数理モデルで読み解く
ウマの群れの維持機構
名古屋⼤ 環境学研究科
学振PD 井上漱太

発表概要
1: イントロダクション: 動物の群れ
2: 実際のウマの群れ
3: ウマの群れの維持機構 (数理モデルから)
4: ウマの群れの維持機構
5: 今後の展望 + まとめ(オスの行動)Westley et al., 2018

Improvements in behavioural solutions to specific social, life
history or ecological problems are also central to the study ofculture12. The accumulation of knowledge through individual
invention and subsequent social learning has been recognized
as an important advantage of group living. In addition, culture
can accumulate progressively, or ‘ratchet’, over generations—a
process referred to as Cumulative Cultural Evolution (CCE)12–15.
CCE can allow groups to develop increasingly complex
knowledge and skills over time, beyond the capacities of asingle individual. Although CCE is a well-established research
field, the interplay between CCE and collective intelligence has so
far remained unexplored.
In the present study, our aim was to investigate the cumulative
potential of collective intelligence—and hence its capacity tosupport CCE—by devising a scenario in which we can systematically quantify both the appearance of novel innovations thatbuild on existing behaviours16 and their cross-generational
maintenance in real time.
We used collective navigation by homing pigeons, Columba
livia, as our model system, examining whether collective
intelligence undergoes cumulative changes over time in an
ecologically relevant, recurring collective problem-solving
scenario. The system has proved valuable in studies of collective
decision-making9,17 because pigeons have been shown to be able
to process information both individually and collectively:
previous work using miniature global positioning system (GPS)
個体数が増えれば正解率があがる
tracking hasrevealed that (i) given sufficient experience,individual birds develop idiosyncratic homing routes, which
can also
they recapitulate faithfully18 and (ii) flocks Nagyet collectively
al. 2009
10
develop distinctive routes , including those obtained by the

集団的知性

Route efficiency improvement. Birds in all three treatment groups
improved steadily in homing efficiency (measured as the beeline
distance between release and home, 8.6 km, divided by the length ofthe path flown) over the first 12 flights (Fig. 2a). The performance of
single birds in the solo control group and in the first generation of theexperimental group did not differ significantly on the twelfth flighta

12 releases

12 releases

12 releases

12 releases

12 releases

Generation 1

Generation 2

Generation 3

Generation 4

Generation 5

ペアフライトにて個体を交換するだけで効率よく⾶べるb
60 releases

Solo(control)

Sasaki & Biro 2017

群れを作るメリット

Please cite this article in press as: Nagy et al., Synergistic Benefits of Group Search in Rats, Current Biolog
j.cub.2020.08.079

ll

交代で⾒回り繁殖機会 ↑

OPEN ACCESS

A

対天敵戦略

C

B

D

採⾷効率↑
迷路の探索効率上昇

Figure 1.
Repeated
Hierarchic
metrical 1(A) Hierarchand 16 end
from 1 to 1
cations (wajunction.
(B) Experim(C) Example
color-codea group tria
inhomogencessible tochamber’’ (marked byWalls werearea with a
automaticaof their un
ure S1 and(D) Examp
search. Tim
visualizatio
correspondthe start ch(Townsend et al. 2011, Nagy
2020)
test; n =et
32; al.
p = 0.21).
Also, indFirst, each rat completes a single search training period (‘‘sin-

296

W.

D.

HAMILTON“どうやって”集まる?
資源に集まるNow suppose that the frogs are given opportunity to move about on therim before the snake appears, and suppose that initially they are dispersedin some rather random way. Knowing that the snake is about to appear, will
all the frogs be content with their initial positions? No; each will have abetter chance of not being nearest to the snake if he is situated in a narrow
gap between two others. 天敵対策として
One can imagine that a frog that happens to haveclimbed out into a wide open space will want to improve his position. The
part of the pond’s perimeter on which the snake could appear and find acertain frog to be nearest
to him may be termed that frog’s “domain of
Selfish herd theory: 敵を避けるために、隣の個体に近づく
danger” : its length is half that of the gap between the neighbours on eitherside. The diagram below shows the best move for one particular frog andhow his domain of danger is diminished by it:

E%zk!%?-aLzi&x...?

xaz

But usually neighbours will be moving as well and one canimagineHamilton,
1971 aconfused toing-and-froing in which the desirable narrow gaps are as elusive(PHOTOGRAPH BY BEN CURTIS, AP)
as the croquet hoops in Alice’s game in Wonderland. From the positions of
the above diagram, assuming the outside frogs to be in gaps larger than any
others shown, the following moves may be expected:

