Modeling fish dynamics around FADs

JL Deneubourg (ULB), L. Dagorn (IRD) & K. Holland (University of Hawaii)

PFRP Principal Investigators WorkshopUniversity of Hawaii, HonoluluNovember 13-14, 2007

OUTLINE

AggregationGeneric conceptsHomogeneous and heterogeneous environment

Modelling

Interaction artificial agents-animalsMobile robotsAutonomous heterogeneities

Mechanisms

In heterogeneous environment : same response of the individuals to the the environmental heterogeneities

Ecologists

Social interaction Clustering around a leader (individuals are different)Inter-attraction between “identical” individuals (signals or cues identical)

Homogeneous environment

Highly widespread from unicellular societies to mammals groupLarge functional diversity (reproduction, feeding,...)Permanent or transitoryImmobile to highly mobile (school, shoal)

Social interaction is often associated to response to the environmental heterogeneities.

Aggregation

(Camazine et al, 2001)

Kinesis : Speed (Temperature)≈ (TM-T)2

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16 18 20

x

Density Temperature

Spatial heterogeneities

Spatial distribution is density independant

QueenWorkers

Leaders

Lasius nigerN = 100T = 2’30”

(From Depickère)

20 cm

Interattraction

Lasius niger

20 cm

N = 100

(From Depickère et al)

Modified from Lebohec et al

Collective choice Sorting

Proportion of cockroaches under the dark shelter

Frac

tion

of e

xper

imen

ts

0-0.2 0.2-0.4 0.4-0.6 0.6-0.8 0.8-1.0

By-product of aggregation: collective choice, sorting, synchronization,....

(Nursery)

0

0.2

0.4

0.6

70% in dark

Individual :55% in dark

75 lux

100 lux

Canonge et al, in prep

Aggregation in heterogeneous environment

Modeling aggregation around FAD

The models are TOOLS

To analyze the relation between individual behavior,population parameters (density) and environmental characteristics AND the spatio-temporal organization of the population around FADs→ to integrate different types of data (acoustic data + tagging data)

To use the FADs to make predictione.g. : is it possible to estimate the total fish density

measuring the populations around FAD?

• Ordinary differential equations (ODE)

•Partial differential equations (PDE) : Advection-diffusion-reaction model

(M.S. Adam & J.R. Sibert, 2002, Aquat. Living Resour., 15, 13-23)

Analytical treatment (Stability analysis,... ) + numerical solution

•Fluctuation : Stochastic simulation (individual based model)Master equation

(Camazine et al., 2001)

Theoretical tools

∂x∂t

= Movement + Birth − death

∂x∂t

= D∂ 2x∂x 2 + D∂ 2x

∂y 2 − λx

dxi

dt= Birth − death = Fi(x1,..., xn ) i =1,...,n

Aggregation in heterogeneous environmentTime evolution of the population around each FAD xi

r

Individual probability of reaching/joining FAD i

Individual probability of leaving FAD i

FAD 1

FAD 2

Xe

FAD 2FAD 2FAD 2FAD 2FAD 2FAD 2

xi

Aggregation in heterogeneous environment

Numerical model : Simple latticeFAD are identical

dxi

dt= −Qixi +

Qj x j

4j

nb

∑

FAD

Differential equation : dynamics of xi and behavior

Model 1: No interaction between the fishes

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 0,05 0,1 0,15 0,2 0,25 0,3

Density of FAD

Fra

ctio

n o

f th

e t

ota

l p

op

ula

tion

aro

un

d F

AD

s

τfad = 5 τopen ocean

Stationary state

FADs are identicalThree parameters: fish population, resting time around FAD (τF),

resting time in others cells (τO)

Stationary state: Population around each FAD≈Total populationx1=...=xn

Fraction fishfad =Dfad

τO

τ F

+ (1−τO

τ F

)Dfad

Comparing different FAD density→Fish density

No interaction between the fishes (2)

0,2

0,22

0,24

0,26

0,28

0,3

0,32

0,34

0,36

0,38

0,4

0 10 20 30 40 50 60 70 80

Time (arbitrary unit)

Fra

ctio

n a

rou

nd

FA

D

FADs FADs are removed

F(resting time)

No interaction between the fishes (3)

Benefit =

Model →strategy: Optimal density/number of FAD

δ = fish density

(R. Hilborn & P. Medley (1999)

Can. J. Fish Aquat. Sci. 46: 28-32)

δDfad

K + Dfad

− χDfad Dopt = ( Kδχ

) − K

-1

-0,8

-0,6

-0,4

-0,2

0

0,2

0,4

0,6

0 2 4 6 8 10 12 14 16

Number of FAD

Ben

efi

t

δ=2

δ=1

Point of view of the fisherman

dxi

dt= −Qixi +

Qj x j

nbj

nb

∑

Qi =θ

1+ βxin

Qi = (1+ βx jn )

Model 2 : Interattraction

Periplaneta americana

An easy case study: collective decision making in cockroach group

Φ=1m, T=0h

T=3h

Identical shelters

(Jeanson &Deneubourg, Am Nat. 2007Amé et al, PNAS 2006,Halloy et al, Science , November 2007)

Pi = μi 1−xi

Si

⎛

⎝ ⎜

⎞

⎠ ⎟

Qi =θi

1+ ρ xi

Si

⎛

⎝ ⎜

⎞

⎠ ⎟

n

Individuals are capable of detecting the sheltersand estimate their quality (θi )The inter-attraction between individuals decreasesthe probability of leaving the shelter.

