Variations on Error Strategyof Foraging Ants
Hiraku Nishimori （HiroshimaUniv.)

Collaborated withHiroyuki Nakagawa (Okasa Pref. Univ.)
Syunsuke Izumi (Hiroshima Univ.)
Toshiharu Akino(Kyoto Inst. Tech.)
Osamu Yamanaka (Hiroshima Univ.)
Akinori Awazu（HiroshimaUniv.)
Shin I. Nishimura(Kyusyu Univ.)
Shinnosuke Kawai (Hokkaido Univ.)Purpose of this study

To investigate

the Strategy of Errors
in the group forging of ants

--Motivation 1--

--Motivation 1-Experiments to quantify the following ability of pheromone pathby 2species of Tetramorium()
nestfood

J.Theor.Biol.(1983)
J.L.Deneubourg et al.
‘ Probabilistic behavior of ants: a strategy of error ? ’3.Computational mode---multi-agent model🐜🐜🐜Setup of Simulation Field

Food f(t)R

Food f(t)Hexagonal latticefieldRθNestθ, R

Environmental Parameters

123Choice of moving direction in each stepby Chemo-taxis

21• Choose one cellamong three frontalcells

31Prob. of choosing i-th cell(i={1,2,3})

P(i) µ (a k ri + z)n(n =10)

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

Walking Modes in foraging trip 1
Food site
1．Exploring mode
explore food
following recruit
pheromone

nest

Recruit pheromone

Walking Modes in foraging trip 2
2.Homing mode
Food site
・Move according to
Chemical cues and/or
Visual cues

Ricruitpheromone・Put recruit pheromone

Chemical cues.
Visual cues.

・On reaching nest, go back to theexploring modenestTime evolution of Pheromone fieldevaporation

pheromonesecretiondiffusionParameters characterizing the error strategyof each colony:{Number of normal ants &n (in totally 500ants)

Accuracy of dull ants }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

What we simulated

Food f(t)RFood f(t)Hexagonal latticefieldRθNestθ, R

Environmental Parameters

123What we measure→Foraging Efficiency E(n, α)

E: Total amount of food which a colonyof 500 ants carry to the nest per unit timeE(n, α): Foraging Efficiency as the function ofNum. of normal ants & Accuracy of dull ants

E: Foraging Efficiency in n--α space(Total Num. of ants 500)E(n, )All extremely dull ants
Mixture of Two Extremes:
Extremely dull & normal
ants

Uniform Colony of
all intermediately
dull ants

50 10-7mini
α0n500

max
50 1

Food

Food

E(n, )
θnest
10-7
Uniform Colony of
all intermediately
dull ants

1

Mixture of Two Extremes:
Extremely dull & normalants

α0500

R=50

Result 1E(n,α):(total number of ants 500)
EFood

R=50
θ=80nest

Max E

50 10-7α0n500 50 1

Food

Optimal colony :Binary-Mixture of two types of extreme ants

Normal ants & Extremely-dull ants

Result 2 E(n,α):E(total number of ants 500)

Max E
Food
10-70500

1

Food

R=50
θ=10nest

Optimal colony :Uniform colony ofAll Weakly(Intermediately) Dull Ants

θ=80

Food

θ=80nest

Food
R=50

θ=50

R=50 :fixed

θ=30
Food

Food
R=50

θ=10nest

θ=10

θ=20

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

10-71

θ=10FoodR=50 fixed

θ=30 ~90

θ=10 ,‥‥, 90nest

θ=20α0500

Summary of simulations
Including inaccurate (=dull) ants within a colony
increase the foraging efficiency of colony→Strategy of Errors
According to the change of foraging environment
the optimal binary distribution of inaccurate ants
in a colony sharply change between:i)a binary mixture of extremely-dull
and accurate antsii)the uniform colony of all-weakly dull ants
→Variations of Strategy of Errors

Remaining Problems
Only numerical results for the model:
Need proof in the reality (in experiment /field )Need some theoretical explanation for the results

Through an more abstract model
we extract the essential feature of theabove results=Emergence of the non-uniform of error strategy

4.Conceptial model🐜 🐜🐜 🐜

E == (500-n) (1-f(α) β(θ))1/β(θ)
Food

Food

θ=80
⇔β=0.5((500-n)f(α)+n)f(α)=αb/(2b + αb)( b=10)

Food

Food

θ=10
⇔β=2.0
nest

nest

EE
peak

n

peak

nf(α)

f(α)

Food

peak

peak
Food

R=50
θ=10nestf (α)

nnf (α)EEMax E

Max E

10-7050 10α0500 1

n50050 1

5 Conclusion

🐜🐜

🐜

🐜

Including inefficient (=dull) ants within a colony
increase the foraging efficiency of colony
According to the change of foraging environment
the optimal binary distribution of inaccurate ants
in a colony sharply change between:i)a binary mixture of extremely-dull
and accurate antsii)the uniform colony of all-weakly dull ants
A simplified mathematical model indicates that thetransition between different strategies of errors is
reduced to the change of optimal division of roleaccording to the feeding environment

6.Perspectives🐜🐜🐜🐜🐜🐜

Remaining Problems
Only numerical results for the model:
Need proof in the reality (in experiment /field )Experimental study of group strategy of ants
Collaboration with a making company of RFID chips)
RFID chips
Produced by SK-Electronics
CO., LTD. (Kyoto, Japan)

Size 0.4mm squre

Camponotus
japonicus

on the RFID chips recognition label of each ants is writtena reading device is set at a gate and is connected to PC
then we can automatically record all the data of ants passing
through the gate with recognizing individual ants

Setup🐜🐜🐜🐜

Nestsensor

PC🐜

Foodgatecorridor(transparent tube)

Number of passages
per hour at the gate

Activity=Example of obtained data 1####

2014/07/15 17:10:15
2014/07/22 23:10:15
2843
15

Time(every one hour)Data extraction and analysis using RFID tips isstarted very recently and still little data has beenobtained
If you are interested in it,

Please come to Poster session
And visit poster P29‘Activity statistics of foraging ants’
Osamu Yamanaka, et al