アリの採餌における意思決定とゆらぎ 	  Decision-­‐making	  and	  Stochas2city	  of	  Foraging	  Ants	  home
広島大 西森拓	  Hiraku	  Nishimori(Hiroshima	  Univ.)	  visual cues	  共同研究者	  chemical cues	  西村信一郎（九州大),	  	  	  粟津暁紀(広島大）	  焼
河合信之輔(北海道大),	  中川寛之（大阪府大)	  Shin	  I.	  Nishimura,(Kyusyu	  Univ.)	  Akinori	  Awazu（HiroshimaUniv.)	  Shinnosuke	  Kawai(Hokkaido	  Univ.)	  Hiroyuki	  Nakagawa(Osaka	  Pref.Univ.)	  	  Thanksto	  秋野順治(京都工繊大)
Toshiharu Akino(Kyoto Inst. Tech.)Hmm

鳥--Motivation 1--

--Motivation 1-Assay (Trail--following experiment) for two species of ants:
Tetramorium impurum and Tapinoma erraticum (シワアリ)
foodnest

Introduc2on	  	Posi2ve	  feedback	
Pheromonechemotaxis

AntsOver-­‐Posi2ve	  feedback			  	appropriate densityof pheromone
10100 times denser
45

1035

40
35

530
52530

nest

25
020

nest
0

20

15

15-5

10

10-5

5

5-10

0
0

5

10

15

20-10

00

5

10

15

20

Time-averaged number
density of ants
By Katsuhito Naka(Hiroshima)

Pheromone

Pheromone
Switchingbetween
two regime
AntsAnts
PheromoneAppropriate densityof pheromone trail
is kept

Antsmotivation2

えさ有りWith food

えさ無し
Without foodInitially
pastedpheromoneWithout
If food isfood
given
Posi2ve	  feedback	
Pheromone
No trail isformed

Ants
条件に依存して  消滅する  
正のフィード・バック  Experimentchemical information

initialy
pastedPheromonevisual information
foodpheromone
line

nest

ants make a combined use of different information

Setup	  of	  Foraging	  Field	  	Food f(t)RFood f(t)Hexagonal latticefieldRθNest
θ, R ：Environmental Parameters

123Choice	  of	  moving	  direc2on	  in	  each	  step	  by	  Chemo-­‐taxis	  	  2• Choose	  one	  cell	  among	  three	  frontal	  cells	

131Prob. of choosing i-th cell(i={1,2,3})	

P(i) ∝ (α k ρi + z)n(n = 10)

ρi: pheromone density in i-th cell	
αk: sensitivity of k-th ant	
(normalization P(1)+P(2)+P(3)=1)

Log P(i)76α=10-354
3α=10-４

2
1

10

20

30

4050

ρ

	  Modes	  in	  foraging	  trip	  	  1	Food site	

1．Explora2on	  mode	  	  	  	  	  explore	  food	  following	  recruit	  pheromone	

Recruit pheromone	nest	  Mode2	  in	  foraging	  trip	  	  2	2.homing	  Food site	  	  	  	  ・	  try	  to	  go	  back	  to	  the	  nest	  aPer	  taking	  food,	  	  	  	  	  	  during	  	  which	  way	  	  	  	  	  	  leave	  recruit	  pheromone	  	  	  	  	  	  	  ・	  the	  choice	  of	  	  homig	  dirce2on;	  	  	  	  	  	  depends	  on	  the	  combina2on	  of	  	  	  	  	  	  Chemical	  informa2on	  (pheromoner)	  and/or	  	  Visual	  informa2on	  Chemical info.	  	  	  	  	  	  	  Visual info.	  	  	  	  	  ・On	  reaching	  nest,	  go	  back	  to	  	  the	  	  	  	  	  	  	  	  	  	  	  	  	  	  exploring	  mode	  Ricruit

nest	

pheromone	A	  set	  of	  Parameters	  characterizing	  foraging	  colonies:	  	   	  	  {Number	  of	  normal	  ants	  	  	  &	  	  	  	  Sensi1vity	  of	  dull	  ants	  	  }	  	  	  	  	  	  	  	  	  	  	  	  n	  (in	  totally	  500ants)	  	  	  	  	  	  	  	  	  	  	  	  	  	  α	  (	  < αnormal=50	  )	  	+Normal Ants
(α=αnormal=50)	