“どうやって”群れを維持する?
資源に集まるだけでも、場合によっては群れは維持されますが、今回は明確に話を分けます

個体間相互作⽤理論的な話COLLECTIVE BEHAVIOUR OF ANIMAL GROUPS
Repulsion, alignment, attractionの3つのzone

Computer simulation

6y(360 - α )°3

I. D. COUZIN ET AL.

An individual will attempt to align itself withneighbours within the zone of orientation, giving
no
X
v ðtÞ
! j !
do ðt þ tÞ ¼
!vj ðtÞ!

zoa
zoo

ð2Þ

j¼1

and towards the positions of individuals within(B)the zone(A)of attraction

zor

na
X
r ðtÞ
! ij !:da ðt þ tÞ ¼
!rij ðtÞ!

x

z

ð3Þ

jai

α°
Fig. 1. Representation of an individual in the model
centred at the origin: zor ¼ zone of repulsion, zoo ¼ zone oforientation, zoa ¼ zone of attraction. The possible ‘‘blind

The attraction represents the tendency of organisms to (C)join groups and to avoid
being on the(D)periphery, whereas the orientation allows collective movementd by minimizing
the numberof
Couzinet al., 2002ccollisions between individuals.
If neighbours areb
1

0.8
0.6

1

1

0.8
0.6
0.4

0.8
0.6

mgroup

1
0.8
0.6
0.4

of ϑ, so that it was greatest when neighbors were at a right angle
to the fish’s current heading (Fig. 2F). This is consistent with theobservation that nearest neighbors were more likely to be founddirectly ahead of or behind each other (Fig. S1B). Unlike acceleration, turning angle did not strongly depend on the distance to

実際の魚の群れでも

2

20

1

10
0

0 −π
−10

−1

−20
−30

−2

−40

−π/2
−40−30−20−10 0 10 20 30 40
distance from neighbour r (cm)ion (cm/s2)

2
1

0

B

2

focal fish acceleration (cm/s )

2

30

3

ケースB. 前⽅に最近接個体がいるとき

−3

6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−40 −30 −20 −10

C

0 10 20 30
distance from neighbour r (cm)6543Herbert-Read et al. 2011(改変、図の中央に⿂をおいた)2
2

A

ion (cm/s )403

ϑ = π/2

acceleration (cm/s )distance from neighbour r (cm)

ケースA. 前⽅に最近接個体がいるとき

we can esfunctions.
eration ofMaterials amapping p

D40

鍵となるクエスチョン

・どんな個体間相互作⽤が起きているのか・個体の意思決定はどのようになされるのか
・その結果、集団レベルで何が創発するのか今回は、空間的近接性をいかに保つか、に焦点
Box 1. Synchrony and ‘Criticality’ in Animal Groups(B)

150 ms

The extremely high speed at which behavioral change (e.g., turning) or density propagates across ﬂocks ofbirds (Figure 1B and Figure I) or schools of ﬁsh (Figure 1C), along with certain statistical properties observedin such groups (e.g., the presence of long-range correlations in individuals’ velocity despite the presence ofhighly local interactions), has caused some researchers to speculate that such animal groups, as has
previously been suggested for the brain, are ‘poised near criticality’ [6]. Taken from statistical mechanics, thetheory of critical phenomena demonstrates that certain generic properties appear in a collective system, be itof physical particles, neurons, or birds,
when local interactions are tuned in a certain way. Near the critical(A)
point, remarkable properties emerge spontaneously, such as individuals’ behavior becoming correlated
irrespective of the distance between them (which is mathematically equivalent to information being able topropagate almost without loss over the entire structure). Biological systems may beneﬁt from being close toa critical state in a variety of contexts since they must often satisfy two, seemingly opposing survival
conditions: to respond quickly to changing environmental conditions, such as the appearance of a predator,
and to remain robust and organized in the face of noise (e.g., in the case of ﬁsh or birds, eddies or gusts ofwind, respectively). While still controversial, criticality provides a fascinating, plausible, and increasingly
testable hypothesis for effective information processing in large collectives.

