of the humane genome, seem to be targetedby balancing selection. Hence, on the host site of a host-parasite system balancing selection seems to besignificant.
In my talk I will focus on the parasite side of the system. Motivated by observations of DNA samples
from the Human Cytomegalovirus I will introduce a model for the evolution of a viral gene locus being
targeted by balancing selection in a host environment driven by primary infection and reinfection.

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9D1-S18-2
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Hiroshi Nishiura
Graduate School of Medicine, Hokkaido University
e-mail: nishiurah@med.hokudai.ac.jp

Mathematical modeling of MERS using epidemiological and genomic data
OBJECTIVES:
To investigate the heterogeneous transmission patterns of Middle East respiratory syndrome (MERS) in
the Republic of Korea, with a particular focus on epidemiological characteristics of superspreaders.
DESIGN:
Retrospective epidemiological analysis.
SETTING:
Multiple healthcare facilities of secondary and tertiary care centres in an urban setting.
PARTICIPANTS and OUTCOMES:
A total of 185 laboratory-confirmed cases with partially known dates of illness onset and most likely
sources of infection. Superspreaders were identified using the transmission tree. The reproduction number,that is, the average number of secondary cases produced by a single primary case, was estimated as afunction of time and according to different types of hosts.
RESULTS:A total of five superspreaders were identified. The reproduction number throughout the course of theoutbreak was estimated at 1.0 due to reconstruction of the transmission tree, while the variance of secondary
cases generated by a primary case was 52.1. All of the superspreaders involved in this outbreak appeared
to have generated a substantial number of contacts in multiple healthcare facilities (association: p<0.01),
generating on average 4.0 (0.0-8.6) and 28.6 (0.0-63.9) secondary cases among patients who visited
multiple healthcare facilities and others. The time-dependent reproduction numbers declined substantiallybelow the value of 1 on and after 13 June 2015.
CONCLUSIONS:Superspreaders who visited multiple facilities drove the epidemic by generating a disproportionate numberof secondary cases. Our findings underscore the need to limit the contacts in healthcare settings. Contact
tracing efforts could assist early laboratory testing and diagnosis of suspected cases.
REFERENCES[1] Nishiura, Miyamatsu, Chowell, Saitoh, Eurosurveillance 2015:20:21181[2] Nishiura, Endo, Saitoh, Kinoshita, Ueno, Nakaoka, Miayamatsu, Dong, Chowell, Mizumoto, BMJ Open
2016;6(2):e009936[3] Chowell, Abdirizak, Lee, Lee, Jung, Nishiura, Viboud. BMC Medicine 2015;13:210[4] Mizumoto, Saitoh, Chowell, Miyamatsu, Nishiura. International Journal of Infectious Diseases 2015;39:7-9[5] Mizumoto, Endo, Chowell, Miayamtsu, Saitoh, Nishiura, BMC Medicine 2015;13:228[6] Nishiura, Miyamatsu, Mizumoto, Emerging Infectious Diseases 2016;22(1):146-8- 112 -

9D1-S18-3
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Yusuke Asai
Department of Hygiene, Graduate School of Medicine, Hokkaido University
e-mail: yusuke.asai@yahoo.de

Identifying the location of virus source by the effective distance approach
The large influenza pandemic occurred all over the world in 2009. More than 100,000 people were
infected and 100 people died in Japan. In order to prevent next pandemic, the estimation of the importrisk of the viruses plays an important role. Recently Nah et al. estimated the effective distance by theairline traffic network data and evaluated the import risk in each country.
In this talk, we apply the idea of the effective distance based on the domestic network data to the locationand date of detection of the influenza viruses and identify the possible location of virus sources.
REFERENCES[1] Shiino et al. Molecular evolutionary analysis of the influenza A(H1N1)pdm, May-September, 2009:

Temporal and spatial spreading profile of the viruses in Japan, PLoS ONE, June 2010, Volume 5, Issue 6.
[2] Nah et al. Predicting the international spread of Middle East respiratory syndrome (MERS), BMC
Infectious Diseases, 2016 16:356, DOI: 10.1186/s12879-016-1675-z- 113 -

9D1-S18-4
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Kiyeon Kim
Research Center for Zoonosis Control, Hokkaido University
e-mail: kiyeon@czc.hokudai.ac.jp
Ryosuke Omori
Research Center for Zoonosis Control, Hokkaido University
e-mail: omori@czc.hokudai.ac.jp
Kimihito Ito
Research Center for Zoonosis Control, Hokkaido University
e-mail: itok@czc.hokudai.ac.jp

Estimating the population dynamics of influenza viruses
from genomic data
The estimation of basic reproduction number is essential to understand the epidemic dynamics, andtime-series data of infected individuals are usually used for the estimation of the basic reproduction number.
However, such data is not always available, and methods to estimate epidemiological parameters using
genealogy constructed from nucleotide sequences of pathogen have been proposed so far. Here, we propose
a new method to estimate epidemiological parameters of outbreaks using time course of Tajima’s D statisticon the nucleotide sequences of their pathogens. We construct a parsimonious mathematical model
describing the transmission process of pathogen among hosts and the evolutionary process simultaneously
to compute the relation between time series of the number of infected individuals and Tajima’s D ofpathogen sequences. Using this model, we estimated the basic reproduction number, recovery rate andmutation rate from Tajima’s D of field data of sequences of pandemic influenza A (H1N1) 2009 viruses.
Our estimated basic reproduction number was consistent with the number estimated by birth–death skyline
plot using the same sequence data, as well as with the number estimated from the time-series of the numberof infected individuals, suggesting that Tajima’s D statistic on nucleotide sequences of pathogens could be
useful to estimate epidemiological parameters of outbreaks.

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9E1-S19
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 9, 9:00 – 10:30, Room E
Mathematical and statistical modeling to bridge the gap between empirical andtheoretical research in ecology
Organizer(s):Michio Kondoh
Faculty of Science and Technology. Ryukoku University, 1-5 Yokotani, Seta Oe-cho,
Otsu 520-2194, Japane-mail: mkondoh@rins.ryukoku.ac.jp

Ecological systems are highly dynamic and complex across a range of organization levels fromindividuals to ecosystems and usually consist of interactions between different organization levels.
Empirical data to reveal the ecological complexity is accumulating, thanks to long-term ecologicalmonitoring and recent technical revolutions (metagenomics, transcriptomics and stable isotope analysis,for example). However, mechanistic understanding of ecological system is still not straightforward, partly
due to the difficulties in identifying the interactions, or causalities, between entities occurring at multiple
spatio-temporal scales. This is especially true when a controlled experiment is not possible - which is often
the case in ecological studies of higher organization levels. In this session, recent development inmathematical or statistical modeling to overcome the difficulty and its application to empirical data of arange of organization levels will be introduced and discussed.
Time

Title & Presenter

09:00 – 00:00

Empirical dynamic modeling for understanding and forecasting dynamic systems
Chih-hao Hsieh (National Taiwan University)

00:00 – 00:00

Environmental triggers of general flowering in a tropical lowland forest in Borneo
Masayuki Ushio (Ryukoku University)

00:00 – 00:00

Imputation of RNA-seq data toward modeling transcriptome dynamics in a field
Koji Iwayama (Ryukoku University)

00:00 – 10:30

Improved statistical recipe for evaluating microbial functional diversity frommetabolic fingerprinting
Takeshi Miki (National Taiwan University)- 115 -

9E1-S19-1
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Chih-hao Hsieh
Institute of Oceanography, Institute of Ecology and Evolutionary Biology, and Department of Life
Science, National Taiwan University
chsieh@ntu.edu.tw

Empirical dynamic modeling for understanding and forecasting dynamic systems
Natural systems are often complex and dynamic (i.e. nonlinear), and are difficult to understand using
linear statistical approaches. Linear approaches are fundamentally based on correlation and are ill posedfor dynamic systems, because in dynamic systems, not only can correlation occur without causation, butcausation can also occur in the absence of correlation. To study dynamic systems, nonlinear time series
analytical methods have been developed in the past decades [1-5]. These nonlinear statistical methods arerooted in State Space Reconstruction (SSR), i.e. lagged coordinate embedding of time series data [6](http://simplex.ucsd.edu/EDM_101_RMM.mov). These methods do not assume any set of equations
governing the system but recover the dynamic from time series data, thus called Empirical Dynamic
Modeling (EDM).
EMD bears a variety of utilities to investigating dynamic systems: 1) determining the complexity(dimensionality) of system [1], 2) distinguishing nonlinear dynamic systems from linear stochastic systems[1], 3) quantify the nonlinearity (i.e. state dependence) [7], 4) determining causal variables [3], 5) tracking
strength and sign of interaction [8], 5) forecasting [5], 6) scenario exploration of external perturbation [4],and 7) classifying system dynamics [2, 9]. These methods and applications can be used for mechanistic
understanding of dynamics systems and providing effective policy and management recommendations on
ecosystem, climate, epidemiology, financial regulation, and much else.
REFERENCES[1]Hsieh, C.H., S.M. Glaser, A.J. Lucas, and G. Sugihara (2005) Distinguishing random environmental fluctuations from ecologicalcatastrophes for the North Pacific Ocean. Nature. 435: 336-340.
[2]Hsieh, C.H., C. Anderson, and G. Sugihara (2008) Extending nonlinear analysis to short ecological time series. American
Naturalist. 171: 71-80.
[3]Sugihara, G., R. May, H. Ye, C. H. Hsieh, E. Deyle, M. Fogarty, and S. Munch (2012) Detecting causality in complex
ecosystems. Science 338: 496-500.
[4]Deyle, E., M. F. Fogarty, C. H. Hsieh, L. Kaufman, A. MacCall, S. B. Munch, C. Perretti, H. Ye, and G. Sugihara (2013)
Predicting climate effects on Pacific sardine. PNAS. 110: 6430-6435.
[5]Ye, H., R. J. Beamish, S. M. Glaser, S. C. H. Grant, C. H. Hsieh, L. J. Richards, J. T. Schnute, and G. Sugihara (2015) Equationfree mechanistic ecosystem forecasting using empirical dynamic modeling. PNAS. 112: E1569–E1576.
[6]Takens, F. 1981. Detecting strange attractors in turbulence. Pages 366-381 in D. A. Rand and L. S. Young, editors. Dynamic
systems and turbulence. Springer-Verlag, New York.
[7]Anderson, C. N. K., C. H. Hsieh, S. A. Sandin, R. Hewitt, A. Hollowed, J. Beddington, R. M. May, and G. Sugihara. 2008. Why
fishing magnifies fluctuations in fish abundance. Nature 452:835-839.
[8]Deyle, E. R., R. M. May, S. B. Munch, and G. Sugihara. 2016. Tracking and forecasting ecosystem interactions in real time.
Proceedings of the Royal Society of London B: Biological Sciences 283.
[9]Liu, H., M. J. Fogarty, S. M. Glaser, I. Altman, C. Hsieh, L. Kaufman, A. A. Rosenberg, and G. Sugihara. 2012. Nonlinear
dynamic features and co-predictability of the Georges Bank fish community. Marine Ecology Progress Series 464:195-207.

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9E1-S19-2
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Masayuki Ushio
Joint Research Center for Science and Technology / Faculty of Science and Technology, Ryukoku
University, Japane-mail: ushio-masayuki@ad.ryukoku.ac.jp

Environmental triggers of general flowering in a tropical lowland forest in Borneo
General flowering, one of the most fascinating phenomena in tropical biology, is a community-wide
masting phenomenon unique to aseasonal dipterocarp forests in SE Asia. As general flowering has
substantial influences on crop yield and reproductive status of forests, ecologists have studied proximate
causes of the general flowering for decades. Long-term phonology census suggested changes in rainfall
and/or air temperature associated with El Niño Southern Oscillation are correlated with the general
flowering [e.g., 1]. However, as correlations usually do not imply causations, proximate causes of themass flowering are still poorly understood. In this study, I applied recently developed statisticaltechniques, convergent cross mapping (CCM) [2] and multivariate S-map [3], in order to detect causal
drivers of the general flowering in Borneo tropical forests.
In a tropical lowland forest in Lambir National Park in Sarawak, Borneo, reproductive activities ofplant individuals were monitored since 1993. Approximately 440 plant individuals of 230 species havebeen monitored twice a month (40 species are Dipterocarpaceae). Plant phenology (i.e., the number offlowering tree individuals) and meteorological data (Southern Oscillation Index [SOI], daily mean
temperature and rainfall and cumulative temperature and rainfall) were used for the time series analysis.
To identify drivers of the general flowering, I applied CCM to the time series. In addition, multivariate Smap method was applied to quantify the influences of causal variables.
CCM showed that cumulative air temperature and rainfall had causal influences on the number offlowering trees in the forest, while SOI did not have causal influences. Multivariate S-map methodsuggested that both of cumulative air temperature and rainfall negatively influenced the number offlowering trees. The result indicated that low air temperature and drought triggered the general floweringin accordance with the previous studies. Changes in air temperature and rainfall associated with recent
climate changes would result in changes in the magnitude and frequency of the general flowering in Borneo.
REFERENCES[1] Sakai et al., 2006. Irregular drought trigger mass flowering in aseasonal tropical forests in Asia. American
Journal of Botany, 93: 1134–1139.
[2] Sugihara et al., 2012. Detecting causality in complex ecosystems. Science, 338: 496–500.
[3] Deyle, E. R., May, R. M., Munch, S. B., Sugihara, G. 2016. Tracking and forecasting ecosystem interactions inreal time. Proceedings of the Royal Society B, 283:20152258- 117 -

9E1-S19-3
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Koji Iwayama
Research Institute for Food and Agriculture, Ryukoku University, Japane-mail: iwayama-kouji@ad.ryukoku.ac.jp
Atsushi J. Nagano
Faculty of Agriculture, Ryukoku University, Japan
Center for Ecological Research, Kyoto University, JapanJST PRESTO, Japan

Imputation of RNA-seq data toward modeling transcriptome dynamics in a field
The field environments is real and natural growth condition for crops and wild plants. In a field,
environmental factors are continuously changing in complex manner and exhibit diurnal oscillations andseasonal changes. To reveal the effects of such environmental changes on organisms, transcriptome data infield environments have been collected and described by the statistical model [1]. However, the cost to
obtain large-scale transcriptome data, required for construction, parameter fitting, and validation of a model,
has restricted the modeling transcriptome dynamics.
Recently, RNA-Seq has become a widely-used technology to quantify transcriptomes [2]. The cost of
RNA-Seq depends on sequencing depth. Whereas shallow-sequencing allows us to obtain transcriptome
data from more samples, the information per sample would decrease. Here, we propose to use the topic
model, which is the statistical model widely used for natural language processing, for precise estimation ofwhole gene expression from data obtained by shallow-sequencing. The topic model represents documents
as a mixture of “topics.” Hierarchical Dirichlet process (HDP) [3] is the nonparametric generalization oflatent Dirichlet allocation [4], the most popular topic model, and automatically select the appropriate
number of topics. We apply HDP to transcriptome data, considering a gene as a “word” and a sample as a“document”. In our application to transcriptome data, the lack of information of each gene expression due
to shallow-sequencing is complemented by co-expression information described by topics. In this talk, wedemonstrate that the topic model can precisely estimate “true” expressions of genes from data obtained byshallow-sequencing.
Using the topic model, we can obtain information from transcriptome data quantified by shallowsequencing comparable to deep-sequencing. Therefore, shallow-sequencing and the topic model enables
quantification of transcriptome of more samples than deep-sequencing with the same cost. Large-scaletranscriptome data obtained by this strategy will facilitate the modeling study of transcriptomic variationin field conditions.
REFERENCES[1] Nagano, A. J., Sato, Y., Mihara, M., Antonio, B. a., Motoyama, R., Itoh, H., Nagamura, Y., and Izawa, T., 2012.
Deciphering and prediction of transcriptome dynamics under fluctuating field conditions. Cell, 151: 1358-1369.
[2] Wang, H., Gerstein, M., and Snyder, M., 2009. RNA-Seq : a revolutionary tool for transcriptomics. Nature
Reviews Genetics, 52: 5277-5286.
[3] Teh, Y. W., Jordan, M. I., Beal, M. J., and Blei, D. M., 2006. Hierarchical Dirichlet processes. Journal of theAmerican Statistical Association, 101: 1566–1581.
[4] Blei, D. M., Ng, A. Y., and Jordan, M. I., 2003. Latent Dirichlet allocation, Journal of Machine Learning
Research, 3: 993-1022.

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9E1-S19-4
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Takeshi Miki
Institute of Oceanography, National Taiwan University
Research Center for Environmental Changes, Academia Sinica
tksmiki@ntu.edu.tw

Improved statistical recipe for evaluating microbial functional diversity frommetabolic fingerprinting
Fingerprinting methods are key tools to describe ecological structures and functions, such as
phylogenetic community profiling (e.g. phylogenetic fingerprinting for microbes and plankton),community-level microbial functional profiling using EcoPlate or through quantifying multiple enzyme
activities, and chemical fingerprinting of plant secondary metabolites such as defense chemicals andvolatiles. For some indices, standard statistical methods have been developed but the statistical analysis on
metabolic fingerprinting using EcoPlate has not been standardized despite the more and more studies use
this technique for evaluating functional diversity and multifunctionality for microbial communities [1]. An
EcoPlate is a 96-well microplate that composed with triplicates of 31 response wells with different solecarbon sources (with three blank wells). The utilization of each carbon source is coupled with theconversion from a chemical dye, which allows the quantification of carbon utilization by the color
development in each well. The color developmental pattern is treated as multivariate (e.g. functional
composition) and can also be converted to univariate (e.g. threshold-based multifunctionality).
The color development patterns from Ecoplate are highly variable because of variabilities in initialcommunity size (inoculum size), those in initial species composition, and shifts in species composition
during incubation. We need to develop an appropriate statistical method to overcome this issue to obtainreliable ecological signatures from the color development patterns. In addition, we need to consider thedissimilarity between carbon substrates in terms of chemical structure for better evaluating the functional
diversity and functional dissimilarity between samples. In this study, we focused on two questions. 1. Whatis the best method for quantifying the color development pattern from 96 well microplates, depending on
the data availability? 2. How is the chemical dissimilarity information between carbon substrates
incorporated and whether does it improve the quantification of microbial functions? We hypothesized thatusing the information along the time evolution of color improves the quantification. For the second question,
we calculated the dissimilarity between carbon substrates from their chemical structure by using
chemoinformatic tools and weighted the ecoplate patterns through using exiting tools in community
ecology analyses. We also hypothesized that consideration of chemical dissimilarity improves thequantification. In order to compare the performance of different calculation methods, we used two datasets:
microcosm experiments and field observation. The basic idea for the evaluation was to compare the powerof explanation (e.g. R2 values) under the identical statistical model, Y~X1+X2+…, where Xk is an
explanatory variable such as temperature and treatment and Y is the univariate or multivariate index that is
calculated from ecoplate patterns such as multifunctionality and functional composition. With different
calculation methods, we had different Y values, which allowed the comparison of explanation power.
REFERENCES[1 Takeshi Miki, Taichi Yokokawa, Kazuaki Matsui* (2014) Biodiversity and multifunctionality in a microbial community: a novel
theoretical approach to quantify functional redundancy. Proceedings of The Royal Society B vol.281 no.1776 20132498- 119 -

9B2-S20
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Mini-Symposium
Sep 9, 10:45 – 12:15, Room B
The role of cost-benefit analysis in ecology and beyond
Organizer(s):Marko Jusup
Center of Mathematics for Social Creativity, Hokkaido University, N12W7 Kita-ku
Sapporo, 060-0812, Japane-mail: mjusup@gmail.com

To inform the audience of recent advances in our understanding of the cost-benefit analysis in biology,
we discuss how mathematical modeling can help decision-making in various practical situations. The
symposium is designed to be a fine example of how, using mathematics in the context of cost-benefit studies,
we can extract unique and novel information that helps advance the knowledge in a number of subfields inbiology (e.g. ecology, epidemiology, virology, etc.).
Time

Title & Presenter

10:45 – 11:01

Foreword by Marko Jusup

11:02 – 11:26

Cost-benefit analysis to guide management of tourist activities in nature protected
areas
Tin Klanjscek (Ruđer Bošković Institute, Zagreb, Croatia)

11:27 – 11:51

The tragedy of the mitigation policy on climate change
Hiroyuki Matsuda (Yokohama National University)

11:52 – 12:15

Statistical physics of vaccination
Zhen Wang (Interdisciplinary Graduate School of Engineering Sciences, Kyushu
University)- 120 -

9B2-S20-1
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Tin KlanjscekRuđer Bošković Institute, Zagreb, Croatia
e-mail: tin@irb.hr
Sunčana Geček
Ruđer Bošković Institute, Zagreb, Croatia
Jasminka KlanjščekRuđer Bošković Institute, Zagreb, Croatia
Tarzan LegovićRuđer Bošković Institute, Zagreb, Croatia

Cost-benefit analysis to guide management of
tourist activities in nature protected areas
Nature protected areas (PAs) are one of the most effective tools in protection of natural and, often,
cultural heritage. The promise of increased well-being through recreation, education, and connection withnature in PAs attracts tourists who, in turn, benefit the local and regional economy. Since even limited
tourist activities (e.g. sightseeing) have negative environmental impacts through pressures ranging from
erosion to habitat fractionation to killing of plants and animals, the recent sharp increases of PA tourism
seriously threatens the protection. Additionally, excessive crowding caused by large visitor numbers cancause stress to tourists and – ultimately – negate any positive effects of the visit. Therefore, managing
visitor numbers to limit crowding can benefit both the environment, and the tourists.
Standard approaches to visitor management in PAs focus on preventing excessive environmental
damage and unacceptable decrease in visitor satisfaction. Typically, the environment is considered wellprotected if values of a number of indicators are better than a (somewhat arbitrary) critical value, and visitor
satisfaction is considered to be in an acceptable range if a percentage (e.g. 80%) of visitors rate theexperience with top marks (e.g. 4 and 5 on a 5-point Likert scale). Since both environmental damage anddecrease in visitor satisfaction are monotonically increasing functions of visitor number, optimization is
not possible. Therefore, the number of tourists that may visit any PA can increase up to the carrying capacity,i.e. the number of visitors for which the critical value of at least one indicator is reached. Managing visitor
numbers to maximum carrying capacity can, therefore, be interpreted as managing for maximum acceptableenvironmental damage and minimum acceptable visitor experience. Clearly, neither goal should beconsidered optimal, and the underlying real-world maximization variable – monetary gain from tourism –is not even considered explicitly, but only implicitly through the idea that more is better. Approaches that
do try to optimize monetary gain typically start by valuating the environment (e.g. approaches based on
ecosystem services) – a step that is wrought with problems such as true monetary value of life.
We develop a new approach in which positive effects of tourism on the environment are taken as anadditional constraint that makes optimization possible, and demonstrate the approach on the example of
National Park Krka. We start by considering the management goals and analyzing both positive andnegative aspects of tourist activities. Next, we estimate the carrying capacity taking into the accountinfrastructural limitations, and negative effects of crowding on the environment, infrastructure, and visitor
experience. Finally, with environmental protection as the optimization target, we perform a cost-benefit
analysis using socio-economic and environmental variables whilst avoiding the need to attach monetary
value to the environment.
The new approach results in recommendations at odds with the traditional analysis. For example,
while traditional analysis recommends distributing tourists throughout the PA to positively affect indicatorsand increase tourist satisfaction, the new approach recommends aggregating the visitors in as small of anarea as possible without unacceptable impact on their satisfaction.

- 121 -

9B2-S20-2
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Hiroyuki Matsuda
Yokohama National University
e-mail: matsuda-hioryuki-vj@ynu.ac.jp
Rejaul Islam
Shota Nishijima
Fisheries Research Agency

The tragedy of the mitigation policy on climate change
Recently adaptation policy on climate change is becoming important because climate change isinevitable. To investigate the best mix of mitigation and adaptation policy, we need to evaluate the impact
cost (I) due to climate change, mitigation cost (M) to prevent climate change, and adaptation cost (A) toclimate change. We consider the mitigation-adaptation policy of each nation, as a non-cooperative game,
although many studies consider the best solution for the world. Policy for climate change of nation s ischaracterized by mitigation and adaptation costs of nation s, denoted by Mi and Ai, respectively. The
magnitude of climate change (t) depends on the sum of Ms of all nations, i.e., t=t(åMs). The magnitude of
impact of nation s due to climate change depends on t and As. Therefore, the magnitude of impact is afunction of the global mitigation cost and the national adaptation cost, i.e., Is = Is[åMs, As].
We simply assume that the net benefit of nation s (Vs) is Vs = B - Is[åMs, As] – Ms – As. We also assume
that the total investment Cs = Ms + As is constant.
If the world is unified (only nation 1 exists), the optimal solution that maximizes V1 is obtained by¶I1[M1, A1]/¶M1 – ¶I1 [M1, A1]/¶A1 = 0.
According to [1], Is[åMs, As]=µ(åMs,)g(As), the optimal solution satisfies that µ’(åMs,)/µ(åMs,) =g’[As]/g[As].
If µ(M) = h1+ (h2– h1)e–bM and g(A)=g0/A, M1* = Max[0,{C1s – 1 – P[-Exp[C1s-1] h1/(h2- h1)]}/s], whereP[x] is the product log function that satisfies x =P(x)eP(x). We can also numerically obtain C1* thatmaximizes I1[M1*, C1 – A1*]. This is a best mitigation-adaptation policy of the world for climate change.
In this paper we consider a multiple nation game:Vs = B - Is[åMs, As] – Ms – As. We obtain the non-cooperative (Nash) solution:¶Is[åMs, As]/¶Ms=0 and ¶Is[åMs, As]/¶As=0 for all nations. We also assume that Is[åMs, As]=µ(åMs)g(As).
The Nash solution must satisfy:µ’(åMs)=1/g(As) and µ(åMs)=1/g’(As) for all s. Note that µ(åMs) and µ’(åMs) are common for all
nations. Therefore the adaptation cost As is common for all nations, while the mitigation cost Ms depends
on the total cost Cs of each nation. This is a similar conclusion by the law of equalization in net incomes[2].
We sincere thank Prof. Managi for valuable information about the preceding studies that did notinclude our idea of non-cooperative game of mitigation-adaptation policy on climate change.
REFERENCES[1] Bréchet, T., Hritonenko, N., Yatsenko, Y. 2013. Adaptation and mitigation in longterm climate policy.
Environmental and Resource Economics, 55:217–243[2] Matsuda, H., Harada, Y. 1990. Evolutionarily stable stalk to spore ratio in cellular slime molds and the law ofequalization in net incomes. Journal of Theoretical Biology 147:329-344.

- 122 -

9B2-S20-3
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Zhen Wang
Interdisciplinary Graduate School of Engineering Sciences, Kyushu University
e-mail: nkzhenwang@163.com

Statistical physics of vaccination
Historically, infectious diseases caused considerable damage to human societies, and they continue to do
so today. To help reduce their impact, mathematical models of disease transmission have been studied tohelp understand disease dynamics and inform prevention strategies. Vaccination–one the most important
preventive measures of modern times–is of great interest both theoretically and empirically [1-3]. And incontrast to traditional approaches, recent research increasingly explores the pivotal implications ofindividual behavior and heterogeneous contact patterns in populations. I review the developmental arc oftheoretical epidemiology with emphasis on vaccination, as it led from classical models assuming
homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that
account for behavioral feedback and/or population spatial/social structure. Many of the methods usedoriginated in statistical physics, such as lattice and network models, and their associated analyticalframeworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms acoupled nonlinear system with analogs in physics. I also review the new paradigm of digital epidemiology,
wherein sources of digital data such as online social media are mined for high-resolution information on
epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics,
and further assisted by new sources of digital data, models that capture nonlinear interactions between
behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improvehealth outcomes.
REFERENCES[1] D. Henderson, P. Klepac, Lessons from the eradication of smallpox: an interview with da henderson, PhilosophicalTransactions of the Royal Society of London B: Biological Sciences 368 (1623) (2013) 20130113.
[2] D. M. Morens, G. K. Folkers, A. S. Fauci, The challenge of emerging and re-emerging infectious diseases, Nature
430 (6996) (2004) 242–249.
[3] P. Bonanni, Demographic impact of vaccination: a review, Vaccine 17 (1999) S120–S125.

- 123 -

9D2-S21
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 9, 10:45 – 12:15, Room D
Recent development of Lyapunov functional approaches in mathematical biology
Organizer(s):Yoichi Enatsu
Department of Mathematical Information Science, Faculty of Science, Tokyo
University of Science 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japane-mail: yenatsu@rs.tus.ac.jp
Toshikazu Kuniya
Graduate School of System Informatics, Kobe University 1-1 Rokkodai-cho, Nada-ku,
Kobe 657-8501, Japane-mail: tkuniya@port.kobe-u.ac.jp

Recently, Lyapunov functional approaches for proving the global asymptotic stability of equilibria
have been widely studied and developed by many researchers in the field of mathematical biology. The
purposes of this minisymposium are to share and extend the knowledge on the theory of Lyapunov
functions and their applications to mathematical models with various structures.
Time

Title & Presenter

10:45 – 11:00

Lyapunov functionals for delayed epidemic models
Connell McCluskey (Wilfrid Laurier University)

11:00 – 11:15

Dynamics of viral infection models incorporating cell-to-cell transmission
Jinliang Wang (School of Mathematical Science, Heilongjiang University)

11:15 – 11:30

Mathematical theory of the global stability of age-structured models forpathogen-immune interactions
Tsuyoshi Kajiwara (Okayama University)

11:30 – 11:45

Asymptotic behaviour of solutions for a virus-immune dynamics model withdiffusion
Toru Sasaki (Okayama University)

11:45 – 12:00

Lyapunov functionals for multi-group models with delay
Yoji Otani (Okayama University)

12:00 – 12:15

Lyapunov functions and some predator-prey differential equations
Yasuhisa Saito (Shimane University)- 124 -

9D2-S21-1
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Connell McCluskey
Wilfrid Laurier University (Canada)e-mail: ccmcc8@gmail.com

Lyapunov functionals for delayed epidemic models
Recent work on modifying a Lyapunov function for an ODE to be a Lyapunov functional for a delaydifferential equation will be presented. The work generalizes the results of many specific examples in thefield of mathematical epidemiology. We identify conditions under which delays are harmless: the delay
does not disrupt the Lyapunov calculation, and therefore does not affect the global asymptotic stability.

- 125 -

9D2-S21-2
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Jinliang Wang
School of Mathematical Science, Heilongjiang University, P.R. Chinae-mail: jinliangwang@hlju.edu.cn

Dynamics of viral infection models incorporating cell-to-cell transmission
In this talk, I will concern with viral infection model incorporating cell-to-cell transmission. For
three types models with cell-to cell mechanism, ODEs with distributed delays and direct cell-to-celltransmission, infection-age model with cell-to-cell transmission, and reaction-diffusion model with cell-tocell transmission, we study the global dynamic properties. Some mathematical arguments, such as the effectof cell-to-cell transmission on viral dynamics, relative compactness and persistence of the solution semiflow, existence of a global attractor, and the principle eigenvalue problem will be addressed. This is a joint
work with Dr. Toshikazu Kuniya (Kobe Univ.), Prof. Xianning Liu (Southwest Univ.) and Prof. Xingfu
Zou (Western Univ. CANADA).
REFERENCES[1] Jinliang Wang*, Min Guo, Xianning Liu and Zhitao Zhao, Threshold dynamics of HIV-1 virus model with cellto-cell transmission, cell-mediated immune responses and distributed delay, Applied Mathematics and Computation,
291 (2016),149-161.
[2] Jinliang Wang, Jiying Lang and Xingfu Zou*, Analysis of a structured HIV infection model with both virus-tocell infection and cell-to-cell transmission, Nonlinear Anal. RWA, Revision[3] Jinliang Wang, Jie Yang, Toshikazu Kuniya*, Dynamics of a PDE viral infection model incorporating cell-to-celltranmission, Journal of Mathematical Analysis and Applications, Accept- 126 -

9D2-S21-3
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Tsuyoshi Kajiwara
Okayama University
e-mail: kajiwara@okayama-u.ac.jp

Mathematical theory of the global stability of age-structured models for pathogenimmune interactions
This talk is based on the joint work with Toru Sasaki and Yoji Otani.
Pathogen-immune interactions in vivo have been studied by ordinary differential equations anddifferential equations with time delay.
Recently, age-structured differential equations are used for the study of various infectious diseases invivo. Lyapunov functional method developed by Korobeinikov in ordinary differential equations andMcCluskey in differential equations with time delay for the global stability is now used in age-structured
differential equations.
Browne and Pilygin [4], Browne [5] and Demasse and Ducrot [3] studied age-structured models of
infectious diseases in vivo. Especially, Browne [5] and Demasse and Ducrot [4] treated multi- strain models.
They proved the competitive exclusion principle for age-structured models. Their model do not contain
immune variables explicitly.
In this talk, we consider multi-strain age-structured models of pathogen-immune interactions.
Ordinary differential equation models of multi-strain pathogen-immune interactions are treated by Iwasa etal. [1] and Inoue et al. [2] Models with infinite delay for multi-strain pathogen-immune interactions aretreated by Otani et al. [6]. By the existence of strain specific immunity, the coexistence of multiple strains
are possible. We show the similar results for the age-structured models. Especially, we present
mathematical detail of the global stability.
REFERENCES[1] Iwasa Y., Michor F. and Nowak M., 2004. Some basic properties of immune selection, J. Theor. Biol. 229:3093–
3114.
[2] Inoue T., Kajiwara T., and Sasaki T., 2010, Global stability of models of humoral immunity against multiple viralstrains, J. Biol. Dyn., 4: 282–295[3] Demasse R.D., and Ducrot A., An age-structured within-host model for multistrain, SIAM J. Appl. Math., 73: 572–
593.
[4] Browne C.J. and Pilygin S.S., 2013. Global analysis of age-structured within-host virus models, Disc. Cont. Dyn.
Sys. Ser. 18: 1999–2017.
[5] Browne C.J., A multi-strain virus model with infected cell age structure: Application to HIV, Nonl. Anal. RWA,
22: 353–372.
[6] Otani Y., Kajiwara T., and Sasaki T, 2016. Lyapunov functionals for multistrain virus-immune models with
infinite delay, submitted.

- 127 -

9D2-S21-4
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Toru Sasaki
Okayama University
e-mail: sasaki@ems.okayama-u.ac.jp
Takashi Suzuki
Osaka University

Asymptotic behaviour of solutions for a virus-immune dynamics model withdiffusion
In this talk, we consider a virus-immune dynamics system with diffusion
𝜕𝑢2= 𝑑2 ∆𝑢2 + 𝜆 − 𝑚𝑣2 − 𝛽𝑢2 𝑢" ,𝜕𝑡𝜕𝑢;= 𝑑; ∆𝑢; + 𝛽𝑢2 𝑢" − 𝑎𝑢; ,
𝜕𝑡
(1)
𝜕𝑢"
= 𝑑" ∆𝑢" + 𝑎𝑟𝑢; − 𝑏𝑢" − 𝑝𝑢" 𝑢@ ,𝜕𝑡𝜕𝑢@
= 𝑑@ ∆𝑢@ + 𝑞𝑢" − 𝑑𝑢@𝜕𝑡with 𝑢B = 𝑢B 𝑥, 𝑡 , 𝑡 ≧ 0, 𝑥 ∈ Ω, where Ω is a bounded set in R3 , with smooth boundary. Here𝑢2 , 𝑢; , and 𝑢" denote the populations of uninfected cells, of infected cells, of infectious agents,
respectively. The variable u4 represents the amplitude of the humoral immunity.
On the boundary of the domain, we impose the Neumann condition:
𝜕𝑢B= 0 on 𝜕Ω 𝑖 = 1,2,3,4
𝜕𝑡
For the ODE model that corresponds to the model (1), a Liapunov function is obtained by Inoue,
Kajiwara, and Sasaki [1]. With a Liapunov function that is derived from that in [1], we can apply themethods described in [2] and [3] to our model, and obtain some basic results on the asymptotic behaviour.
REFERENCES[1] Inoue, T., Kajiwara, T., and Sasaki T., 2010, Global stability of models of humoral immunity against multiple
viral strains. J. Biol. Dyn., 4: 282–295[2] Latos, E., Suzuki, T., and Yamada, Y., 2012, Transient and asymptotic dynamics of a prey-predator system withdiffusion. Math. Meth. Appl. Sci. 35: 1101–1109,[3] Sasaki, T. and Suzuki, T., Asymptotic behaviour of solutions for virus dynamics models with diffusion, in
preparation.

- 128 -

9D2-S21-5
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Yoji Otani
Graduate School of Environmental and Life Science, Okayama University
e-mail: gev421104@s.okayama-u.ac.jp
Tsuyoshi Kajiwara
Graduate School of Environmental and Life Science, Okayama University
Toru Sasaki
Graduate School of Environmental and Life Science, Okayama University

Lyapunov functionals for multi-group models with delay
For the multi-group models with infinitely distributed delay, the global stability of the equilibria canbe shown by using well-known Lyapunov functionals. We refine the proof of the nonpositivity of those
Lyapunov functionals.
When R0>1 we show the well-definedness of the Lyapunov functionals for good solutions. It
completes the mathematical proof of the global stability.
The irreducibility of the next generation matrix and the properties of the Laplace transform play
important roles.
REFERENCES[1] Y. Otani, T. Kajiwara, T. Sasaki, 2015. Lyapunov functionals for virus-immune models with infinite delay.
Dsicrete Contin. Dyn. Syst. Ser. B, 9: 3093–314.
[2] M. Y. Li, Z. Shuai, C. Wang, 2010. Global stability of multi-grup epidemic models with distributed delays. J.
Math. Anal. Appl., 361: 38–47.
[3] C. J. Browne, 2015. A Multi-Strain Virus Model with Infected Cell Age Structure Application to HIV. Nonlinear
Analysis: Real World Applications 22: 354–372.

