Post on 19-May-2020
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