群れの形は様々
0 ms(C)

150 ms

450 ms

6. Bialek, W. et al. (2014) Social interactions domin
control in poising natural ﬂocks near criticality.
Acad. Sci. U. S. A. 111, 7212–7217

7. Dell, A.I. et al. (2014) Automated image-baseand its application in ecology. Trends Ecol. Evo428

8. Centola, D. (2010) The spread of behavior insocial network experiment. Science 329, 1194

(B)

9. Rosenthal, S.B. et al. (2015) Revealing the hworks of interaction in mobile animal groups a
diction of complex behavioral contagion. Proc. N
Sci. U. S. A. 112, 4690–4695

10. Ugander, J. et al. (2012) Structural diversity intagion. Proc. Natl. Acad. Sci. U. S. A. 109, 59

11. Strandburg-Peshkin, A. et al. (2013) Visual seworks and effective information transfer in anim
Curr. Biol. 23, R709–R711

12. Noy, L. et al. (2011) The mirror game as a pa
studying the dynamics of two people improvis
together. Proc. Natl. Acad. Sci. U. S. A. 10
20952

Special Issue: Time in the Brain

Forum
300 ms

450 ms(C)

Stuck in the Presen
Constraints on
Children’s Episodic
Prospection
Simona Ghetti1,2,* andChristine Coughlin3

750 mshronized Behavior in Animal Collectives. (A) An image sequence, with intervals of 150 ms, showing the propagation of a spiral waves (Apis dorsata) (ﬁlmed by Gerald Kastberger) [5]. (B) A ﬂock of bronzewing pigeons (Phaps histrionica) taking ﬂight together in innerof Damien Farine. (C) Visualization of the trajectories of 150 schooling golden shiner ﬁsh (Notemigonus crysoleucas) demonstrating the
600 ms
750 ms(by Vivek Sridhar and Matt Grobis).
Figure I. A ‘Murmuration’ of Starlings (Sternus vulgaris). Here the ﬂock is being attacked by a

The examination of childability to simulate their futur
gained increased attention
recent discoveries highlight ltions in this ability that e

Portugal et al., 2014, Lukeman et al., 2010, Couzin et al., 2018
peregrine falcon (Falco peregrinus) just to the left of the center of the ﬂock. Photograph courtesy of thedent, less-corre- evolved to be in a special ‘critical’ regime projected future state of the world, and ifウマを対象にした⼤型哺乳類の研究例は極めて少ない (Torney et al. 2018)-飼育できない-よく動く≒観察が難しい-体が⼤きいので、広範囲に広がる

ようはデータが取りづらい

Strandburg-Peshkin et al., 2015

ウマとドローン

ドローンの良さ

-

データ精度
機動力
撮影範囲
行動の文脈

ウマの良さ

-

寛容
高い社会性
個体識別
体の向き

2: 実際のウマの群れ

ウマの群れはどんな”かたち”をしているのか
調査地: ポルトガル アルガ⼭
調査期間: 2016-2019年 合計8ヶ⽉半♂: 1-2頭♀: たくさん

ウマの群れはハレム群&バチェラー群

社会順位ありデータ収集法
いまはMavic シリーズを使っています
Phantom 3 standard&
Phantom 3 advanced (DJI)

25 - 80m
Kyoto
1 ♂ + 7 ♀ + 2 foals

10 - 50m

単語の定義個体の位置
首の付け根とお尻の中点
個体の向き
お尻から首の付け根に向かうベクトル

距離の単位
お尻と首の付け根の間の距離(body length; abbrv. BL)

正確な距離はPinto&Hirata 2020を参照

個体間距離は?
個体間距離 (全ペア)
100

80

80

60

60

40

40

20
0
0

b b

120 120100 100

Frequency

100

Frequency

120

Frequency

a a120

最近接個体間距離

FrequencymmMamm
Res Res

80

80

60

60

40

40

20

20

20

0

0

0

0

20

20

40

40

60

60

Distance(BL) (BL)Distance

80

80

100

100

0

0

20

20

40

40

60

60

80

80

100 100

Distance(BL)(BL)
Distance

4 Histogramsof inter-individual
distance.
Binissizeis 1 bodylengtha Histogramofdistances
the distances
betweenall pairs.
of thishistogram. 4 Fig.
Histogramsof inter-individual
distance.
Bin size
1 bodylength(BL).(BL).
a Histogramof thebetweenall pairs.
TheThepeakpeakof thishistogram
ピークは3BLくらい- ピークは4BLくらい
was aroundb Histogram
the distanceto nearest
neighbor.
The peakof histogram
this histograms around
4 BL.4bBL.
Histogramof theofdistanceto nearest
neighbor.
The peakof thiswas was3 BL3 BL20 othergroups,includingbachelorgroups,werelocatedtowardthe rear.
Finally,grooming
frequency
the spatial 20 othergroups,includingbachelorgroups,werelocatedin inward
the rear.
Finally,grooming
frequency
and andthe spatial
et al. 2019the same(Ringhoferal. 2017).
To Inoue
betterunderstandcohesion
didcorrelate
not correlate
other.
the samefieldfield(Ringhofer
et al.et2017).
To betterunderstandthethehesion
did not
withwith
eacheachother.

where v⃗pi indicates a unit vector from the central point of an individual to the central point of their nearest neighbour i (Appendix& Agostinelli, 2017), R 3.3.2 and RStudio (V1.1.447, Rstudio, Inc.).