- 129 -

9D2-S21-6
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Yasuhisa Saito
Department of Mathematics, Shimane University
e-mail: ysaito@riko.shimane-u.ac.jp

Lyapunov functions and some predator-prey differential equations
Lyapnov methods can be used to determine local stability and asymptotic stability of equilibria, butalso global behavior of solutions such as global stability and permanence for ecological models describedby ordinary differential equations. However, the problem of how to find an appropriate Lyapunov function
is even more challenging in global behavior than in local behavior for their solutions. This talk mainlypresents a Lyapunov method to show that the classical Lotka-Volterra predator-prey model (which has theneutrally stable equilibrium surrounded by a family of periodic orbits whose amplitudes depend on theinitial population sizes) can be permanent by species migration.

- 130 -

9E2-S22
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 9, 10:45 – 12:15, Room E
Geometry and Patterning in Tissue, Cell, and Nucleus
Organizer(s):Yoshihiro MORISHITA
Laboratory for Developmental Morphogeometry, RIKEN, Quantitative Biology
Center, Japane-mail: morishita@cdb.riken.jp
Sungrim SEIRIN LEE
MLS, Hiroshima University
e-mail: seirin@hiroshima-u.ac.jp

Mathematical studies have contributed to biology from different aspects. For example, one directcontribution is to find tendencies or rules by analyzing data, which can be bases for revealing mechanisms
underlying focal phenomena. In addition to this, proving concepts by developing minimal models that can
reproduce observations, and providing testable hypotheses or predictions for issues unsolved or difficult toexperimentally approach. The purpose of this symposium is to show those different approaches to cellularand developmental biological phenomena with different theories such as differential geometry, cellularmechanics, and dynamical system.
Time

Title & Presenter

10:45 – 11:15

An equation of chemical field to be satisfied for achieving optimal encoding of
positional information during organ development
Yoshihiro MORISHITA (RIKEN)

11:15 – 11:45

Controlling contractile instabilities in the actomyosin cortex
Masatoshi NISHIKAWA (Hosei University)

11:45 – 12:00

A challenging interdisciplinary approach to elucidate a mystery of remodelingprocess in nuclear architecture (Part I: Theory)
Sungrim SEIRIN LEE (Hiroshima University)

12:00 – 12:15

A challenging interdisciplinary approach to elucidate a mystery of remodelingprocess in nuclear architecture (Part II: Experiment)
Hiroshi OCHIAI (PRESTO, JST)- 131 -

9E2-S22-1
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Yoshihiro Morishita
Laboratory for Developmental Morphogeometry, RIKEN, Quantitative Biology Center, Japane-mail: yoshihiro.morishita@riken.jp

An equation of chemical field to be satisfied for achieving optimal encoding of
positional information during organ development
Robust positioning of cells in a tissue against unavoidable noise is important for achieving normal
and reproducible morphogenesis. The position in a tissue is represented by morphogen concentrations,and cells read them to recognize their spatial coordinates. From the engineering viewpoint, these
positioning processes can be regarded as a problem of information coding. Organisms are conjectured toadopt good coding designs with high reliability, and to answer the questions of how good coding is
adopted, and subsequently when, where, and to what extent each morphogen contributes to positioning,
we need a way to evaluate the goodness of coding. In this study, we tried to find a general rule that thechemical field or concentration distribution should satisfy for achieving an optimal coding. In physics,
using tensorial or differential-geometrical description, coordinate-free general forms of fundamental
equations governing diverse physical phenomena have been derived. After this, we here differentialgeometrically formulated the process of morphogen-dependent positioning and then derived a generalequation for optimal encoding. We also discuss the interpretation of the equation and the possibility ofextending our theory.
REFERENCES[1] Hironaka, K. and Morishita, Y. (Review) Encoding and decoding of positional information in morphogendependent patterning, Current Opinion in Genetics & Development, 22: 553?56, (2012)[2] Morishita, Y. and Iwasa, Y. Coding design of positional information for robust morphogenesis, BiophysicalJournal, 101: 2324-2335, (2011)[3] Morishita, Y. and Iwasa, Y. Accuracy of positional information provided by multiple chemical gradients withcorrelated noises, Phys. Rev. E, 79: 061905, (2009)[4] Morishita, Y. and Iwasa, Y. Optimal placement of multiple morphogen sources, Physical Review E, 77: 041909,(2008)- 132 -

9E2-S22-2
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Masatoshi Nishikawa1, 2, 3, 4
1. BIOTEC Technical University Dresden, 2. Max Planck Institute for the Physics of Complex Systems, 3
Max Planck Institute of Molecular Cell Biology and Genetics, 4. Hosei University
e-mail: masatoshi.nishikawa.93@hosei.ac.jp
Sundar R. Naganathan1, 2, 3,
Frank Jülicher2
Stephan W. Grill1, 2, 3

Controlling contractile instabilities in the actomyosin cortex
Cells and tissues represent active materials that generate stresses for driving morphogenesis. A
fundamental challenge is to understand how spatiotemporal patterns arise in such active biological materials,
driven by the interplay of active mechanical processes and regulation by signaling pathways. We study themechanism of spatiotemporal pattern formation in the highly contractile actomyosin cortical layer, wheretransient accumulations of myosin motor proteins tend to form pulsatile networks to drive morphogenetic
events. Using a novel image-based quantification technique (COmoving Mass Balance Imaging, COMBI)
we determine the kinetic diagram of myosin activation by RhoA in the cell cortex of the polarizing onecell stage Caenorhabditis elegans embryo. We find that the complete system of myosin activation by RhoA,
active stress generation by myosin, and RhoA advection by actomyosin gel flow is unstable. Interestingly,
a RhoA pacemaking oscillator controls the spatiotemporal myosin patterns that emerge beyond theinstability. This endows the zygote with the ability to use a highly contractile and unstable system to drive
polarizing flows. Taken together, these results highlight how introducing regulatory processes to active
materials gives rise to novel pattern forming states.

- 133 -

9E2-S22-3, 4
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
S. Seirin Lee (Part I:Theory)
Department of Mathematical and Life Sciences, Hiroshima University
e-mail: seirin@hiroshima-u.ac.jp
Hiroshi Ichiai (Part II: Experiment)
PRESTO, JSTe-mail: ochiai@hiroshima-u.ac.jp

A challenging interdisciplinary approach to elucidate a mystery of remodelingprocess in nuclear architecture: Theory and Experiment
Nuclear architecture, which plays an important role in organizing the function of the nucleus, iscomposed of heterochromatin and euchromatin. Conventional nuclear architecture is found when the
distribution of heterochromatin is enriched in the periphery of the nucleus. Conventional architecture is theprimary structure in the majority of eukaryotic cells, and the rod cells of diurnal mammals contain thisstructure. In contrast, inverted nuclear architecture occurs when the heterochromatin is distributed in thecenter of the nucleus; this occurs in the rod cells of nocturnal mammals. Surprisingly, the inverted
architecture found in the rod cells of the adult mouse is formed through reorganization of the conventionalarchitecture during terminal differentiation. Although an experimental approach has shown the relationshipbetween these two types of nuclear architecture at the molecular level, the mechanisms mediating the longrange reorganization processes remain unknown. Here, we suggest a new mathematical approach tounderstanding the dynamics of nuclear architecture, by which we found that the deformation of nucleus canplay a critical role in the process of chromatin remodeling. With the interdisciplinary work, we succeeded
in developing an in vitro experiment and found that the dynamical deformation of nucleus promotes theclustering of chromocenters. With the basis of theoretical observation, we prove that the deformation of
nucleus is sufficient condition to induce the remodeling of chromatin architecture. This interdisciplinary
work has been started from the theoretical hypothesis and we suggest a new framework of interdisciplinary
research in life sciences.

- 134 -

9B3-S23
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 9, 14:00 – 15:30, Room B
The role of cost-benefit analysis in medicine
Organizer(s):Shingo Iwami
Department of Biology, Kyushu University, 744 Motooka Nishi-ku Fukuoka, 819-0395,
Japan
e-mail: siwami@kyushu-u.org

To inform the audience of recent advances in our understanding of the cost-benefit analysis in biology,
we discuss how mathematical modeling can help decision-making in various practical situations. The
symposium is designed to be a fine example of how, using mathematics in the context of cost-benefit studies,
we can extract unique and novel information that helps advance the knowledge in a number of subfields inbiology (e.g. ecology, epidemiology, virology, etc.).
Time

Title & Presenter

14:00 – 14:25

Health technology assessment and mathematical biology: A possibility for better
economic evaluation
Naoko Tomita (National Institute of Public Health, Japan)

14:25 – 14:50

Mathematica modeling vaccination against infectious diseases including dengue
and influenza
Eunha Shim (Soongsil University, Korea)

14:50 – 15:15

Characterization of cost-effectiveness of multidrug treatment - Case study on
HCV treatment
Shingo Iwami (Kyushu University, JST PRESTO & CREST, Japan)

15:15 – 15:30

Debate discussion
Marko Jusup (Hokkaido University, Japan) & Shingo Iwami (Kyushu University,
JST PRESTO & CREST, Japan)- 135 -

9B3-S23-1
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Naoko Tomita
National Institute of Public Health, Saitama, Japane-mail: Naoko.Tomita@niph.go.jp

Health Technology Assessment and Mathematical Biology: A Possibility for Better
Economic Evaluation
Health Technology Assessment (HTA) is defined as a “systematic evaluation of the properties andeffects of a health technology, addressing the direct and intended effects of this technology, as well as its
indirect and unintended consequences, and aimed mainly at informing decision making regarding healthtechnologies”.1 It consists of assessment by economic evaluation and appraisal to take into accounteconomic, ethical, social and medical issues. Subjects of HTA include not only pharmaceuticals but also
devices, procedures, vaccines and prevention.
In recent years, HTA has been adopted and has informed decision making in health care in several
countries. From April 2016, a pilot introduction of HTA has started in Japan and five hepatitis C drugs
and two cancer drugs are scheduled to be assessed.
This presentation will introduce the audience to HTA methodology and issues in HTA and consider
the applicability of mathematical biology to HTA for better decision making in health care.
REFERENCES[1]International Network of Agencies for Health Technology Assessment. http://www.inahta.org. Accessed 27 July
2016.

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9B3-S23-2
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Eunha Shim
Department of Mathematics, Soongsil University, Seoul, South Korea
e-mail: alicia@ssu.ac.kr

Mathematica modeling vaccination against infectious diseases including dengue
and influenza
Mathematical modeling of infectious diseases and the evolution of pathogens can contribute to theprediction of health policy effectiveness and best practices. Integrating mathematics, epidemiology,
economics, and evolutionary biology, this interdisciplinary research generates predictions that could not bemade by these disciplines alone, and has important impacts on these fields as well as for policy makers
world-wide. For instance, dengue is one of the most problematic vector-borne diseases worldwide, and in
December 2015 the first dengue vaccine was approved for use. In light of the recent approval of the dengue
vaccine, we present its epidemiological and economic impact based on mathematical model of dengue
vaccination. As such, health policies must be developed to maximize the benefit to the public and to balance
health, social, and economic considerations. Achieving this aim requires combining molecular, individual,
population, and national scales with evolutionary perspectives to understand the importance of trade-offs
between disease control and the risk of pathogen replacement.
REFERENCES[1] Shim, E., Brown, S.T., DePasse, J., Nowalk, M.P., Raviotta, J.M., Smith, K.J., Zimmerman, R.K. Cost effectivenessof influenza vaccine for U.S. children: live attenuated and inactivated influenza. Vaccine. In press[2] Shim, E. Dengue dynamics and vaccine cost-effectiveness analysis in the Philippines. In submission.
[3] Shim, E. Cost-effectiveness of dengue vaccination in Mexico using a dynamic dengue transmission model. In
submission- 137 -

9B3-S23-3
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Shingo Iwami 1, 2
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan. 1
PRESTO, JST, Saitama 332-0012, Japan. 8CREST, JST, Saitama 332-0012, Japan. 2
e-mail: siwami@kyushu-u.org

Characterization of cost-effectiveness of combination anti-HCV drugs
With the introduction of direct-acting antivirals (DAAs), treatment against hepatitis C virus (HCV)
has been rapidly improving. To eradicate this worldwide infectious disease, the “best” multidrug treatment
is demanded based on scientific evidence. However, there is no method available that systematicallyquantifies and compares the antiviral efficacy and drug-resistant profiles of drug combinations. Based on
experimental anti-HCV profiles in an HCV cell culture system, we quantified the instantaneous inhibitory
potential (IIP), which is the logarithm of the reduction in viral replication events [1], for both single andmultiple drug combination treatments. From the calculated IIP of 15 anti- HCV drugs, we found thatinterferon-alpha (IFN-α) and a nucleoside polymerase inhibitor, sofosbuvir (SOF), had the largest potential
to inhibit viral replication events. Profiling of 52 double-combination treatments indicated that the
combinations based on a protease inhibitor, simeprevir (SMV), achieved high IIP. Our modeling also
predicted the treatment amount of SOF in a SOF plus SMV combination could be reduced to 41% incomparison to the amount of SOF needed when combined with ledipasvir.
REFERENCES[1] B. L. Jilek, M. Zarr, M. E. Sampah, S. A. Rabi, C. K. Bullen, J. Lai, L. Shen, R. F. Siliciano, A quantitative basis
for antiretroviral therapy for HIV-1 infection. Nat Med 18, 446-451 (2012).

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9D3-S24
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka

Mini-Symposium
Sep 9, 14:00 – 15:30, Room D
Real-time modeling approaches to vaccination and emerging infectious diseases
joint hosting symposium of The Toyota Physical and Chemical Research Institute,
Specially Promoted Project
Organizer(s):Kenji Mizumoto
Hokkaido University
e-mail: mizumotokenji@gmail.com
Hiroshi Nishiura
Hokkaido University, Kita 15 Jo Nishi 7 Chome, Kita-ku, Sapporo-shi, Hokkaido 0608638, Japane-mail: nishiurah@med.hokudai.ac.jp

It is increasingly recognized that real-time mathematical modeling plays a key role in clarifying thetransmission dynamics of infectious diseases and estimating the effectiveness of interventions including
immunization practice. This session aims to elaborate the formality of mathematical modeling of emerging
infectious diseases and propagate the trend of real time modeling studies in the field of mathematicalbiology. A series of case studies on emerging infectious diseases including Middle East respiratory
syndrome (MERS) and Zika virus infection are presented, along with modeling of vaccine preventabledisease, especially vaccination against rubella is designed using a variety of mathematical models.
Time

Title & Presenter

14:00 – 14:18

Estimating Seasonal Influenza-Associated Deaths in Japan
Kenji Mizumoto (Hokkaido University)

14:18 – 14:36

Estimating risks of importation and local transmission of Zika virus infection
Kyeongah Nah (Hokkaido University)

14:36 – 14:54

Optimizing vaccination program against rubella in JapanRyo Kinoshita (Hokkaido University)

14:54 – 15:12

A Meta-Analysis of Risk and Risk Factors related mortality of Middle East
Respiratory syndrome
Ryota Matsuyama (Hokkaido University)

15:12 – 15:30

Spatiotemporal forecasting of rubella and its vaccination
Masaya Saitoh (Institute of Statistical Mathematics)- 139 -

9D3-S24-1
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Kenji Mizumoto
Graduate School of Medicine, Hokkaido University
e-mail: mizumotokenji@gmail.com
Hiroshi Nishiura
Graduate School of Medicine, Hokkaido University

Estimating Seasonal Influenza-Associated Deaths in Japan
Influenza is highly contagious respiratory disease caused by influenza viruses. It can cause mild tosevere illness, and sometimes it leads to death. In Japan, the number of deaths caused by seasonal influenza
is estimated to reach to thousands in previous studies, and it is important to measure the disease burden of
seasonal influenza, which is an indirect indicator of the lethality of an infection.
The purpose of present study is to examine the disease burden caused by influenza, mainly attributable
to seasonal influenza, employing various robust models.
Statistical analysis:
Excess number of deaths were calculated by subtracting the expected from the observed data for each monthincluded in the epidemic periods. CUMSUM method is used to calculate the annual excess number ofdeaths. Bayesian approach is used for parameter estimation
We set season is from September to August, and population size is modified accordingly.
Following methods are used:
1) Serfling least squares cyclical regression model:
2) Serfling-Poisson regression3) Autoregressive integrated moving average (ARIMA) model4) Rate-difference:
Dataset:Two secondary datasets of census data and national surveillance reports, are analysed to quantify thedisease burden.
Population size and monthly(weekly) deaths with codes from the international Classification of Diseases(ICD) for 2004-2014 were obtained from the Vital Statistics of Japan.
Monthly(weekly) number of influenza virus isolation/detection by virus type and subtype are obtained fromthe published report from National Institute of Infectious Diseases in Japan.
Result:Here we report a preliminary estimate of the disease burden (e.g. mortality) we obtained using above
modeling techniques.
REFERENCES[1]Thompson WW et al. Estimates of US influenza-associated deaths made using four different methods. Influenza
Other Respi Viruses. 2009 Jan;3(1):37-49..
[2] Park M, Wu P, Goldstein E, Kim WJ, Cowling BJ. Influenza-Associated Excess Mortality in South Korea. Am J
Prev Med. 2016 Apr;50(4):e111-9.

- 140 -

9D3-S24-2
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Kyeongah Nah
Graduate School of Medicine, Hokkaido University, Sapporo, Japane-mail: kynah@med.hokudai.ac.jp
Yohei Yasuda
Graduate School of Medicine, The University of Tokyo, Tokyo, Japan
Kenji Mizumoto, Yuichiro Miyamatsu, Ryo Kinoshita, Hiroshi Nishiura
Graduate School of Medicine, Hokkaido University, Sapporo, Japan

Estimating risks of importation and local transmission of Zika virus infection
An international spread of Zika virus (ZIKV) infection has attracted global attention. Potentially highimportation risk of ZIKV in many temperate countries motivates us to explore the risks of importation andlocal transmission fueled by mildly infected travelers. Considering that the public health concerns overZIKV infection stems from microcephaly, it is important to estimate the risk of local transmission that
could involve pregnant women. In this study, we develop a statistical model that predicts the risk of local
transmission of ZIKV in each country.
We collect arrival time of ZIKV importation (i.e., the time at which the first imported case wasdiagnosed) in each imported country from publicly available data sources. In addition to the importation
data, we collected the list of countries with local transmission of ZIKV. Employing a survival analysis
model in which the hazard is an inverse function of the effective distance as informed by the airlinetransportation network data, and using dengue and chikungunya virus transmission data, risks ofimportation and local transmission were estimated.
As a result, the predicted risk of local transmission was frequently seen in tropical and subtropicalcountries with dengue virus or Chikungunya virus epidemic experience, while the risk of importation was
more scattered around the world. The diagnostic performance of risk model for local transmission was well
supported by AUC value of 0.90. Whereas the risk of importation was well explained by the airlinetransportation network data, the risk of local transmission appeared to be best captured by additionallyaccounting for the presence of dengue and chikungunya viruses.

- 141 -

9D3-S24-3
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Ryo Kinoshita
Hokkaido University
e-mail: kinoshitaryo@gmail.com
Hiroshi Nishiura
Hokkaido University

Optimizing vaccination program against rubella in Japan
Vaccination program against rubella in Japan has become questioned after experiencing an epidemic
in 2012-2014, involving more than 12,000 cases of rubella and yielding 45 congenital rubella syndrome(CRS) cases. While rubella is a vaccine-preventable disease, Japan has yet to be successful to implement
an effective vaccination program to supplement against cohorts remaining susceptible to fully control thedisease.
When rubella vaccination was first introduced in 1976, only women at childbearing age were targeted
to prevent CRS. From 1995, both men and women were targeted to construct and maintain the herd
immunity. After the shift in vaccination policy, the proportion seronegative has steadily declined, andsusceptible birth events have been reduced. However, clusters of male adults born prior to the change invaccination policy remained susceptible and has induced the recent epidemic. Moreover, the age at
infection was elevated to 32.0 (17.0–42.0) years among men and 27.0 (7.0–37.0) years among women,
which has allowed to increase the risk of infection of women at childbearing age allowing to increase CRS.
To intervene to prevent future epidemic of rubella in Japan, a convincing vaccination strategy must
be considered. A mathematical model was constructed to optimize the vaccination considering the age
dependent transmission dynamics. R0 was calculated against the early exponential phase of the epidemic in
2012-14 to be 1.34. By accounting different scenarios of vaccination against different age groups, an
optimal target of vaccination was defined to be against age group of 20s.

- 142 -

9D3-S24-4
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Ryota Matsuyama
Graduate School of Medicine, Hokkaido University
e-mail: rmatsu0618@gmail.com
Hiroshi Nishiura
Graduate School of Medicine, Hokkaido University

A Meta-Analysis of Risk and Risk Factors related mortality of
Middle East Respiratory Syndrome
The Middle East respiratory syndrome corona virus (MERS-CoV) infection can cause a severe
respiratory disease, with often fatal cases, and the risk and risk factors related mortality of the infection
have been reported in many studies. However, those risk and risk factors sometimes differ among eachstudies or study types. A comprehensive understanding of risk and risk factors of MERS-CoV infection areneeded.
The aim of the present study is to systematically understand results in each report including risk andrisk factors of MERS-CoV by a meta-analysis.
Statistical analysis
To evaluate the risk of MERS-CoV infection, case fatality ratios (CFRs) in 25 studies were extracted or
calculated. Combined value of 25 CFRs were calculated by weighted means of each CFR derived fromvariance of samples in each study. These analysis were also conducted among stratified study types thatclassified by study designs. In addition to CFRs, we also analyzed the risk factors of severity (sex andcomorbidities) using odds ratio of each indexes.
In these analyses, heterogeneities among studies were also assessed by the Cochran’s Q and I2
statistics.
Dataset:Dataset from 25 eligible studies selected from 571 articles were used in the analyses. These studies include
data from outbreaks of MERS-CoV in Saudi Arabia and Korea.
Results and Discussions
CFRs were ranged from 14.5% to 100% and the combined values among total studies was 39.1 %.
CFR was high in ICU patients. Male and presence of comorbidities (diabetes mellitus, respiratory disease,
hypertension, heart disease, renal disease) increased the odds of mortality. However, ICU patients possibly
tend to become fatal without comorbidities. Risk factors of ICU admission should be clarified in futurestudies.
REFERENCES[1]. Alsahafi AJ and Chen AC. The epidemiology of Middle East respiratory syndrome coronavirus in the Kingdomof Saudi Arabia, 2012–2015. Int J Infect Dis. 2016. 45:1-4.
[2]. Assiri A et al. Epidemiological, demographic, and clinical characteristics of 47 cases of Middle East respiratory
syndrome coronavirus disease from Saudi Arabia: a descriptive study. Lancet Infect Dis. 2013.13: 752–761.

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9D3-S24-5
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Masaya M. Saito
The Institute of Statistical Mechanics
e-mail: saitohm@ism.ac.jp
Ryo Kinoshita
Graduate School of Medicine, Hokkaido University
Hiroshi Nishiura
Graduate School of Medicine, Hokkaido University

Progress report on modelling of rubella epidemic in Japan
In Japan, the proportion of rubella susceptible person's is currently near the threshold above which amajor epidemic may occur. During 2012/13 the number of rubella cases in Japan was relatively large inrecent years. The maximum number of weekly reported cases was 168 in Tokyo Prefecture and 268 in
Osaka Prefecture while 1-2 or no cases are reported per week in usual years in each prefecture. Thisepidemic is almost limited to the metropolitan area while below ten cases per week were reported in 30
prefectures. Such a geographical contrast in reported cases reflects that the susceptibility is very close to
the threshold of major outbreak. It is necessary to take into account a spillover of the disease via theperson's movement and stochastic nature of transmission in order to reproduce such an infection trend.
In the present study, it is shown that the 2012/13 epidemic is reproduced better by a stochastic metapopulation model than a standard SIR model, under an appropriate model parameter.
REFERENCES[1]. Colizza V, Barrat A, Barthe'lemy M, Vespignani A (2006) The modeling of global epidemics: Stochastic dynamics
and predictability. Bulletin of Mathematical Biology 68: 473–481.
[2]. Kinoshita R, Nishiura H (2016) Assessing herd immunity against rubella in japan: a retrospective
seroepidemiological analysis of age-dependent transmission dynamics. BMJ Open 6: 1–7.

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9E3-S25 (Special)
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka

Special Symposium
Sep 9, 14:00 – 15:30, Room E
Wanders will never cease: the current and future studies of the evolutionary
ecology of dispersal
Organizer(s):Ryosuke Iritani
Kyushu University, Japane-mail: lambtani@gmail.com
Yuuya Tachiki
Kyoto University, Japane-mail: tachiki@bio-math10.biology.kyushu-u.ac.jp

Dispersal and migration influence arrays of ecological setups of organisms, from allelic distribution
to community compositions. Dispersal is, at the same time, subject to diverse selective pressures, and thus
an evolving trait by natural selection (e.g., kin competition, sib-mating avoidance, resource heterogeneity).
Therefore, studies on evolutionary ecology of dispersal and migration have been of pivotal importance inpopulation ecology. In the present symposium, we review our current understandings of dispersal andmigration from evolutionary and ecological points. Specifically, we illustrate different theoretical
approaches to model the evolution of dispersal and migration. Each speaker briefly reviews their recent
projects, and highlight the future directions and steps to enhance the elaboration of studies of dispersal.
Time

Title & Presenter

14:00 – 14:05

Introduction

14:05 – 14:25

Who escapes from whom: disease transmission among kin can drive the evolutionof conditional dispersal in viscous host populations
Ryosuke, Iritani (Kyushu University, Japan)

14:25 – 14:45

Evolution of dispersal in spatially and temporally heterogeneous environments
Florence, Débarre (College de France, France)

14:45 – 15:05

The evolution of marine larval dispersal kernels in spatially structured habitats
Allison, K. Shaw (University of Minnesota, US)

15:05 – 15:25

Evolutionary and ecological consequences of individual decisions, whether they
stay or go, under environmental fluctuations
Yuuya Tachiki (Kyoto University, Japan)

15:25 – 15:30

Discussion- 145 -

9E3-S25-1
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Ryosuke, Iritani
Department of Biology, Faculty of Sciences, Kyushu University
e-mail: Lambtani@gmail.com

Who escapes from whom: disease transmission among kin can drive the evolutionof conditional dispersal in viscous host populations
In viscous populations, horizontal transmission of parasites can occur among closely related
individuals, and sickness-dependent dispersal (individuals disperse conditionally according to their own
disease status) might relax this menace. That is, infected individuals can lower the risk of transmission to
siblings if they disperse, while uninfected individuals can escape from such a risk by dispersing. Empiricalstudies have indeed found evidence for both patterns of sickness-dependent dispersal. However, the costs
and benefits of sickness-dependent dispersal have been poorly investigated so far. Here, I develop
mathematical models to study the effect of transmission among kin on the evolution of sickness-dependent
dispersal. The model reveals that at evolutionary endpoints, infected individuals are more dispersive, or
uninfected individuals are more dispersive, and these two endpoints are bistable, i.e., evolution can lead toeither outcome depending on the initial conditions. In particular, if horizontal transmission makes thegenetic structuring for uninfected individuals more pronounced, then selection favours higher dispersal for
uninfected individuals and lower dispersal for infected individuals. I discuss the mechanism accounting forsuch a concomitant effect of transmission avoidance in terms of altruism-spite interpretation of social
evolution theory.

- 146 -

9E3-S25-2
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Florence, Débarre
Centre Interdisciplinaire de Recherche en Biologie (CIRB), Collège de France (Paris, FRA)
e-mail: florence.debarre@normalesup.org

Evolution of dispersal in spatially and temporally heterogeneous environments
Variations in environmental conditions, among locations and in time, have been suggested to affectthe evolution of traits such as dispersal, habitat selection or local adaptation. Depending on whether
environmental variations is averaged over a population in a single generation or in every single genotype
over several generations, these variations select for generalist or specialist strategies, and may induce
stabilizing or disruptive selection on studied traits. Here, we investigate the effect of the order of events inthe life cycle on the evolution of dispersal in a spatially heterogeneous, temporally varying landscape. Our
results show that the occurrence of intermediate singular strategies and disruptive selection are conditionedby the autocorrelation in patch state and the life cycle. With unconditional dispersal, “soft selection” and“hard selection” life cycles give different evolutionary outcomes. With informed dispersal, even the two“hard selection” life cycles disagree on evolutionary predictions. Our results highlight the importance ofaccounting for life cycle specificities when predicting the effects of the environment on evolutionarily
selected trait values, as well as the need to check the robustness of evolutionary model conclusions against
modifications of the life cycle.

- 147 -

9E3-S25-3
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Allison, K. Shaw,
Deparment of Ecology, Evolution, and Behavior, University of Minnesota (US)e-mail: ashaw@umn.edu
Cassidy C. D’Aloia,
Dept. of Ecology & Evolutionary Biology, University of Toronto (CANADA)
andPeter M. Buston
Department of Biology and Marine Program, Boston University (US).

The evolution of marine larval dispersal kernels in spatially structured habitats
Understanding the patterns, causes and consequences of dispersal is a major goal of ecology. However,most research on the causes of variation in dispersal in marine systems focuses on proximate causes(physical oceanography, larval behavior). Here, we investigate the ultimate, evolutionary causes ofdispersal variation. Building on classic work by Hamilton and May, we develop a combination of analytic
and simulation models for the evolution of larval dispersal kernels in spatially structured habitats. First,
considering a world without bound, we find that the evolutionarily stable strategy (ESS), paradoxically,
allocates most offspring to the longest dispersal distance class. Second, considering a world with boundresolves the first paradox, but creates its own paradox: the ESS strategy allocates next to nothing beyond
the shortest dispersal distance class. Third, considering a patchy world with bound, we find a more realistic
result: the ESS allocates most offspring to short distances classes, but still some to longer distance classes.
Finally, we test our model predictions against an empirically derived dispersal kernel (the neon
goby Elacatinus lori) from a real, spatially-structured habitat (the Belizean Barrier Reef System). The
model’s predictions are qualitatively similar to the empirical data: both data sets predict a high level ofshort-distance dispersal (< 2 km from source), and low levels of long-distance dispersal. This study provides
a framework that can be used to model the evolution of dispersal kernels in other species and seascapes,
which will provide new insights into variation in patterns of population connectivity.

- 148 -

9E3-S25-4
Sep 9, Fri (mini-symposia)
JSMB2016 Fukuoka
Yuuya, Tachiki,Institute for Virus Research, Kyoto University;
Department of Biology, Kyushu University.
e-mail: tachiki@bio-math10.biology.kyushu-u.ac.jp
andItsuro, Koizumi
Faculty of Environmental Earth Science, Hokkaido University.

Evolutionary and ecological consequences of individual decisions, whether they
stay or go, under environmental fluctuations
Species sometimes choose one of alternative tactics in their life history. To explain this phenomenon,a threshold value for individual status is assumed, above and below which each individual should adopt
either tactic to attain higher fitness. This framework is called the status dependent strategy and implicitly
assumes the existence of an “absolute” value, so each individual chooses a tactic based only on its own
status. However, it is also possible that animals assess their status based on surrounding individuals. This
“relative” assessment considers that a threshold value can change depending on individual situations. Here,
we incorporated Bayesian decision-making and adaptive dynamics frameworks to explore the conditionsof each assessment to be an evolutionarily stable strategy (ESS). Our model demonstrates that absoluteassessment is always an ESS under a stable environment, whereas relative assessment can be an ESS understochastic environments; a mixed strategy was also selected as the intermediate [1]. Individuals’ responses
to stochasticity are different between absolute and relative assessment. The proportions of alternative tactics
fluctuate under stochasticity when animals adopt absolute assessment, while they are stabilized when
animals adopt relative assessment. Our results underscore the need to better understand how individuals
assess their own status to choose alternative tactics.
REFERENCES[1] Tachiki, Y. and Koizumi, I. 2016. Absolute versus Relative Assessments of Individual Status in Status-Dependent
Strategies in Stochastic Environments. The American Naturalist.188. 113-123.

- 149 -

JSMB2016 Fukuoka

Oral Session Abstract- 150 -

7A1-O1-1
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Genki Ichinose
Department of Mathematical and Systems Engineering, Shizuoka University
e-mail: ichinose.genki@shizuoka.ac.jp
Takehiro Kurisaku
Department of Computer Science and Engineering, Toyohashi University of Technology

Effect of peer pressure on the evolutionary vaccination game
Preventing infectious disease like flu from spreading to large communities is one of the most important
issues for humans. One effective strategy is voluntary vaccination, however, there is always the temptation
for people refusing to be vaccinated because once herd immunity is achieved, infection risk is greatly
reduced. Fu et al. and Cardillo et al. revealed that voluntary vaccination is effective despite the high cost inheterogeneous networks compared to homogeneous networks, because once hub nodes are vaccinated, thebehavior immediately spreads to the whole population [1, 2]. In those networked models, when imitationof the strategy is conducted, only the payoff information of one particular neighbor is obvious. If people
use broader information, what happens to the dynamics? Fukuda et al. investigated the effect of social status
information in which each individual can use the information of the average payoff of its neighbors insteadof the payoff of one randomly selected neighbor [3]. They showed that the effectiveness of the social statusdepends on both network structures and the cost of vaccination. In this paper, we study the effect of peerpressure on the vaccination behavior resulting in preventing infectious disease in networks. The
evolutionary simulation results show that the peer pressure has both positive and negative effects on thevaccination behavior. Especially, in heterogeneous networks, if the vaccination cost is low the behavior ismore promoted than the case without peer pressure. In contrast, if the cost is high, the behavior is reduced
compared to the case without peer pressure. Moreover, the vaccination behavior is effective inheterogeneous networks more than in homogeneous networks. This implies that the peer pressure puts
people at risk in homogeneous networks.
REFERENCES[1] Fu, F., Rosenbloom, D. I., Wang, L. and Nowak, M. A., 2011. Imitation dynamics of vaccination behaviour onsocial networks, Proc. R. Soc. B, 278: 42–49.
[2] Cardillo, A., Reyes-Suarez, C., Naranjo, F. and Gomez-Gardenes, J., 2013. Evolutionary vaccination dilemma incomplex networks, Phys. Rev. E 88: 032803.
[3] Fukuda, E., Kokubo, S., Tanimoto, J., Wang, Z., Hagishima, A. and Ikegaya, N., 2014. Risk assessment for
infectious disease and its impact on voluntary vaccination behavior in social networks, Chaos, Solitons & Fractals
68: 1–9.

- 151 -

7A1-O1-2
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Masayuki Kakehashi
Hiroshima University (Graduate School of Biomedical & Health Sciences), Hiroshima, Japane-mail: kakehashi@hiroshima-u.ac.jp
Shoko Kawano
Kurume University (School of Nursing), Kurume, JapanAn analysis on the effect of school closure against influenza:'Back Monte Carlo' data approach
Taking advantage of infectious disease spread data collected in small sized groups such as schoolclasses, using individually based stochastic model is considered to be appropriate. In spite that collected
data are usually the numbers of cases (patients) on each time interval, the data required to estimateparameters in the model are those of persons just infected on each interval. To reconstruct infection datafrom case report data taking the effect of latent period into account, we proposed 'back Monte Carlo'
calculation approach to analyze properly the effect of school closure.
Data used in our analysis were collected during September 2009 - March 2010 at schools in Oita inJapan. Totally 51,872 pupils or students in 134 schools (kindergartens, elementary schools, junior highschools and high schools) were reported their absence due to Pandemic flu by class and by day. Whether
or not school or class closure was implemented was also reported.
In addition to the stochasticity due to latent period, there was an effect of reporting delay: i.e., thenumbers of cases reported on Saturdays and Sundays were smaller than those on other week days in contrast
to those on Mondays that were larger. This took place because some of the case reports were postponed to
the next working day avoiding reporting on holidays. This was also observed on national holidays. We
assumed constant rate of postponing report as 67% based on the observed data. We also assumed average
duration of latent period was 3 days. Transmission were divided into three types: within class, within school
and within whole school community. An addition of baseline level of transmission was also considered.
Based on the assumptions described above, parameters in the model were estimated by maximum likelihood
method where transmission were assumed not to happen in classes nor schools when on holidays or whenclass or school was under closure. Analyses were carried out for the data during September 1 - December
24 (115 days) when school vacations were not involved. Simulations based on the estimated parameters
were also carried out.
In the analysis, transmission coefficients due to individual in the same class and due to those in thesame school were separately and found the former was approximately 15 times larger than that of the latter.
It was also found that the transmission coefficients due to individual in the same school was approximately
10 times larger than that in a different school.
We also examined the effect of successive days of school closure (the duration of each school closure),
which was set 4 days according to relevant regulations. Among 2 - 5 days as the duration of each school
closure, 3 days realized the best performance as a preventive measure.
‘Back Mont Carlo’ data approach was useful to estimate parameters involved in stochastic infectious
disease spread model. The reason why 3 day school closure attained the best performance may be
attributable to the fact that average latent period was assumed to be 3 days. In the evaluation of the effectof school closure, disadvantage of school closure must be incorporated in addition to benefit of school
closure, i.e., the reduction of the number of cases, etc. It was then useful to calculate ‘the person-years ofclosure’ required to reduce one case. The results of simulation did not reproduce the rapid increase of casesin the last decade of October, which were considered to be attributed to specific episode not considered in
the model. It was also considered useful to improve prediction that the spread of infection in wholecommunity was considered.
REFERENCES[1] Kawano, S. and Kakehashi, M., 2015. Substantial Impact of School Closure on the Transmission Dynamics
during the Pandemic Flu H1N1-2009 in Oita, Japan. PLOS ONE, 10: e0144839.

