collective states and transitional behavior in schooling fish...local rules and emergent behavior...
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Collective states and transitional behavior in schooling fish
Collective Animal Behavior
CouzinLab@PrincetonUniversity
KOLBJØRN TUNSTRØM
Local rules and emergent behavior
Couzin, I.D. et al., 2002. Collective memory and spatial sorting in animal groups. Journal of Theoretical Biology, 218(1), pp.1–11.
Experiments: schooling fish in 2D environment
30 fish
70 fish
150 fish
300 fish
2.1 m
1.2
m
Water depth: 5 cm
•Notemigonus crysoleucas (golden shiners) •30-150 fish: 7 replicates of 56 min each •300 fish: 3 replicates of 56 min each •Video frame rate: 30 fps
1.2
m
16x normal speed
30 fish 70 fish 30 fish30 fish
150 fish 300 fish
Collective states
Swarm (S) Polarized (P)Milling (M)
Low dimensional representation: Order parameters
Rotational order parameter:
Polarization order parameter:
Swarm (S) Milling (M) Polarized (P)
Or =1
N
NX
i=1
|ui ⇥ ncm,i|
Op =1
N
NX
i=1
|ui|
Time series of order parameters
MODELSDATA
Relativeheading
Dis
tan
ce f
ron
t-b
ack
Distance left-right
Force
Velo
city
FocalFish
Vel
ocity
NeighboringFish
Turning force
Ssp
ee
din
g f
orc
e
Katz et al. PNAS 2011
A force model of social interactions
? ? ? Inferring interaction rules: revisited
30 golden shiners
Physical properties of individuals !1. Varying tail beat frequency. 2. Strength of tail beat. 3. Dissipative force on fish. 4. Form of blind zone. 5. Geometric shape. 6. Reaction time lag. 7. Interactions: Metric, topological, visual field. 8. Stochastic behavior. 9. Fish memory.
Model assumption !1. Constant update frequency. 2. Speed limited to v_max. 3. Dissipative force set constant. 4. No blind zone. 5. Point particle. 6. Instantaneous reaction time. 7. Metric interactions. 8. Deterministic rules. 9. No memory.
Considerations
!2 !1 0 1 2
!2
!1
0
1
2
Distance !Body length"
Distance!Body
length"
!21.
0
21.Par. a !m#s2"
0.0 0.5 1.0 1.5 2.0 2.5!20
!10
0
10
20
Distance !Body length"Forceparametera!m#s2
" Sector 1
0.0 0.5 1.0 1.5 2.0 2.5!20
!10
0
10
20
Distance !Body length"Forceparametera!m#s2
" Sector 2
0.0 0.5 1.0 1.5 2.0 2.5!20
!10
0
10
20
Distance !Body length"Forceparametera!m#s2
" Sector 3
0.0 0.5 1.0 1.5 2.0 2.5!20
!10
0
10
20
Distance !Body length"Forceparametera!m#s2
" Sector 4
Force matching example: attraction/repulsion
30 fps
Observational time scale: simulations
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
20
40
60
80
100
Radius
Pairw
iseforce
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4!0.2
0.0
0.2
0.4
0.6
0.8
1.0
Radius
Pairw
iseforce
0 1 2 3 4 5!0.5
!0.4
!0.3
!0.2
!0.1
0.0
0.1
0.2
Radius
Pairw
iseforce
Original
dt = 50
dt = 30
dt = 10
dt = 1Lennard-Jones Quadratic
Morse
0.0 0.5 1.0 1.5 2.0 2.5!0.6!0.4!0.2
0.00.20.40.6
Distance !Body length"Forc
epa
ram
eter
c!unitl
ess" sector 1
0.0 0.5 1.0 1.5 2.0 2.5!0.6!0.4!0.2
0.00.20.40.6
Distance !Body length"Forc
epa
ram
eter
c!unitl
ess" sector 2
0.0 0.5 1.0 1.5 2.0 2.5!0.6!0.4!0.2
0.00.20.40.6
Distance !Body length"Forc
epa
ram
eter
c!unitl
ess" sector 3
0.0 0.5 1.0 1.5 2.0 2.5!0.6!0.4!0.2