最近接個体はどこにいる? -> 真後ろにはいない

D). A Rayleigh test was used to investigate whether the populationƒՊ|Պ! " & $ "of circular data from which a sample was drawn differed from randomness, by comparing the sum of random vectors and the sum of

For nearest neighbours within two body lengths, circular varianceobserved vectors (Wilkie, 1983).

among directions was 0.52, which means that the distribution differed

Front
0°

50

1
0.5

90°

270°

180°
Back

0

  & !  Ɛ Պ Heat map showing thedensity of nearest neighbours within twobody lengths (BL) around an individual. In
total, 308 points were used to create thismap and bin sizes were Δx = Δy = 0.67 BL;
there were 17 points per square unit

10

20

30

0

Density of nearest neighbor

60

1.5

40

(Body length)2

右脳-左脳の機能と関係あるかもしれない

n = 308

Inoue et al. 2019individual had
value calculation because he was located in the periphery.
Figure 5 shows the q-value histogram. The peak was
性に応じて位置が変わる?
->0.5
オスは外側にいるaround 0.5, but the cases less thanoutnumbered thosegreater than 0.5.
Discussionn = 61
Error bar: standard error
BL: Body length30

periphery

Distance (BL)

25
20
15
10
5
center

0
Uzu

Uj

Kis

kat

Aya

Gio

Fus

Aka

Fig. 3 Average distance (+SE) between each individual and the central
point of the group. Uzu is the only male in this group

In the present
individual spa
a test case usi
positioning inof the group m
breeding an
Distribution oin that it fit w
distributions w
the q-value th
were located

まとめ- 個体間距離の分布がわかった- 最近接個体は真後ろにはいないことがわかった- オスは群れの外側にいた3: ウマの群れの維持機構

数理モデルからどんな相互作用で群れが維持されているのか
これを再現したい- 個体間距離の分布がわかった- 最近接個体は真後ろにはいないことがわかった- オスは群れの外側にいた使用モデルの基本
3

COLLECTIVE BEHAVIOUR OF ANIMAL GROUPS

An individual will attempt to align itself withneighbours within the zone of orientation, givingy(360 - α )°

no
X
v ðtÞ
! j !
do ðt þ tÞ ¼
!vj ðtÞ!

zoa
zoo

ð2Þ

j¼1

and towards the positions of individuals within
ただし、連続的な動きは考えないthezone of attraction

zor

x

z

na
X
r ðtÞ
! ij !:da ðt þ tÞ ¼
!rij ðtÞ!

ð3Þ

jai

α°
Fig. 1. Representation of an individual in the model
Couzin et al. 2002
centred at the origin: zor ¼ zone of repulsion, zoo ¼ zone of

The attraction represents the tendency of organisms to join groups and to avoid being on the
periphery, whereas the orientation allows collective movement by minimizing the number ofcollisions between individuals. If neighbours areモデルのイメージt = 0 (Random position)
Attractive force

t=1

Repulsive zone

Repulsive force

⼒の”かたち”と”範囲”が重要

t=2

力のかたち
a=0.1

a=0.2

a=0.4

1

b=0.5

0

F>0
-> Repulsive force

c
force

1

1
b=0.6

F<0
-> Attractive force

−1

0

5
10
15

−1

30
1

b=0.8

0
−1
0.0

2.5

5.0

7.5

10.0 0.0

2.5

5.0

distance

7.5

10.0 0.0

2.5

5.0

7.5

10.0

Metric

Topological

Voronoi

VisualT

Current Biology Vol 23 No 17
R710

A

B

Log marginal likelihood

力の範囲

C

D

0
gr

ransitivity–8000

fficiency

ginal likelihoodTa

rg ConTa et strg dis an
et ta t
vi nc
si e
bi
G litylo
To M bapo et llo ricg
Vo ica
ro l
n
Vi oi
su
al

Efficiency

fis
to
0.6
–7500
nonsocialinTarget0.4
Topologicaldi
Metric–8000
social
fo
0.2
pr
–8500
a
10
FeedersDena
Voronoi
Visualtr
50time (sec)
ge
C
E
D
0.8
th
0.6
p
–7500
0.7spread of information through fish
Figure 1. The
nonsocial“⾒えているかどうか”が⼀番⼤事(A) Different models for the neighbors with whomco0.6
image from our dataset. Metric: all individualsinw
0.4Strandburg-Peshkin et al. 2013

number of 0.5
nearest neighbors. Voronoi: those ind

相互作用モデル
Numeric

Topological

半径r以内の個体全てと相互作⽤する

近い順にN個体と相互作⽤する

このケースはN=3r

相互作⽤は対称相互作⽤は⾮対称

⼀度、群れから外れると帰還出来ない

⼀度、群れから外れても帰還可能

or not the drone
viors performed
ar to a previous
essive behaviors
ng were considup. We then calper hour and per