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7A1-O1-3
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Takaaki Funo
Department of Biology, Kyushu University, Japane-mail: funoseisu@gmail.com
Shingo Iwami
Department of Biology, Kyushu University, Japan

Corrilation between malaria cases and rainfall
Malaria is a vector-borne disease transmitted by mosquitoes. In area of highly seasonal transmission,
it is believed that asymptomatic patients persist over the course of the dry season and to reseed transmission
when mosquito populations increase along with wetter conditions. In this study, we investigated how theMalthusian coefficient correlates with climate factors such as rainfall and temperature.

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7C1-O2-1
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Yuji Sakai
Theoretical Biology Laboratory, RIKEN, Hirosawa, Wako, Saitama, 351-0198, Japan
interdisciplinary Theoretical Science iTHES, RIKEN, Hirosawa, Wako, Saitama, 351-0198, Japane-mail: ysakai@riken.jp
Masashi Tachikawa, Atsushi Mochizuki
Theoretical Biology Laboratory, RIKEN, Hirosawa, Wako, Saitama, 351-0198, Japan
Kazuya Kinoshita, Tatsuya Hirano
Chromosome Dynamics Laboratory, RIKEN, Hirosawa, Wako, Saitama, 351-0198, Japan

Chromosome condensation effects on the organization and segregation
The spatial organization of chromosomes in mitosis is a fundamental question of biology. Upon entry
into mitosis, a mass of chromatin distributed in the interphase nucleus is converted into a discrete set ofchromosomes with high condensed rod-shape structures.
The condensen protein complex is responsible for the chromosome condensation [1]. In thechromosome condensation, the condensin is associated with chromosomes, enriched on chromosome axes,
and have distinct contributions to the chromosome organization.
It is experimentally considered that the condensin has two functions, making twisted loops inchromosome and attracting between near ones [1]. However since the chromosome condensation is very
complex phenomena, it is not clear how the condensin functions contribute to the chromosome organizationand the segregation.
In this study, we investigate effects of the condensin functions on the chromosome organization andthe segregation by using coarse-grained molecular dynamics simulations. We model the chromosome as
the rigid beads and the connecting springs, the condensin as the rigid beads. We model two condensinfunctions as follows. First, the one condensin bead attracts with the two chromosome beads and make atwisted loop structure in the chromosome. Second, the condensin beads attract with each other when they
are in some distance.
By changing the strengths of the chromosome-condensin attraction and condensen-condensin
attraction, we investigate the effects of the two condensin functions on the chromosome organization andthe segregation. We show that these functions apparently affect on both the organization and the segregation.
Particularly both the functions are necessary for both the organization of the rod-shape chromosomes andthe segregation of the entangled chromosomes.
We also discuss the condensin spatial pattern formation. The condensing is enriched on chromosome
axes, i.e., the condensin axis, in the chromosome condensation. Recently, the experiment shows that thecondensin does not make the axis but makes many spot patters on the chromosome when the condensin
subunit is knocked out [2]. We show that the spatial pattern changes can be reproduced by lack of thecondensin looping function in our model.
REFERENCES[1] Hirano, T., 2016, Condensin-Based Chromosome Organization from Bacteria to Vertebrates. Cell, 164: 847-857.
[2] Kinoshita, K. and Hirano, T., 2016. Balancing Acts of Two HEAT Subunits of Condensin I Support Dynamic
Assembly of Chromosome Axes. Developmental Cell, 33: 94–106.

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7C1-O2-2
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Hisao Honda
Kobe University Graduate School of Medicine, Kobe.
Center for Developmental Biology, RIKEN, Kobe.
e-mail: hihonda@hyogo-dai.ac.jp
Takaya Abe
Division of Bio-function Dynamics Imaging, RIKEN, Kobe.
Toshihiko Fujimori
National Institute for Basic Biology, Okazaki.
Division of Bio-function Dynamics Imaging, RIKEN, Kobe.

Mechanism of cardiac looping of the embryonic heart
We investigated a mechanism of heart looping using a mathematical model, the cell-based vertex dynamics
for tissues. A simple straight tube consisted of polygonal cells could be deformed by various factors in themodel. We considered two factors, left-right (LR) asymmetric expression of nodal cassette genes in thelateral plate mesoderms (LPM) and cell chirality that was recently recognized experimentally. Cells in theleft side of tube were derived from the left LPM, and their growth was assumed to be rapid. In the computer
simulation, the tube protruded one-side or bent, but did not loop. On the other hand, we assumed chiralbehavior of cells. Most of cells divided along anterior-posterior (AP) axis of the heart. After cell division,
two daughter cells assumed to rotate for small angle in counterclockwise direction (the chiral behavior). In
the simulation the cells migrated on surface of the tube, but the tube did not loop. Finally, we performed
the two assumptions (LR asymmetry of the tube and chiral rotation of the cells) simultaneously, the tube
looped. We succeeded in recapitulation of the heart looping. The assumptions of difference of cell growth
between the left and right sides of the tube, tendency of cell division along the AP axis and thecounterclockwise rotation of daughter cells were substantiated by in vitro experiments of mouse embryos.
In conclusion the cardiac looping was caused by asymmetry of LPM and chiral behavior of dividing cells.

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7C1-O2-3
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Kenichi Nakazato
Theoretical Biology Lab, RIKEN
e-mail: na@riken.jp
Atsushi Mochizuki
Theoretical Biology Lab, RIKEN
Yuta Takase, Yoshiko Takahashi
Zoology Lab, Graduate school of science, Kyoto Univ.

Understanding Vascular Remodeling from the View of Continuum Mechanics
We are studying the vascular remodeling from immature vascular plexus to stable vascular networkby combining experimental and mathematical methods. Experimentally, we found two types ofendothelial cellular behavior. (1) Cells show migration in the tissue against the blood flow. (2) Cells show
detachment from the tissue when blood flow is surpressed. Based on those observations, we developed
mathematical framework to study macroscopic deformation of vascular organs from microscopic cell
behaviors to determine responsible mechanisms for remodeling. Endothelial tissue should compensate forthe density change brought by cellular behaviors in some way to keep its thickness constant. Assuming
expansion and contraction of the tissue as the compensation, we construct mathematical model of
remodeling. In our model, cellular behavior results in stress field on the tissue. Here, positive stress field
generates expansion and negative one generates contraction. Analyzing the model, we show the directionof local deformation of the tissue is determined by two factors, the sign of stress field and the local
curvatures of the tissue. In addition, we compared effect of two hypotheses on cellular behavior: increaseof migration speed and decrease of ablation rate against the increase of speed of blood flow. As theresults, we show (a) the directions of deformation are different between them and (b) migration has only
minor effects compared to detachment to explain actual patterning.
In my talk, I will focus on another description of continuum, namely particle dynamics. Since the particle
dynamics can be directly interpreted as cell center dynamics, we can capture the biological meanings ofour model more intuitively.

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7A2-O3-1
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Joe Yuichiro Wakano
Meiji Univeristy
e-mail: joe@meiji.ac.jp
Kenichi Aoki
Meiji University
William Gilpin, Marcus Feldman
Stanford University

Traveling waves of cultural invasion
Human range expansion has been studied based on genetic data (mainly modern human DNA + someancient DNA of Neanderthals). It is estimated that the second wave of out-of-Africa by Homo sapiens took
place roughly 50-100 kya, and they completely replaced the pre-existing hominids. On the other hand,
Homo sapiens and Neanderthals are so closely related that the evidence of introgression is found [1,2]. In
this study, we assume that the genetic difference between these species is negligible. We postulate that therelatively quick replacement is triggered not by genetic but by cultural differences. When a group with highcultural level (e.g., advanced stone-tools) appears, they might increase their population density and hence
the spatial distribution of such high culture groups might spatially spread. Previous empirical [3] andtheoretical [4,5,6] studies suggest the existence of positive feedback loop between cultural level andpopulation size. There could exist two locally stable equilibria: "low" equilibrium consisting of low
population density and low cultural level and "high" equilibrium consisting of high population density andhigh cultural level. Since previous models did not explicitly model spatial structure, theoretical predictions
are made based on the basins of attractions of these equilibria in ODE systems. In this study, we propose
spatially explicit reaction-diffusion model. We consider a traveling wave solution (TWS) connecting theseequilibria, and obtain the condition under which "high" equilibrium expands its spatial distribution.
REFERENCES[1] Viola B, Pääbo S (2013) What’s new in Central Asia? Basic Issues in Archaeology, Anthropology and Ethnographyof Eurasia: Festschrift on the Occasion of Anatoly Derevianko’s 70th Birthday, eds Shunkov MV, Molodin V (SB RAS
Press, Novosibirsk, Russia), pp 555–565.
[2] Prüfer K, et al. (2014) The complete genome sequence of a Neanderthal from the Altai Mountains. Nature
505(7481):43–49.
[3] Henrich J (2004) Demography and cultural evolution: How adaptive cultural processes can produce maladaptive
losses: The Tasmanian case. Am Antiq 69:197–214.
[4] Aoki K (2014) Modeling abrupt cultural regime shifts during the Palaeolithic and Stone Age. Theor Popul Biol
100:6–12.
[5] Ghirlanda S, Enquist M (2007) Cumulative culture and explosive demographic transitions. Qual Quant 41(4):591–
600.
[6] Gilpin W, Feldman MW, Aoki K (2016) An ecocultural model predicts Neanderthal extinction through competition
with modern humans. Proc.Nat.Acad.Sci.USA 100:6–12.

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7A2-O3-2
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Riccardo Pansini
Kunming Institute of Zoology (CAS) and Yunnan University of Finance and Economics
e-mail: r.pansini@gmail.com

High cooperation levels in a PGG by Chinese subjects to mitigate climate change
Cooperation theories assume that interacting individuals can change their strategies under different
expected payoffs, depending on the social situations. The willingness to invest into partners and tocooperate may therefore shift in China as opposed to Western countries partly as a result of culturaldifferences. An experiment was implemented to test the willingness of young Chinese subjects tomitigate the consequences of climate change in a country severely affected by air pollution. Following adesign already implemented in Germany [1], we set up a Public Good game in which groups comprisedof six students had to reach a minimum threshold of earned points to be able to invest the convertedmoney into planting trees. Differently from the German model whose subjects did not manage to reachthe threshold, the Chinese subjects were very successful at investing for this cause. These results are
discussed in relation to a Social Value Orientation questionnaire we presented the subjects with toascertain the social value profile of cooperators and non-cooperators.
REFERENCES[1] Jacquet, J., Hagel, K., Hauert, C., Marotzke, J., Rohl, T. & Milinski, M. 2013. Intra- and intergenerational
discounting in the climate game. Nature Clim. Change, 3, 1025-1028, 10.1038/nclimate2024.

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7A2-O3-3
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Cinthia Marie Tanaka
Department of Applied Mathematics, University of Sao Paulo, Brazil
e-mail: cimarie@ime.usp.br
Yoh Iwasa
Department of Biology, Kyushu University, Japan

Persistence of local dialect in the face of a national standard language:a mathematical study
Many languages had gone extinct or were put in the endangered list of languages in the last century,with the number of languages decreasing at a faster rate than mammals and birds species. Since late 1990s,
mathematical models have been proposed to study the language change dynamics and language survival
dynamics [1][4]. In particular, Abrams and Strogratz [1] proposed a simple model for the competition of
two languages and concluded that when there are no bilinguals in the population, one of the two languages
will eventually become extinct.
Dialects can be defined as different speech systems of the same language which are mutually
intelligible [2]. The rise of a dialect as a national language is relatively common, and it has happened inhistory many times, e.g. Tokyo dialect (Japanese), Paris dialect (French) and Athens dialect (Greek). The
standardization process of a language may cause other dialects to be perceived as a lower-class or ruralspeech. This endangers the survival of different dialects; in the case of Japan, there was a fear that dialects
would disappear after the language unification [3]. However, the persistence of dialects, as the Piedmontese
dialect (Italy) or the Kansai dialect (Japan), proves that dialects dynamics are more complicated thaninitially thought.
Here we propose a deterministic model to investigate the dynamics of the survival of a local dialect(B) when competing against a national language (A). We assume individuals may be able to use different
dialects, in response to different situations. For example, in public situations, e.g. in a formal workplace,they may use the national language, while in private situations, e.g. in family or close friend meetings, they
may use a local dialect.
We consider the choice of a dialect (for private situations) is guided by, mainly, two forces: (i) prideof the local language (negatively affects probability of changing dialect π); and (ii) willingness to speak thesame dialect (conformity parameter, ξ) inside a private group.

Figure 1. Dialect change dynamics for different groups. Conformity parameter ξ affects the change from mixed
groups, where A and B dialects are both spoken, to homogeneous groups (all A or all B). Pride of the language A
negatively affects the probability of changing to language B (𝜋P ), and vice-versa.

Our preliminary results show that the conformity parameter has no influence in the final outcome if
the private group has only two individuals (married couple). In particular, in this case, the stable frequencyof speakers of the standard language A is given by 𝜋Q 𝜋Q + 𝜋P . However, this result does not hold when
we increase the number of individuals per group. This may indicate that the number of individuals matterswhen it comes to the fate of a dialect.
REFERENCES[1] Abrams, D. M., & Strogatz, S. H., 2003. Linguistics: Modelling the dynamics of language death. Nature, 424(6951):
900.
[2] Crystal, D., 2000. Language Death. Cambridge University Press.
[3] Inoue, F., 1993. The significance of new dialects. Dialectologia et Geolinguistica, 1: 3-27.
[4] Nowak, M. A., & Krakauer, D. C., 1999. The evolution of language. Proceedings of the National Academy of
Sciences, 96(14): 8028-8033.

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7C2-O4-1
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Hiromi SENO
Research Center for Pure and Applied Mathematics
Department of Computer and Mathematical Sciences
Graduate School of Information Sciences
Tohoku University
Aramaki-Aza-Aoba 6-3-09, Aoba-ku, Sendai 980-8579
JAPANe-mail: seno@math.is.tohoku.ac.jp

Mathematical Modeling of Metapopulation Dynamics: Revisiting Its Meaning
The following 2-state metapopoulation dynamics model is well known as Levins model [2,3]:dE= eP P – cPE
dt
dP= cPE – eP P
dt

In a patchy habitat, E and P mean the frequency (or the probability of existence) of patches with ‘vacant’state and that with ‘occupied’ state, respectively. Since E and P satisfy the condition that E + P = 1
independently of time, this model can be described in a mathematically equivalent form by the following
single ordinary differential equation as known well:dP= cP(1 – P) – eP P
dt
The parameter eP means the coefficient for the occurrence of transition from the state ‘occupied’ to ‘vacant’
which is due to the extinction of population in the ‘occupied’ patch, and c means the coefficient for thetransition of vacant patch to the ‘occupied’ state due to the successful settlement of some immigrants fromthe ‘occupied’ patches.
Interesting and valued point of mathematical modeling by Levins [2, 3] is its treatment of dynamics
in terms of ‘state’ transition of each patch without considering the temporal variation of population size
itself in each patch [1]. However, the frequency of migration, that is, the strength of migration effect on
the state transition is significant in the modeling since it takes the effect of immigrants into account for thecause of state transition, and the strength of migration effect necessarily depends on the size of migrating
population. Therefore it requires a rational combination of patch states and population size for themodeling by the idea of Levins [2, 3] to aggregate the population dynamics in a patchy habitat into a
dynamics of patch state transition.
In the work [4], we will discuss a mathematical modeling, focusing on how the strength of migration
could be involved in it to construct a metapopulation dynamics model, with the same idea with Levins’.
Although the similar problem has been discussed in some previous papers, we will independently consider
the mathematical modeling of Levins’ idea, and try to discuss the problem about the rationality of its
modeling typical with the mass-action terms.
REFERENCES[1] Hanski, I. and M. Gilpin, M., 1991. Metapopulation dynamics: Brief history and conceptual domain. Biol. J.
Linnean Soc., 42: 3–16.
[2] Levins, R., 1969. Some demographic and genetic consequences of environmental heterogeneity for biologicalcontrol. Bull. Entomol. Soc. Am., 15: 237–240.
[3] Levins, R., 1970. Extinction. In M. Gerstenhaber (ed.), Some Mathematical Problems in Biology, Lectures onMathematics in the Life Sciences, Vol. 2, pp. 75–107, American Mathematical Society, Providence, Rhode Island.
[4] Seno, H., 2016. Mathematical modeling of metapopulation dynamics: Revisiting its meaning. Math. Model. Nat.
Phenom., (in press).

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7C2-O4-2
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Kei Tokita
Department of Complex Systems Science, Graduate School of Information Science, Nagoya University
e-mail: tokita@nagoya-u.jp

Species abundance patterns of a food web model
In community ecology, the relation between diversity, stability and species abundance patterns (SAP)
has been discussed as one of the ``unanswered questions in ecology in the last century'' [1]. In special,theoretical understanding of SAP for a system in a single trophic level has been greatly progressed in thiscentury, based on Hubbell's neutral theory [2, 3]. Meanwhile, for more complex systems occurring on
multiple trophic levels and including non-neutral species with various types of interspecies interactions
among them, a pioneering work by May [4], which triggered a controversial debate on the relation between
diversity and stability [5], has demonstrated efficacy of a linear analysis and the theory of random matrices.
Beyond the linear model, statistical mechanics have been employed for analyzing nonlinear models
and have provided global and quantitative information for diversity, stability and SAP [6-10]. Recently, we
presented that sparse interactions essentially change SAP and it reveals multiple peaks that have been
discovered in several field researches [11, 12]. Our analyses also give the first theoretical prediction thatthe sparse (specialist-specialist) interactions stabilize the system and realize all-species coexistence at finite
intraspecific competition that was never predicted in a model with all-to-all interactions.
In my talk, statistical mechanics of SAP for a food web model is presented. Based on the classicaltheory of Edward Kerner for the antisymmetirc Lotka-Volterra equations [13, 14], we analytically obtained
species abundance distributions such as a lognormal distribution and the Fisher’s logseries in a limit of the“eco-temperature” parameter value. We also discuss the corresponding species-area curve.
REFERENCES[1] May, R.M., 1999. Unanswered questions in ecology. Phil. Trans. R. Soc. London, B 264: 1951-1959.
[2] Hubbell, S.P., 2001. The United Neutral Theory of Biodiversity and Biogeography. Princeton University Press.
[3] Etienne, R.S. and Alonso, D., 2007. Neutral community theory: how stochasticity and dispersal limitation can
explain species coexistence. J. Stat. Phys. 128: 485-510.
[4] May, R.M., 1972. Will a large complex system be stable? Nature 238: 413-414.
[5] McCann, K.S., 2000. The diversity-stability debate. Nature 405:228-233.
[6] Tokita, K., 2004. Species abundance patterns in complex evolutionary dynamics. Phys. Rev. Lett. 93: 178102.
[7] Galla, T., 2006. Random replicators with asymmetric couplings, J. Phys. A: Math. Gen. 39: 3853-3869.
[8] Yoshino, Y., Galla, T. and Tokita, K., 2007. Statistical mechanics and stability of a model eco-system. J. Stat.
Mech.: P09003.
[9] Yoshino, Y., Galla, T. and Tokita, K., 2008. Rank abundance relations in evolutionary dynamics of random
replicators. Phys. Rev. E, 78: 031924.
[10] Tokita, K., 2015. Analytical theory of species abundance distributions of a random community model. Popul.
Ecol., 57: 53-62.
[11] Obuchi, T., Kabashima, Y. and Tokita, K. 2016. Multiple peaks of species abundance distributions induced bysparse interactions. Phys. Rev. E, in print. [http://arxiv.org/abs/1605.09106][12] Obuchi, T., Kabashima, Y. and Tokita, K. 2016. Relative species abundance of replicator dynamics with sparseinteractions. J. Stat. Mech., submitted. [https://arxiv.org/abs/1605.09490][13] Kerner, E. H. 1957. A statistical mechanics of interacting biological species. Bull. Math. Biophys. 19: 121-146.
[14] Kerner, E. H. 1974. Why are there so many species? Bull. Math. Biol. 36:477-488.

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7C2-O4-3
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Ryo Oizumi

Ministry of Health, Labour and Welfare
e-mail: oizumi@ms.u-tokyo.ac.jp

Twofold stochasticity in structured population models
Organisms are faced with twofold stochasticity that are internal and external stochasticity. The
fomer belongs to scale of individuals and generates heterogeneity in life schedules. The latter affects
population scale as environmental stochasticity [1]. The internal stochasticity brings about diversity ofstrategies in individual life history which is represented stochastic processes [2]. On the other hand, apaper argued that the external stochasticity conditionally reduces the population growth rate in the longterm perspective [3]. The paper vilified the argument by use of an innovative perturbation method whichis referred to as Tuljapurkar’s approximation. The method clarifies the relationship between effects ofexternal stochasticity on life history and population dynamics in matrix population models. In this study,
by adapting Tuljapurkar’s approximation to a matrix model containing twofold stochasticity, we revealthat the relationship between internal and external stochasticity in life histories.
REFERENCES[1] Oizumi, R., and Takada, T. 2013. Optimal life schedule with stochastic growth in age-size structured models:Theory and an application. Journal of Theoretical Biology, 323: 76–89.
[2] Oizumi, R., 2014. Unification theory of optimal life histories and linear demographic models in internal
stochasticity. PLOS ONE, 9 (6) e98746.
[1] Tuljapurkar, S., 1982. Population dynamics in variable environment III Evolutionary dynamics of r-selection.
Theoretical population Biology, 21: 141–165.

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7C2-O4-4
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Takashi Shimada
Department of Applied Physics, Graduate School of Engineering, The University of Tokyo 1
e-mail: shimada@ap.t.u-tokyo.ac.jp
Fumiko Ogushi
Advanced Institute for Material Research, Tohoku University 2
e-mail: fumiko.ogushi.e3@tohoku.ac.jp

Robustness of evolving open systems with mutual interactions
An important and universal feature of ecosystems, and also other many real complex systems such as
biological, social, economic, and engineering systems, is that those are open: in those systems, constituting
elements are not fixed and the complexity emerges (at least persist) under successive introductions of newelements. Those systems sometimes grow, but also sometimes collapse. A fundamental question that why
and when, in general, we can have such open and complex systems is still not fully understood.
We have revisited this classical problem using a very simple graph-dynamics model in which theinteraction between species are modeled by directed and weighted links. This model gives either continuous
growth or stagnation in system size, depending on the model's unique parameter: the average number ofweighted links per node m. Systems can grow only if the connection is moderately sparse, i.e. 4 < m < 19.
This transition is found to originate from an essential balance of two effects: although having moreinteractions makes each node robust, it also increases the impact of the loss of a node [1, 2]. This novel
relation might be a one scenario for solving the diversity-stability paradox [3]. The non-trivial distributionfunction of the lifetime of species is also reproduced in this model [3].
An important feature we should consider next on applying this theory to dynamical systems such as
population dynamics models of ecological systems is that interaction often should have considerably highchance to be bidirectional [5]. Therefore we here consider the system with bidirectional interactions. In thetalk, we will report how the phase portrait of the system’s growing nature is changed by the introduction of
bidirectional interactions. The model with a mix of unidirectional and bidirectional interactions will be also
discussed.
REFERENCES
[1]
[2]
[3]
[4]
[5]

T. Shimada, in Mathematical Approaches to Biological Systems: networks, Oscillations and Collective Motions(Springer, 2015) p. 95-117.
T. Shimada, Scientific Reports Vol. 4, 4082 (2014).
M. R. Gardner and W. R. Ashby, Nature 228 784 (1970).
Y. Murase, T. Shimada, & N. Ito, New J. of Physics 12, 063021 (2010).
T. Shimada, Y. Murase, & N. Ito, Proceedings of the International Conference on Social Modeling and Simulation,plus Econophysics Colloquium 2014, p. 99-109 (2015).

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7A3-O5-1
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Akane Hara
Kyushu University
e-mail: hara.akane32a@gmail.com
Yoh Iwasa
Kyushu University

When is the allergen immunotherapy effective?
Allergen immunotherapy is one of the methods to treat Japanese cedar pollen allergy (JCPA). In the
immunotherapy of JCPA, patients have a small amount of pollen every week over several years, whichmight suppress severe allergic symptoms when they are exposed to a large amount of environmental pollen
later [1]. In the mechanism of this therapy, Regulatory T cells (Treg cells) play an important role [2]. Treg
cells suppress overreaction of immune system and help avoiding allergic responses [3]. Since it takes
several years to be effective, it is important to choose participants who are likely to benefit from this therapy.
We develop a simple mathematical model and identify the conditions for success of allergen
immunotherapy. In the model, two differential equations (1) and (2) describe the dynamics of type-2helper-T-cells (Th2) and regulatory-T-cells (Treg). H and R represents the number of Th2 and Treg cells,
respectively, and A(t) stands for the amount of pollen the participant takes in. Both of them are differentiatedfrom naive T-cells stimulated by pollen (Fig.1). During therapy period of several years, the patient receivesa small dose every week, and then he or she becomes exposed to a large amount of environmental pollen.
We assume that Treg cells live much longer than Th2 cells, which makes Treg cells accumulate over thetherapy period. Accumulation of Treg cells leads the therapy to be effective. We define that the therapy is
successful if all the following three conditions are satisfied: (1) without therapy the patient develops allergic
symptoms upon exposure to the environmental pollen, (2) with therapy the patient does not develop allergic
symptoms upon exposure, and (3) the patient does not develop allergic symptoms caused by the therapy
itself.

(1)(2)

Fig. 1 Scheme of the model
As a result of analysis of the model, we find the conditions of each parameter for successful therapy.
For example, Treg cells should have a long life span, and many naïve T cells should be stimulated anddifferentiated per unit amount of pollen. We also find that the therapy with dose linearly increasing time,rather than constant dose, is more able to reduce allergic symptoms caused by the therapy itself. We can
extend this model to other kind of allergy, such as food allergy.
REFERENCES[1] Okubo, K., Gotoh, M., 2009. Sublingual immunotherapy for Japanese cedar pollinosis. Allergol Int, 58, 149-54.
[2] Radulovic, S., Jacobson, M. R., Durham, S. R., Nouri-Aria, K. T., 2008. Grass pollen immunotherapy induces
Foxp3-expressing CD4+ CD25+ cells in the nasal mucosa. J Allergy Clin Immunol 121, 1467-72, 1472.e1.
[3] Sakaguchi, S., Yamaguchi, T., Nomura, T., Ono, M., 2008. Regulatory T cells and immune tolerance. Cell 133,
775-787.

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7A3-O5-2
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Yoshiki Koizumi
School of Medicine, College of Medical, Pharmaceutical and Health Sciences, Kanazawa University,
Ishikawa, Japane-mail: koizumi.yoshi@gmail.com

Mathematical modeling of drug administration schedule in HCV infection
In the era of direct-acting antiviral agents (DAAs), hepatitis C virus (HCV) infection can be cured by
combining several DAAs. Although DAAs have achieved the success of drug combination therapy against
HCV infection, the cost of drug treatments has increased and imposed a financial burden on the patients.
In Japan, for instance, the price of a drug combination of sofosbuvir and ledipasvir, the first-line DAAs
treatment on HCV genotype 1, is about 54,000 yen per pill and more than 4,500,000 yen per standard 12week treatment. Such the heavy financial burden may increase the national medical expenses and threaten
the national health insurance system. To save the high cost of DAAs treatment, one possible solution is to
reduce the treatment duration with optimizing a drug regimen for a rapid eradication of HCV. Using theprevious mathematical model[1,2] of viral dynamics and PK/PD, here we try to compare the treatment
duration between double and triple drug combinations, and discuss the optimized drug regimen from thefinancial aspect of DAAs treatments.
REFERENCES[1][2]

Adiwijaya, B. S., et al. "A viral dynamic model for treatment regimens with direct-acting antivirals for chronic
hepatitis C infection." PLoS Comput Biol, 8.1 (2012): e1002339.
Ke, R., et al. "Rational design and adaptive management of combination therapies for Hepatitis C virus
infection." PLoS Comput Biol, 11.6 (2015): e1004040.

- 165 -

7A3-O5-3
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Tatsuya Kurusu
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan.
e-mail: b.c.kurupon11rm16@gmail.com
Koichi Watashi
Department of Virology II, National Institute of Infectious Diseases, Tokyo 162-8640, Japan
Shingo Iwami 1,2
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan. 1 PRESTO,
JST, Saitama 332-0012, Japan. 8CREST, JST, Saitama 332-0012, Japan. 2

Modeling Hepatitis B Virus entry
Hepatitis B virus (HBV) is one of the major factors of hepatic disease, and there is few specificmedicine. For antiviral drugs, virus entry is important target, but there is no quantitative model describing
the viral entry. With the model, we can estimate how percentage virus replication decrease when virus entry
is inhibited, so we propose a novel mathematical model for HBV entry. In this study, we analyzed HBVexperimental dataset, and estimated viral cell-attachment and detachment rate, cell-entry rate and nuclearentry rate. Using this parameter, we simulated our mathematical model and predict the kinetics of HBV
entry. In addition, we would like to discuss about the relationship between the entry inhibitive ratio and thedecrease of cccDNA, the factor of replication.
REFERENCES[1] Watashi, K., Urban, S., Li, W., Wakita, T., 2014. NTCP and Beyond: Opening the Door to Unveil Hepatitis B Virus
Entry. International Journal of Molecular Sciences, 67: 2892–2905.
[2] Seeger, C., Locarnini, S., 2015. The Hepatitis and Delta Viruses. New York, Cold Spring Harbor Laboratory Press.

- 166 -

7A3-O5-4
Sep 7, Wed (Oral)
JSMB2016 Fukuoka

Haru Negami- 167 -

7C3-O6-1
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Gen Kurosawa
Theoretical Biology Laboratory, RIKEN, Wako 351-0198, Japan
Core Research for Evolutional Science and Technology, JSTe-mail: g.kurosawa@riken.jp

Theoretical studies on temperature and biological clocks
Biological phenomena are often sensitive to temperature. For example, cell growth gets faster athigher temperature. In contrast, the period of daily rhythms is robust to temperature. This phenomenon ispeculiar because the system level property (period) is insensitive to temperature while the elements of thesystem (biochemical reactions) are sensitive to temperature. The phenomenon is called "temperaturecompensation", and the mechanism has been elusive for more than 60 years. Thanks to molecular biology
studies, we now know genes and proteins essential for daily rhythms. In our study, we aim to uncover themechanism for the robustness of daily rhythms to temperature by combining computational modeling andquantitative experiments
Regulation of gene expression is essential for the autonomous daily rhythms in mouse, Drosophila,
and Arabidopsis. On the other hand, the autonomous rhythm in Cyanobacteria can be reconstituted in vitro
using three key proteins and ATP [1]. While temperature compensation is observed at both mouse andCyanobacteria, the mechanism for temperature compensation might be different between the two species.
To address this possibility, we used published mathematical models for mammalian [2] and Cyanobacterial[3] daily rhythms. Under the assumption that all reactions should accelerate with temperature, we
numerically analyzed the condition for the robust period in the two models. Unexpectedly, we found thatgeometrical mean of amplitudes should be larger at higher temperature to generate the robust period totemperature in both mammalian [2] and Cyanobacterial [3] models, suggesting that the mechanism fortemperature compensation might be shared between mammals and Cyanobacteria. From the numericalresults, we predict that amplitudes of state variables should be larger at higher temperature in temperaturecompensated systems.
To test the theoretical prediction, we measured expression of genes essential for mammalian daily
rhythm at different temperature in mammalian cultured cells. We found that amplitudes of gene-expressions
tend to be larger at higher temperature in the cells, consistent with the prediction. Moreover, we re-visitedthe time-series of yeast respiration rhythms [4] whose 4hr period is also temperature compensated. We
confirmed that amplitude of the respiration rhythm increases with temperature.
By combining computational modeling and quantitative experiments in mammalian cultured cells,
we conclude that amplitudes of oscillations should be larger at higher temperature to generate the robust
period to temperature. This study has been conducted in the collaboration with Atsuko Fujioka(Kindai), Satoshi Koinuma (Kindai), Tu Benjamin (UT Southwestern), Atsushi Mochizuki (RIKEN), andYasufumi Shigeyoshi (Kindai).
REFERENCES[1] Nakajima, M., Imai, K., Ito, H., Nishiwaki, T., Murayama, Y., Iwasaki, H., Oyama, T., and Kondo, T., 2005
Reconstitution of circadian oscillation of cyanobacterial KaiC phosphorylation in vitro. Science, 308: 414.
[2] Kim, J.K. and Forger, D.B., 2012 A mechanism for robust circadian timekeeping via stoichiometric balance.
Molecular Systems Biology, 8: 630.
[3] Kurosawa, G., Aihara, K., and Iwasa, Y., 2006 A model for the circadian rhythm of cyanobacteria thatmaintains oscillation without gene expression. Biophysical Journal, 91: 2015.
[4] Chen, Z. and McKnight, S.L., 2007 A conserved DNA damage response pathway responsible for coupling the cell
division cycle to the circadian and metabolic cycles. Cell Cycle, 6, 2906.

- 168 -

7C3-O6-2
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Koichiro Uriu
Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Japane-mail: uriu@staff.kanazawa-u.ac.jp
Tei Hajime
Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Japan

Genetic Oscillations by Positive and Negative Feedback Loops Interlocked atCompetitive Binding Sites
Positive and negative feedback loops are often present in regulatory networks for genetic oscillations.
Motivated by the mammalian circadian clock and synthetic genetic oscillators, we study genetic oscillations
caused by positive and negative feedback loops interlocked at competitive binding sites.
In the mammalian circadian clock, a key clock gene Bmal1 is regulated by a repressor Rev-erb and an
activator Ror. Bmal1 activates both of them, forming interlocked feedback loops. The activator andrepressor compete for the same binding sites in the Bmal1 promoter region. Moreover, their time scales andpeak phases are predicted to be very close in the central clock tissue, intensifying competition. Thus, itremains unclear how the positive and negative feedback loops interlocked at competitive binding sites
regulate oscillations of Bmal1 expression. To address this question we develop a theoretical model
describing the time evolution of these three components as a system of delay differential equations. We
find an optimal ratio of dissociation constants of the activator and the repressor for the binding sites toenhance the amplitude of Bmal1 oscillations. The optimal ratio allows them to switch occupancy in thebinding sites over time. In addition, numerical simulations indicate that sharp switch like oscillation of therepressor and small amplitude oscillation of the activator are required for the amplification of Bmal1
oscillation.
Secondly, it has been shown that interlocked positive and negative feedback loops can produce
synthetic genetic oscillations even in the absence of long time delays in the negative feedback loop. To
generate oscillation, however, the time scale of the activator needs to be faster than that of the repressor.
Non-competitive binding sites for the activator and repressor have been used previously, but whether they
are suitable to generate oscillations remains to be revealed. We show that competitive binding sites are
more likely to generate oscillation than the non-competitive binding sites when the time scales of theactivator and repressor are not well separated.
Taken together, our results suggest that the dynamics of the activator and repressor needs to be tightly
linked with their binding sites for effective use of the interlocked positive and negative feedback loops forrobust genetic oscillations.

- 169 -

7C3-O6-3
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Shingo Gibo
Theoretical Biology Laboratory, RIKEN
e-mail: shingo.gibo@riken.jp
Gen Kurosawa
Theoretical Biology Laboratory, RIKEN

Toward understanding the mechanism of the regulation for circadian clocks
by RNA methylation
Methylation of mRNA stabilizes or destabilizes its mRNA. Considerable attention has been paid toregulation of RNA methylation because RNA methylation possibly links metabolic to gene regulatory
systems. Recently, RNA methylation inhibition was found to elongate circadian period by as-yetunidentified mechanism in vitro and in vivo [1]. Revealing this phenomenon helps understand theinteraction between metabolic and gene regulatory systems. In this study, we theoretically investigate themechanism of period-alteration by RNA methylation.
According to experimental results [1], a methylation inhibitor (DAA) stabilizes mRNAs of many (notall) circadian related genes. Thus, we analyzed a published realistic model for mammalian circadian clock[2] by incorporating the changes in kinetics under RNA methylation inhibitor. We estimated the changes
in mRNA under a methylation inhibitor using experimental data, and confirmed that calculated circadianperiod should elongate under RNA methylation inhibitor, consistent with experimental data.
RNA methylation possibly changes other reaction rates in gene regulatory system. To predict which
reaction processes can be activated by methylation, we analyzed period sensitivity of realistic model [2].
We found that when fast reaction rate elongates the circadian period, the inhibitor abundance tends toincrease, possibly slowing down the transcription process.
To understand these results, we simplified the realistic model into 4 variables model, which keeps
multiple protein modification processes. Using Fourier analysis [3, 4], we derived the exact period formulaof our simplified model. The period formula states that fast reaction rate tends to shorten the period. It also
states that fast reaction rate can lengthen period only when amplitudes of inhibitor changes. By using oursimplified model, we can understand the result of realistic model. The present approach opens the way forunderstanding how variation in kinetics parameters changes oscillatory period.
REFERENCES[1] Fustin, JM. Doi, M., Yamaguchi, Y., Hida, H., Nishimura, S., Yoshida, M., Isagawa, T., Morioka, MS., Kakeya,
H., Manabe, I., and Okamura, H., 2013. RNA-Methylation-Dependent RNA Processing Controls the Speed of the
Circadian Clock. Cell, 155: 793–806.
[2] Zhou, M., Kim, JK., Eng, GWL., Forger, DB., and Virshup, DM., 2015. A Period2 Phosphoswitch Regulates andTemperature Compensates Circadian Period. Molecular Cell, 60: 77-88.
[3] Panter, PF., 1965. Modulation, Noise, and Spectral Analysis, Applied to Information Transmission (McGraw-Hill,
New York) p viii.
[4] Forger, DB., 2011. Signal processing in cellular clocks, PNAS, 108: 4281-4285.