0.00.20.40.6
Distance !Body length"Forc
epa
ram
eter
c!unitl
ess" sector 4
dt = 1dt = 10
dt = 30dt = 50
0.0 0.5 1.0 1.5 2.0 2.5!20
!10
0
10
20
Distance !Body length"Forceparametera!m#s2
" Sector 1
0.0 0.5 1.0 1.5 2.0 2.5!20
!10
0
10
20
Distance !Body length"Forceparametera!m#s2
" Sector 2
0.0 0.5 1.0 1.5 2.0 2.5!20
!10
0
10
20
Distance !Body length"Forceparametera!m#s2
" Sector 3
0.0 0.5 1.0 1.5 2.0 2.5!20
!10
0
10
20
Distance !Body length"Forceparametera!m#s2
" Sector 4
Observational time scale: experiments
Effects of tracking difficulties
Tracking accuracy per frame
0 10 20 30 40 50 600
0.2
0.4
0.6
0.8
1Statistics of individual track lengths
Length of individual track [s]
Frac
tion
of tr
acks
Individual track lengths
Tracking accuracy: Simulations
Original
dt = 50
dt = 30
dt = 10
dt = 1
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
20
40
60
80
100
Radius
Pairw
iseforce
0 1 2 3 4 5!0.5
!0.4
!0.3
!0.2
!0.1
0.0
0.1
0.2
Radius
Pairw
iseforce
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4!0.2
0.0
0.2
0.4
0.6
0.8
1.0
Radius
Pairw
iseforce
Lennard-Jones Quadratic
Morse
Observational time scale: simulations
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
20
40
60
80
100
Radius
Pairw
iseforce
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4!0.2
0.0
0.2
0.4
0.6
0.8
1.0
Radius
Pairw
iseforce
0 1 2 3 4 5!0.5
!0.4
!0.3
!0.2
!0.1
0.0
0.1
0.2
Radius
Pairw
iseforce
Original
dt = 50
dt = 30
dt = 10
dt = 1Lennard-Jones Quadratic
Morse
0.0 0.5 1.0 1.5 2.0 2.5!2
!1
0
1
2
Distance !Body length"Forc
epa
ram
eter
a!m#s2 " Sector 1
0.0 0.5 1.0 1.5 2.0 2.5!2
!1
0
1
2
Distance !Body length"Forc
epa
ram
eter
a!m#s2 " Sector 2
0.0 0.5 1.0 1.5 2.0 2.5!2
!1
0
1
2
Distance !Body length"Forc
epa
ram
eter
a!m#s2 " Sector 3
0.0 0.5 1.0 1.5 2.0 2.5!2
!1
0
1
2
Distance !Body length"Forc
epa
ram
eter
a!m#s2 " Sector 4
> 24 fish> 25 fish
> 26 fish> 27 fish
> 28 fish> 29 fish
Test: short interaction length (2.5 BL)
0.0 0.5 1.0 1.5 2.0 2.5!20
!10
0
10
20
Distance !Body length"Forceparametera!m#s2
" Sector 1
0.0 0.5 1.0 1.5 2.0 2.5!20
!10
0
10
20
Distance !Body length"Forceparametera!m#s2
" Sector 2
0.0 0.5 1.0 1.5 2.0 2.5!20
!10
0
10
20
Distance !Body length"Forceparametera!m#s2
" Sector 3
0.0 0.5 1.0 1.5 2.0 2.5!20
!10
0
10
20
Distance !Body length"Forceparametera!m#s2
" Sector 4
Force matching: three examples
Attraction/repulsion
Attraction/repulsionAlignment
Attraction/repulsionTurning
Force matching: three examples
Inspired by Daniel Strömbom
!4 !2 0 2 4
!4
!2
0
2
4
Distance !Body length"
Distance!Body
length"
!6.9
0
6.9Par. a !m#s2"
Attraction/repulsion with blind angle
Colin Twomey@CouzinLab
Interaction network: field of view
Colin Twomey@CouzinLab
Interaction network: field of view
Individual decision making
Colin Twomey@CouzinLab
Individual decision making
Colin Twomey@CouzinLab
Individual decision making
0 500 1000 1500
-300
-200
-100
0
100
200
300
0 20 40 60 80 100 1200
20
40
60
80
Scale free velocity correlations
Square root of group area [cm]
Cor
rela
tion
leng
th [c
m]
Physical properties
Thanks.
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