シミュレーションの評価
Mamm Res

個体間距離の分布

Observation

Simulationcomparing the length of the grid in the photo with its actual
length. Before we corrected the distortion using Photoshop
CC, the maximum error was 12% and around the peripheryof the photo. After correction, it was 3% or less. This was
acceptable, and we thus based our analysis on the distortioncorrected images.

Calculation of distance and direction
We used three measures to characterize the spatial positions ofindividuals within the group: inter-individual distance, nearest

Parameter survey

Error (root-mean-square error)近傍3個体と相互作用させると良さそう

観察値との誤差

近傍何個体と相互作⽤するか

観察結果を(概ね)説明できた
この⼒をrepulsion

attraction

Topological distance = 3で作⽤させる

まとめ- 個体間距離をエージェントベースシミュレーションによって再現できた- ウマは近傍3個体と相互作⽤させると良いみたい

個体に依存しない群れの維持機構の⼀端を説明した

4: ウマの群れの維持機構

オスの役割

群れの維持機構

個体に関係ないメカニズム + 個体に依存したメカニズム

例えば、オスがいない状況では、メスは⼀群になる

オスはハーディングという行動をみせる
Male

Femalesx4

74

個体の反応機序

Journal of Ethology (2020) 38:71–77

最初に反応するメスはオスに対して次に反応するメスは、すでに動いているメスに対してカスケード反応

Ringhofer et al., 2020

牧羊犬のモデルで説明できる

Fig. 3 Schematic diagram of the zones and forces of interaction experienced by a mare while being herded by a stallion
Go et al., 2020

ところで、本当に群れの維持に役立っている?
…the herding behavior of the male, where themale chases the females from behind, which isconsidered to maintain group cohesion …

検証した研究がない

Ringhofer et al., 2020

Less cohesive

Highly cohesive

Herdingまずはトラッキングする
individual tracking (uavTracker)

Body parts tracking (DeepLabCut)本当にメスは集まっているのか?
event A

herding start

event B

全イベント重ねてみた

個体間距離

メスが集まってない?

メスが集まる要因は?
cohesiveness increase

ハーディング前
2. females behavior

1. maleʼs behavior

cohesiveness decreaseオスの行動を分析してみた

1. turning angle

3. Male’s position to center of femalesθ
2. velocity
5. straightness
4. duration

特に何も出てこなかった

最終⾯積/初期⾯積

ハーディング直前の広がりが重要

仮説: オスは行動を変えていないが結果が異なる
Less cohesive

Highly cohesive

attraction > repulsion
attraction < repulsion
repulsion area

male

他の機能はないの?

秩序パラメータ

体の向きを揃えているのかも?

まとめ- オス特有の⾏動”ハーディング”は群れの維持に役⽴っている(状況に応じて)- メスが集まらないケースでは、体の⽅向を揃えているのかも (もしくは失敗した)個体に依存した群れの維持機構が存在する

全体まとめウマの群れの”かたち”を⾼精度で明らかにした個体に依存した群れの維持機構
個体に依存しない群れの維持機構

Current Biology Vol 23 No 17
R710

今後の展望

A

B
視野が極めて重要

MetricTopologicalhood

VoronoiC

VisualStrandburg-Peshkin et al., 2013

D

TargetRosenthal et al. 2015

これはあくまで数理モデル
実際は、それぞれの複合では?
Feeders0

Etime (sec)0.8群れ間の関係にも応用できる?

Acknowledgements
Horse team

Collaborators

Prof. Satoshi Hirata
Prof. Shinya Yamamoto
Dr. Monamie Ringhofer
Dr. Renata Mendonça
Pandora Pinto
Tamao Maeda
Sakiho Ochi
Dr. Tetsuro Matsuzawa
Dr. Carlos Pereira

Dr. Colin Torney
Prof. Keiichiro Fukazawa
Mikolaj Kundegorski

Field site
Lorenço Almada
Jose Maria Costa
Almando Pereira
Agostinho Costinha
People in Montaria
Viana do Castelo City

Comments
Prof. Dora Biro
Dr. Thomas Morison
Dr. Nobuaki Mizumoto
Dr. Valéria Romano
People in WRC
People in PWS

52