- 170 -

7C3-O6-4
Sep 7, Wed (Oral)
JSMB2016 Fukuoka
Prabhat Shankar
Lab for Physical Biology, Riken QBiC, Kobe, Japane-mail: pshankar@cdb.riken.jp
Tatsuo Shibata
Lab for Physical Biology, Riken QBiC, Kobe, Japan
Hitoshi Niwa
Department of Pluripotent Stem Cell Biology, Kumamoto University, Kumamoto, Japan

Inference of Gene Regulatory from Experimental Data
Many important functions of a cell are governed by gene regulatory networks, where a set of genes activateof repress the functions of other genes, working in synchrony to regulate some function. Recent
developments in experimental methods have enabled collection of gene expression profile data from anumber of gene simultaneously. But the gene expression data by itself is not sufficient to uncover the
regulatory principles, and need the help of mathematical models and analysis for deeper insight. Such a
network model leads into understanding of the regulatory principles underlying the function. Number ofapproaches have been proposed in this direction recently [1]. In this work, we present an algorithm to infera gene regulatory network in terms of a deterministic Boolean Network, obtained from a stationary gene
expression data. This algorithm is based on the principle of consistency, that is, identical inputs must haveidentical outputs. Using time evolution, the number of candidate networks satisfying the gene expression
data can further be reduced.
Using our algorithm, we analyzed a set of gene expression data obtained from the mouse pluripotent ES
cells, and inferred the regulatory interactions underlying beneath. The approach uncovered hitherto
unknown interactions. We hope our simple and intuitive approach can be applied to many other cellular
systems as well.
REFERENCES[1] Dunn, S-J., et al. Defining an essential transcription factor program for naive pluripotency.

Science 344.6188 (2014): 1156-1160.

- 171 -

8A1-O7-1
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Hisashi Ohtsuki
SOKENDAI, Hayama, Japane-mail: ohtsuki_hisashi@soken.ac.jp
Kalle Parvinen
University of Turku, Turku, Finland
IIASA, Laxenburg, Austria
Joe Yuichiro Wakano
Meiji University, Tokyo, Japan

Does spatiality hinder evolutionary branching?
Convergent stable evolutionarily singular points are classified into two types. One is an evolutionarily
stable point where no mutants can invade. The other is an evolutionary branching point where nearby
mutants can invade and thus the population splits into two morphs. A recent study has shown a generalcondition for evolutionary branching in a spatially structured population in terms of fitness derivatives[1],yet it was too general to obtain insights into practical questions, such as “whether spatiality hinders
evolutionary branching” or “whether there exists a case where spatiality promotes evolutionary branching”.
In this study, we have adopted Wright’s island model with non-overlapping generations as our model
framework and studied fecundity selection there. In particular, we have assumed that social interactions
within an island affect one’s fecundity, f. We have then derived conditions for evolutionary branching interms of first-order and second-order fecundity derivatives, as well as of island size, migration rate, and thesurvival probability in migration.
Our results show that evolutionary branching is always hindered when either the migration rate or thesurvival probability in migration is close to zero. We also provide two simple necessary conditions for the
inhibition of evolutionary branching by spatial structure. These results are consistent with the previous
finding that evolutionary branching is hindered in a deme-structured population[2]. We can construct,
however, a 3-person game example where evolutionary branching does not occur in a well-mixed
population but it does in Wright’s island model with an intermediate migration rate. Overall, our results
help us intuitively understand the effect of spatial structure on conditions for evolutionary branching.
REFERENCES[1] Ajar, É., 2003. Analysis of disruptive selection in subdivided populations. BMC Evol. Biol., 3(22): 1–12.
[2] Wakano, J.Y., Lehmann, L., 2014. Evolutionary branching in deme-structured populations. J. Theor. Biol., 351:
83–95.

- 172 -

8A1-O7-2
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Ryo Yamaguchi
Department of Biology, Kyushu University
e-mail: ryamaguchi@bio-math10.biology.kyushu-u.ac.jp
Yoh Iwasa
Department of Biology, Kyushu University

A tipping point in speciation with gene flowMore than two loci are involved in reproductive isolation in most cases of putative recent speciation.
We study the speciation between two geographically isolated populations connected by infrequentmigration, in which incompatibility is controlled by quantitative loci. Incompatibility genetic distance isdefined as the fraction of compatibility controlling loci different between individuals. Complete
reproductive isolation is established when the distance reaches a threshold level in spite of occasionalmigration and subsequent hybridization that reduce it.
Here we study how the time to speciation depends on the manner the magnitude of incompatibility
increases with the genetic distance. Both the increases of the genetic distance due to the accumulation of
separate mutations and the decrease due to rare migration and subsequent hybridization include
stochasticity.
Results are: (1) The time to speciation is short if the migration rate is smaller than the mutation rate,or if intermediate levels of genetic distance cause mild incompatibility, making migrants less effective in
reducing genetic distance. (2) Genetic distance may fluctuate around a positive quasi- equilibrium level fora long time, and suddenly show a quick passage to speciation when it goes beyond a “tipping point.” (3)Speciation becomes very slow if incompatibility is effective for individuals differing only one locus. Thesefindings provide testable predictions that reproductive traits controlled by specific incompatibility
accumulation forms can facilitate the speciation process.
REFERENCES[1] Yamaguchi, R. and Y. Iwasa. 2013. First passage time to allopatric speciation. A contribution to a special issue of‘Modelling biological evolution: recent progress, current challenges and future direction" Interface Focus 2013 3,
20130026. doi: 10.1098/rsfs.2013.0026[2] Yamaguchi, R. and Y. Iwasa. Smallness of the number of incompatibility loci can facilitate parapatric speciation.
Journal of Theoretical Biology (in press)- 173 -

8A1-O7-3
Sep 8, Thu (Oral)
JSMB2016 Fukuoka

Yuma Sakai- 174 -

8A2-O8-1
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Norio Yamamura
Culture and Information Science, Doshisha University, Kyoto, Japane-mail: nyamamur@mail.doshisha.ac.jp

Population Dynamics and Optimal Management of 4 Species(Grass, Shrub, Sheep and Goat) in Nomadism
It is an urgent subject to make rich life of people without deterioration of environment. I describe
population dynamics of grass, shrub, sheep and goat in nomadism, and examine the optimal selling rates of
sheep and goat in order to attain a high economical gain with a rich biomass of grass.
In the dynamics, grass and shrub grow as Logistic equations that are grazed by sheep and goat, andhuman sell animals at constant rates with proportion of their biomass. Assuming parameter conditions thatsheep prefer grass and goats prefer shrub [1], only one equilibrium among the following six equilibria is
globally stable, depending on values of two selling rates: (1) four species, (2) three species other than goat,(3) three species other than sheep, (4) sheep and shrub, (5) goat and grass, and (6) grass and shrub. Indirect
effects are observed such that raising sheep selling rate induces reduction of grass through increase in shrub
and goat, although direct effect should increase grass.
On the stable equilibria, I obtained optimal selling rates by environmentally-optimized model,
economically-optimized model, and both-optimized model. In the environmentally-optimized model, highselling rates without no animals give an optimum as I maximized the sum of grass and shrub biomass. In
the economically-optimized model, intermediate selling rates give an optimum where four species coexist
when prices of sheep and goat per biomass do not much differ as I maximized selling proceed. In the bothoptimized model, higher selling rates with less animals give an optimum than in the economicallymaximized model as I maximized the sum of selling proceed and plant biomass. Finally, I examined how
the optimal solution changes corresponding to changes in environmental awareness, trend of economy, andglobal climate.
REFERENCES[1] Fujita, N., Amarrtuvshin, N. and Ariunbold, E., 2013. Vegetation interaction for the better
understanding of a Mongolian ecosystem network. In: The Mongolian ecosystem network (Yamamura,N., Fujita, N. and Maekawa, A. eds.), Springer, pp.157-184.

- 175 -

8A2-O8-2
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Shigeo YACHICenter for Ecological Research, Kyoto University
e-mail: yachi@ecology.kyoto-u.ac.jp

Dynamics of community-based ecosystem management:
the role of context-dependent ecosystem services
In this paper, I present a dynamic model of a community-based ecosystem restoration processcatalyzed via ecosystem services which stakeholders of the community can evaluate in their own contexts
of interests. It has long been worried that biodiversity and ecosystem services on earth have been degraded
intensively by human activities. IPBES (Intergovernmental Panel on Biodiversity and Ecosystem
Services), for example, has started to improve this situation by promoting collaborative framework
between researchers and diverse stakeholders including governments, local governments, enterprises,
NGOs and communities through publishing scientific assessment reports on biodiversity and ecosystemservices, and developing tools for communication and capacity building between stakeholders such asmodels and scenarios.
Among the difficulties to overcome between stakeholders in large-scale management issues is themismatch with the pressing issues of the concerned stakeholders. In the context of ecosystem restoration,
management at the watershed scale is regarded as effective; however, as the management scale becomeslarger, the diversity of stakeholders increases and so the mismatch on what is the pressing issue. One of
the representative mismatches of urgent issues typically observed in local communities in Japan expresses
as ecosystem restorations at the watershed scale vs. restoration or revitalization of communities of smallerscales in the watershed, which are to be driven to extinction by depopulation and aging. Ecosystem
restoration would fail if there is keen mismatch with the pressing issue of the concerned stakeholders.
Here, community-based ecosystem management which focuses on the role of ecosystem services
evaluated in the stakeholders' context is suggested as a candidate to resolve this mismatch (K. WAKITA).
The essential mechanism lies in the emergence of multiple functions or multiple services of an ecosystem
which can work as effective services in the context of community restoration as the ecosystem restoration
proceeds.
A dynamic model was constructed to evaluate the role of community-context dependent ecosystemservices, by introducing supply of multiple ecosystem services evaluated in the context of ecosystem
restoration context and community restoration context. Frequencies of multiple preferences of
stakeholders corresponding to ecosystem services, too, are formulated as variables which changes
dynamically as ecosystem restoration proceeds and, in turn, affect the improvement of ecosystem
restoration. By combining these two kinds of variables, an ecosystem restoration process is formulated. I
will report under what conditions community-based ecosystem restoration would overcome the mismatchof issues between stakeholders.

- 176 -

8A2-O8-3
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Yuki Kubo
Graduate School of Sistems Life Sciences, Kyushu University
e-mail: yukikubo@kyudai.jp
Joung-Hun Lee
Institute of Decision Science for Sustainable Society, Kyushu University
Takahiro Fujiwara
Institute of Decision Science for Sustainable Society, Kyushu University
Yoh Iwasa
Department of Biology, Faculty of Science, Kyushu University

Management of tropical forests with agroforestry and profit sharing
Illegal logging is a very serious problem for plantation management in tropics [1]. Here we study the
profit-sharing and agroforestry as management strategies [2-4].
Owner chooses the age of trees to cut, and the workers choose their monitoring effort to prevent illegal
logging.
We derived two recursive formulas for the values of a site with trees of age t to the owner and to theworkers. After the trees were removed, either by cutting, physical disturbances, or illegal logging, the ownerhires workers to replant young trees. While trees are young, the land is also used as agriculture. In addition,
the owner may share a fraction of profit obtained by selling logs with the workers. Illegal logging may be
prevented by hiring forest guards or by monitoring effort of the workers.
Results are: (1) As the fixed cost of harvesting increases, the foresters delay the tree harvesting age.
(2) If the discount rate is high, the foresters may use the land for continual agriculture by cutting trees attheir young ages. (3) Under the presence of illegal logging pressure, the owner may find it profitable toshare the income with the workers to solicit their monitoring efforts. We discuss policy implications ofthese results.
REFERENCES[1] Tacconi, L., 2012. Illegal logging: law enforcement, livelihoods and the timber trade. Earthscan.
[2] Fujiwara, T., Awang, S.A., Widayanti, W.T., Septiana, R.M., Bariatul, H., Rahmat, M., Suyanto, A. and Sato, N.,
2011. Overcoming vulnerability of privately owned small-scale forest through collective management unit
establishment: a case study of Gunung Kidul district, Yogyakarta in Indonesia. International Journal of Social
Forestry, 4(2), pp.95-120.
[3] Nawir, A.A., Santoso, L. and Mudhofar, I., 2003. Towards mutually-beneficial company-community partnerships
in timber plantation: lessons learnt from Indonesia (No. CIFOR Working Paper no. 26, pp. xvi-77p). CIFOR, Bogor,
Indonesia.
[4] Peluso, N.L., 1992. Rich forests, poor people: Resource control and resistance in Java. Univ of California Press.

- 177 -

8A2-O8-4
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Mayuko Nakamaru
Department of Innovation Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo,152-8552, Japane-mail: nakamaru.m.aa@m.titech.ac.jp
Hayato Shimura
Department of Value and Decision Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro,
Tokyo, 152-8552, Japan
Yoko Kitakaji
Research Center for Future Design, Kochi University of Technology, Eikokuji Campus: 2-22 Eikokuji,
Kochi City, Kochi 780-8515, Japan
Susumu Ohnuma
Department of Behavioral Science, Hokkaido University, North 10 West 7, Kita-ku, Sapporo, Hokkaido,
060-0810, JapanThe evolution of cooperation in the division of labor:
Industrial waste illegal dumping as an example
Cooperation is a foundation of our society. The evolution of cooperation is an unsolved research topic
and has been investigated from the viewpoint of not only evolution but also other research areas such associal sciences. We are on an equal footing and cooperation among peers is essential in some social
situations. Many previous researches have focused on the evolution of cooperation among peers. While,
we are on a different footing, different players play different social roles such as leaders and subordinatesin a group and hierarchy in some organizations, and then players playing different social roles cooperate toachieve their goal. In this talk, we focus on cooperation in the division of labor.
The industrial waste treatment process is an example of the division of labor and consists of five typesof industry: generators (or W1), the 1st waste haulers (or W2), the intermediate treatment facilities (orW3), the 2nd waste haulers (or W4) and the landfill sites (or W5) [1]. The player of Wi can choose two
strategies: legal treatment or illegal dumping (i = 1−5). In legal treatment, the player of Wi pays a cost to
have the player of Wi+1 treat the waste (i = 1−4). In illegal dumping, the player of Wi does not pay any cost(i = 1−5). However, the illegal dumping damages the environment, and all players suffer from the damage
or have to pay for the environmental restoration. This situation is equivalent to social dilemma and thestudies about the evolution of cooperation can be applied into this situation. The previous studies about theevolution of cooperation show that cooperators punishing defectors promotes the evolution of cooperation.
In reality, the administrative organ introduces two punishment systems to solve the illegal dumping
problem: the actor responsibility system and the producer responsibility system. In the actor responsibility
system, if players who choose illegal dumping are discovered, they are penalized a fine. However, it is hardto discover those who choose illegal dumping, and this system may not work. While, in the producer
responsibility system, the generator is penalized a fine if the generator cannot hand the manifest to the local
administrative organ as the players of Wi (i = 1−5) who choose illegal dumping do not hand the manifest
to the generator. We investigate whether the producer responsibility system can restrain the illegal dumping
more than the actor responsibility system.
We analyzed the replicator dynamics when (i) there are two types of industry, generators and thelandfill sites, and (ii) there are three types of industry, generators, intermediate treatment facilities, andlandfill sites. Then we found that (1) the three-industry model explains the present situation of illegal
dumping more than the two-industry model, and (2) both the actor responsibility system and the producer
responsibility system promote the evolution of cooperation in the division of labor more than the system
without penalty. While, the actor responsibility system promotes the evolution of illegal dumping morethan the producer responsibility system.
REFERENCES[1] Kitakaji, Y. and Ohnuma, S., 2014, Demonstrating that monitoring and punishing increase non-cooperative
behavior in a social dilemma game. The Japanese Journal of Psychology, 85:9-19. (In Japanese)- 178 -

8C2-O9-1
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Akira Sasaki
Department of Evolutionary Studies of Biosystems, The Graduate University for Advanced Studies,
Hayama, Kanagawa, 240-0193, JAPANe-mail: sasaki_akira@soken.ac.jp

A Bayesian updating model for the antigenic escapes of influenza virus subtypes
Human influenza viruses are known to escape continuously from hostimmune defense by accumulating mutations on hemagglutinin. A recent multivariate
statistic technique has extracted their surprisingly simple evolutionary trajectories on alow dimensional projected trait spaces. Here I propose a simple Bayesian update model
to reproduce such evolutionary trends.
The antigen space is assumed to be two dimensional. The evolutionary
dynamics is made up of the series of the following 3 processes in each year: (1) an
epidemic of a particular strain, (2) the change in fitness landscape (the probability that amutant can establish itself in host population) on antigen space according to the buildup
of herd immunity against the epidemic strain, (3) a mutant that will cause epidemic in
the next year is chosen randomly according the its probability of being generated by theparental strain, multiplied by its fitness determined by the past past infection history inthe host population.
This model generates nearly linear trends in the series of epidemic strains
placed on antigen space with a randomly chosen direction. The angles made byconsecutive axes of annual antigenic changes are narrowly distributed around 0, and the
distance between epidemic strains has a peaky distribution around the characteristic
width of cross-immunity. An extension that allows more than two epidemic strains
sampled in each year, and its relation to occasional turns in trajectories are discussed.
a)
b)
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Figure 1. The time sequence of epidemic strains on two-dimensional antigen space. a)
The epidemic strain in year t (blue point) newly introduced in host population, and thelikelihood for the position of the next epidemic strain (contours -- the lighter the grayscale, the greater the probability is). Red point is the strain actually sampled with thisprobability distribution. b) The likelihood after two epidemic strains (blue in year t, andred in year t+1) has a skewed, hammer-head like landscape. c) The chosen epidemic strainof the year t+2 (green point) and the likelihood for the year t+3.

- 179 -

8C2-O9-2
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Kazunori Sato
Shizuoka University
e-mail: sato@sys.eng.shizuoka.ac.jp

Lattice model of foot-and-mouth disease revisited
Ringa and Bauch (2014)[1] analyze the lattice model of foot-and-mouth disease (FMD), in which farmto-farm disease spatially transmits, using pair approximation. Their SEIRV (susceptible-exposedinfectious-recovered-vaccinated) model includes both ring and prophylactic vaccinations, and they
consider the effects of these vaccinations depending on duration of vaccine immunity and disease reintroduction rate. Then they clarify the differences in dynamics between FMD-free countries and FMDendemic ones, and argue the necessity of these kinds of mathematical models to examine the case of FMDendemic countries.
Generally speaking in epidemics, the basic reproduction number R0 is a key estimator by which we
can expect whether the disease outbreak occurs or not. We can find several previous studies of R0 for some
infectious disease models on lattice space (e.g. Bauch 2005[2]; Keeling 1999[3] Trapman 2007[4]) and thenwe should carefully choose the method of calculation to estimate the value of R0. Ringa and Bauch (2014)[1]
obtained R0 for their FMD model based on the procedure by Bauch (2005)[2]. Even for the case withoutboth ring and prophylactic vaccinations, the parameter dependence of their R0 much differs from R0 by
corresponding completely mixing model (or no spatial-structured model). Then I will examine the reason
why that difference takes place. In addition I would like to compare R0 by usual approach with their R0 andconsider the effect of spatial structure of the model on R0. Finally, I will propose an appropriate R0 for themodeling of FMD.
REFERENCES[1] Ringa, N. and Bauch, C.T., 2014. Dynamics and control of foot-and-mouth disease in endemic countries: A pairapproximation model. Journal of Theoretical Biology, 357: 150–159.
[2] Bauch, C.T., 2005. The spread of infectious diseases in spatially structured populations: an invasory pairapproximation. Mathematical Biosciences, 198: 217–237.
[3] Keeling, M.J., 1999. The effects of local spatial structure on epidemiological invasions. Proceedings of the Royal
Society B, 266: 859-867.
[4] Trapman, P., 2007. Reproduction numbers for epidemics on networks using pair approximation. Mathematical
Biosciences, 210: 464–489.

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8C2-O9-3
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Noriyuki Suzuki
College of Science and Engineering, Aoyama Gakuin University, Kanagawa 252-5258, Japan.
e-mail: c5616003@aoyama.jp
Shinji Nakaoka
Graduate School of Medicine, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 133-0033, Japan.
e-mail: shinzy.nakaoka@gmail.com
Yasuhiro Takeuchi
College of Science and Engineering, Aoyama Gakuin University, Kanagawa 252-5258, Japan.
e-mail: takeuchi@gem.aoyama.ac.jp

HIV infection dynamics with pyroptosis of target cells
In ethical reasons, it is impossible to perform experimental operations to humans when a person is
infected with human immune-deficient virus (HIV). In such a situation, mathematical modeling andsimulation is powerful and useful approach to investigate mechanisms underlying the cause of disease. In[1], it is reported that pyroptosis may play a promoting role in HIV infection cycle, leading to a vicious
cycle in HIV infection. Although pyroptosis is a type of cell death which induce secretion of proinflammatory cytokines such as IL1-beta to inform immune cells to be recruited and initiate proinflammatory response, recruitment of CD4 positive T cells via pytoptosis is suggested to be important in
HIV infection. In order to take into account for the effect of cell recruitment via pyroptosis, we construct amathematical model for HIV infection which describes cell recruitment and HIV infection. A simplified
one-dimensional mathematical model is derived from our original model to understand clearly how
pyroptosis mediates HIV infection. In our mathematical analysis, typical time scale to develop to acquire
immune-deficiency (AIDS), defined as the declined CD4 positive T cell counts below 200 per micro-liter,
can be explained by our simplified mathematical model.
REFERENCES[1] Gilad Doitsh et al, Cell death by pyroptosis drives CD4 T-cell depletion in HIV-1 infection, Nature 505, 509–514.

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8A3-O10-1
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Tsuyoshi Mizuguchi
Department of Mathematical Sciences, Osaka Prefecture University, Sakai, Osaka, Japane-mail: gutchi@ms.osakafu-u.ac.jp
Makoto Yomosa
Department of Mathematical Sciences, Osaka Prefecture University, Sakai, Osaka, Japan
Yoshinori Hayakawa
Center for Information Technology in Education, Tohoku University, Sendai, Miyagi, Japan
Gábor Vásárhelyi
Department of Biological Physics, Eötvös Univeristy, Budapest, Hungary
Máté Nagy
Department of Collective Behaviour, Max Planck Institute for Ornithology, Konstantz, Germany

Spatial and temporal structure of flying bird flocks
Collective behavior of animals such as flock of birds, school of fish, swarm of insects and crowds ofhumans fascinate people for a long time. There are rather “regular” behaviors such as V-shape formed bylarger birds while the swarm of insects seems to be irregular. One key concept to characterize theseregularities is their relative positions with respect to their moving direction, which are important to describe
the internal structure of the flock[1].
The development of measurement devices makes it possible to extract three-dimensional position dataof distant objects like flying birds. And collective motions of birds in flocks are studied based on real datausing these devices such as GPS or digital camera[2-5]. We focus on flocks of hooded gull (Larus
ridibundus) which fly around and along Yamatogawa River in Osaka, Japan[6]. Behaviors of birds in flocks
are analyzed with time series of their velocities and relative positions, which are three-dimensionallyreconstructed from pictures taken by a portable stereo camera system. We define "bird coordinates" basedon the averaged motion of each individual. The distribution of lateral component of relative position has
two peaks around zero, which suggests that individuals avoid the position just behind others by aninteraction between them. The time series of oscillating velocity component caused by a flapping motion
are also analyzed.
Analysis of pigeon flocks obtained by GPS system is also introduced[7]. By focusing on the free
flight state their internal structure of the flocks are analyzed and are compared with those of hooded gull
flocks.
REFERENCES[1] Bajec, I. L. & Heppner, F. H., 2009. Organized flight in birds. Animal Behaviour, 78: 777-789.
[2] Ballerini, M., et al., 2008. Interaction ruling animal collective behavior depends on topological rather than metricdistance: Evidence from a field study. PNAS, 105:1232-1237.
[3] Nagy, M., et al, 2010. Hierarchical group dynamics in pigeon flocks. Nature, 464: 890-894.
[4] Portugal, S. J., et al. 2014. Upswash exploitation and downwash avoidance by flap phasing in ibis formation flight.
Nature, 505: 399-404.
[5] Hayakawa, Y., 2010. Spatiotemporal dynamics of skeins of wild geese. Europhysics Letters, 89:48004.
[6] Yomosa, M., Mizuguchi, T. and Hayakawa, Y., 2013. Spatio-temporal structure of hooded gull flocks. PLoS ONE,8: e81754.
[7] Yomosa, M., et al., 2015. Coordinated behavior in pigeon flocks. PLoS ONE, 10: e0140558.

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8A3-O10-2
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Yumino Hayase
Hiroshima Universit
e-mail: yumino@hiroshima-u.ac.jp
Shota Fujii
Hiroshima University
Ryo Kobayashi
Hiroshima University

An active undulation of centipede locomotion
A centipede can move very fast with a velocity more than 200mm/s although his body length is only
a few centimeters. It is obvious that a centipede does not control each leg independently, but a central
control rule of legs is still unknown. From observations of centipedes, we found that some species use its
body undulation and others do not. For example, we compare centipede “Scolopendra subspinipes
mutilans”(Fig. a) with centipede “Scolopcryptos rubiginosus”(Fig, b). Both belong to the same order“Scolopendramorpha” and their physical sizes are almost the same. “Scolopendra subspinipes mutilans”
uses the body undulation, but “Scolopcryptos rubiginosus” does not. The difference is not only the bodyundulation, but also the locomotory wave. At a low velocity of about 30mm/s, both take on the retrograde
wave. At a high velocity, while “Scolopendra subspinipes mutilans” takes still the retrograde wave,“Scolopcryptos rubiginosus” changes the locomotory wave to direct wave. From this observation, we
assume that “Scolopendra subspinipes mutilans” converts a transversal oscillation into a longitudinalmotion.
We propose a simple mathematical model with an active body undulation. We discuss the relation
between the body undulation and the wave direction. The efficiency of the locomotion with/without
undulation is also discussed.
Figure(a) Scolopendra subspinipes mutilans(b) Scolopendra subspinipes multians- 183 -

8A3-O10-3
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Nariya Uchida
Department of Physcis, Tohoku University
e-mail: uchida@cmpt.phys.tohoku.ac.jp

Collective dynamics of bacteria at interfaces
Collective dynamics of swimming bacteria attached to solid walls are investigated by numericalsimulations. A monolayer of bacteria (bacteria carpet) exhibits collective reorientation as the flagellar
activity is tuned by sodium concentration, which resembles a second-order phase transition [1,2]. We
propose a simple model incorporating the three-dimensional rotational degrees of freedom of the flagella,hook elasticity, and hydrodynamic interaction between flagella. Densely packed bacteria chains exhibit
collective waving due to steric repulsion. The waving behavior is reproduced by a model based on semiflexible and self-propelling chains with excluded volume interaction.
REFERENCES[1] Y.-T. Hsiao, J.-H. Wang, K.-T. Wu, J. Tsai, C.-H. Chang, and W.-Y. Woon, 2014. Collective flow dynamics acrossa bacterial carpet: Understanding the forces. Appl. Phys. Lett., 105: 203702-1–203702-5. [2] Y.-T. Hsiao, K.-T. Wu,
N. Uchida, and W.-Y. Woon, 2016. Impurity-tuned non-equilibrium phase transition in a bacterial carpet. Appl. Phys.
Lett., 108: 183701-1–183701-5.

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8A3-O10-4
Sep 8, Thu (Oral)
JSMB2016 Fukuoka
Takahiro Kamioka
Department of Biology, Faculty of Science, Kyushu University
e-mail: t.kamioka.530@gmail.com
Yoh Iwasa
Department of Biology, Faculty of Science, Kyushu University

Evolution of density dependence and juvenile hormone regulation in wing
polymorphic insects
The wing-polymorphic insects show two wing types within species. The experienced density
affects the wing determination [1]. Physiologically, the level of juvenile hormone is responsible in thisprocess [1]. However, the action of the density is different among species or local population [1,2,3].
To observe the factor of this various result, we studied the evolution of density-dependent dispersal
and juvenile hormone (JH) regulation in wing-polymorphic insects.
The population dynamics is shown in Fig. 1. Assumptions are: An asexual species with larval
and adult stages live in many patches. Larval growth rate depends on the amount of renewable
resources within a patch, which are consumed by the larvae. Dispersal type adults migrate out of thenatal patch just before reproductive stage; which reproductive type adults in contrast have a large
fertility but no dispersal ability. The fraction of dispersal type may change with the density experienced
in larval stages. Genotypes differ in the way in which the fraction of dispersal type responds to thedensity experienced in the larval stages. The carrying capacity of the resources fluctuates between highand low values.
Density-dependent dispersal evolved if the environmental fluctuation was large. Some dispersal
type adults were produced if the density was above a threshold, with the rate increases with the density.
In contrast, no dispersal type appeared if the environmental fluctuation was small.
The rate of production of dispersal type increased with the density more rapidly in more severely
fluctuating environment. The growth rate of larva and the recovery of resource also affect the
production of dispersal type at high density.
We also examined the evolution in a situation in which the JH level to produce has a fixedvariance and the mean responding to the density experienced by the larvae, in which wing type isdetermined by whether the JH level is higher than a threshold (Fig. 2). In more severely fluctuating
environment, the density-dependent degradation of JH evolved to be faster and the variance of JH
level evolved to be smaller, both leading to an enhanced fraction of dispersal type adults.

REFERENCES[1] Zera and Denno, 1997. Annual review of entomology, 42: 207–230.
[2] Iwanaga and Tojo, 1985. Entomologia experimentalis et applicata, 38: 101–108.
[3] Denno, 1991. The American Naturalist, 138: 1513–1541.

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9A1-O11-1
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Masato S. Abe
National Institute of Informatics, JST ERATO Kawarabayashi Large Graph Project, Tokyo, Japane-mail: masatoabee@gmail.com
Shin-ichiro Nakayama
National Research Institute of Fisheries Science, Kanagawa, Japan
Haruna Fujioka
Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan
Masakazu Shimada
Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan

Detecting interaction patterns in ant society by cross-embedding method
Collective behavior is ubiquitous in living systems ranging from cells to animal groups, andcan lead to rapid and accurate responses to environments or efficient division of labor at grouplevel. Especially, it has shown that social insects such as ants and bees often exhibit sophisticatedcollective behavior including searching foods through pheromone trails, quorum sensing, and soon. Although it is crucial to understand how collective behavior in social insects can emerge frominteractions between individuals, it is less understood due to difficulty in obtaining and analyzing
data. Here, to investigate who influences whom and untangle collective dynamics, we
automatically obtained the trajectory of movements in ant individuals (Diacamma sp.) by image
analysis, and detected interactions and their strength between individuals using time-series
analysis based on state space reconstruction and cross-embedding [1, 2]. We show that theinteraction patterns driving collective dynamics depends on the behavioral castes (i.e., nurses andforagers), and discuss how the collective dynamics emerges from interactions in ant society.
REFERENCES[1] Sugihara, G., May, R., Ye, H., Hsieh, C. H., Deyle, E., Fogarty, M., & Munch, S., 2012. Detecting causality incomplex ecosystems. Science, 338(6106), 496-500.
[2] Deyle, E. R., May, R. M., Munch, S. B., & Sugihara, G., 2016. Tracking and forecasting ecosystem interactions inreal time. Proc. R. Soc. B, 283, 20152258.

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9A1-O11-2
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Wataru Nakahashi
SOKENDAI, Hayama, Japane-mail: w.nakahashi@gmail.com
Hisashi Ohtsuki
SOKENDAI, Hayama, Japan

Cost and benefit of emotional contagion in group-living animals
Many animals including humans show emotional contagion, the phenomenon that a strong emotionof an individual (demonstrator) triggers similar emotions and behaviors in other individuals (observers).
This may cause consistent group behaviors of many animals. Although we have already investigatedconditions for emotional contagion to be adaptive in a two-player (a demonstrator and an observer) situation[1], it remains unclear whether emotional contagion is adaptive in a large group. As group size increases,
two probabilities may increase, the probability that someone recognizes a change in the situation to behave
correctly (e.g., finds a predator to escape) and that someone misrecognizes the situation to behave wrongly.
Therefore, we may suppose that individuals with emotional contagion may receive both cost and benefit
from the increasing group size. Taking this into account, we theoretically study the effect of group size on
the evolution of emotional contagion in group-living animals.
REFERENCES[1] Nakahashi, W. and Ohtsuki, H., 2015. When is emotional contagion adaptive? Journal of Theoretical Biology, 380:
480–488.

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9A1-O11-3
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Emmi SchlichtPeter Santema
Bart Kempenaers
Department of Behavioural Ecology and Evolutionary Genetics,
Max Planck Institute for Ornithology, Seewiesen, Germany
Robert Schlicht
Department of Forest Sciences,
Technische Universität Dresden, Tharandt, Germany
e-mail: robert.schlicht@tu-dresden.de

Evidence for conditional cooperation in biparental care systems?
In species with biparental care, the joint benefit from care by each parent makes it possible to free rideon the partner’s investment. As an evolutionary solution to this conflict over care, Johnstone et al. [1]propose conditional cooperation, where parents show a tendency to take turns in feeding their young. Usinga simple Markov process based model they show for data from a great tit (Parus major) population thatparents indeed reduce their feeding rates after feeding and before the partner feeds next. Additionally, by
randomizing intervisit times, they show that this effect is not merely due to the adoption of constant rates
between feeding events.
We here argue [2] that fundamental assumptions of this model are violated in many biologically
relevant settings, and that alternating feeding patterns result from many simple realistic processes. Byslightly modifying the randomization, we demonstrate that patterns such as those observed occur without
any form of conditional cooperation when feeding rates are affected by both time of absence and changing
external conditions, as is biologically plausible. We therefore believe the conclusion of conditional
cooperation is premature.
In this talk I first introduce the original model, then present our alternative randomization procedureand its conclusions, and finally discuss the response to our analysis by Johnstone et al. [3].
REFERENCES[1] Johnstone, R.A., Manica, A., Fayet, A.L., Stoddard, M.C., Rodriguez-Gironés, M.A., Hinde, C.A., 2014.
Reciprocity and conditional cooperation between great tit parents. Behavioral Ecology, 25: 216–222.
[2] Schlicht, E., Santema, P., Schlicht, R., Kempenaers, B., 2016. Evidence for conditional cooperation in biparental
care systems? A comment on Johnstone et al. Behavioral Ecology, 27: e2–e5.
[3] Johnstone, R.A., Manica, A., Fayet, A.L., Stoddard, M.C., Rodriguez-Gironés, M.A., Hinde, C.A., 2016.
Evidence for conditional cooperation: a response to Schlicht et al. Behavioral Ecology, 27: e6–e7.

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9A1-O11-4
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Shinsuke Satoi
Kyushu Univ.
e-mail: ssatoi257n@gmail.com
Yoh Iwasa
Kyushu Univ.

Theoretical study of chemical mimicking strategy in ants
Mimicry is widely observed strategy for avoiding attacks by other animals and preying on other animals
efficiently. There is a strategy of mimicry simulating chemical trait and this strategy is called chemical
mimicry. One typical example of chemical mimicry is parasites of ants. Their strategy is classified in two
types: simulating host’s chemical trait (mimic) and reducing the total amount of body chemicals (cryptic)[1]. Since newly emerged workers of ants lack chemicals, host ants cannot distinguish cryptic parasites
from callow workers. Mimic parasites are more common than cryptic parasites.
Here, we report theoretical study for the evolution of mimicking strategies, especially focusing on
the evolution of these two strategies. We consider multi-dimensional space indicating mixtures ofchemicals. Assumptions: Ants of a nest accept an individual if its ratio of chemical traits is close to theirown and if the absolute amount of chemical traits is smaller than their own. For any colony of a parasite,
there exist conspecific colonies with similar chemical composition. We define the fitness of a parasite asa combination of the benefit of being accepted by the host and the risk of accepting those parasites fromother colonies. Results: Crypsis is advantageous if the strength of intraspecific competition is week.
Mimicry evolves if the recognition accuracy of host is high and the competition with other colonies isintense. We discuss the chemical strategies of ant parasites.
REFERENCE[1] Kilner, R. M. and N. E. Langmore (2011). "Cuckoos versus hosts in insects and birds: adaptations,counter-adaptations and outcomes." Biol Rev Camb Philos Soc 86(4): 836-852.

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9A2-O12-1
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Makoto Douge
Kyushu University
e-mail: makotodouge@gmail.com
You Iwasa
Kyushu University

Advantage of sex due to sibling diversity in an environment fluctuating over space
and time
Many hypotheses for the maintenance of sex have been presented after Maynard
Smith proposed a concept of "two-fold cost of sex". However the general answer has
not been found yet. There is a potent following idea. In an environment with intense sibcompetition, phenotypic diversity among sexual siblings might favor sexual
reproduction over asexual reproduction. Maynard Smith studied it by computer
simulation called sib-competition model. From the simulation result he concluded thatin a certain condition sexual had advantage. However if there was an environmental
correlation the advantage disappeared.
We investigated the model and knew that the diversity of sexual was not reflected
well. Then we revised the model in which the diversity was more reflected. In therevised model, the sexual had more advantage irrespective of there is an environmental
correlation or not. Suppose, N is the number of siblings of a mother, the simplest idea
is that the sexual has N-fold advantage and asexual has 2-fold advantage due to the 2fold cost of sex. However the simulation showed more complicated result, not sosimple, and we found some factors for the difference. However we could show that therelative fitness of sexual is basically N/2.
From the simulation result and analysis, we think that the sib-competition has
important roll for the evolutionally maintenance of sex.