Dull Ants(α < αnormal =50×10-1, 50×10-2
50×10-3, 50×10-4, ‥,50×10-7 )	

number ratio ｎ ： 500－ｎ	Foraging	  Eﬃciency E	  E:	  Total	  amount	  of	  food	  which	  a	  colony	  	  	  	  	  	  of	  500	  ants	  carry	  to	  the	  nest	  per	  unit	  2me	  	  	What	  we	  measure	  	  	  E(n,	  α):	  Foraging	  Eﬃciency	  as	  the	  func2on	  of	  	  	  	  #	  of	  normal	  ants	  	  	  &	  	  	  	  Sensi1vity	  of	  dull	  ants	  	  	  	E: Foraging Efficiency in (n, α) space(Total Num. 500)E(n, )All extremely dull ants

All normal ants alongThese lines

50×10-750×1 0
Num. of nαormal ants

n500

Result 1E(n,α): Foraging Efficiency in the space ofn: num. of normal ants &α: Sensisitvity of dull ants

(total number of ants 500)
EMax E

Food	

50×10-70α
n500 50×1

Food	
R=50
θ=80°nest		  	  	  Op2mal	  colony	  :	  	  	  	  	  	  	  	  	  	  	  	  	  	  Binary-­‐Mixture	  of	  two	  types	  of	  extreme	  ants	  	  	  	  	  	Normal ants & Extremely-dull ants＋

Result 2E(n,α): Foraging Efficiency in the space ofn: # of normal ants & α: Sensisitvity of dull ants
(total number of ants 500)
EMax E
Food	 Food	
10-70500

1R=50
θ=10°nest		  	  	  Op2mal	  colony	  :	  	  	  	  	  	  	  	  	  	  	  	  	  	  Uniform	  colony	  of	  All Weakly Dull Antsθ=80°

Food	

θ=80°
nest	

Food	
R=50

θ=50°

R=50 :fixed

θ=30°
Food	

Food	
R=50

θ=10° θ=10°

nest	

θ=20°

Shift of Optimal Colony According to the change of θFood	E(n, )

Food	
R=50 fixed

θ=10° ,‥‥, 90°
nest	-710	  Uniform	  Colony	  of	  	  weakly	  dull	  ants	

1 0

θ=10°

θ=30°~90°
Mixture	  of	  Two	  Extremes:	  	  Extremely	  dull	  &	  normal	  ants	  	  	   	  θ=20°α# of normal ants

n500

We tried to formalize the phenomena
and proposed one of possible scenariosin the workshop
However, in this note,
we are sorry to omit the part of formalism

It is because, details of theoretical discussions
are still in the level of private communication
among authors.

peak

peak
Food	 Food	
R=50
θ=10°nest	
Log αnn
Log αResults obtained by formalism

Max EEE10-70500 1

Max E

50×100αnResults obtained by numerical calulation

50050×1

Conclusion○Including inefficient (=dull) ants within a colony
increase the foraging efficiency of colony○The optimal way of including inefficient (=dull) ants
sharply change depending on foraging environment
From a binary mixture of extremely-dull and sensitive
normal ants to the uniform colony of all-weakly dull ants
○A mathematical formulation for the above phenomena
is made.
But on the half-way

Perspective
Is the generalization of this story possible?

Transition of noise–induced efficient behavior
in many-body systems:
From homogeneous noise to heterogeneous noiseExample
Stochastic resonance under inhomogeneous noise

鳥越章吾修士論文

inhomogeneous noiseWeak coupling

Strong coupling

ASPA: degree of stochastic resonance averaged overelements 1 and 2.
D1,D2: amp. of noise induced to 1 and 2,respectively
1.R. Kawai, A. Awazu , and H. Nishimori, PRE. Vol.84,021135-1-5 (2011)
2. R. Kawai, S. Torigoe, K. Yoshida , A. Awazu , and H. Nishimori, PRE. Vol.82,051122-1-7 (2010)