Individuals randomly explore the system & encounter the sheltersThey are constrained by a crowding effect

Collective decision making in cockroach groupbased on inter-attraction

xi number of individuals in shelter i xe number of individuals outside the sheltersSi carrying capacity of the shelters p number of shelters present in the systemn inter-attraction factor (n≈2) N total number of individuals = xe+ x1 …+ xp

Collective decision making:experimental bifurcation diagram

Amé et al, PNAS, 2006

dxi

dt= −Qixi +

Qj x j

nbj

nb

∑

Qi =θi

1+ βxin

Model 2 : Interattraction

Diversity of responses but some generic properties

FAD Density : 0.1, 20 simulations

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60

Total Population

Po

pu

lati

on

aro

un

d F

AD

s

Influence of the total population ortotal population estimation from FAD population (1)

Influence of the total population... (2) : “selection” of a FAD 2 FADs

0

0,2

0,4

0,6

0,8

1

1,2

0 1 2 3 4 5 6

Total fish population

Fra

ctio

n o

f p

op

ula

tion

aro

un

d F

AD

1

(1) Acoustic data + tagging data → Model

(2) Model → Relation between population around FAD and the totalpopulation

(3) Data collection with j FADs →estimation of the total population

Influence of the total population... (3)

Influence of the # of FADs

0

0,2

0,4

0,6

0,8

1

1,2

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

Density of FAD

Fra

ctio

n o

f si

mu

lati

on

s w

ith

sele

ctio

n

50 simulations per condition with random initial conditions(Stationary states)

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

Density of FAD

Mean

fra

ctio

n o

f th

e t

ota

l p

op

ula

tio

n

Influence of the # of FADs (2)

Mixed societies: mixed groups of social animals and robots.Animals and robots (artificial agents) interact and communicate.

Control means: That it is possible to trigger the emergence of somenew global patterns by adding artificial agents with specific behaviors to the society.

Society is a network of interactionsXi,Ai : number of agent i Negative feedback Positive feedback Flow

X0

Dynamics, attractors New dynamics, new attractors

X1 X2

X3

Living units X0

X1 X2

X3

Living units + Artificial agents

A5 A6

A0

Lure/Decoy

Bird of prey≈ 1925-1926Arctic (Canada)

Behavioural StudyManagement & Monitoring

Function

Artifici

al ag

ents

Mounte

d dev

ices

Mobile

Robots

Network

of se

nsors-

actua

tors

The artificial agents are passive→The feedback loop is not closed

Patterns Synchronization, collective choice,…

Smart collar (Mounted device): GPS, PDA, sound amplifier & wireless networking, affects the behaviour of some individuals & of the group (D. Rus et al, MIT)What about schools with some fishes tagged with a smart device?

Mounted devices

Collective decision making in mixed groups of robots and cockroaches

?

?

+

The lure robots allow the implementation of new feedbacks and the modification of the collective choice (dynamics).

Building interactions and communication:Perception of individual presence Modulation of the behavior according to individual presence

+

Adding feedbacks

Caprari G., Colot A., Siegwart R., Halloy J. and Deneubourg, J.-L..Animal and Robot Mixed Societies- Building Cooperation Between Microrobots and Cockroaches. IEEE Robotics & Automation Magazine. Vol.12, No 2, June, pp 58-65. 2005.

MarkingIdentification

analysis

Extraction/Synthesis of the blendConcentration

C. Rivault, I. SaidV. Durier

Cuticularhydrocarbons

F. Tâche, M. Asadpour, A. Colot

G. Caprari, F. Mondada,

R. Siegwart

12 IR Proximity Sensors⇒ Cockroach detection⇒ Wall detection⇒ Robot detection

2 Photodiodes⇒ Shelter detection

Linear Camera⇒ Cockroach detection

≈ 40mm

Robot-insect

Summary

Both machines and insects are capable, independently of each other, to perform such collective decision (don’t show here).

The robots are accepted by the cockroaches groups and actively take part in the collective choice. Most of the time, they gather with the cockroaches under the same shelter.

When the robots are programmed to have an opposite preference compared to insects, they are able to induce a change in the global pattern by reversing the collective shelter preference. The mixed group of robots and insects gather in the less preferred shelter by the insects.

G Sempo et al. LNCS, 4095 2006J. Halloy et al. Social Integration of Robots in Groups ofCockroaches to Control Self-organized Choices. Science November 15 2007.

Experimental demonstration : 12 cockroaches & 4 robots

Shared collective decision between identical sheltersy = 0.3446x + 0.1935

R2 = 0.8443

0

1

2

3

4

0 2 4 6 8 10 12Number of insects under shelter

Num

ber o

f rob

ots

unde

r she

lter

0.63

0.38

0.20

0.80

0.00

0.20

0.40

0.60

0.80

1.00

Ligth shelter Dark shelter

Freq

uenc

y of

sel

ectio

n by

inse

cts

Insects & robots Insects

2 shelters: dark & lightInsects prefer dark & Robots prefer light

dxi

dt= μixe −

θixi

1+ ρ xi

Si

⎛

⎝ ⎜

⎞

⎠ ⎟

n

dθi dt

= Fi(x1,x2,θ1,θ2)

Different patterns, responses of the systems→Information on the total population →Optimal control

Network of sensors-actuators : shelters, FADs,...

From FADIO (Quality of Life; FP5)

Aggregation-sorting : by-catch

<<Amé et al, Anim. Behav. 2005 <<

Selective attraction?Robot-decoy acting selectively on one species e.g. by imitation

?

Aggregation-sorting : by-catch