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9A2-O12-2
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Daisuke Shikayama
Graduate School of Integrated Science and Technology Department of Engineering Mathematicaland System Engineering course, Shizuoka University, Japane-mail: tennsitann@gmail.com
Kazunori Sato
Graduate School of Integrated Science and Technology Department of Engineering Mathematicaland System Engineering course, Shizuoka University, Japan

Improvement of the overestimation for invasion speed inhigher birth-rate population
Population invasion speed and critical birth-rate for successful invasion in lattice space are calculated
by pair-edge approximation that estimate the wave front position by using pair approximation.[1] That
approximation is imperfect in two-dimensional lattice space and gives the method of calculation byconsidering lattice space as height-3 stripes. We calculated invasion speed in higher lattice space applying
the approximation and confirmed that both invasion speed and critical birth rate become farther fromsimulation value than 3-line calculation. In this research, we aim to improve the way of calculation andgain better approximation for critical value and invasion speed above it.
Ellner et al. (1998)[1] use Growing Phase Approximation (they assume that density of front is zero,GPA) and Look Both Ways approximation (they assume that density of front is half of internal density,
LBW). However, their approximations strongly reply on a newly introduced parameter, which rather seems
to be an artifact Then we consider all the possible states of front and use their occurrence probabilities forthe invasion calculation. Using this method, in height-3 stripe lattice space, we got higher critical birth-rate
than both GPA and LBW, so approximation got worse, but for the range above critical birth-rate, we got
lower and better invasion speed than both GPA and LBW. In height-5 stripe lattice space, we got lower
critical birth-rate than 3-line space and lower and worse invasion speed than GPA.
Considering all the possible states on the front, we can see that approximation value somewhat got
worse, but this method of calculation enables us to gain invasion speed that has good approximation value
without artificially assuming front shape as GPA or LBW.
REFERENCES[1] Ellner, S.P., Sasaki, A., Haraguchi, Y. and Matsuda, H., 1998. Speed of invasion in lattice population models: pairedge approximation. J. Math. Biol, 36: 469–484.

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9A2-O12-3
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Takuji Oba
Graduate School of Informatics, Kyoto University
e-mail: takuji_oba@acs.i.kyoto-u.ac.jp
Jun Kigami
Graduate School of Informatics, Kyoto University

When does invasion implies substitution?
Suppose that a monomorphic population, called the resident, with a trait A is in a stationary state
under stable environment. When small number of mutants with a new trait B will emerge, plausible
outcomes of the resulting competition are typically the following (a), (b) and (c):(a) eventually the original resident will win the battle and the population will return monomorphic with thetrait A,(b) eventually the mutants will drive out the original resident and the population will become
monomorphic with the trait B,(c) original resident and the mutants will coexist with certain ratio, i.e. the population will become
dimorphic with traits A and B.
Under a suitable mathematical model associated with adaptive dynamics(See [1] and [2] for example),we study general sufficient conditions for (a) and (b). More precisely we consider a model of competitionof two traits and show sufficient conditions for (a) and (b). If our two traits' model is a restriction of a three
traits' model, our result corresponds to the condition for “invasion implies substitution” proven by Dercole
and Rinaldi[3]. On the other hand, in the case when the two traits' model is not derived from a three traits'model, we obtain a class of simple examples where the “invasion implies substitution” condition is satisfied
but the situation (c) occurs, i.e. the population will become dimorphic with two different traits.
REFERENCES[1] Metz, J.A.J., Geritz, S.A.H., Meszéna, G., Jacobs, F.J.A. and van Heerwaarden, J.S., 1996. Adaptive dynamics, ageometrical study of the consequences of nearly faithful reproduction. IIASA Working Paper WP-95-099, 1: 183– 231.
[2] Geritz, S.A.H., Kisdi, E., Meszéna, G. and Metz, J.A.J., 1998. Evolutionarily singular strategies and the adaptive
growth and branching of the evolutionary tree. Evolutionary Ecology, 12: 35–57.
[3] Dercole, F. and Rinaldi, S., 2008. Analysis of evolutionary processes. Princeton Series in Theoretical andComputational Biology.

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9A2-O12-4
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Shota Nishijima
National Research Institute of Fisheries Science
Yokohama, Japane-mail: nishijimash@gmail.com
Hiroyuki Matsuda
Yokohama National University
Yokohama, Japan

Eco-evolutionary dynamics of a plant-pollinator system under climate change
It is challenging but important to predict the impacts of climate change on organisms withconsideration for species interactions and adaptive evolution. Pollination provides an ecosystem service,
but climate change is one of the causes of the declines in pollinators such as bumblebees. A previous study
has shown that a bumblebee population has shortened their tongue in order to adapt to resource scarcity
due to climate change, causing functional mismatch between the pollinators and deep flowers [1]. However,the underlying mechanism and eco-evolutionary consequences of the plant-pollinator interaction remain
poorly understood.
In this study, we develop and analyze a mathematical model to understand and predict ecoevolutionary dynamics of the plant-pollinator system under climate change. In the model, a bumblebee
population consumes two prey items (deep and shallow flowers) according to optimal foraging theory. We
assume that the length of bumblebee controls the handling times for these prey items and can evolve so as
to increase the fitness of bumblebee. We also assume that foraging by the bumblebee elevates plant growthand climate change increases the mortality rates of plants with deep flowers.
As a result, the bumblebee shortens its tongue under moderate climate change and, thereby, becomesa generalist from a specialist to short flowers, because climate change decreases the resource availabilityof shallow flowers. This prediction is consistent with empirical observation [1]. Severe climate change
makes the length of bumblebee’s tongue further shorter, increasing shallow flower density. Therefore, thebumblebee can become specialist to shallow flowers, leading to sudden extinction of deep flowers because
they do not ever receive benefit from the bumblebee pollinator. When the adaptive evolution is absent, suchextinction does not occur, indicating adaptive dynamics increase extinction risk of plants in this pollinatorsystem. However, the extinction can be avoided when shallow flowers are moderately sensitive to climatechange, because shallow flowers are unlikely to increase. This suggests that a negative impact of climatechange on a species can rescue another species through interspecific interactions and adaptive dynamics.
To conserve deep flower species in this system, inhibiting pollinator evolution and population managementof shallow flowers are important as adaptation strategy to climate change.
REFERENCES[1] Miller-Struttmann, N. E., Geib, J. C. Franklin, J. D. Kevan, P. G. Holdo, R. M. Ebert-May, D. Lynn, A. M.
Kettenbach, J. A. Hedrick, E. and Galen, C. 2015. Functional mismatch in a bumble bee pollination mutualism underclimate change. Science 349:1541–1544.

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9C2-O13-1
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Mizuho Nagata
College of Science and Engineering, Aoyama Gakuin University, Kanagawa 252-5258, Japan.
e-mail: minmi.unya@gmail.com
Yasuhiro Takeuchi
College of Science and Engineering, Aoyama Gakuin University, Kanagawa 252-5258, Japan.
e-mail: takeuchi@gem.aoyama.ac.jp
Shinji Nakaoka
Graduate School of Medicine, The University of Tokyo, Bunkyo-ku, Tokyo 133-0033,Japan.
e-mail: shinzy.nakaoka@gmail.com

Mathematical model of T and NK cell therapy against cancer
Different types of immune response can be induced in response to cancer associated antigen
expressed MHC class I molecules. While high expression level of MHC class I molecules on thesurface of cancer cells are required to activate CD8 T cells, NK cells specifically detect a type ofcancer cells expressing low level of MHC class I (missing-self hypothesis). To incorporate different
expression levels of MHC class I molecules, we construct a mathematical model which describes
dynamics of immune response against cancer by introducing two different types of cancer in termsof the expression level of MHC class I. Cancer is assumed to be classified to high or low MHC class
I expression. Different types of immune responses (implicitly assumed CD8 T cells and NK cells)
eliminate corresponding cancer phenotype. By stability analysis and numerical simulations of ourmathematical model, a key parameter was found which covers major qualitatively different
behaviors of cancer-immune dynamics. Biological implications derived from our mathematicalanalysis and numerical computation results will be discussed.
REFERENCES[1] Mizuho Nagata, Yutaro Furuta, Yasuhiro Takeuchi, and Shinji Nakaoka, Dynamical behavior of combinational
immune boost against tumor, Japan Journal of Industrial and Applied Mathematics 32 (2015) 759–770.
[2] Naoki Nakada, Mizuho Nagata, Yasuhiro Takeuchi and Shinji Nakaoka, Mathematical modeling and analysis ofcombinational immune boost for tumor elimination, AIP Conference Proceedings 1723 (2016) 020002.

- 194 -

9C2-O13-2
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Shoya Iwanami
Graduate School of Systems Life Sciences, Kyushu University, Fukuoka 819-0395, Japane-mail: iwanamishoya@gmail.com
Ryo Yamamoto
Institute for Stem Cell Biology and Regenerative Medicine, Stanford University, Stanford, CA 94305,
USA
Shingo Iwami
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 819-0395 Japan
Hiroshi Haeno
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 819-0395 Japan

Mathematical model of hematopoietic system withmyeloid-restricted progenitors with long-term repopulating activity
Hematopoietic system is maintained by hematopoietic stem cells (HSCs) with dual abilities of longterm self-renewal and differentiation to all types of blood cells. Recently, using a single-cell transplantation
system and mice expressing a fluorescent protein, myeloid-restricted progenitors with long-term
repopulating activity (MyRPs) were found. Moreover, by using paired daughter cell assay, MyRPs weredirectly differentiated from HSCs. Because of the non-step division from HSCs, myeloid cells wererepopulated faster than lymphoid cells after transplantation.
In this study, we investigated hematopoietic system incorporating the novel insight that there existed
a cell type that exclusively differentiated to myeloid lineages. There were five populations in the model: (i)long-term HSCs, (ii) short-term HSCs, (iii) MkRPs; one of MyRPs which are directly differentiated from
LT-HSCs, (iv) myeloid cells, and (v) lymphoid cells. Myeloid cells were produced after transplantation ofa single HSC via short-term HSCs or MkRPs, while lymphoid cells were produced via only short-term
HSCs. This is the first study of investigating hematopoiesis with MkRPs. From the analysis of the model,
we successfully reproduced the experimental observation that myeloid cells were repopulated faster thanlymphoid cells after transplantation of a single HSC. Moreover, we estimated differentiation rates, selfrenewal rates and death rates of all cell types that fitted the published data. Finally, MkRPs are importantto reproduce platelets in emergency such as transplantaion.
REFERENCES[1] Yamamoto, R., et al. 2013. Clonal analysis unveils self-renewing lineage-restricted progenitors generated directlyfrom hematopoietic stem cells. Cell 154(5): 1112-1126.

- 195 -

9C2-O13-3
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Min YuCollege of Science and Engineering, Aoyama Gakuin University, Sagamihara 252-5258, Japane-mail: yumin8618@gmail.com
Yueping Dong2, Yasuhiro Takeuchi1
Graduate school of Medicine, The University of Tokyo, Tokyo 113-0033, Japan 2
College of Science and Engineering, Aoyama Gakuin University, Sagamihara 252-5258, Japan 1

Dual role of delay effect in a tumor immune system
In this paper, a previous tumor immune interaction model is simplified by considering a relatively
weak immune activation, which can still keep the essential dynamics properties. Since the immune
activation process is not instantaneous, we incorporate one delay effect for the activation of the effector
cells by helper T cells into the model. Furthermore, we investigate the stability and instability region of thetumor-presence equilibrium state of the delay-induced system with respect to two parameters, the activation
rate of effector cells by helper T cells and the helper T cells stimulation rate by the presence of identified
tumor antigens. We show the dual role of this delay that can induce stability switches exhibiting
destabilization as well as stabilization of the tumor-presence equilibrium. Besides, our results show that theappropriate immune activation time plays a significant role in control of tumor growth.
REFERENCES[1] J. Arciero, T. Jackson and D. Kirscher, 2004. A mathematical model of tumor-immune evasion and siRNAtreatment. Discrete Contin. Dyn. Syst., Ser. B 4: 39–58.
[2] Y. Dong, H. Gang, R. Miyazaki and Y. Takeuchi, 2015. Dynamics in a tumor immune system with time delays,
Appl. Math. Comput. 25: 99–113.

- 196 -

9A3-O14-1
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Sachi Yamaguchi
Department of Information Systems Creation, Kanagawa University
e-mail: sachi.dwarfmale@gmail.com

Time required for sex change in teleost fishes: hormonal dynamics shaped by
selection
Sex change is observed in many species of teleost fishes. The evolution of sex change has been
explained by size advantage hypothesis, which postulates that each individual chooses the more profitablesex given its body size and social condition. In haremic species, when the dominant (harem) maledisappears, the largest female changes to male. When social condition changes, transition of sex takes forseveral days to a few months. In some species, the length of the time required for sex change is similar
between two directions (male-to-female, and female-to-male); in other species, male-to-female transition
takes clearly longer time than female-to-male transition. To understand the difference in the length of time
for sex change in two directions, I propose a simple mathematical model for the hormone-enzyme dynamics.
Aromatase (P450arom) catalyzes the synthesis of estradiol (female hormone) from testosterone (malehormone). I assume that the change of the social condition for the individual affects the rates of production
and degradation of P450arom. I then consider the evolution of parameters in the dynamics. The optimal
parameter values are those that minimize the total fitness cost, defined as the sum of the fitness losses by
the delay as a functional male and as a functional female, and the cost for the acceleration of the degradationof P450arom in changing from female to male. The model predicts that, in haremic species, as the numberof females in a harem increases, the sex changer promotes the faster degradation of P450arom, realizing afaster female-to-male transition than the transition in the opposite direction. In contrast, in monogamous
species, or when the number of females is small, faster degradation of P450arom when changing to male isnot beneficial, resulting in about equal length of the time for sex change in two different directions.
REFERENCES[1] Yamaguchi, S., 2016. Time required for sex change in teleost fishes: hormonal dynamics shaped by selection.
Journal of Theoretical Biology (in press).

- 197 -

9A3-O14-2
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Kouki Uchinomiya
RIKEN, iTHES
e-mail: kouki.uchinomiya@riken.jp

Modeling optimal resource allocation in plant-fungi mutualism
Mycorrhizal fungi colonize roots of terrestrial plant. The relationship of plant and fungi becomesmutualism by trading resource. The host plant produces carbohydrate by photosynthesis and allocates it to
the fungi. The fungi can get soil nutrition more efficiently than plant. Mycorrhizal fungi supply soil
nutrition to its host plant. In nature, one plant has many mycorrhizal fungi. Some studies show growth ofplant is better when there are many mycorrhizal fungi (e.g. Gustafson and Casper, 2006). In this study, I
discuss resource allocation when one plant has one fungus and one plant has multiple fungi.
I assume plant can get only carbon and fungi can get only phosphorus. Plant and fungi allocateacquired resource to the partner for maximizing their biomass at the end of mutualistic relationship. I
express dynamics of carbon and phosphorus in plant and fungus by differential equations.
According to Pontryagin’s maximum principle and conditions of singular control (Bryson&Ho,
1975), allocation fraction is affected by resource acquisition ability and resource allocation efficiency when
there are only one plant and one fungus. In addition, when one plant has two fungi, total phosphorus
supplied by fungi become larger than the case one plant has only one fungus. On the other hand, total carbon
supply to the fungi decreases.
REFERENCES[1] Gustafson, D. J., & Casper, B. B., 2006, Differential host plant performance as a function of soil arbuscular
mycorrhizal fungal communities: experimentally manipulating co-occurring Glomus species. Plant Ecology,183(2), 257-263.
[2] Bryson, A. E., & Ho, Y., 1975, Applied optimal control: optimization, estimation and control. CRC Press- 198 -

9A3-O14-3
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Ross D. Booton
University of Sheffield, UKe-mail: r.booton@sheffield.ac.uk
Ryo Yamaguchi
Kyushu University
Yoh Iwasa
Kyushu University

The Role of Cannibalism in Determining Insect Voltinism Patterns
Pupa-eating cannibalism occurs naturally in several subfamilies of Lepidoptera. Within the subfamily
Papilionidae, Byasa alcinous is a multivoltine species of Red-bodied Swallowtail butterfly found in East
Asia which diapauses over the winter, and whose larvae cannibalise eggs and pupae. We investigate theeffects on population dynamics of increasing the cannibalistic attack rate of B. alcinous larvae in changing
environmental conditions. We do this by theoretically formulating the change in weight functions of ageneralised system of univoltine and bivoltine larvae over two generations in the spring and summer months.
We predict that a declining resource over summer can force the population to become entirely univoltine,
unless the second generation bivoltine larvae increase their cannibalistic attack rate, and consume thediapausing pupae. The model shows that under extreme environmental conditions, the persistence of
univoltine larvae is favoured when faced with the threat of extinction. The model also predicts conditions
for coexistence of both univoltine and bivoltine larvae, and the degree to which they can both coexist, which
decreases as the resource in the second generation increases. This work provides the grounding for future
theoretical and experimental consideration on the role of cannibalism in the onset of diapause in a
multivoltine insect setting.

- 199 -

9A3-O14-4
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Toru Osaki
Shizuoka University Graduate School at Science and Technology Graduate School, Hamamatsu City
Nakaku Johoku 3-5-1,Japane-mail: osaki311@icloud.com
Kazunori Sato
Shizuoka University Graduate School at Science and Technology Graduate School, Hamamatsu City
Nakaku Johoku 3-5-1,Japan

Spatial pattern and its stability formed by algal blooms
Algae, in order to protect themselves from predators, is known to have the morphological changes.
The shape change is considered to be one of the most important protective strategies to avoid predationfrom grazing zooplankton. For example, algae aggregation makes herbivorous zooplankton difficult topredate.
The morphological changes between the colonial algae and unicellular algae depend the density of theherbivorous zooplankton . If the density of herbivorous zooplankton is low, change from the colonial algae
to the unicellular algae occurs. On the other hand, if the density of herbivorous zooplankton is high, a large
proportion of the changes to the colonial algae from unicellular algae is observed.
As pioneering researches, Vos et al. (2004)[2] and Serizawa et al. (2008)[1], which improved Vos et al.
(2004)[2], are known.Furthermore, in the model including the diffusion into Serizawa et al.
(2008)[1], it has been shown to produce a complex spatial pattern from around the unstable equilibrium
point.
In this study, it focuses on the morphological change between the colonial algae and the unicellularalgae, induced by predators of herbivorous zooplankton, to consider the spatial pattern and its stability,
which is formed by the algae bloom. In particular, with respect to some of the models, including theprevious researches, changing the parameters and initial conditions, we would like to consider what kindof spatial patterns to appear.
REFERENCES[1]Serizawa et al , 2008. Mathematical modeling of colony formation in algal blooms:phenotypic plasticity incyanobacteria. Ecol Res23:841–850.
[2]Vos et al,2004.Inducible defences and the paradox of enrichment.OIKOS105:471-480.

- 200 -

9C3-O15-1
Sep 9, Fri (Oral)
JSMB2016 Fukuoka

Hiroshi Ueno

- 201 -

9C3-O15-2
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Yoshihiro Morishita
Laboratory for Developmental Morphogeometry, RIKEN, Quantitative Biology Center, Japane-mail: yoshihiro.morishita@riken.jp
Ken-ichi Hironaka
Laboratory for Developmental Morphogeometry, RIKEN, Quantitative Biology Center, JapanThe Japan Society for the Promotion of Science, Japan
Sang-Woo Lee
Laboratory for Developmental Morphogeometry, RIKEN, Quantitative Biology Center, Japan
Takashi Jin
Laboratory for Nano-Bio Probes, RIKEN Quantitative Biology Center, Japan
Daisuke Ohtsuka
Laboratory for Developmental Morphogeometry, RIKEN, Quantitative Biology Center, Japan

Reconstructing 3D deformation dynamics for curved epithelial sheet
morphogenesis from positional data of sparsely-labelled cells
Quantifying global tissue deformation patterns is essential for understanding how organ-specificmorphology is generated during development and regeneration. However, due to imaging difficulties andcomplex morphology, little is known about deformation dynamics for most vertebrate organs such as thebrain and heart. To better understand these dynamics, we propose a method to precisely reconstruct global
deformation patterns for 3D morphogenesis of curved epithelial sheets using positional data from labeledcells representing only 1-10% of the entire tissue with limited resolution. By combining differentialgeometrical and Bayesian frameworks, the method is applicable to any morphology described with arbitrary
coordinates, and ensures the feasibility of analyzing many vertebrate organs. Application to data from chick
optic vesicle formation demonstrated that our method provides not only a quantitative description of tissue
deformation dynamics but also predictions of the mechanisms that determine organ-specific morphology,
which could form the basis for the multi-scale understanding of organ morphogenesis.
REFERENCES[1] Y. Morishita, K. Hironaka, S.-W. Lee, T. Jin, and D. Ohtsuka, “Reconstructing 3D deformation dynamics for curved
epithelial sheet morphogenesis from positional data of sparsely-labelled cells” (under review)[2] Morishita, Y. Kuroiwa, A. and Suzuki, T. "Quantitative analysis oftissue deformation dynamics reveals threecharacteristic growth modes and globally-aligned anisotropic tissue deformation during chick limb development",
Development, 142: 1672-1683 (2015)[3] Morishita, Y. and Suzuki, T. Bayesian inference of whole-organ deformation dynamics from limited space-time
point data, Journal of Theoretical Biology, 357: 74-85,(2014)- 202 -

9C3-O15-3
Sep 9, Fri (Oral)
JSMB2016 Fukuoka

Masashi Tachikawa- 203 -

9C3-O15-4
Sep 9, Fri (Oral)
JSMB2016 Fukuoka
Takashi Okada
Theoretical Biology Laboratory, RIKEN, Wako 351-0198, Japane-mail: takashi.okada@riken.jp
Atsushi Mochizuki
Theoretical Biology Laboratory, RIKEN, Wako 351-0198, Japan
CREST, JST 4-1-8 Honcho, Kawaguchi 332-0012, Japane-mail: mochi@riken.jp

Law of Localization in Chemical Reaction Networks
In living cells, many biochemical reactions connect to one another and form complex networks, likethe carbon metabolism pathway. One experimental approach to study such network systems is sensitivity
analysis where the amount or activity of the enzymes is perturbed and responses (concentrations ofchemicals and fluxes) are measured. However, due to the complexity of the systems, it has been unclear
how the network structures influence the responses of the systems. In this study, we introduce amathematical method, named structural sensitivity analysis, to determine responses of chemical reaction
systems to the perturbation of the enzyme amount/activity based only on information of network topology.
We found that (1) qualitative responses at steady state are determined from network structure only. We also
found that (2) nonzero responses of chemicals exhibit two characteristic features, localization and hierarchy.
Finally, we found (3) a general theorem that directly connects network topology and response patterns,
which we call the law of localization. These results also imply that network topology is an origin of
biological adaptation and robustness. We also apply our method to several hypothetical and real life
chemical reaction networks, including the metabolic network of the E. coli metabolic network.
REFERENCES[1] Mochizuki A. & Fiedler B. J. Theor. Biol. (2015) 367, 189-202.
[2] Okada T. & Mochizuki A. (2016) Phys. Rev. Lett. 117, 048101.

- 204 -

JSMB2016 Fukuoka

Poster Session Abstract- 205 -

P-1
JSMB2016 Fukuoka
Kazumasa Kaneko
Department of Electrical Engineering and Information Systems, The University of Tokyoe-mail: kaneko@sat.t.u-tokyo.ac.jp
Ryo Yokota
Institute of Industrial Science, The University of Tokyo
Taishin Akiyama
Institute of Medical Science, The University of Tokyo
Tetsuya J. Kobayashi
Institute of Industrial Science, The University of Tokyo

Modeling and inferring dynamics of T cell population in thymus
A development of T cell, a type of immune cells, in the thymus is a dynamic process that generates
the repertoire of T cell population. During the maturation of T cells, they interact with thymic epithelial
cells (TECs) and TECs positively and negatively select functional and nonself-reactive T cells respectively.
Although the chemical reactions that constitute the positive and negative selection has been revealed, thedynamic aspects of the selection and differentiation of T cells is not fully understood [1]. While T cell
population and its generation in thymus is homeostatically maintained normally, various external
perturbations such as stress and drug lead to its failure [2,3]. Mathematical modeling is indispensable tounderstand the dynamics of the thymic functionality and to infer the mechanism of the disorder.
In this study, we construct a mathematical model on the recovery dynamics of CD4-CD8- double
negative, CD4+CD8+ double positive T cells after X-ray irradiation by employing experimental data on
joint dynamics of T cell and TEC populations. The inferred model suggests that cortical TECs controls
division and differentiation rates of double negative T cells and shows positive/negative correlation
between medullary/cortical TECs and the stable population size of the double positive T cells. We also
analyze the possibility on cell division of CD4+CD8+ double positive T cells. An extended model to include
CD4-CD8+/CD4+CD8- single positive T cells may also be discussed.
REFERENCES[1] Akiyama, T., Tateishi, R., Akiyama, N., Yoshinaga, R., & Kobayashi, T. J. 2015. Positive and negative

regulatory mechanisms for fine-tuning cellularity and functions of medullary thymic epithelial cells.
Frontiers in Immunology, 6(SEP).
[2] Billiard, F., Kirshner, J. R., Tait, M., Danave, A., Taheri, S., Zhang, W., … Skokos, D. (2011). Ongoing Dll4-Notch
signaling is required for T-cell homeostasis in the adult thymus. European Journal of Immunology, 41(8), 2207–
2216.
[3] Gruver, A. L., & Sempowski, G. D. (2008). Cytokines, leptin, and stress-induced thymic atrophy. Journal of
Leukocyte Biology, 84(4), 915–923.

- 206 -

P-2
JSMB2016 Fukuoka
Naoki Nakada
e-mail: c5615017@aoyama.jp
College of Science and Engineering, Aoyama Gakuin University,
Kanagawa, 252-5258, Japan.
Shinji Nakaoka
e-mail: shinzy.nakaoka@gmail.com
Graduate School of Medicine, The University of Tokyo, Hongo 7-3-1,
Bunkyo-ku , Tokyo, 133-0033, Japan.
Yasuhiro Takeuchi
e-mail: takeuchi@gem.aoyama.ac.jp
College of Science and Engineering, Aoyama Gakuin University,
Kanagawa, 252-5258, Japan.

Mathematical modeling and analysis of cancer immunotherapy:
exploring the effect of cytokine mediated communication among T and NK cells
Treatment of cancer is broadly classified as surgical, radiotherapy, and chemotherapy.
Immunotherapy is an emerging type of cancer therapy which attracts attention in late years because of
its therapeutic potential and less burden of side effects. Immune cell transfer therapy boosts immune cells
taken from a body, and then activates cells ex vivo, and finally returns the activated cells to a body.
The populations of natural killer (NK) cell and T cell are known as candidates of cancer immunetherapy. Two types of cell attack cancer in a different manner according to the expression level of MHC
class I molecules which are expressed on the surface of cancer cells. NK cell is a member of innate
immunity which attacks cancer cells exhibiting low MHC class I expression (missing-self hypothesis).
On the other hand, CD8 positive T cells specifically recognize cancer associated antigen directly, orpresented by antigen presenting cells as MHC class I complex. Hence CD8 positive T cells kill high
MHC class I expressing cancer cells. To investigate dynamical behaviors of cancer killing by two
different immune cell types, we construct a mathematical model that describes mutual interactions among
NK cells, T cell via produced interferon gamma.
Mathematical analysis and numerical simulations are performed to investigate dynamical behaviorof immune response against cancer. We specifically focus on the role of interferon gamma as a mediatorof mutual activation of two different cell types. Our computational results imply the possibility of cancer
elimination which is mediated by the establishment of mutual activation among NK and CD8 T cells.
Biological implications based on our mathematical and computational results will be discussed.
REFERENCES[1] Mizuho Nagata, Yutaro Furuta, Yasuhiro Takeuchi, and Shinji Nakaoka, Dynamical behavior of combinational
immune boost against tumor, Japan Journal of Industrial and Applied Mathematics 32 (2015) 759–770.
[2] Naoki Nakada, Mizuho Nagata, Yasuhiro Takeuchi and Shinji Nakaoka, Mathematical modeling and analysis ofcombinational immune boost for tumor elimination, AIP Conference Proceedings 1723 (2016) 020002.

- 207 -

P-3
JSMB2016 Fukuoka
Shinji Nakaoka
Graduate School of Medicine, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, 133-0033,
Japan
e-mail: shinzy.nakaoka@gmail.com

Development of a computational grammar for immune cell processes
Immune response against foreign antigen is dynamics and mediated by a considerable number of
immune cell types [1]. Both inflammatory and regulatory cell types are associated with antigen clearance.
Cytokines are extracellular proteins which mediate cellular communication among immune cell types.
Some cytokines such as IL-6 and IL-10 are pleiotropic as they promote and suppress immune cell activities.
On the other hand, some cytokines are known to be redundant: IL-4 and IL-13 share a common biological
function as to promote allergic immune response.
One of challenging tasks in the field of computational immunology is to correctly describe a context
dependent manner of interactions among immune cell types mediated by cytokine communications.
Although case specific description of cytokine function on immune cell activation and suppression has beenmassively found, a computationally available framework to describe immune cell dynamics has been poorly
investigated.
The aim of this study provides a description of immune cell dynamics based on transcriptional gene
regulatory networks associated with cytokine production. In this talk, I would like to present recent research
progress on construction of computational grammar to describe immune cell dynamics.
REFERENCES[1] Gérard Eberl, A., 2016. Immunity by equilibrium. Nature Reviews Immunology, doi:10.1038/nri.2016.75.

- 208 -

P-4
JSMB2016 Fukuoka
Seiya Nishikawa
Department of Electrical Engineering & Bioscience, Waseda University, Tokyo, Japane-mail: seiya.nskw@gmail.com
Shoko Baba
Graduate School of Biostudies, Kyoto University, Kyoto, Japan
Shizue Ohsawa
Graduate School of Biostudies, Kyoto University, Kyoto, Japan
Tatsushi Igaki
Graduate School of Biostudies, Kyoto University, Kyoto, Japan
Atsuko Takamatsu
Department of Electrical Engineering & Bioscience, Waseda University, Tokyo, Japan

Fate after ‘cell competition’ depending on initial states
in tumor-suppressor system
Coordinated cell population forms multicellular organisms. In tissue of multicellular organisms,
interaction among different cell-species would play important roles for normal organ development andmaintaining organs themselves. A phenomenon called ‘cell competition’ discovered in Drosophila
system [1] is considered to be one of the candidates for such the interaction. ‘Cell competition’ is defined
as follows: cells with higher fitness (called “winner”) eliminate cells with lower fitness (called “loser”) by
inducing cell death among the loser cells [2]. The elimination occurs only at their interface between the
two types of cells.
Interestingly, it is reported that an experimental system consisting of tumor-suppressing-functiondefecting mutant, Rab5, shows initial-state dependent fates [3]. Although the mutant cells possess strong
growth competence, they can be “loser” once introduced in a normal tissue, when the mutant populationis small. In contrast, Rab5 cells survive and form tumor when the initial population is larger than a certain
value.
To elucidate fate after ‘cell competition’, namely, a condition determining whether the Rab5 cells
are exterminated or survive, we performed both-side analysis with a mathematical model and an
experimental system. We constructed a mathematical model for ‘cell competition’ based on LotkaVolterra competition equation, by introducing the predator-prey interaction at interface [4]. As
experimental approach, Rab5 cells were induced in Drosophila imaginal wing disc by using heat shock
method in which the initial number of Rab5 cells and the time can be controlled.
As a result of analyzing our mathematical model, we obtained the condition in which the fate after‘cell competition’ is depends on initial states of numbers of mutant cells and normal cells. After a numberof combinations in initial states tested in the experiment, we verified that the phase portrait and vector
field depicted using the mathematical model can roughly explain the experimental observations. To refine
the mathematical model, we are trying to introduce a phenomenon observed in the experimental system[3] that mutant cell death induced by ‘cell competition’ has context-dependent effect on controlling
proliferation.
REFERENCES[1] Morata, G. and Ripoll, P., 1975. Differential mitotic rates and patterns of growth in compartments in the
Drosophila wing. Dev. Biol., 42: 211–221.
[2] Baker, N, E., 2011. Cell competition. Curr. Biol., 21: R11–R15.
[3] Ballesteros-Arias, L., Saavedra, V. and Morata, G., 2014 Cell competition may function either as tumoursuppressing or as tumour-stimulating factor in Drosophila. Oncogene, 33: 4377–4384.
[4] Nishikawa, S., Takamatsu, A., Ohsawa, S. and Igaki, T., 2016. Mathematical model for cell competition:
Predator–prey interactions at the interface between two groups of cells in monolayer tissue. J. Theor. Biol, 404:
40–50.

- 209 -

P-5
JSMB2016 Fukuoka- 210 -

P-6
JSMB2016 Fukuoka
Kentaro Inoue
Laboratory for Integrated Cellular Systems, RIKEN Center for Integrative Medical Sciences,
Yokohama, Japane-mail: kentaro.inoue.hv@riken.jp
Hisaaki Shinohara
Laboratory for Integrated Cellular Systems, RIKEN Center for Integrative Medical Sciences
Gouhei Tanaka
Institute of Industrial Science, The University of Tokyo
Kazuyuki Aihara
Institute of Industrial Science, The University of Tokyo
Mariko Okada-Hatakeyama
Laboratory for Integrated Cellular Systems, RIKEN Center for Integrative Medical Sciences
Laboratory of Cell Systems, Institute for Protein Research, Osaka University

Mathematical model for NF-kB signal transduction system
A mathematical model of molecular networks can explain molecular mechanism of a complex
biological system and also predict dynamical behaviors of individual molecules in cells. Signal transduction
can transmit extracellular information to intracellular transcription factors (TFs). The activation of TFs can
induce gene expression and lead to cell differentiation, proliferation and apoptosis. Nuclear factor-kappa B(NF-kB) is a transcriptional factor and relates to a variety of cellular functions, such as immune response.
Dynamic behaviors of NF-kB activity after cell stimulation show damping oscillation [1] and switch-like
response [2] necessary for target gene induction. To reveal the molecular mechanism of the NF-kB activity
dynamics, we constructed and analyzed a mathematical model which can recapitulate both the oscillationand switch-like response.
The model consists of 47 differential equations with 190 kinetic parameters and contains multiple
positive and negative feedback loops. Simulation of the model reproduced experimental results. We
performed sensitivity analysis and identified sensitive components in the model critical for oscillation andswitch-like response of NF-kB. In addition, we constructed a core model regarding those components. The
core model explained one of the roles of the switch-like activation on the oscillation.
The model proposed here is the first model which can recapitulate both oscillation and switch-like
response of NF-kB, and provides valuable insights for understanding the regulatory mechanisms of NF-kB
signaling.
REFERENCES[1] A. Hoffmann, A. Levchenko, M. L. Scott, D. Baltimore, 2002. The IkappaB-NF-kappaB signaling module: temporalcontrol and selective gene activation. Science 298, 1241-1245.
[2] H. Shinohara et al., 2014. Positive feedback within a kinase signaling complex functions as a switch mechanism
for NF-kappaB activation. Science 344, 760-764.

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P-7
JSMB2016 Fukuoka
Masashi Kamo
Advanced Industrial Science and Technology, Research Institute of Science for Safety and Sustainability,
Tsukuba, Ibaraki, Japane-mail: masashi-kamo@aist.go.jp
Hiroyuki Yokomizo
National Institute for Environmental Studies, Center for Health and Environmental Risk Research

Explanation of non-additive effects in mixtures of similar mode of action chemicals
The risk assessments of chemical substances are often carried out to evaluate the risk by single
substance. Even though risk by single substances is negligibly small, there is an anxiety that total risk by
many chemical substances cannot be neglected if exposed all together. Recently, there is an increased
interest for a risk assessment of combined effect by multiple chemicals.
Researches for combined effects have a long history. They have started in the pharmacology to predict
combined effects of drug efficacies. Loewe’s concentration addition (CA) in 1926 [1] and Billis’
independent action (IA) in 1936 are the two major models [2]. Bliss considered that effects by drugs are
random events and tried to predict a total effect by multiple of effects by single drug. Whereas, Loewe tried
to predict a total effect by a sum of concentrations of each drug. When combined effects of drug are
predicted by the CA, the effect is termed additive. When the combined effects are not additive, it isconsidered that there is a synergism, or an antagonism among drugs. The synergism is the effects to pursue
in pharmaceuticals but to avoid in the risk assessment of chemical.
The CA is somehow a heuristic model and it cannot offer answers to questions such as what an
applicability domain of the model is. There are a couple of belief such as (1) the CA yields accurate
prediction for chemicals having the same or similar modes of action, (2) if slopes of dose-response curveof each chemical are the same, CA is applied to predict toxic effect of chemical mixture, and (3) due to a
non-additive effects (synergism/antagonism), CA may not predicts an accurate toxicity when number ofchemicals in mixture is small; however, prediction becomes accurate as number of chemicals in mixture
are large because synergism and antagonism are canceled out (the funnel hypothesis [3]). In this paper, we
use a simple model of enzyme catalysis to investigate if these beliefs are true or not [4].
We found that the belief (1) is partially true. The CA is true for chemicals having exactly the samemodes of action, but the synergism or antagonism appear for chemicals having the similar modes of action.
The belief (2) is also not always true. Chemicals having the same slope in dose-response curve may lead tothe synergism or antagonism when they are mixed. The funnel hypothesis in the third belief is true, but thereasoning for the accuracy for the CA prediction is wrong. Additivity in the chemical mixture appears notby the cancelation of synergism and antagonism, but appears by the linear approximation of the multiple
terms of concentration in the model. In toxicity tests with many chemicals in mixture, concentrations ofeach chemical are held low (otherwise all die immediately). For chemicals leading to non-additive effects,
deviation from the CA prediction rises by multiple terms of concentrations. When the concentration ofchemicals are low, such non-linear terms can be neglected, and the effects can be approximated by the CA
in which the toxicity is predicted by a sum of concentrations. The number of chemicals is not the key inFunnel Hypothesis, but the low concentrations of chemical are.
In the risk management chemical mixture, it is often criticized that the use of the CA is dangerous
because the model cannot predict the non-additive effects. According to our results, use of the CA are nots
so dangerous because environmental concentrations of chemicals are low in many cases.
REFERENCES[1] Loewe, S., Muischnek, H. (1926) Effect of combinations: mathematical basis of the problem. Arch. Exp. Pathol.
Pharmakol. 114, 313–326.
[2] Bliss, C.I. (1939) The toxicity of poisons applied jointly. Ann. Appl. Biol. 26, 585–615[3] Warne, M.S., Hawker, D.W. (1995) The number of components in a mixture determines whether synergistic andantagonistic or additive toxicity predominate: the funnel hypothesis. Ecotoxicol. Environ. Saf. 1:23-8.
[2] Kamo, M,. Yokomizo, H. (2015) Explanation of non-additive effects in mixtures of similar mode of action
chemicals. Toxicology, 1: 1–10.

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P-8
JSMB2016 Fukuoka
Isao Kawaguchi
Center for Radiation Protection Knowledge,
National Institute of Radiological Sciences,
National Institutes for Quantum and Radiological Science and Technology
e-mail: kawaguchi.isao@qst.go.jp
Tetsuya Sakashita
Department of Radiation-Applied Biology Research,
Takasaki Advanced Radiation Research Institute,
National Institutes for Quantum and Radiological Science and Technology

Mathematical model approach to understand abscopal effect with radiotherapy
Since Roentogen's discovery of X-rays, the medical use of the radiation has been increased andapplicable scope of radiation was extended not only to diagnosis but also to treatment. Especially,effectiveness of localized irradiation to cancer has been recognized and application of the radiotherapy tocancer treatment is extended. By progression of radiotherapy, indirect effect of the localized radiotherapy
referred as "abscopal effect" was reported from around the 1970's, where the non-irradiated tumors wereshrunk by irradiation to primary tumor. According to review by UNSCEAR[1], it was suggested that
immune reaction induced by radiation exposure could be related to abscopal effect. In addition, an effectof the tumor immunity in late years attracts attention, and interest increases for the use of abscopal effectby the combination with the radiation therapy. On the other hand, there were also known that relations
between immunity and tumor progression are very complicated, so that it is still unknown how abscopal
effect stably is induced by localized irradiation treatment.
In this study, a mathematical model for the abscopal effect by radiotherapy to the primary tumor wasdeveloped and analyzed to find the condition for abscopal effect induced stably. We assumed cell death isinduced by radiation exposure for the primary tumor, and tumor antigen is produced from irradiated tumor
cells. And immune response to the tumor antigen is induced and activated immune cells are diffused toother tumor cites which metastasized. It is also assumed that the tumor cells evolve in the direction escaping
from immune reaction with time.
From the analysis of the model, it was found that it was difficult to decrease a metastasized tumor
successfully only by abscopal effect with the radiation therapy. In addition, it was suggested that the tumor
size could be decrease by the combination with the immune therapy.
REFERENCES[1] United Nations Scientific Committee on the Effects of Atomic Radiation, UNSCEAR 2006 Report to theGeneral Assembly, with scientific annexes Volume II: Scientific Annexes, 2009.

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P-9
JSMB2016 Fukuoka
Masahiko Higashi
Nagoya University, Nagoya, Japane-mail: higashi@alife.cs.is.nagoya-u.ac.jp
Reiji Suzuki
Nagoya University, Nagoya, Japan
Takaya Arita
Nagoya University, Nagoya, Japan

A Coevolution Model of Individual and Social Learning
in a Rugged Fitness LandscapeThe role and importance of social learning have been investigated by many researchers, because it isobserved in many animals and it is expected to play a significant role in cultural phenomena. We explore
the coevolution between individual learning and social learning in a rugged fitness landscape, as a realistic
condition in which they can interact with each other. This rugged fitness landscape was designed by Suzuki
and Arita [1], and they revealed how learning facilitates the evolution in the fitness landscape. Our purpose
is to investigate how social learning affects evolution and how it interacts with individual learning. We
constructed an agent-based evolutionary model in which each individual can accommodate its plastic
phonotypes using both individual learning based on trial-and-error and social learning based on imitationof phenotypes from the most adaptive individual. We found that social learning has two important roles toenhance individual fitness through the two-step evolution process of the Baldwin effect (i.e., the evolutionof learning ability and the subsequent occurrence of the genetic assimilation of acquired traits). First, social
learning can spread and keep the adaptive phenotypes that are acquired by individual learning in the
population (Fig. 1). Second, such an effect of social learning allows individuals to explore a wide range offitness landscape (Fig. 2). The first role of social learning affects each of two steps of Baldwin effect, andthe second role of social learning affects first step of Baldwin effect. Therefore, the 2 steps of the Baldwin
effect will be reformulated as follows. 1) the first and second roles of social learning accelerate the firststep of Baldwin effect. 2) the first role of social learning enables individuals to acquire adaptive phenotypes
culturally, so the second step of Baldwin effect is compensated by cultural inheritance.

REFERENCES[1] Suzuki, R. and Arita, T., 2007. Repeated occurrences of the Baldwin effect can guide evolution on rugged fitness
landscapes. In Proceedings of the First IEEE Symposium on Artificial Life (IEEE-Alife’07), pp. 8-14.

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P-10
JSMB2016 Fukuoka
Mariko Ito
Department of Evolutionary Studies of Biosystems, The Graduate University for Advanced Studies(Sokendai), Hayama, Kanagawa Japane-mail: ito_mariko@soken.ac.jp
Hisashi Ohtsuki
Department of Evolutionary Studies of Biosystems, The Graduate University for Advanced Studies(Sokendai), Hayama, Kanagawa Japan
Akira Sasaki
Department of Evolutionary Studies of Biosystems, The Graduate University for Advanced Studies(Sokendai), Hayama, Kanagawa Japan

Emergence of opinion leaders in reference networks
An opinion of an individual is often influenced by those of other members of the society. We
describe this situation by a network model with nodes representing individuals and edges representing
information flow as is assumed in many studies of opinion formation [1][2]. In such networks,
individuals who have a large number of reference links are greatly influential to others, so we call themopinion leaders. Here we ask how opinion leaders emerge in an evolving network where each agent
rewires one’s reference links adaptively, and what role they will play in the evolved network.
To answer these questions, we constructed a network model where, in each iteration round, eachagent makes a decision sequentially on a given problem with the majority vote among oneself and his or
her neighbors’ opinions, and rewires his or her links according to the performance of the linked
individuals. Since each agent makes decision with majority vote, his or her probability to find a correct
answer by oneself, which we call his/her “ability”, is different from his or her actual probability of finding
a correct answer by referring to others, which we call “performance”. The rewiring rule is as follows;each individual monitors his or her neighbors’ performance and breaks the link if the neighbor’s
performance becomes worth than a preset threshold. We also assume that individuals vary in their ability.
Our analysis shows the following results. (1) The threshold for breaking a link, which stands forhow strictly agents assess their neighbors, strongly affects whether or not opinion leaders emerge, or,more strictly, whether or not the distribution for the number of followers becomes significantly different
from binomial distribution under random connection. When opinion leaders emerge in the model, (2) themean number of followers each individual has increases more than linearly with his or her ability, and(3) the average performance of agents becomes higher but shows more temporal fluctuation than wheneach individual makes a decision independently. Furthermore, as long as the threshold value for rewiringlinks is greater than 0.5, which is the minimum ability an individual may have, the lower the threshold
we set, the higher the mean performance each agent will have. Some of these results can be explainedby considering a random walk of the monitoring value of the neighbor’s performance and its first hitting
time to the threshold: for example, the effect of a threshold on the emergence of opinion leaders, and themean number of followers that an agent with a given ability can attract.
REFERENCES[1] C. Castellano, S. Fortunato, V. Loreto, 2009. Statistical physics of social dynamics, Rev. Mod. Phys. 81, 591.
[2] T. Gross, B. Blasius, Adaptive coevolutionary networks: a review, 2008. J. R. Soc. Interface 5, 259-271.

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P-11
JSMB2016 Fukuoka
Mitsuhiro Nakamura
Department of Evolutionary Studies of Biosystems,
SOKENDAI (The Graduate University for Advanced Studies),
Hayama, Kanagawa 240-0193, Japane-mail: nakamuramh@soken.ac.jp
Ai Kawamori
Department of Data Sciences,
The Institute of Statistical Mathematics,
10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan

Learning processes and matching behavior in domestic chicks' foraging
Environmental harshness in food resources varies in nature, thus foraging animals should adapt their
cognitive ability to environment in different levels [1]. Learning mechanism is in particular importantamong several aspects of animal cognition. However, how they adapt their learning strategies toenvironment is unclear. Rescorla–Wagner (RW) and Roth–Erev (RE) learning rules are classicalreinforcement learning models that explain animals’ choice behavior regarding their implicit estimation of
resource amounts, namely values, of different patches. RW-rule learning maximizes the expected value,
whereas RE-rule learning does not. However, RE-rule learning has been often observed in nature andlaboratory experiments. What kind of environmental condition makes animals maximize their fitness?
Performing a Bayesian model-fit analysis to behavioral data of domestic chicks in laboratory tests affectedby environmental change, we show that chicks use RW-rule learning in high risk environments. In low risk
environments, they show diverse behavioral patterns; thus, it is not easy to identify which learning rule they
adopt. Nonetheless, we found that in low risk environments, chicks show a generalized matching law,
implying that they select a choice that has provided resources at past. RE-rule learning satisfies suchproperty.
REFERENCES[1] Shettleworth, S. J., 1998. Cognition, Evolution, and Behavior. Oxford, NY: Oxford University Press.
[2] Rescorla, R.A., Wagner, A.R., 1972. A theory of Pavlovian conditioning: variations in the effectiveness ofreinforcement and nonreinforcement. Classical Conditioning II, 64–99.
[3] Roth, A., Erev, I., 1995. Learning in extensive-form games: experimental data and simple dynamic models in theintermediate term. Games and Economic Behavior 8, 164–212.

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P-12
JSMB2016 Fukuoka
Junepi Okuno
Dept. of Elec. Eng. & Biosci.Waseda University, Tokyo, Japane-mail: wsd.j.o@asagi.waseda.jp
Atsuko Takamatsu
Dept. of Elec. Eng. & Biosci.Waseda University, Tokyo, Japan

Foraging strategy using multi-tentacles in plasmodial slime mold
Decision making during foraging is important problem for every organism even for brainless primitive
organisms. Plasmodium of true slime mold, Physarum policephalum is a giant multinucleated unicellularorganism. The plasmodium extrudes the portion of the body as tentacles to explore food in environment.
Latty and Beekman found trade-off between decision speed and accuracy, and trade-off between harmful
light stimulation and food reward in foraging decision in plasmodiums, where the decisions are that of final
states [1,2]. In fact, the plasmodium can explore multiple food simultaneously by using multiple tentacles.
Therefore, we focus on the process of decision making with the multi-tentacles.
In our observation, three food blocks were placed in contact with tentacles extending in three
directions (Fig.1a). It was observed, after 3-12 hours cultivation, that the tentacles extend over the foodblocks alternatively (Fig.1b).
The relationship between nutrient concentration of food sites and extending speed of the tentacles(activity), capturing time of the food sites, or the resident period was quantified. The results of analysis
suggest that priorities during foraging decision depend on activity of tentacles when nutrient concentrations
are equal. In contrast, when the concentrations are different, the priorities depend on complex factors of theconcentration and the activity.

(a)

( b)
1

2

3

Fig.1: Experimental set-up. (a) A plasmodium extrudes three tentacles contacting with each food block.
(b) A plasmodium forages three food sites (The food sites 1-3 contain extraction of 10, 5, 3w/v% groundoat flakes).
REFERENCES[1] Latty, Tanya, and Madeleine Beekman., 2010. "Food quality and the risk of light exposure affect patch-choice decisions in the slime mold Physarum polycephalum." Ecology, 91.1: 22-27.
[2] Latty, Tanya, and Madeleine Beekman., 2011. "Speed–accuracy trade-offs during foraging decisions in

the acellular slime mould Physarum polycephalum." Proceedings of the Royal Society of London B:
Biological Sciences, 278.1705: 539-545.

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P-13
JSMB2016 Fukuoka
Chikoo OOSAWA
Department of Bioscience and Bioinformatics, Kyushu Institute of Technology,
680-4 Kawazu Iizuka Fukuoka JAPAN 820-8502
e-mail: chikoo@bio.kyutech.ac.jp
Yamato HAMADA
Dept. of Biosci. Bioinfor. Kyushu Institute of Technology

Gathering animals by escaping
Introduction:
Simple models for relationship between sheep and sheepdogs have developed to capture major factors
behind collective behavior of sheep. Even with the simple model can provide show gathering behavior of
sheep without using famous Boids model [1]. We also find that effective conditions of moving sheepdogs
for gathering sheep.
Model:
In our model, two-dimensional squared lattice sheep farm with fence (zero-flux boundary conditions)is considered. Each site is empty or occupied by one animal: a sheep or sheepdog. A large number of the
sheep can only escape from the nearest sheepdog as far as possible [2]. On the other hand a small numberof sheepdogs are controllable: (1) running along the fence, (2) running in circle, (3) chasing the nearest
sheep, (4) running at random (no chase).
To evaluate differences of sheepdog behaviors, 2~8 sheepdogs are placed along the fence and sheep
are distributed at random and gathering efficiency is defined by density of sheep in the central region offarm.
Results and discussions:
Most of conditions show that the density increases with time, demonstrating that even simple model
can generate collective behavior of sheep. In general the higher efficiency of gathering sheep are shownwith larger number of sheepdogs as well as the more regular behaviors of sheepdogs can provide the higher
efficiency.
REFERENCES[1] C.W.Reynolds, Flock,Herds, and Schools: A Distributed Behavioral Model ,1987, Computer Graphics, 21(4):25.
[2] A. Kimura, T. Ohhira, 2010. Group chase and escape, New Journal of Phyiscs, 12:053013.

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P-14
JSMB2016 Fukuoka
Hemma Philamore
Kyoto University, University of Bristol, Bristol Robotics Laboratory.
e-mail: hemma.philamore@bristol.ac.uk
Tomohiro Hayakawa
Kyoto University
Bo Hyeon Kim
Kyoto University
Jonathan Rossiter
University of Bristol, Bristol Robotics Laboratory.
Ioannis Ieropoulos
University of the West of England, Bristol BioEnergy Centre
Fumitoshi Matsuno
Kyoto University

Trophallaxis for Swarms of Energy-Scavenging Artificial Organisms.
One of the greatest challenges in robotics is to achieve operation with the degree of autonomy weobserve in natural organisms. For complete autonomy, in addition to actuation and computation, a robot
must be capable of independent energy self sufficiency. Robots that supplement their power demand by
conversion or direct use of environmentally scavenged sources of energy have shown great potential forenergy autonomous operation [1]. However, the stochastic conditions that typify most real world
environments mean that it is often challenging for a single energy-scavenging robot to maintain its energy
needs. In the case of robots with limited power generation or on-board energy storage capabilities, periodsof starvation can be a threat to survival [2]. This applies to small, simple agents that typify a swarm ofubiquitous robots [3] and those which take their energy from relatively low power sources such as microbial
fuel cell technology [4]. Properties that demonstrate system robustness when operating in real environments,
such as increased power generation with prolonged environmental exposure [5], inherent fault tolerance[6], and bio-remediative effects, may be compromised due to the low energy capabilities of individual
robots.
Here we demonstrate the use of a bio-inspired decentralised control strategy using a swarm ofsimulated robots, tasked with cleaning up a biodegradable environmental pollutant, which simultaneously
serves as their sole source of energy. The simulated robots ingest the pollutant and convert it to electricalenergy using on-board artificial stomachs. Trophallaxis; inter-agent feeding inspired by the behaviour ofsocial organisms including ants, bats and bees, is employed for group energy distribution andcommunication. Communication and sensing are minimised to conserve stored agent energy. Additionally,
relay-chain formation is employed as a means to connect distal swarm members to the food supply.
Increased robot aggregation at the food supply is shown in response to the use of social mechanisms;
trophallaxis and relay chain formation in combination. Notably using only trophallaxis results in the longest
swarm survival time. In contrast, use of relay chains alone is detrimental to overall performance. We expect
the outcomes of this study to have impact in the adoption of swarm robots for real world applications andradically new designs for future robots.
REFERENCES[1] Mars Exploration Rover Landings Press Kit. Technical Report January, NASA, 2004.
[2] McFarland D and Spier E, Basic Cycles Utility and Opportunism in Self-Sufficient Robots. Robotics andAutonomous Systems, pages 179-190, 1997.
[3] Kim B.H, Fukushima H, and Matsuno F. Cooperative Transportation of a Disk Object by Multiple Robots without
Communication. In SWARM 2015: The First International Symposium on Swarm Behavior and Bio-Inspired Robotics,
pages 94–95, 2015.
[4] Ieropoulos I, Greenman J, Melhuish C, and Horsfield I. EcoBot-III : a robot with guts. In Proceedings of the Alife
7 Conference, pages 733-740, 2010.
[5] Tender L, Microbial Fuel Cells for Powering Navy Devices, Naval Research LaboratoryWashington, DC,

2014.
[6] Winfield AFT, Nembrini J, Safety in Numbers: Fault Tolerance in Robot Swarms, International
Journal of Modelling Identification and Control, 1:30-37 (2006)- 219 -

P-15
JSMB2016 Fukuoka
Motohide Seki
Kyushu University, Fukuoka, Japane-mail: seki.evol@gmail.com

Optimality and evolutionary stability of life histories with stages for culturaltransmission of information
Social leaning, by which a leaner acquires pieces of information held by an exemplar regardlesswhether the information is adaptive or harmful, is essentially a free-riding behaviour; it can evolve when it
poses less learning cost than individual learning does. Game-theoretic approaches are required to predict
evolutionary consequences of individual and social learning.
It has been shown that social learning rarely contributes to the total amount of information carried by
the whole population. Specifically, a coexisting state of individual and social learners can be
evolutionarily stable depending on the environment, where the total amount of information carried by themixed population is exactly the same as that carried by the population purely consisting of individual
learners [1]. This finding was counterintuitive because we often attribute the ecological success of humanspecies based on high technology to our innate ability of social learning.
It is believed that one of a few exceptional cases in which social learning improves the level ofcollective knowledge is cross-generational transmission of cumulative information. A previous study
considered the case that infant individuals acquire information held by random post-reproductive
individuals from the parental generation (i.e. oblique transmission) [2]. It predicted that life history
including such an infant period evolves when efficiency of the cross-generational information transmission
is sufficiently high. Though the study included the cost for having and extending the infant period, it did
not explicitly consider cost for post-reproductive period during which an individual plays a role of exemplar.
The present model examines the effect of benefit and cost for living after reproduction on the life
history evolution. It also focuses on the difference between oblique and vertical transmission of
information. The results suggest that a post-reproductive period longer than the infant period, which isobserved in human species, may be a complex outcome of cultural transmission and the improved
efficiency of parental care due to the cumulative information.
REFERENCES[1] Rogers, A., 1988. Does biology constrain culture? American Anthropologist, 90: 819–831.
[2] Lehmann, L. et al., 2013. On optimal learning schedules and the marginal value of cumulative cultural evolution.
Evolution, 67: 1435–1445.

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P-16
JSMB2016 Fukuoka
Shohei Utsunomiya
Dept. of Elec., Eng. & Biosci., Waseda University, Japane-mail: shohei.utsunomiya.ant@gmail.com
Atsuko Takamatsu
Dept. of Elec., Eng. & Biosci., Waseda University, Japan

Diversity of behavioral preference on cooperative transport in ants
reduces obstacle passing time
Cooperative transport is known as an action, in which two or more individuals move a single itemfrom a location to another (Fig.1) [1]. The advantages are, as reported in previous studies, that group ofindividuals can drag heavier items and move faster than a single does [2, 3]. It was observed that some ants
try to drag the item from the opposite site against the nest, which seems to disturb the effective transport
toward the nest. We focus on the behavior of the disturbing ants, and its advantage in the group duringpassing through obstacles.
We found two characteristics through a quantitative analysis of experimental observation: First,
increase in number of ants participating the transport reduces the obstacle passing time. Second, individual
ants do not always move straightforwardly toward their nest and some go toward unexpected directions
during their solo transportation. From these experimental results, we hypothesize that diversity of
behavioral preference in ants could optimize something during cooperative transportation of an item. To
verify it, we performed numerical simulation using a mechanical model.
In the model, the diversity of behavioral preference is assumed to be directional preference during
item transportation to the nest. The simulation result revealed that the behavioral diversity reduces the
obstacle passing time.

Fig.1: Cooperative transport in ants.
REFERENCES[1] Czaczkes, T. J. and Ratnieks, F. L. W., 2013. Cooperative transport in ants (Hymenoptera: Formicidae) andelsewhere. Myrmecol News, 18: 1-11.
[2] Czaczkes, T. J., Nouvellet, P. and Ratnieks, F. L. W., 2011. Cooperative food transport in the Neotropical ant,
Pheidole oxyops. Insectes Sociaux, 58: 153-161.
[3] Hölldobler, B., Stanton, R. C. and Markl, H., 1978. Recruitment and food-retrieving behavior in Novomessor(Formicidae, Hymenoptera). Behavioral Ecology and Sociobiology, 4: 163-181.

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P-17
JSMB2016 Fukuoka
Fumiko Ogushi
Advanced Institute for Material Research, Tohoku University
e-mail: fumiko.ogushi.e3@tohoku.ac.jp
Takashi Shimada
Department of Applied Physics, Graduate School of Engineering, The University of Tokyo

A mean-field analysis of the simple model of evolving open systems
A graph dynamical model of evolving open systems (EOS) with uni-directional interactions gives anovel transition in the robustness. The system keeps growing in the case that a newly incoming species has
a moderate number of initial interactions m (4 < m < 19, diverging phase). In the cases that the newly
introduced species have sparser or denser interactions, the system remains in a finite size (m ≤ 4 or m ≥ 19,
finite phase). In addition, the structure of the interaction network of the emergent system has no strong
correlation. It suggests that the emergent system is composed of simple tree structures without any loop
structures. On a basis of such mean-field treatment, the total number of extinctions of resident species per
introduction of a new species is found to be a function of the product of the extinction probability of a
species at single link-change event and the average out-degree of the species, m/2. A further simplified
theoretical process suggests that the extinction probability should monotonically decreases with m but
slower than 1/m. This means that increasing of m makes each node stronger but makes the whole systemfragile, predicting the transition from the diverging phase to the finite phase.
However, the transition point estimated from this simple theoretical process mc=13 is considerably
apart from the real transition point (i.e. 18.5). This difference in the point of transition can stem either orboth from the neglected structure of the emergent systems and/or the inaccurate estimation of the meanfield extinction probability. Therefore, in this study, we investigate the validity of the mean-field approachin detail, with improving the estimation of extinction probabilities using the information of emergent
systems. The transition point estimated from the mean-field treatment with the empirically calculated
extinction probabilities is found to agree with the true transition point. This result suggests that the error in
the transition point we had in the previous study is due to the not accurate estimation of true mean-field
extinction probabilities. And the correlation in the interaction network of the emergent system does notplay a major role to the determination of the transition point.
REFERENCES[1] T. Shimada, Scientific Reports, 4 (2014) 4082.
[2] T. Shimada, in Mathematical Approaches to Biological Systems (Springer, 2015), p.95-117.
[3] T. Shimada and F. Ogushi, to appear in J. of Physics Conference Series- 222 -

P-18
JSMB2016 Fukuoka
Shota Shibasaki
Graduate School of Arts and Sciences, the University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 1538902, Japane-mail: shibasaki.sh@gmail.com
Yuka Shirokawa
Graduate School of Arts and Sciences, the University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 1538902, Japan
Masakazu Shimada
Graduate School of Arts and Sciences, the University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 1538902, JapanThe evolutionary game in sexual reproduction of the social amoeba
The evolution of cooperation is one of the most important problems in biology because of its
vulnerability to cheating. Dictyostelium discoideum, or the social amoeba, is used as a model organism tosolve this problem. The social amoeba lives as free-living cells in most of the time, but it has also two
dormant phases in starvation; one is the fruiting body and the other is the macrocyst. Although each dormant
phases is hypothesized to be kin cooperation, it is unclear how these cooperative systems are maintained
where the genetic diversity has been reported [1]. Here, we suggest the coexistence with fruiting bodies
makes macrocyst formation stable.
In fruiting body formation, ten thousands of cells are attracted by the chemoattractant, cyclic AMP(cAMP). After the aggregation, the cells form the fruiting body, which is regarded as cooperation because
nonviable stalk cells help the dispersal of spore cells. In chimeric fruiting bodies, cheater strains whosecell-type ratio is weighted toward spore cells are reported [2]. Many studies have focused on why fruiting
body formation has been maintained though cheaters exist in nature [3].
On the other hand, the social amoeba also cooperates in during sexual reproduction called macrocyst
formation. In darkness, some cells become gametes but the others stay vegetative cells [4]. After the gamete
fusion, the zygotes secrete cAMP and collect the surrounding vegetative cells. Then, the zygotescannibalize the cells, which leads to macrocyst formation. If these cannibalized cells have high relatedness
with the zygotes, this sexual cannibalism is regarded as kin cooperation. However, there has been no
empirical study, to our knowledge, why such a cooperative cannibalism has been maintained in the social
amoeba.
In this study, we formed a mathematical model to test the hypothesis that the coexistence with fruiting
bodies enabled macrocysts to be maintained. This hypothesis reflects the fact that both macrocysts andfruiting bodies use the common chemoattractant, cAMP. In the model, we assume there exist residents ofeach mating types and a mutant in either of the mating types. We investigate whether the mutant can invade
the population in following two cases. When fruiting bodies are excluded from the model, it shows
macrocyst formation is not maintained. Including fruiting bodies, however, the model predicts one strategy
with macrocyst formation is not invaded by any other strategy; i.e. macrocyst formation is the evolutionarily
stable strategy (ESS). Moreover, our experiment showed the coexistence of macrocysts with fruiting bodies
at the same time. Therefore, it is suggested that macrocyst formation has been maintained due to thecoexistence with fruiting bodies.
REFERENCES[1] Fortunato, A., Strassmann, J. E., Santorelli L. and Queller, D. C. 2003. Co-occurrence in nature ofdifferent clones of the social amoeba, Dictyostelium discoideum. Mol. Eco., 12: 1031-1038.
[2] Strassmann, J. E., Zhu, Y. and Queller, D. 2000. Altruism and social cheating in the social amoeba
Dictyostelium discoideum.Nature, 408: 695-697.
[3]Li, S. I. and Purugganan, M. D. 2011. The cooperative amoeba: Dictyostelium as a model for social
evolution. Trends Genet.. 27: 48-54.
[4] McConachie, D. R. and O'Day, D. H. 1986. The immediate induction of extensive cell fusion by
Ca2+ addition in Dictyostelium discoideum. Biochem. Cell Biol., 64: 1281-1287.

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P-19
JSMB2016 Fukuoka
Masanori Tsuchiya
Graduate School of Information Science, Nagoya University, Nagoya 464-8601, Japane-mail: tsuchiya@alife.cs.is.nagoya-u.ac.jp
Reiji Suzuki
Graduate School of Information Science, Nagoya University, Nagoya 464-8601, Japan
Takaya Arita
Graduate School of Information Science, Nagoya University, Nagoya 464-8601, JapanAn agent-based evolutionary model for diversification ofphenotypic plasticity and personality in resource partitioning
Organisms have plasticity and personality in their phenotypes. Phenotypic plasticity is the ability ofan organism to change its phenotype in response to changes in the environment. Personality is individual
differences in behavior that are consistent over time or contexts. The evolutionary significance of the interand intra- specific diversity in plasticity and personality has been discussed recently [1, 2, 3]. Wolf et al.
showed that, in the hawk-dove game, the presence of responsive individuals can trigger a coevolutionary
process which gives rise to populations in which responsive individuals coexist with unresponsive
individuals who show high levels of adaptive consistency in their behavior [2]. Suzuki et al. constructed a
coevolutionary model of behavioral plasticity in which several different species participate in a partitioningof their shared niches, and evolve their behavioral plasticity to avoid an overlap of their niche use. They
showed that the two different types of asymmetric distributions of phenotypic plasticity among species
emerge depending on the settings of the degree of congestion of the shared niches [3].
Our purpose is to further consider the evolutionary significance of such inter- and intra- specificdiversity in behavioral plasticity and personality in the context of resource sharing. As a first approach, weconstructed an agent-based evolutionary model of behavioral plasticity and personality in a single species[4]. The whole population is composed of groups in which there are some individuals sharing several niches.
Each individual in the group chooses one of niches at each time step, obtains the fitness contribution if the
focal individual has dominated a niche. With a genetically determined probability (i.e., plasticity), eachindividual has a chance to change the niche to use in the next time step by choosing one of the othercurrently unused niches if the current niche use of the focal individual overlapped with the use of others.
Otherwise, in the case of the non-plastic behavior, the focal individual chooses consistently a geneticallydetermined niche (i.e., personality) irrespective of the use of others. The results showed that diversity inthe behavioral plasticity and personality emerged when the number of niches was slightly smaller than thenumber of individuals in a group. That is, individuals with high and low plasticity coexisted and they also
had different personality due to the balances between benefit and cost of overlap avoidance behaviors.
We further extended this model to be able to adjust the numbers of species and the ratio of inter- to
intra- specific interactions. In preliminary experiments under the condition of the evolution of phenotypic
plasticity only (i.e., an individual keeps its own choice of niche in the case of non-plastic behavior), we
observed that the intra-specific and unstable differentiation of phenotypic plasticity emerged when there
were the necessary and sufficient number of niches and intra-specific interactions occur often in groups.
On the other hand, the inter-specific differentiation of the phenotypic plasticity emerged, which is similar
to the results in [3], when inter-specific interactions occur frequently. We also observed that both inter- andintra- specific diversity of phenotypic plasticity sometimes emerged when the ratio of inter- to intraspecific interactions was intermediate.
REFERENCES[1] Dingemanse, N. J. and Wolf, M., 2013. Between-individual differences in behavioural plasticity within populations:causes and consequences, Animal Behavior, 85, 1031-1039.
[2] Wolf, M., Van Doorn, G. S. and Weissing, F. J., 2011. On the coevolution of social responsiveness and behaviouralconsistency, Proceedings of the Royal Society B, 278, 440-448.
[3] Suzuki, R. and Arita, T., 2014. Emergence of a dynamic resource partitioning based on the coevolution ofphenotypic plasticity in sympatric species, Journal of Theoretical Biology, 352, 51-59.
[4] Tsuchiya, M., Suzuki, R. and Arita, T., 2016. An evolutionary model for diversification of phenotypic plasticity
and personality in resource partitioning (written in Japanese), Proceedings of the78th National Convention of theInformation Processing Society of Japan, Vol. 1, pp. 293-294.

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P-20
JSMB2016 Fukuoka
Yu Uchiumi
Department of Evolutionary Studies of Biosystems, SOKENDAI (The Graduate University for Advanced
Studies), Hayama, Kanagawa 240-0193, Japane-mail: uchiumi_yu@soken.ac.jp
Hisashi Ohtsuki
Department of Evolutionary Studies of Biosystems, SOKENDAI (The Graduate University for Advanced
Studies), Hayama, Kanagawa 240-0193, Japan
Akira Sasaki
Department of Evolutionary Studies of Biosystems, SOKENDAI (The Graduate University for Advanced
Studies), Hayama, Kanagawa 240-0193, Japan

Evolution of vertical transmission of symbionts by reducing the rate of cell division
Chloroplasts and mitochondria evolved from free-living bacteria via intracellular symbiosis. Throughthe evolutionary transition from symbionts to organelles, symbionts has become transmitted vertically andremained persistently in a host cell. In intracellular symbiosis, such as the relationship between protists andalgae, vertical transmission is ensured by synchronized cell divisions of symbionts and hosts. If symbiont
division is faster or slower than the host, symbionts accumulate in or are lost from their host cell. In
particular, excessive accumulation makes symbionts a burden to their host and will induce host cell death.
Indeed, the regulation of symbiont division rate is well observed in various symbiotic systems, for example
in the symbiosis between ciliates (Paramecium bursaria) and green algae (Chlorella spp.)[1].
There are two hypotheses for the maintenance of synchronized cell divisions. The first hypothesis isthat a host suppresses excessive cell divisions of symbionts. The second hypothesis is that a symbiont
restrains its own cell division for the synchronization. The latter may seem paradoxical because symbionts’
growth rate may increase by virtue of symbiotic interaction, and it is actually unclear whether symbionts
self-restrain their own division evolutionarily.
Therefore, we theoretically explored the condition for the evolution of self-restraints in symbiont cell
division. We analyzed a mathematical model, in which symbiont dynamics within a host cell is explicitly
taken into account. We assumed that excessive accumulation of symbionts in a host cell leads to the hostdeath and its burst. We also assumed that the host may acquire free-living symbionts, and, once in host cell,
symbionts can be inherited randomly in daughter cells during host cell division. These assumptions leadthe tradeoff between horizontal and vertical transmission as in many protist-algae symbiotic systems. If thedivision rate is higher in symbiont than in host, symbionts tend to accumulate in a host cell, leading to thehost burst and their release into the environment. As a result, such symbionts tend to be transmitted
horizontally and lose the opportunity of vertical transmission. Additionally, we also assumed that bothhost’s and symbiont’s symbiotic benefits are to reduce their death rates.
An analysis of our model reveals that a low cell division rate evolves if symbiotic benefit is large inboth host and symbiont. This is because a larger symbiotic benefit given to hosts makes infected hosts
advantageous over uninfected ones, leading to lower density of uninfected hosts, with which released
symbionts from dead host become difficult to find next hosts. In contrast, sybmiont cell division rate
evolves to a large value or increase without limit if either symbiont’s or host’s benefit is not sufficiently
large. Thus, our results suggest that if symbiotic benefit is large both in host and symbiont, synchronizedcell division can result from symbionts’ self-restraint of their own division even if host’s suppression ofsymbiont’s division is absent.
We also examined the case where host, rather than symbiont, regulates the division rate of symbionts,
and found that the evolutionarily stable cell division rate is different (and is smaller) than when it is selfregulated by symbionts, suggesting unresolved evolutionary conflict in either evolutionary equilibrium.
REFERENCES[1] Kadono, T., Kawano, T., Hosoya, H., & Kosaka, T., 2004. Flow cytometric studies of the host-regulated cell
cycle in algae symbiotic with green paramecium. Protoplasma 223: 133-141.

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P-21
JSMB2016 Fukuoka
Takahiro Yamagishi
Center for Ecological Research, Kyoto University, Japane-mail: yamagishi@ecology.kyoto-u.ac.jp
Ross Booton
School of Mathematics and Statistics, The University of Sheffield
Atsushi Yamauchi
Center for Ecological Research, Kyoto University, Japan

Joint Evolution of cytoplasmic male sterility and selfing rate in plant
It has been reported in some plants species that their populations consist of hermaphrodite individuals
and female individuals. This type of sexual system is called gynodioecy. There are cases where cytoplasmic
factor cause male sterility and change plant population from hermaphrodite into gynodioecy. Thisphenomenon is also known as cytoplasmic male sterility (CMS) [1]. In self-compatible species,
hermaphrodite individuals can reproduce by both outbreeding and selfing, whereas female individual
reproduce outbreeding only. That’s why a selfing rare has influence on the evolution of gynodioecy [2]. On
the contrary, sexual system, or sex ratio, would affect the evolution of selfing rate. In order to investigate
joint evolution of the gynodioecy and selfing, we analyzed the evolutionary process by using mathematicalmodel.
We considered that sexual system is determined by two types of mitochondria. The wild typemitochondria do not disturb the original hermaphrodite, although mutant mitochondrial prevent pollen
production, resulting in feminization. Each individual possesses either mitochondria that inherit from theirmother. On the other hand, a selfing rate is governed by quantitative gene on nuclear genome in theconsidered diploid organism. Our analysis has two steps. First, we assumed selfing rate as fixed value fora while, and found equilibrium frequency of CMS as previous studies did [2, 3]. Subsequently, It can be
discussed whether the nuclear mutant allele which bring higher or lower selfing rate can invade thepopulation or not. This two-step way allows us to analyze evolutionary process of gynodioecy andselfing.
Our analysis suggests that higher selfing rate can evolve as anti-CMS strategy of plants. In
gynodioecious population, higher selfing rate is easy to be selected, and it suppress increase in CMS. The
evolutionary branching about selfing rate is also expected, and demonstrated by individual based model.
These are unique results, which have not been found in previous studies with fixed selfing rate, and thisjoint evolution is worthy to study in more detail.
REFERENCES[1] Jacobs, M. S., & Wade, M. J. (2003). A synthetic review of the theory of gynodioecy. The American Naturalist,
161(6), 837-851.
[2] Dornier, A., & Dufay, M. (2013). How Selfing, inbreeding depression, and pollen limitation impact nuclearcytoplasmic gynodioecy: a model. Evolution, 67(9), 2674-2687.
[3] Dufay, M., Touzet, P., Maurice, S., & Cuguen, J. (2007). Modelling the maintenance of male-fertile cytoplasm ina gynodioecious population. Heredity, 99(3), 349-356.

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P-22
JSMB2016 Fukuoka
NOBUYUKI ISHIZUKA
e-mail: ousiryu@gmail.com
College of Science and Engineering, Aoyama Gakuin University, Kanagawa
252-5258, Japan.
Shinji Nakaoka
e-mail: shinzy.nakaoka@gmail.com
Graduate School of Medicine, The University of Tokyo, Hongo 7-3-1,
Bunkyo-ku, Tokyo,133-0033, Japan.
Yasuhiro Takeuchi
e-mail: takeuchi@gem.aoyama.ac.jp
College of Science and Engineering, Aoyama Gakuin University, Kanagawa
252-5258, Japan.

Analysis of Lymph tissues network model of HIV infection dynamics
HIV infection is known to be difficult to eradicate from a body of an infected person. One of major
reason of HIV persistence is existence of reservoir cells that maintain HIV virions despite sufficient levelof multiple types of drug injection. Moreover, reservoir cells are believed to stay in tissue. Importantly,
lymph nodes are the main place of reservoir cells to stay. Since lymph nodes constitute a network
structure, it is important to understand how network structure can mediate HIV persistence.
Here we report our progress on analyzing a mathematical model when all the migrations between N
lymph nodes have equal immigration rate m. The objective of this talk is to derive explicit form of disease
free equilibrium of our network model. To obtain an insight, we start with using symbolic calculation
package Sympy to perform symbolic computation for disease free equilibrium of our model for N = 2, 3,
4. Based on the result, we conjecture an explicit form of the disease free equilibrium. Finally, based on
the conjecture derived from symbolic computation, we have succeeded in obtaining explicit values ofthe disease free equilibrium for general N. We will show another progress on numerical simulation of
HIV infection dynamics in lymph node network.
REFERENCES[1] Shinji Nakaoka, Shingo Iwami, and Kei Sato, Dynamics of HIV infection in lymphoid tissue network,
Journal of Mathematical Biology, 72:909–938 (2016) (DOI:10.1007/s00285-015-0940-x).

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P-23
JSMB2016 Fukuoka
Yusuke Ito
Department of Biology, Kyushu University, Japan e-mail: uks3tkwbft@gmail.com
Azaria Remion
U941, INSERM, France
Alexandra Tauzin
U941, INSERM, France
Yoh Iwasa
Department of Biology, Kyushu University, Japan
Fabrizio Mammano
U941, INSERM, France
Shingo Iwami
Department of Biology, Kyushu University, Japan

Estimating the number of HIV-1 to infect target cells in nonrandom co-infection
Co-infection is a simultaneous infection event by multiple viruses and largely causes the diversity of
HIV-1 through recombination. One interesting recent finding is “nonrandom HIV-1 co-infection”, in which
co-infection of HIV-1 occurs more frequently than it would be random, reported by Q. Dang et al., 2004[1].
“Heterogeneity of susceptibility of target cell” but not any other viral factors is thought to be a potential
factor for this phenomenon[1,2].
In this study, we developed the mathematical model for nonrandom co-infection including“heterogeneity of susceptibility of target cell” and analyzed co-infection experiments. Our results show thatthe number of infection events per target cell based on different amount of inoculated HIV-1 is 1.02 to 1.62,
and are consistent with previous experimental one[3]. Furthermore, using the parameters, we revealed thatup to 40% of infected cells are co-infected, which indicates co-infection is likely to promote the HIV-1
diversity through recombination. Taken together, our experimental-mathematical approach quantitatively
revealed that the frequency of co-infection events in infected cells is surprisingly high and co-infection canbe a major factor to drive the diversity of HIV-1.
REFERENCES[1] Dang, Q. et al, Nonrandom HIV-1 infection and double infection via direct and cell- mediated pathways, Proc. Natl.
Acad. Sci. USA, 101, (2004), 632-637.
[2] Chen J. et al, Mechanisms of Nonrandom Human Immunodeficiency Virus Type 1 Infection and Double Infection:
Preference in Virus Entry Is Important but Is Not the Sole Factor, J. Virol, 79, (2005), 4140-4149.
[3] Portillo. A. D et al Multiploid Inheritance of HIV-1 during Cell-to-Cell Infection, J. Virol, 85 (2011), 7169–7176[4] Robertson D. L et al, Recombination in HIV-1, Nature, 374, (1995), 124-126.
[5] Remion A.et al,Kinetics of the establishment of HIV-1 viral interference and comprehensive analysis of thecontribution of viral genes, Virology, 487, (2015), 59-67.

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P-24
JSMB2016 Fukuoka
Nao Yamamoto
Hokkaido University
e-mail: nao.m.yamamoto@gmail.com

How Does Correlation between Condom Use and Partner Type Influence theTransmission Dynamics of STI?
Background:No systematic review of prospective studies has been reported on the relationship between condom use andpartner type or the number of sexual partners. It is pressing to clarify how this relationship has an impact
on epidemic dynamics.
Objectives:
To examine under what kind of sexual relationships individuals are more likely to use condoms and toclarify its population impact on the dynamics of sexually transmitted infections using a mathematical model.
Methods:
A systematic review and meta-analysis of published studies are performed, analyzing literature thatepidemiologically examined the relationship between condom use and sexual partnership. Subsequently,
we compute the reproduction number accounting for the number of partners and incorporating the condom
coverage, which is different dependent on the partnership (single or multiple). Finally, we evaluated theeffect of reducing multiple partnerships on R0 varying condom coverage of the people with multiple
partnerships.
Results:
A greater number of people used condoms during sexual intercourse outside of an ongoing relationshipthan with a steady partner. Furthermore, people with multiple partners use condoms more frequently thanpeople with a single partner. Through the computational simulation, we have ascertained that as people
with multiple partnerships increase, effective reproduction numbers increase in conjunction, which implies
that multiple partnerships accelerate the HIV epidemic. However the association can change depending on
the relative condom use of multiple partnerships, which implies we cannot conclude that multiple
partnerships are the only cause of the epidemic.
Conclusions:
In spite of the high frequency of sexual contact that people with multiple partnerships have, the HIV
epidemic may be primarily maintained by individuals with single partnerships due to low condom coverage.
The intervention should be implemented towards peoples with single and multiple partnerships.

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P-25
JSMB2016 Fukuoka
Kenta Yashima
The Graduate University for Advanced Studies (Sokendai), Kanagawa, Japane-mail: yashima_kenta@soken.ac.jp
Akira Sasaki
The Graduate University for Advanced Studies (Sokendai), Kanagawa, Japan

Network centrality measure based onsensitivity analysis of the basic reproductive ratio
Identification of epidemiologically high-risk communities in a metapopulation network is required for
effective and efficient intervention strategies. The network centrality measure, which quantifies the relative
importance of each community, is commonly utilized for this purpose. As the condition for the invasion of
disease is given from the basic reproductive ratio R0, we have introduced a novel centrality measure basedon the sensitivity analysis of this R0 and shown its capability of revealing the characteristics that has been
overlooked by the conventional centrality measures. The epidemic dynamics over the commute network of
the Tokyo metropolitan area is theoretically analyzed by using this centrality measure. We found that, theimpact of countermeasures at the largest station (Shinjuku station) is more than 1,000 times stronger
compare to that at the second largest station (Tokyo station), even though the population sizes are onlyaround 1.5 times larger. Other population has even minor effect, but its relative importance incountermeasures is again most strongly determined by the existence and the number of commuters to thelargest station (Shinjuku). It is well known that the hubs are the most influential nodes, however, ouranalysis shows that only the largest among the network plays an extraordinary role. Lastly, we also foundthat, the location that is important for the prevention of disease invasion does not necessarily match thelocation that is important for reducing the number of infected.

Figure: Final size of epidemic (the proportion of hosts that are eventually infected) at
each local station (left: daytime, right: nighttime).
⚫︎: 0.00~0.25, ⚫︎: 0.25~0.50, ⚫︎: 0.50~0.75, ⚫︎: 0.75~1.00- 230 -

P-26
JSMB2016 Fukuoka
Shiori Abe
Department of Information and Computer Science, Nara Women's University
e-mail: abe-shiori1201@ics.nara-wu.ac.jp
Fugo Takasu
Department of Information and Computer Science, Nara Women's University

Population viability analysis of the Japanese rock ptarmigan
The Japanese rock ptarmigan (Lagopus muta japonica) is endangered species that breeds in limited
alpine zones in Japan. Total population size was estimated around 3,000 in 1980. But the population has
decreased in number and the present estimation is about 1,700. To conserve the Japanese rock ptarmigan,several protective measures have been undertaken such as guarding fledgling by human attendants andartifitial incubation of eggs in order to increase the survivability of young.
In this study, we work on population viability analysis of the Japanese population based on breeding
parameters estimated by field studies in the past. Suzuki at al. 2013 [1] has carried out PVA of the Japaneserock ptarmigan and concluded that the local population in Mt. Norikura is stable and the risk of local
extinction is low based on breeding parameters collected by 2011. In this study, we include breeding
parameters collected after 2011 [2].
We first evaluate sensitivity and elasticity of the eventual population growth rate λ on breeding
parameters using matrix model [3]. We then study stochastic population dynamics using an individualbased approach in which each individual is assigned a set of properties (age, sex, holding a breeding
territory or not, etc.) and reproduces and survives one year stochastically according to the breeding
parameters (age-dependent annual survival probability, and clutch size, etc.)
The model analysis show that 1) increasing survival rates of young is effective to raise λ, and 2) therisk of local extinction is higher when we consider recent breeding parameters.
Based on the model analyses, we discuss effective protective measure to conserve the Japanese rockptarmigan population.
REFERENCES[1] Suzuki, A., Kobayahi, A., Nakamura, H., Takasu, F, 2013. Population viability analysis of the Japanese rockptarmigan. Wildlife Biology, 19: 339–346.
[2] Kobayahi, A., Nakamura, H. and Takada, M, 2014. Life history and population dynamics of the Japanese rockptarmigan in alpine belt. Toho University. (In Japanese).
[3] Caswell, H, 2001. Matrix population models. 2nd edition. Sinauer Associates, Inc. Publishers, Sunderland,
Massachusetts, USA, 722pp.

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P-27
JSMB2016 Fukuoka
Miki Hamada
Graduate School of Human and Sciences, Nara Women’s University
e-mail: u1284018@gmail.com
Fugo Takasu
Department of information and Computer Science, Nara Women’s University

Spatial SIS model as a point pattern dynamics
The SIS model is one of the classical models of mathematical epidemiology [1]. The model describes
the dynamics of susceptible S and infections I under the assumption that S and I are well mixed andinfection occurs by the law of mass action. This deterministic model has been served as a conceptual model
to study the dynamics of disease that confers no immunity. However, this model completely ignores spatial
distribution of S and I. In order to explore disease spread over a space, we need to somehow extend themodel to be spatial.
In this study, we extend the SIS model as a point pattern dynamics [2]. Each individual is represented
by a point in two dimensional space and its status can change from S to I to S according to the following
rules. Infection (S to I) occurs with the infection rate as a function of the distance from a focal S to I’s.
Recovery (I to S) occurs with a constant recovery rate. We simulate stochastic point pattern dynamics as
an individual-based model and study the dynamics of the number of S and I and spatial distribution. A point
pattern can be quantified by focusing on the number of points (1st order structure) and the number of pairs
displaced by a certain distance (2nd order structure), etc. We derive deterministic dynamics of the singlet
probabilities (an arbitrary chosen point is in status S and I) and the pair probabilities (an arbitrary chosen
pair is in status S-S, S-I, I-S, I-I). We explore to what extent this deterministic description can explain
simulation results.
REFERENCES[1] Matt J. Keeling and Pejman Rohani. 2008. “Modeling infectious diseases in humans and animals.” Princeton.
[2] Law Richard, David J. Murrell, and Ulf Dieckmann. 2003. “Population growth in space and time: spatial logistic
equations.” Ecology, 84.1: 252–262.

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P-28
JSMB2016 Fukuoka
Yusuke Ikegawa
Ryukyu Sankei Co., Ltd., Maji 123, Naha, Okinawa, 902-0072, Japane-mail: y.ikegawa224@gmail.com

Effects of spatial and temporal homogeneity of releases of sterile insects on controlof pests with limited dispersal ability
Sterile insect technique (SIT) is a genetic pest control method by periodically releasing mass-reared
sterile insect and thereby impeding successful reproduction of fertile pests [1]. In Okinawa Prefecture, theSIT project against West Indian sweet potato weevil, Euscepes postfasciatus (Fairmaire), which is an
important agricultural pest of sweet potato, Ipomoea batatas (L.), have been initiated after success in thatagainst some species of fruit flies. However, E. postfasciatus is flightless and usually shows much lower
mobility than the fruit flies. It might lead to spatial segregated distributions of the wild and sterile weevils,
for instance due to spatially biased releases of the latter, and consequently inhibit eradication of the former.
Recently, considering a trade-off between the number of released sterile insects per release and the numberof patches where the insects were released, a metapopulation model predicted that the spatially biased
releases of the sterile insect could inhibit success in the SIT [2]. However, no studies proposed effective
measures to improve the negative effect.
In this study, I consider that managers can vary the number of released sterile insects toward each ofpatches at every release so that the spatial bias for the previous release is counterbalanced (hereafter called'temporal balancing'), as a measure to improve the negative effect of the spatially biased releases. Extendinga non-spatial SIT model [3], I constructed a simple two-patch Ricker model comprised of the pest andsterile insect moving between the two habitats. I examined effectiveness of the temporal balancing on
eradication of the pest in the two habitats, by numerically simulating the model with some release strategies(the number of released sterile insects, release intervals, and spatial evenness of the releases). Demographic
parameter values were derived from some previous empirical works on E. postfasciatus.
I confirmed that the spatially biased releases inhibited successful eradication of the pest in both thetwo habitats as shown in previous models, and revealed that the negative effect of the spatially biased
releases was dramatically improved by the temporal balancing. This was because the pests lost the spatialrefuge arisen from the spatially biased releases, due to the temporal balancing of the releases. However,shortening releases intervals was necessary for efficient pest control, because the sterile insect
monotonically decreased during no-release terms and the pest could temporally enjoy lower reproductive
interference from the sterile insect.
In this model, the failure in the SIT is primarily mediated by too low mobility of the target insect. If I
assume that the mobility of the target insect becomes sufficiently high, regional eradication of the pest isachieved, irrespective of the spatial evenness of the releases. It indicates that the spatially even release of
the sterile insect is much more crucial for eradication of the pest with low mobility (e.g., E. postfasciatus)
than for that with high mobility (e.g., some species of fruit flies), and that this is the reason why the
temporally balancing spatial distribution of the sterile insect is a reasonable measure to control less mobile
E. postfasciatus.
REFERENCES[1] Knippling, E.F., 1955. Possibilities of insect control or eradication through the use of sexually sterile males. J.
Econom. Entomol. 48: 459-462.
[2] Evans, T.P.O., Bishop, S.R., 2014. A spatial model with pulsed releases to compare strategies for the sterile insect
technique applied to the mosquito Aedes aegypti. Math. Biosci. 254: 6-27.
[3] White, S.M., Rohani, P., Sait, S.M., 2010. Modelling pulsed releases for sterile insect techniques: fitness costs ofsterile and transgenic males and the effects on mosquito dynamics. J. Appl. Ecol. 47: 1329-1339.

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P-29
JSMB2016 Fukuoka
Takahiro Irie
Atmosphere and Ocean Research Institute, The University of Tokyoe-mail: irie@aori.u-tokyo.ac.jp

A hierarchical Bayesian estimation of wild population size
From the neutral genetic information
In conservation biology and fishery science, there is a strong need to improve the estimating
techniques for wild population sizes of marine organisms. Current estimation methods have problems withboth accuracy and precision, because of heavily relying on fishery-derived data, collected in a non-randommanner. A new technique based on the neutral genetic information of randomly sampled individuals acrossgenerations is expected to be the next generation alternative. This procedure is referred to as the Close-Kin
approach, in which the numbers of parent-offspring pairs (POPs) and half-sibling pairs (HSPs) are assumed
to be the metrics of population size. These kinships are quantified by comparing neutral allele frequencies(e.g., those at SNPs) by means of the RAD-sequencing. However, no statistical procedure has been
established yet to estimate population size from kinship information. Accordingly, the present study
proposes a hierarchical Bayesian model to compute the posterior distribution of wild population size fromthe numbers of parental and offspring samples, POPs, and HSPs. This task begins with formulating theprobability mass function (pmf) describing the stochastic behavior of POPs and HSPs, in which theparameters are population size (N), parental sample size (n), and offspring sample size (m). The author
tentatively termed this pmf as the modified multivariate Hypergeometric (MMHG) distribution. The
parameters N, n, and m are given as vectors because of being stratified with the parental reproductive
success (= the number of surviving offspring from the focal parent). For the same reason, both POPs and
HSPs are matrices rather than scalars. The model also considers the parental reproductive success follows
the negative binomial (NB) distribution with two parameters. These NB-parameters affect the values ofparametric vectors N, n, and m, which is the reason why this model has a hierarchical structure. In theory,the joint posterior distribution of population size (N) and two NB-parameters can be generated by evaluating
MCMC using the Metropolis–Hastings algorithm, under the given parental sample size, offspring sample
size, POPs, and HSPs. However, this method suffers from a technical difficulty, in which computational
steps rapidly increases with increasing sample sizes, because the multidimensional convolution based on
repeated integer partitioning is required when calculating the probability from the MMHG distribution. In
this paper, I will propose some technical ideas to avoid the computational complexity due to combinatorial
explosion.

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P-31
JSMB2016 Fukuoka
Kenta Suzuki
Center for Environmental Biology and Ecosysteme-mail: suzuki.kenta@nies.go.jp

Studies, National Institute for Environmental Studies

Katuhiko Yoshida
Center for Environmental Biology and Ecosystem Studies, National Institute for Environmental Studies

Resilience of hydrothermal vent communities: a metacommunity framework
Hydrothermal vent communities have a patchy spatial distribution that is well-suited to ametacommunity framework. To evaluate the effect of disturbance on local community structure causedby resource mining, we developed a spatially explicit, multi-species competition model, implementing
the distribution of hydrothermal vents in Okinawa trough and the connectivity between these local
habitats. Using this model, we performed numerical experiments to understand the resilience of local
communities in the metacommunity context. It was difficult for a community to recover its original state
when it is distant from other communities. More interestingly, in some cases when a disturbed
community could not recover its original state, other non-disturbed communities were "infected" withthe alternative community structure without any disturbance. The result suggests that when evaluating
the effect of resource mining, one should not only consider the recoverability of community at the focal
location, but also its effect on other communities that are not directly disturbed.

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P-32
JSMB2016 Fukuoka
Takenori Takada
Hokkaido University, Japane-mail: takada@ees.hokudai.ac.jp

Population statistics of random matrices
Projection matrix models have been often employed as an effective tool to quantify the population
dynamics of both trees and herbs. Elasticity analysis is the most frequently-used analytical method, andFranco and Silvertown published a famous paper, where they mapped elasticity vectors of survival, growthand fecundity for 102 plant species in triangle simplex and found that they are located in specific regions
depending on groups of plants with different life history and growth forms.
To understand and clarify why they are located in specific regions, we constructed four types ofrandom matrices. 4 by 4 random matrices is compose of two parts: fecundity and transition probabilities
from a stage to another. The distribution of fecundities is a Poisson distribution with the average p. The
transition probabilities range from zero to one, whose row sums are less than 1. The elasticities for survival,
growth and fecundities are calculated using 3000 random matrices and the elasticity vectors are plotted in
the triangle map. Four types of matrices are as follows: (1) random matrices with no zero-element, (2)random matrices with no zero-element and the survival probabilities increase as individuals grow, (3)random matrices which have non-zero elements only on diagonal and sub-diagonal positions, (4) randommatrices which have non-zero elements only on diagonal and sub-diagonal positions and the survival
probabilities increase as individuals grow. The results are: (a) distribution of elasticity vectors moves toupper-left region of the triangle map as the average of fecundity increases (Fig. 1a). (b) In the third andfourth types of random matrices, the distribution is located on a line whose slope is equal to 46 degrees(Fig.1b). The slope can be proved by the following formula:tan θ =

(n −1) 3(n +1)

when n = 4, where n is the size of projection matrix. The angle, q, ranges from 30 to 60 degrees with n= 2
to infinity. (3) There is no elasticity vectors in the bottom half of the triangle map.
Fig.1 The triangle map of elasticity vectors of survival, growth and fecundity.
(a) For random matrices with no zero-element.

(b) When individuals don’t grow rapidly- 237 -

P-33
JSMB2016 Fukuoka
Takahiro Hiraga
Department of Mathematical and Life Sciences, Hiroshima University
e-mail: m164154@hiroshima-u.ac.jp
Ryo Kobayashi
Department of Mathematical and Life Sciences, Hiroshima University

Mathematical study of the rising movement and its support from the chair
Japan is facing to the serious situation of declining birthrate and a growing proportion of elderly
people. It is expected that the number of people who need nursing care drastically increase in near future.
Thus it is important to reduce the physical load of care workers, and caring robots are developed for the
purpose.
We propose a mathematical model of standing up motion and its support by preparing a imaginary
doll named “Tachiagari-san” which consists of body, thighs, lower leg and foot connected by waist, knee
and uncle joints. Firstly, we construct a healthy people’s model using the standing up data of one of theauthors. Time sequence of the torque at each joint was calculated by ODE. After that, we restricted the
maximum torque at the selected joint, which causes falling down of the doll. It is a model of a person who
requires nursing care. Then we apply the support power to the point of the chest in three different ways.
Support of Type 1 is pulling the supporting point from the same direction at all time. Support of Type 2 ispulling the supporting point from the fixed point. Support of Type 3 is pulling the supporting point so as tofollow the healthy people’s model. Comparing these 3 types by appropriate criteria, it turned out that Type
3 was the best.
I simulated the standing up motion and supporting. I made a standing up simulation doll named“Tachiagari-san” consists of body, thighs, lower leg, and foot. It has waist, knee, and uncle joints. I madethe “healthy people model.” It is my standing up data. After that, I weakened its torque, so it fells in thestanding up motion. And I apply the support power for it. I researched the way to the 3 types support. Type
1 is pulling same direction at all time. Type 2 is pulling from the fixed point. Type 3 is pulling the user tohealthy people model. Type 3 is the best support of the 3. Type 3 support applies a force that is proportional
to the distance between the location of the chest and the location of the chest of the healthy people model.
In the support of Type 3, the supporting force is proportional to the displacement vector between the
supporting point of the doll and the corresponding point of the healthy people’s model. It seems to be betterto take larger constant of proportion. However, too large constant not only causes an uncomfortable feelingto the users, but also makes a cared person not to use their own muscles, which is an essential problem. In
contrast, too small constant fails in supporting itself. The constant of proportion was searched bysimulations, in which the less the machine uses energy the better constant is under the restriction of
successful rising up. We obtained the best constant of proportion in various situations.

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P-34
JSMB2016 Fukuoka
Shigehide Iwata
Tokyo University of Marine Science and Technology
e-mail: siwata0@kaiyodai.ac.jp

The catch control by the allocation of number boat
Marine species, especially fish lives with migration among some area. To correspond the spatial
pattern of fish, fisherman moves to fish ground to maximize catch. This means the allocation of effort. The
allocation of effort is important issue in two meanings; one is to increase a benefit for fisherman, the otherone is taking care of stock (to take care of special area i.e. marine protected area, MPA or by the miss judgeof the fisherman). Both points are trade-off. Recently, electronic searching system were developed. Rosset. al., [1] were assessed the efficiency of multiple electrofishing scenarios by comparing various strategies
for the spatial and temporal allocation of sampling effort so as to improve a coastal fish community survey.
This situation is same as fisherman. Therefore, the stock may not sustain if catch amount increase or there
is no management. So, the optimal strategy of the allocation of boat (effort) for fishing is theoreticallyconsidered in the talk.
The optimal strategy of the fish boat, catch and fish amount, we suggest the model incorporating thesefactors. We consider a simple model which is constructed by two fishing ground and one port. Total fishboat is constant in the port. These one takes two states, one is operating fishery, and the other is absent
among total boat. Of course, operating fish boat can be separate the boat going to one fishing ground orothers.
For an analysis, we consider several situations on the fish stock dynamics, in other words, to assume
the several types of movement, and population dynamics. Under the situation, we virtually operate fish boat
allocation. Furthermore, all boat has same fishing ability, so the effort is proportional to the fish boat.
Finally, we discuss the balance of allocation of fish boat based on several types of fish.
REFERENCES[1] J. E. Ross, C. M. Mayer, J. T. Tyson & E. J. Weimer, 2016. Comparison of Electrofishing Techniques and Effort
Allocation across Diel Time Periods, Seasons, Sites, and Habitat in the Ohio Coastal Waters of Western Lake Erie.
North American Journal of Fisheries Management, 36: 85–95.

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P-35
JSMB2016 Fukuoka
Kodai Sato
Dept. of Elec., Eng. & Biosci., Waseda University, Tokyo, Japane-mail: kodaisato1@gmail.com
Shin Watanabe
Dept. of Elec., Eng. & Biosci., Waseda University, Tokyo, Japan
Atsuko Takamatsu
Dept. of Elec., Eng. & Biosci., Waseda University, Tokyo, Japan

Zone planning for emergency evacuation using physarum algorithm
Natural disasters, e.g. the Greatest East Japan Earthquake, sometimes bring a large number ofcasualties. Effective emergency evacuation planning is very important to save such people. In this poster,a zone planning method for emergency evacuation is proposed using a bio-inspired algorithm of physarum[1]. The easiest method for zone planning is that using Voronoi diagram. It is known as a method forpartitioning of a plane into regions each of which includes a specific point as a shelter. In this method,
distance between any points inside the specific regions and the shelter is minimized. However, this method
takes no account of actual routes on the road network. The physarum algorithm mimics adaptive network
formation observed in plasmodium of phsarum [1]. The algorithm can be applied to multi-objective
optimization problem on networks.
Zone planning for emergency evacuation was calculated using physarum algorithm (PA). The results
are evaluated using two performance functions related to cost and congestion degree [2], comparing withthe results calculated by network Voronoi diagrams (ND) [3].
Congestion degree calculated by PA increases according to a control parameter µ, which represents
an adaptive process of tubular structures in the road network, while the value by ND is always large thanthose by PA (1.2≤µ≤2.2). In contrast, cost calculated by PA degreases monotonically, while the value by
ND is in the middle of those in PA. The network performances calculated using PA are optimized multiobjectively under certain range of parameter µ.
REFERENCES[1] Tero, Atsushi, Ryo Kobayashi, and Toshiyuki Nakagaki. "A mathematical model for adaptive transport networkin path finding by true slime mold." Journal of theoretical biology 244.4 (2007): 553-564.
[2] Watanabe, Shin, et al. "Traffic optimization in railroad networks using an algorithm mimicking an amoeba-likeorganism, Physarum plasmodium."Biosystems 105.3 (2011): 225-232.
[3] Okabe, Atsuyuki, et al. "Generalized network Voronoi diagrams: Concepts, computational methods, andapplications." International Journal of Geographical Information Science 22.9 (2008): 965-994.

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P-36
JSMB2016 Fukuoka
Takuya Sekiguchi
National Institute of Informatics
e-mail: sekiguchi_takuya@nii.ac.jp
Kohei Tamura
Tohoku University
Naoki Masuda
University of Bristol

How population clusters predict the population growth in Japan
Population trends are often measured and discussed on the basis of administratively defined
subdivisions of countries. However, residential mobility and the birth rate can be affected by thesocioeconomic and geographic factors, which are independent of administratively defined borders. In thepresent study, we extract population clusters, applying the city clustering algorithm [1, 2] to Population
Census of Japan, and analyze the population growth in each cluster during the period from 2000 to 2010.
Our statistical analyses show that the population density, the male-to-female ratio, and the shape of thecluster have significant effects on the population growth within the cluster. We also report how those factors
affect the changes in the shape of the cluster.
REFERENCES[1] Rozenfeld, H. D., Rybski, D., Andrade, J. S., Batty, M., Stanley, H. E., & Makse, H. A. (2008). Laws of population
growth. Proceedings of the National Academy of Sciences of the United States of America, 105(48), 18702-18707.
[2] Rozenfeld, H. D., Rybski, D., Gabaix, X., & Makse, H. A. (2011). The area and population of cities: New insightsfrom a different perspective on cities. American Economic Review, 101(5), 2205-2225.

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P-37
JSMB2016 Fukuoka
Mayumi Seto
Faculty of Sciences, Nara Women’s University, Nara, Japane-mail: seto@ice.nara-wu.ac.jp
Koichiro Uriu
Graduate School of Natural Science and Technology, Kanazawa University, Ishikawa, Japan
Isao Kawaguchi
Research Center for Radiation Protection, National Institute of Radiological Sciences, Chiba, Japan
Hiroyuki Yokomizo
Center for Health and Environmental Risk Research, National Institute for Environmental Studies,
Ibaraki, Japan

Cost-benefit analysis of food safety management:
The case of radioactive contaminantPublic concerns about food risks have increased due to repeating food safety incidents (e.g., bovine
spongiform encephalopathy (BSE), microbial and chemical contaminations) in the past few decades.
Early hazard identification and prompt safety regulation on sale and consumption of contaminated foodare important for the protection of consumers’ health. Strict food safety regulations can reduce consumers’
health risk, whereas food safety policy attempting to achieve zero risk may increase economic costs
involved with prolonged regulations.
In this study we propose a theoretical approach to analyze consumers’ benefit by avoiding food risk
and producers’ cost by restriction on food export, both of which are associated with food restriction
period. The food restriction period is controlled by the probability of food samples passing a safety test,
which depends on both food safety regulation policy (e.g., the number of samples, the condition forremoval of food restriction) and the dynamics of contaminants [1]. Consumers’ risk and benefit are
estimated from the amount of dose that is avoided until the restriction is removed. Meanwhile, producers’
cost is evaluated from the economic losses due to product bans during the food restriction period.
We applied our approach to the case of radioactive contamination (especially 134Cs and 137Cs
contamination) on food caused by the nuclear accident at the Fukushima Daiichi nuclear power plant on
March 11, 2011, and following food safety management adopted by the Japanese Ministry of Health,Labour and Welfare. The results suggested that the rapid decrease of radioactive cesium in the mostcommon foods could keep the potential dose exposure per consumer lower than the permissible dose
limit, which is consistent with the previous studies (e.g., [2]). Although the consumers’ benefit tends tobe bounded, the producers’ cost is accumulated throughout the food restriction period, which emphasis
the importance of considering both cost and benefit of food safety regulation when adopting a food safety
policy.
REFERENCES[1] Seto, M. and Uriu, K., 2015 Organizer, 2016. Sample Size Allocation for Food Item Radiation Monitoring and
Safety Inspection. Risk Anal. 35, 409–422.
[2] Harada, K. H., Fujii, Y., Adachi, A., Tsukidate, A., Asai, F., Koizumi, A., 2012. Dietary intake of radiocesiumin adult residents in Fukushima prefecture and neighboring regions after the Fukushima nuclear power plant
accident: 24-h food-duplicate survey in December 2011. Environ. Sci. Technol., 47(6): 2520–2526.

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P-38
JSMB2016 Fukuoka
Hironori Fujita
National Institute for Basic Biology, Okazaki, Aichi 444-0867 Japane-mail: hfujita@nibb.ac.jp
Masayoshi Kawaguchi
National Institute for Basic Biology, Okazaki, Aichi 444-0867 Japan
Keiko U. Torii
Howard Hughes Medical Institute, University of Washington, Seattle, WA 98195 USA

Pattern density control in Turing systems
The self-organization of stable patterns is critical in the field of developmental biology and has been
explained by the Turing mechanism, in which the interactions among diffusible molecules translate into
stable patterns. However, such stable patterns induced by the Turing mechanism are difficult to be predictedfrom model dynamics. Thus, these patterns are usually investigated using numerical simulations. In thisstudy, we found that the pattern density (proportion of area with a high concentration of dynamics
molecules) is correlated with the relative equilibrium position between the upper and lower constraints.
Based on this finding, we established a theoretical method that can predict pattern density according tomodel dynamics and successfully applied this method to a representative case of animal skin color
patterning. This relationship between pattern density and equilibrium position is detected in various Turingsystems, including linear and nonlinear dynamics, activator–inhibitor-type dynamics, and substrate–
depletion-type dynamics. Our method may be widely applicable to self-organized patterns induced by theframework of local activation and long-range inhibition. Thus, this application would be a powerful andreliable tool for elucidating developmental mechanisms in biological systems.
REFERENCES[1] Shoji, H., Iwasa, Y., Kondo, S., 2003. Stripes, spots, or reversed spots in two-dimensional Turing systems. J. Theor.
Biol. 224: 339-350.
[1] Miyazawa, S., Okamoto, M., Kondo, S., 2010. Blending of animal colour patterns by hybridization. Nat. Commun.
1: 66.

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P-39
JSMB2016 Fukuoka
Ryosuke_Kohno
Graduate School of Life and Medical Sciences, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe,
Kyoto, Japan
Yoshiki_Kamiya
Graduate School of Life and Medical Sciences, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe,
Kyoto, Japan
Hiroshi_Kawakami
Faculty of Engineering, University of Tokushima, 2-1 Minamijohsanjima-cho, Tokushima, Japan
Masatomo_Matsushima
Faculty of Life and Medical Sciences, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe, Kyoto,Japane-mail: mamatsus@mail.doshisha.ac.jp

Classifying of synchronization pattern in oscillator circuits with optical signal
In this presentation, We introduce the synchronization phenomenon patterns of the square wave
oscillator. These oscillators were introduced SEKIKAWA et al., 2011[1].
They are controlled by an optical signal. There are three kinds of oscillator circuits. Two kinds of theircircits are designed by arranging the position of a electornic element (phototransistor), and another circit
are designed without a phototransistor. Phototransistor plays a role to sense light of the LED. Therefore,
these oscillator circits are called “Electric fireflies’’ or “LED fireflies’’.
This time, we inform new discovery. When three oscillator circits are coupled circularly, Blinking of
the lights of the LED turn around. Example, clockwise or counterclockwise. This phenomenon does notlast long. After having done about ten laps, blinking of the lights become the different mode. This mode isthat reversing synchronization by two circits (forward synchronization) and another circit. Thisphenomenon has multiple stability.
We consider that this phenomenon resembles the transmission circits of the brain. And so, we callthese circits “Optical network’’. Analysis of the multiple stability is necessary for the control of the optical
network. But, the multiple stability is too complicated, and it is difficult to analyze it by a true circit.
We model these oscillators circits in substitution for a true circit. We use “MapleSim’’ for modeling.
We introduce analysis by MapleSim.
REFERENCES[1]

Munehisa SEKIKAWA, Keiko KIMOTO, Takashi KOHNO, Hiroshi KAWAKAMI, and Kazuyuki AIHARA,
2011. Synchronization phenomena in square-wave oscillators with optical coupling. IEICE Technical Report,
CAS2011-45,NLP2011-72: 73–78.

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P-40
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P-41
JSMB2016 Fukuoka
Naoto Shingu
Kyushu University
e-mail: kiani127x525y@gmail.com
Akiko Nakamasu
Kyushu University
e-mail: nakamasu@anat1.med.kyushu-u.ac.jp
Takashi Miura
Kyushu University
e-mail: miura_t@anat1.med.kyushu-u.ac.jp

Mathematical analysis for aging effects of endothelial cells on their self-organizedpattern size
Vascular networks spread around the body and deliver nutrients and oxygen to various tissues.
Vascular endothelial cells cover the lumen of blood vessels and have the capacity to make self-organizedpatterns. When HUVECs are cultured on Matrigel, a kind of extracellular matrix, they generate the net-likepattern autonomously.
With this culture system, we found that their pattern size varies depending on the passage numbers ofcomponent cells, suggesting ageing of cells affect the pattern size. Consistent with this observation, it has
been reported that vascular endothelial cell specific ARIA (apoptosis regulator through modulating IAP
expression) gene, inhibitor of apoptosis, is increased in the aged cells [1]. Gene knock down experimentsshows that the ARIA functions to reduce apoptosis then accelerated chemotactic cell migration and tube
formation (i.e. the reduction of the pattern size) [1],[2].
In this work, we mathematically analyze these two effects (apoptosis and chemotaxis) on pattern size.
We used well-known Keller-Segel model that was reaction-diffusion system with a chemotaxis term to theanalysis of this system. To consider the effects of apoptosis and chemotaxis, at first we performed linear
stability analysis to obtain the fastest growing wavenumber. Then the Monte Carlo methods were used toreveal the qualitative change of the most-unstable wavelength as particular parameters (related to apoptosis
and chemotaxis) were increased. For qualitative understanding of effects of the parameters, geometricalanalysis using null clines was also performed. We plot null clines of two components against the wave
number k. It was predicted that the wavelength became approximately most unstable when the differenceof the slopes of two null clines was maximum. The wavelength derived from dispersion relation wascompared to that obtained by null clines.
REFERENCES[1] Ikeda, K., et al., 20011. Apoptosis regulator through modulating IAP expression (ARIA) controls thePI3K/Akt pathway in endothelial and endothelial progenitor cells. PNAS, 108: 9472–9477.
[2] Koide, K., et al., 2009.Identification of ARIA regulating endothelial apoptosis and angiogenesis by mofulating
proteasomal degradation of clap-1 and clap-2. PNAS, 106: 8227–8283.

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P-42
JSMB2016 Fukuoka
Hiroto Shoji
Kyoto Prefectural University of Medicine
e-mail: shoji@koto.kpu-m.ac.jp

Physical Analysis of Branching Patterns of Sinusoidal Networks in Hepatic Lobule
The liver is one of the most important organs and is capable of regenerating itself [1]. The sinusoid isdefined as a small blood vessel and the bile canaliculi is a thin tube that collects bile secreted fromhepatocytes; these two tubes are arranged along cords of hepatocytes, without crossing each other. Sincemorphology changes of branching networks cannot be fully understood in two dimensions, threedimensional (3D) analysis is needed for mathematical understanding of morphology. Confocal microscope
images are useful for observing 3D structures; however, it is necessary to explicitly describe the vessel
structures using 3D images of sinusoidal endothelial cells. For this purpose, we proposed a new approach
for image segmentation based on the Turing reaction-diffusion model, in which temporal and spatial patters
are self-organized. Turing conditions provided reliable tools for describing the 3D structures. Using the
proposed method, the sinusoidal patterns of rat fed a high-fat/high-cholesterol diet were examined; theserat exhibited pathological features similar to those of human patients with nonalcoholic steatohepatitis
related to metabolic syndrome. The findings showed that the parameter in diffusion terms differedsignificantly among the experimental groups [2]. Moreover, we also discuss the relationship between
structures and functions of the biological branching system of sinusoid. To quantify the structural propertiesof the branching systems and the physical properties of fluid dynamics on the systems, a branching networkmodel introduced [3].
REFERENCES[1] Sheila, S. and Dooley, J., 2002. Diseases of the liver and billary systems. Willey-Blackwell.
[2] Shoji, H. and Yamada, K., A reaction-diffusin algorithm for segmentation of three-dimensional sinusoidal networks
in rats fed a high-fat and high-cholesteril diet. (submitted).
[3] Shoji, H., Sakuma, S., Hontani, H., Akahoshi, K. and Kudoh, A., 2016. Three-dimensional periodic network patternsof micro structures in rat liver from a view of fractal analysis. RIMS Kokyuroku, 1994: 94–100.

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P-44
JSMB2016 Fukuoka
Takaaki Yonekura
Botanical Gardens, Graduate School of Science, The University of Tokyo
Hakusan 3-7-1, Bunkyo, Tokyo 112-0001, Japane-mail: yonekura@ns.bg.s.u-tokyo.ac.jp
Munetaka Sugiyama
Botanical Gardens, Graduate School of Science, The University of Tokyo

Analysis of orixate phyllotactic patternwith expanded Douady and Couder's model
Phyllotaxis is the arrangement of leaves around a stem. Research on phyllotaxic pattern generation
has a long history, and already in the early days, morphological studies attributed phyllotactic patterning to
the nature that a new leaf primordium is formed in the largest gap between existing primordia, and as far
away as possible from them on the periphery of the shoot apical meristem (SAM), which later led to the
hypothesis that the position of primordium formation is determined under the influence of the inhibitory
effect by the preceding primordia. Many mathematical models have been constructed based on thishypothesis and succeeded in the generation of several major types of phyllotactic patterns. Of these, here
we focus on the simple and powerful models proposed by Douady and Couder (DC models); DC model I
and DC model II [1, 2].
DC model I assumes periodical formation of leaf primordia one by one at the position on the SAM
periphery where the sum of inhibitory effects from preceding primordia is smallest, and thus it is specialized
for alternate phyllotaxis. DC model II assumes that a leaf primordium develops on the SAM peripherywhen and where the sum of inhibitory effects falls below a given threshold, and it allows whorledphyllotaxis as well as alternate phyllotaxis. In both models, the inhibitory power of each existing
primordium is fixed to be constant, and the inhibitory effect is supposed to decline with the distance fromthe primordium.
Computer simulations with DC models revealed that most of common phyllotactic patterns, such as
distichous, spiral (with divergence angles close to the golden angle), decussate, and tricussate patterns, aregenerated by the models according to parameter settings. There are, however, still some phyllotactic
patterns that cannot be produced by DC models, an interesting example of which is orixate phyllotaxis.
Orixate phyllotaxis is a specific type of alternate phyllotaxis named from Orixa japonica, and ischaracterized by repetition of a sequence of different divergence angles; 180˚, 90˚, 180˚, and 270˚. Althoughspecies that show orixate phyllotaxis are rare, they are found in several distant taxa, suggesting that orixate
phyllotaxis occurred independently in each taxon. It is therefore likely that orixate phyllotaxis is generated
by a common regulatory mechanism of leaf primordium formation under some particular condition rather
than by an orixate-unique mechanism. If this is true, mathematical models that fully account for spatial
regulation of leaf primordium formation should be able to produce not only major phyllotactic patterns but
also orixate phyllotaxis.
In the present study, we expanded DC models by introducing primordial age-dependent changes of
the inhibitory power, and examined them for the abilities of generation of orixate phyllotaxis. The expanded
versions of both DC models I and II returned orixate phyllotaxis in computer simulation with definite rangesof parameters. Morphometrically, the orixate phyllotactic pattern produced by computer simulation using
expanded DC model II fitted well with the actual orixate patterns observed in the winter buds of Orixa
japonica.
REFERENCES[1] S. Douady and Y. Couder, 1996. Phyllotaxis as a dynamical self organizing process part I: the spiral modes resulting
from time-periodic iterations. Journal of Theoretical Biology, 178: 255–274.
[2] S. Douady and Y. Couder, 1996. Phyllotaxis as a dynamical self organizing process part II: the spontaneous
formation of a periodicity and the coexistence of spiral and whorled patterns. Journal of Theoretical Biology, 178: 275–
294.

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P-45
JSMB2016 Fukuoka
Yoshinori Hayakawa
Theoretical Biology Laboratory, RIKEN
e-mail: y.hayakawa@riken.jp
Masashi Tachikawa
Theoretical Biology Laboratory, RIKEN
Atsushi Mochizuki
Theoretical Biology Laboratory, RIKEN

Mathematical study of gene expression and morphogenesis coupling that realizes
flat leaf formation
Most of the land plants generally have dorsoventrally flat leaves, maximizing the surface area of both
upper (adaxial) side and lower (abaxial) side. The former is specialized for light capturing forphotosynthesis and the latter is specialized for gas exchange. From findings of molecular genetics, it has
been considered that the coupled dynamics between tissue morphogenesis and gene regulation for cell
identity is responsible for making flat leaves. The hypothesis claims that a flat leaf is generated under two
assumptions, i) regulations between two groups of genes specifying adaxial and abaxial sides are mutuallyrecessive, ii) cell divisions are induced at the limited region in the leaf margin where expressions of twogroups are overlapped. We examined the plausibility and possibility of this hypothesis from the dynamical
point of view. We studied a mathematical model where two processes are coupled, tissue morphogenesis
induced by cell division and deformation, and dynamics of gene regulations. We used vertex dynamics formodeling of the cell-based morphogenesis. For the second process of gene expression, we used an ODE
for the dynamics of activity of each gene in each cell under the assumption that gene activities are uniform
inside of each cell. From the analysis of the model we found that the classically believed hypothesis is not
sufficient to generate flat leaves with high probability. We examined several different modifications andrevision of the model. Then we found that a simple additional rule of polarized cell division facilitates flat
leaf formation. The result of our analysis gives prediction of possible mechanism, which can be easily
verified in experiments.

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P-46
JSMB2016 Fukuoka
Kazuya Horibe1
e-mail: kazuya-horibe@ist.osaka-u.ac.jp
Ken-ichi Hironaka2,3,4
Katsuyoshi Matsushita2
Koichi Fujimoto2
1

Graduate School of Information Science and Technology, Osaka University
1-4, Yamadaoka, Suita-shi, 565-0871, Japam
2
Graduate School of Science, Osaka University
1-1, Machikaneyama-cho, Toyonaka-shi, 560-0043, Japan
3
JSPS Research Fellow(PD)Kojimachi Business Center Building, 5-3-1 Kojimachi, Chiyoda-ku, Tokyo, 102-0083, Japan
4
RIKEN Center for Developmental Biology
2-2-3 Minatojima-minamimachi, Chuou-ku, Kobe, 650-0047, Japan

Curvature-driven splitting of a planar traveling wave
Although reaction-diffusion equations provide the variety of traveling waves dynamics such as collision
and annihilation mainly on a flat surface1, little is known about the role of curved surface. Here wenumerically show the sequence of dynamics, i.e., bending, collision, annihilation and splitting of a travelingwave, can be driven by a curved surface represented by the two dimensional Gaussian function. When aplanar traveling wave of Fitzhugh-Nagumo reaction-diffusion equation2 passed through the bell-shaped
surface, its traveling direction varied depending on the local curvature; The wave first bended backwardly
into a wedge shape outlining the bell shape. Next, parts of wave passing on the both sides of the bell shaperotated into opposite directions and then collided head-on. Finally, these collision parts annihilated eachother whereas the other parts split into two parts, i.e., a ring wave surrounding the bell shape traveling to
the peak and a planar wave traveling behind the bell shape to same direction as the initial condition. The
sequence to wave splitting occurred above a threshold ratio of the height and width of the bell shape. The
wave split utilizing the curvature information could function as a signal processing on convoluted surface
such as amoeboid cells3 and brain cortex4.
REFERENCES[1] S.Ei, M.Mimura, M, Nagayama, Physica D, 165 (2002): 176-198[2] R. Fitzhugh, Biophys. J., 1 (1961): 445–466[3] D. Taniguchi et al., PNAS, 110 (2013): 5016-5021[4] E. Santos, M. Schöll, R. Sánchez-Porras et al., Neuroimage, 99 (2014): 244–255- 251 -

P-47
JSMB2016 Fukuoka
Osamu Iizuka
Kyushu University School of Medicine, Fukuoka, Japane-mail: 1MD14002G@s.kyushu-u.ac.jp
Akiyoshi Uemura
Graduate school of Medicine, Nagoya City University
Takashi Miura
Kyushu University Graduate School of Medical sciences, Fukuoka, Japan

Mechanism of Scaling law formation in developing retina vasculature
During retina development, the endothelial cells migrate from optic disk on part of preexisting fineastrocyte mesh to form initial network structure [1]. Later blood flow is established, results in remodelingof initial vascular network. In adult retina vasculature, certain scaling law was observed by box countmethod [2]. In the present study, we tried to understand how the scaling law is established during
development.
At first, we measured the number and size distribution of islands surrounded by capillary meshwork.
The log-log plot showed single peak sandwiched by two linear relationships in larger and smaller scale.
We try to understand these characteristics separately.
(1) Existence of peak can be reproduced by assuming repulsive cell-cell interaction. Single peak
represents there is a mechanism to generate structure of similar size. We tried to understand thischaracteristic by voronoi division. We considered astrocyte meshwork structures as voronoi polygon
generated by repulsion by Muller glia cells [3], and investigated features of voronoi polygon. In thisprocess, we derived the size distribution of 1D voronoi division and predicted the size distribution ofmultidimentional voronoi division. By using this prediction formula, we found that astrocyte meshwork
structures are considered as voronoi division.
(2) Larger scale relationship can be interpreted by the formation of avascular zones around arteries. Largeislands are mainly distributed in avascular zone in which some of the meshwork is removed stochasticallyaround the arteries. We model this phenomenon by a size distribution of one dimensional rectangularmesh whose boundary are randomly removed. Simple analysis showed that the size distribution should be
linear on log-linear plot.
(3) Smaller scale relationship comes from formation of random connection between endothelial cells.
REFERENCES

[1]

[2]
[3]

A. Uemura, M. Ogawa, M. Hirashima, T. Fujiwara, S. Koyama, H. Takagi, Y. Honda, S. J. Wiegand, G. D.
Yancopoulos, and S.-I. Nishikawa, “Recombinant angiopoietin-1 restores higher-order architecture of
growing blood vessels in mice in the absence of mural cells,” Journal of Clinical Investigation, vol. 110, no.
11, pp. 1619–1628, Dec. 2002.
P. Ball, Flow. Oxford University Press, 2011.
A. Reichenbach and A. Bringmann, “New functions of Müller cells,” Glia, vol. 61, no. 5, pp. 651–678, Feb.
2013.

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P-48
JSMB2016 Fukuoka
Sang-Woo Lee
RIKEN QBiC, Kobe, Japane-mail: ledman97@gmail.com
Yoshihiro Morishita
RIKEN QBiC, Kobe, Japan

Neutral cell competition and tissue growth efficiency
Cell competition was originally reported as the competition between two cell populations withdifferent genetic backgrounds. On the other hand, recent studies reported that non-negligible number ofcells are extruded from developing tissues even in a genetically-identical cell population [1-4]. Not only insuch experimental studies, in mechanical simulations for epithelial tissue, cell extrusion is observed evenwhen mechanical/growth parameters are identical for all cells. In this manner, the extrusion of a portion ofcells from tissues itself is not necessarily due to the difference in genetic background, and not programmeda priori. In that sense, the extrusion from a genetically homogeneous tissue may be referred as a result of“neutral” cell competition (NCC). In contrast to NCC, the competition between the cell populations withdifferent genetic background which is caused through specific signaling pathways may be called“regulatory” cell competition (RCC). We here studied mechanisms of NCC because we can approach itfrom a pure mechanical viewpoint independently of specific chemical signaling and gene regulation thatare not fully understood.
In this study, we first introduce two kinds of fitness, cellular and tissue-level ones. Regarding eachcell population with a certain growth/mechanical trait as “species”, the time derivative of its logarithmic
growth curve defines a fitness measure of the species. On the other hand, when different cell populations
with different traits are mixed, the growth rates of each population and the whole tissue are different ingeneral. Then tissue-level fitness is defined as the average of cellular fitness between species weighted by
the frequency of each species. Importantly, in the mixed situation, both cellular and tissue-level fitness
varies over time as a result of the change in the frequency distribution of species constituting the focal
tissue through competition between them.
After defining the fitness, by numerical simulations of vertex dynamics model, we examined thedependence of cell extrusion rate or cellular fitness on mechanical/growth parameters of cells in the casesof pure population. We found that the dependence was summarized in how those parameters affectgeometrical and stress heterogeneity in tissues. By using the results, we proposed possible feedback
mechanisms depending on cellular stress state, which reduces the energetic loss due to cell extrusion.
Furthermore, we examined what happens through competition in a population where cells withdifferent mechanical traits are mixed. When daughter cell epigenetically inherited its parent’s trait, the trait
distribution within the tissue drastically changed with the tissue growth and, as a result, the fitness at thetissue-level increased, clearly showing that the NCC can improve tissue growth efficiency through theselection of cell mechanical traits, i.e., intra-tissue “evolution”. Further, through the selection, cellular
phenotype was homogenized, which is considered to be another possible role of NCC. From a moretheoretical side, we proposed another differential equation model of competition dynamics that permits toapproximately calculate the time evolution of tissue-level fitness and trait distribution. The model is usefulin predicting what happens when the tissue size is much larger, e.g., reached at fully-developed size with106 cells, because direct simulations of cell-based mechanical model require immense amount ofcomputation time.
REFERENCES[1] Marinari, E. et al., 2012. Live-cell delamination counterbalances epithelial growth to limit tissue overcrowding.
Nature, 484: 542-545.
[2] Eisenhoffer, G.T. et al., 2012. Crowding induces live cell extrusion to maintain homeostatic cell numbers inepithelia. Nature, 484: 546-549.
[3] Etournay, R. et al., 2015. Interplay of cell dynamics and epithelial tension during morphogenesis of the
Drosophila pupal wing. eLife, 4: e07090.
[4] Guirao, B. et al., 2015. Unified quantitative characterization of epithelial tissue development. eLife, 4: e08519.

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P-49
JSMB2016 Fukuoka
Fumito Mori
Theoretical Biology Laboratory, Riken, Wako, Japane-mail: fumito.mori@riken.jp
Atsushi Mochizuki
Theoretical Biology Laboratory, Riken, Wako, Japan

Origin of cell diversity: Analysis of fixed points in Boolean networks
In cell differentiation, identity of cell is determined by a gene expression pattern, where a subset ofgenes is constantly active. Therefore, dynamics of gene activities based on regulatory network are expected
to have ability to generate at least as many gene expression patterns as the number of cell types. To clarify
the mechanism providing a sufficient number of gene expression patterns is important for discussing originof diversity of cell types. Boolean network model [1] has been employed to describe gene regulatory
dynamics, where a fixed point in the state space corresponds to a gene expression pattern for cell identity.
Interestingly, the average number of fixed points in randomly constructed Boolean network is just one [2].
Thus, real gene regulatory systems would have special characteristics, which may be expected to beeffective network structure of regulations and effective regulatory functions for generating various gene
expression patterns.
In this study, we investigate how the average number of fixed points in Boolean network is dependenton network structure and also biased choice of Boolean functions. Here, a network consists of a set of genes
and directed links representing existence of gene regulations. We fix network and assign a Boolean function
consistent with the network structure to every gene at random. Under the condition, we prove that the
average number of fixed points is independent of network structure and exactly one.
Next, we introduce biases in choice of functions to examine influence of them to the average numberof fixed points. We pick up one or several genes and apply bias to the choice of Boolean functions only forthese genes while the other genes have no bias. It is proven that the average number of fixed points is also
one unless the subgraph consisting of genes biased and links between them has a cycle in the regulatory
network. Moreover, we demonstrate that positive and negative feedback respectively increases anddecreases the average number of fixed points. Consequently, real regulatory networks would have positive
feedbacks appropriately.
REFERENCES[1] Robeva Raina, and Terrell Hodge, eds. Mathematical concepts and methods in modern biology: using modern
discrete models. Academic Press, 2013.
[2] Mochizuki, Atsushi. "An analytical study of the number of steady states in gene regulatory networks." Journal of
Theoretical Biology 236.3 (2005): 291-310.

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P-50
JSMB2016 Fukuoka
Shigeru Moriyama
Department of Developmental Biology, Shimane University Faculty of Medicine, Shimane,693-8501, Japane-mail: moriya12@vega.ocn.ne.jp
Junko Kuramoto
Department of Developmental Biology, Shimane University Faculty of Medicine, Shimane,693-8501, Japan
Hiroki Otani
Department of Developmental Biology, Shimane University Faculty of Medicine, Shimane,693-8501, Japan

Mathematical representation and analysis of the number of cells in the intestinal
epithelium of mouse embryos
We have been trying to represent developmental phenomena in mathematical models, and conducted
the present study on the intestinal epithelium.
We measured the number of total cells in the intestinal epithelium of mouse embryos by stereology atembryonic day (E) 11.5, 13.5, 15.5, and analyzed the data using Excel and Image J software.
We examined whether the exponential growth model of cultured cells in culture media is applicablefor the growth of the cells in the intestinal epithelium in vivo, and showed that the proliferation of cells in
the intestinal epithelium in vivo is represented by an exponential function curve.
We also confirmed that the growth of epithelial cells using an Excel built-in formula, and estimatedthe epithelial cell numbers for the other embryonic days every 0.5 day.
Whereas sections of the intestine are elliptic, we hypothesized that the genuine intestinal tract is acylinder. We measured the minor axis of the ellipses of the epithelial-mesenchymal boundary, built an
approximation formula, and using the formula we predicted the minor axis of the other parts of theintestinal tract.
We also measured the length of the inner circumference of the epithelium and observed that itchanges in a similar manner with the minor axis of the ellipse. We calculated the tilting angle of theellipse of each cross-section against the cylinder, and corrected the length of the inner circumference.
We showed that epithelial outside diameter and the inner circumference of E15.5 changed in a
stepwise manner along the long axis of the intestinal tract.
REFERENCES[1] 巌佐庸，数理生物学入門 1998, 2-7.
[2] 倉本純子，2015. マウス胎仔の腸管上皮における細胞数の計測，島根大学大学院医学系研究科修士論
文， 2015, 3.
[3] Matsumoto A., Hashimoto K., Yoshioka T., Otani H., 2002. Occlusion and subsequent re-canalization in early
duodenal development of human embryos: integrated organogenesis and histogenesis through a possible
epithelial-mesenchymal interaction. Anatomy and Embryology, 205: 53-65.
[4] 森山茂，2016. マウス胎仔の腸管上皮における細胞数と発生過程の数理表現と解析，島根大学大学院
医学系研究科修士論文，2016, 3.

This work was supported by KAKENHI (23112006)
COI: None- 255 -

P-51
JSMB2016 Fukuoka
Yuto Naroda
Kyushu University Faculty of Medicine
e-mail: nrdyt0117@yahoo.co.jp
Kenji Yoshimura
Department of Neurology, Osaka City General Hospital
Yoshinaga Kajimoto
Department of Neurosurgery, Osaka Medical College
Tomohisa Ohmura
Department of Neurosurgery, Osaka Medical College
Takashi Miura
Kyushu University Graduate School of Medical Sciences

Mathematical analysis of fractality of skull sutures
Skull suture has been regarded as typical example of fractal structure in biology. Theoretical models
based on Eden front [1] or Diffusion-Limited Aggregation (DLA) [2] had been proposed. We havepreviously shown that the maintenance of suture tissue width and formation of interdigitation in skull
suture can be reproduced by reaction-diffusion framework [3]. Simple reaction-diffusion model can only
produce structure with single characteristic length. To generate a fractal structure in this framework, we
introduced a time-dependent parameter in the model. By this effect, the model generates larger structure
at first, and it gradually adds smaller structures to preexisting larger structures.
To examine whether this mechanism is actually working in vivo, we observed time course of humanskull suture development by 3DCT. Contrary to our expectation, small and large structures appeared
simultaneously during suture development. These data are more consistent with Eden and DLA typemechanisms. Therefore, we need to modify the model to generate fractal structure from the early phase ofpattern formation.
We are now trying to incorporate Eden like effect in biologically plausible context. At first wedeveloped an intuitive explanation why random growth of interface can generate fractal pattern using
simplified Eden model. Next, we formulated a model with biologically plausible assumption in which
mesenchyme cells differentiate into bones in situ, and their differentiation capacity is stochastic.
Numerical simulation of the model generated fractal structure, and we found that simplified version of themodel is equivalent to simplified Eden model.
REFERENCES
[1]
[2]
[3]

Y. Oota, T. Nagamine, K. Ono, and S. Miyazima, “A Two-Dimensional Model for Sagittal Suture of Cranium,”
Forma, vol. 19, pp. 197–205, 2004.
C. P. E. Zollikofer and J. D. Weissmann, “A bidirectional interface growth model for cranial interosseous suturemorphogenesis,” J Anat, vol. 219, no. 2, pp. 100–114, May 2011.
T. Miura, C. A. Perlyn, M. Kinboshi, N. Ogihara, M. Kobayashi-Miura, G. M. Morriss-Kay, and K. Shiota,“Mechanism of skull suture maintenance and interdigitation,” J Anat, vol. 215, no. 6, pp. 642–655, Dec. 2009.

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P-52
JSMB2016 Fukuoka
Toshiki Oguma
School of Medicine, Kyushu University
e-mail: t.oguma.111@s.kyushu-u.ac.jp
Tomoharu Shinoda
Graduate school of Medicine, Nagoya University
Shuntaro Ogura
Graduate school of Medicine, Nagoya City University
Akiyoshi Uemura
Graduate school of Medicine, Nagoya City University
Takaki Miyata
Graduate school of Medicine, Nagoya University
Takashi Miura
Graduate school of Medicine, Kyushu University
The effect of cell dynamics on Delta-Notch pattern formation during retinal angiogenesis
Delta-Notch interactions have an important role for development and maintenance of vascular pattern inangiogenesis. Delta and Notch are membrane proteins, the former is ligand and the latter is receptor.
Lateral inhibition by Delta and Notch results in spatially alternate pattern in 1D [1]. The expression
pattern of Dll4 in retinal vasculature falls into three categories: alternate, sporadic and homogeneous [2].
Arteries show alternate pattern and veins show homogeneous pattern. Expression of Dll4 contribute toprevent oversprouting [3].
We examined the effect of endothelial cell movement [4] and proliferation [5] on Delta-Notch patternformation during retinal angiogenesis. We experimentally observed cell dynamics in retina organ culture,and the results show random endothelial cell movements and cell divisions in a region-specific manner.
Based on these experimental results, we formulated a minimal model of Delta-Notch interaction and cell
dynamics that is analytically manageable. In the model, we regarded random cell movement as a flip of
two the neighboring cells and cell division as duplication of a cell. We reproduced the three patterns
observed in vivo by numerical calculations and analytically derived the instability condition. These results
are consistent with experimental results and suggest that local differences of mobility and cellproliferation critically affect Delta-Notch patterns in endothelial cells.
REFERENCES[1] Collier, J. R., Monk, N. A. M., Maini, P. K., & Lewis, J. H. (1996). Pattern Formation by Lateral Inhibition with
Feedback: a Mathematical Model of Delta-Notch Intercellular Signalling. Journal of Theoretical Biology, 183(4), 429–
446. http://doi.org/10.1006/jtbi.1996.0233[2] Claxton, S., & Fruttiger, M. (2004). Periodic Delta-like 4 expression in developing retinal arteries. Gene
Expression Patterns. GEP, 5(1), 123–7. http://doi.org/10.1016/j.modgep.2004.05.004[3] Kim, J., Oh, W. J., Gaiano, N., Yoshida, Y., & Gu, C. (2011). Semaphorin 3E-plexin-d1 signaling regulates VEGF
function in developmental angiogenesis via a feedback mechanism. Genes and Development, 25(13), 1399–1411.
http://doi.org/10.1101/gad.2042011[4] Arima, S., Nishiyama, K., Ko, T., Arima, Y., Hakozaki, Y., Sugihara, K., … Kurihara, H. (2011). Angiogenic
morphogenesis driven by dynamic and heterogeneous collective endothelial cell movement. Development (Cambridge,
England), 138(21), 4763–76. http://doi.org/10.1242/dev.068023[5] Uemura, A., Ogawa, M., Hirashima, M., Fujiwara, T., Koyama, S., Takagi, H., et al. (2002). Recombinantangiopoietin-1 restores higher-order architecture of growing blood vessels in mice in the absence of mural cells. Journalof Clinical Investigation, 110(11), 1619–1628. http://doi.org/10.1172/JCI200215621- 257 -

P-53
JSMB2016 Fukuoka
Daiki Sasaki
Department of anatomy and cell biology, Graduate School of Medical Sciences, Kyushu University, 3-1-1
Maidashi, Higashi-ku, Fukuoka, Japane-mail: s-daiki@anat1.med.kyushu-u.ac.jp
Takashi Miura
Department of anatomy and cell biology, Graduate School of Medical Sciences, Kyushu University

A mathematical model for meshwork formation of endothelial cells in fibrin gel
Vasculogenesis is the process that the first primitive vascular plexus is made from endothelial
progenitor cells in the embryo. In vitro experimental system of vasculogenesis is extensively studied. In
this culture system, Human Umbilical Vein Endothelial Cells (HUVECs) are cultivated on Matrigel.
Within 24 hours, these cells form meshwork structure that resembles capillary plexus. To make amathematical model for vasculogenesis, Murray et al. used a deformation of the extracellular matrix [1].
Serini et al. use chemotaxis model based on vascular endothelial growth factor (VEGF) [2].
In this study, we focused on the pattern formation of HUVECs embedded in the fibrin gel. The cells
also produce meshwork spontaneously. This system was considered to be particularly useful since it
develops perfusable capillary meshwork. However, the deformation of substrate and the gradient of
VEGF in fibrin gel is not observed as in the Matrigel system described above. In fibrin system, cells
themselves do not move but make protrusions actively to connect to the adjacent cell.
Time-lapse observation revealed
1. Cells do not move, but make protrusions actively.
2. Protrusions repeat extension and collapse.
3. Whenever the protrusion collides with the surface of the adjacent cell, connection is established.
4. Formation of the protrusion is not affected by the neighboring cells.
5. Collapse speed is higher than extension speed.
6. Two neighboring cells have higher probability to connect when they are closer.
.
Based on these findings, we constructed a mathematical model for the extension of a protrusion,using discrete-time stochastic process. A protrusion extends at a rate c per unit time, and it connects to aneighboring cell when it collides with the surface of the adjacent cell. The protrusion collapses at
probability p per unit time, and the length becomes 0 instantaneously. We assume the time for meshwork
formation as t, the distance between the cell membranes as l. Then, the connection probability function
P(t, l) is expressed as following recurrence equation

P (t + 1, l) = P (t, l) + {1P (tl, l)}p(1
c

l

p) c

.
We obtained an analytical solution of P(t, l) by taking continuous limit of the recurrence equationand the boundary conditions (When t < l/c, P(t, l) = 0, When t = l/c, P(t, l) = (1-x)^(l/c) ) as follows:

Using the solution, we can evaluate connection probability of two cells in two dimensions.
Numerical simulation of connection formation of randomly dispersed cells reproduces morphology ofobserved endothelial meshwork.
REFERENCES[1] Manoussaki, D., Lubkin, S. R., Vernon, R. B. & Murray, J. D., 1996. A mechanical model for the formation ofvascular networks in vitro. Acta Biotheor. 44: 271–82.
[2] Serini, G. et al., 2003. Modeling the early stages of vascular network assembly. EMBO J. 22: 1771–9.
[3] Miura, T. & Tanaka, R., 2009. In vitro Vasculogenesis Models Revisited - Measurement of VEGF Diffusion in
Matrigel. Math. Model. Nat. Phenom. 4: 118–130.

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P-54
JSMB2016 Fukuoka
Hisako Takigawa-Imamura
Anatomy and Cell Biology, Graduate School of Medical Sciences, Kyushu University, Fukuoka, Japane-mail: hisaima@med.kyushu-u.ac.jp
Takashi Miura
Anatomy and Cell Biology, Graduate School of Medical Sciences, Kyushu University, Fukuoka, Japan

Emergence of hierarchical structure of lung: a model and observation of cellularresponse to FGF
We investigated how the hierarchical branch formation is regulated during lung developmental
process. It has been considered that the high sensitivity of cells to the distribution of FGF within thedeveloping lung is the principle mechanism guiding shape change. We experimentally examined thecellular responses to FGF10 in lung epithelium. It was demonstrated that uptake of FGF10 by epithelial
explants of the pseudoglandular stage lung in Matrigel was sensitive over a wide range of FGF10
concentrations. It was also shown that MAP kinase activity downstream of FGF10 was affected by theepithelial explant size and shape as well as the FGF10 concentration. The cellular responses of lungepithelium showed higher dependency on the FGF10 concentration in embryonic day 13.5 (E13.5) thanE14.5. To assess how these cellular responses result in shape formation of the lung epithelium, weconstructed a mathematical model in which an epithelial tip splits depending on the proliferative andchemotactic activities. It was revealed that higher contrast in the activities resulted in the longer segment
length of branches, which is reminiscent of the actual lung pattern where segment lengths are longer inearlier branches.

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P-55
JSMB2016 Fukuoka
Masaki Sekiguchi
Tokyo Metropolitan Ogikubo High School, Tokyo, Japane-mail: emafarms@gmail.com
Emiko Ishiwata
Tokyo University of Science, Tokyo, Japane-mail: ishiwata@rs.tus.ac.jp
Yukihiko Nakata
Shimane University, Shimane, Japane-mail: ynakata@riko.shimane-u.ac.jp

Effect of time delay for an ultra-discretized logistic equation
Ultra-discretization is proposed as a special procedure to obtain a discrete system. There are various
ultra-discrete models related to the cellular automaton and traffic flow, but few examples of the applicationof ultra-discretization in mathematical epidemiology.
In this presentation we introduce two ultra-discrete models derived from logistic type differential
equations and discuss dynamical properties regarding global attractivity as in [2, 3] and periodicity of thesolution. Here logistic equations appear from epidemiological models with waning immunity, such as SIS
and SIRS models. It is shown that our ultra-discrete model capture the qualitative dynamics of a delayed
SIS epidemic model by Cooke [1]. Potential use of the ultra-discrete model to analyze the periodic
oscillation is also discussed.
REFERENCES[1] Cooke, K. L., 1979. Stability analysis for a vector disease model. Rocky Mt. J. Math., 7: 253–263.
[2] Kocic, V. L. and Ladas, G., 1993. Global behavior of nonlinear difference equations of higher order with application.
Kluwer Academic Publishers.
[3] Ruan, S., 2006. Delay differential equations in single species dynamics. Delay Differential Equations andApplications. Springer, 477-517.

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P-56
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P-57
JSMB2016 Fukuoka
Yohei Saito
Institute of Industrial Science, University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505 Japane-mail: yoheis@sat.t.u-tokyo.ac.jp
Yuki Sughiyama
Institute of Industrial Science, University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505 Japan
Kunihiko Kaneko
Department of Basic Science, University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153-8505 Japan
Tetsuya J. Kobayashi
Institute of Industrial Science, University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505 Japan

Discreteness-induced transition in multi-body reaction systems
Finiteness of system size may cause qualitative change in dynamics and small-system size
effect attracts much attention in various fields of study, e.g., systems biology (stochastic chemical
reactions), ecology (population dynamics), game theory, and social networks (agent dynamics).
Increase in multiplicative noise-intensity owing to smaller system size can induce qualitativetransition of stationary distribution, which has been known as noise-induced transition and has been
investigated well since 1970s [1]. Although finite system size not only increases noise intensity but
also emphasizes the state space discreteness, the role of discreteness of state space has rarely beenstudied [2].
In this work [3], we propose a simple 1- and 3-body reaction system as a toy model which
exhibits pure discreteness-induced transition and obtain a sufficient condition under which thediscreteness induced transition arises. Furthermore, we find that the critical size of discretenessinduced transition can become quadratically large, if multi-body reactions are allowed.
REFERENCES[1] W. Horsthemke and R. Lefever, Noise-Induced Transitions in Physics, Chemistry, and Biology (Springer, 2006).
[2] Y. Togashi and K. Kaneko, Phys. Rev. Lett. 86, 2459 (2001).
[3] Y. Saito, Y. Sughiyama, K. Kaneko, and T. J. Kobayashi, arXiv:1605.06273.

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P-58
JSMB2016 Fukuoka
Yuki Sughiyama
Institute of Industrial Science, The University of Tokyoe-mail: yuki.sughiyama@gmail.com
Tetsuya J. Kobayashi
Institute of Industrial Science, The University of Tokyo

Steady State Thermodynamics in Population Dynamics
Prediction and control of a population of growing cells are relevant for understanding evolution of
microorganisms and for designing effective drug treatment to pathogenic and cancer cells. Methods ofstatistical physics can contribute to resolving these problems because of a mathematical similarity between
statistical physics and population dynamics. The long term expansion rate of population size (population
growth) is an important observable in the population dynamics. In a fixed environment, the population
growth converges to a stationary growth rate, and can be evaluated mathematically by the largest eigenvalueof the time-evolution operator of the population dynamics by using the Perron-Frobenius theorem. In
contrast, in a changing environment, the evaluation of the population growth is a more difficult problem
because the higher eigenvalues non-negligibly contribute to the population growth due to disturbance ofthe convergence by the changing environment. In this study, to extract and evaluate the contribution of thehigher eigenvalues from the population growth, we employ the framework of steady state thermodynamics(SST), which is used in nonequilibrium statistical physics.
SST was established for understanding a “thermodynamics” of transitions between nonequilibrium
steady states (NESS). The core of this theory is a decomposition of total heat during environmental change
into housekeeping and excess parts. The housekeeping heat represents the sum of the stationary heatdissipations in each NESS, and the excess heat is the heat generated due to the change of environment. By
using this decomposition, Clausius inequality is formulated for the excess heat.
In this talk, by using the SST framework, we decompose the population growth into two parts, thesum of the stationary growth for each environmental condition (i.e. the contribution of the largest
eigenvalues) and the excess growth, which is generated by the switching of environment (i.e. thecontribution of the higher eigenvalues). Focusing on the excess growth, we obtain a Clausius inequality for
population dynamics, which gives the upper bound of the excess growth. The equality is achieved inquasistatic changes. We also clarify that this bound can be evaluated by ``lineage fitness”, which is anexperimentally observable quantity.
REFERENCES[1] Y. Sughiyama and T. J. Kobayashi, arXiv:1509.06448 (2015).
[2] T. J. Kobayashi and Y. Sughiyama, Phys. Rev. Lett. 115, 238102 (2015).
[3] Y. Sughiyama, T. J. Kobayashi, K. Tsumura and K. Aihara, Phys. Rev. E 91, 032120 (2015).

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JSMB2016 Fukuoka

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StairsGalleria

Stairs

1st floor
South lobbyWC

1st floor
North lobby

WC

WC

WC

2F

WC

WC

WC

Break room is open while
1st floor
Sep 7 (Wed) 13:00 – 18:00
South lobby
Sep 8WC(Thu) 13:00 – 18:00
Sep 9 (Fri) 09:00 – 15:00

StairsBreak room

WC

WC

Galleria

Stairs

1st floor

1st floor
North lobby

1F

StairsStairsReception desk

2nd floor
South lobby

StairsStairs2nd floor
North lobby Stairs

Outdoor stairs

2nd floor

A

E

Shiiki Hall

WC

WC

B

D

C

3rd floor

WC

WC

C

Plenary talkAward lecture
Board meeting
General meeting

D(304)A(301), C(303)

B

D

Oral session

A

E

B(302), D(304), E(305)

StairsStairsMini-symposia

2nd floor
East lobby

Poster exhibit area

3F