Collective states and transitional behavior in schooling fish KOLBJØRN TUNSTRØM Collective Animal Behavior CouzinLab@ PrincetonUniversity
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 1.2 m 1.2 m Water depth: 5 cm 2.1 m • 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
30 fish 70 fish 30 fish 30 fish 150 fish 300 fish 16x normal speed
Collective states Swarm (S) Milling (M) Polarized (P)
Low dimensional representation: Order parameters N O p = 1 X Polarization order parameter: | u i | N i =1 N O r = 1 X Rotational order parameter: | u i × n cm ,i | N i =1 Swarm (S) Milling (M) Polarized (P)
Time series of order parameters
MODELS DATA
A force model of social interactions Relative y heading t i c o l e Sspeeding force V Force Velocity Distance front-back Turning force Neighboring Neighboring Fish Fish Focal Focal Distance left-right Fish Fish Katz et al. PNAS 2011
Inferring interaction rules: revisited ? ? ?
30 golden shiners
Considerations Physical properties of individuals Model assumption � � 1. Varying tail beat frequency. 1. Constant update frequency. 2. Strength of tail beat. 2. Speed limited to v_max. 3. Dissipative force on fish. 3. Dissipative force set constant. 4. Form of blind zone. 4. No blind zone. 5. Geometric shape. 5. Point particle. 6. Reaction time lag. 6. Instantaneous reaction time. 7. Interactions: Metric, topological, visual field. 7. Metric interactions. 8. Stochastic behavior. 8. Deterministic rules. 9. Fish memory. 9. No memory.
Force matching example: attraction/repulsion Sector 1 Sector 2 Force parameter a � m � s 2 � Force parameter a � m � s 2 � 20 20 10 10 Par. a � m � s 2 � 21. 0 0 2 � 10 � 10 Distance � Body length � � 20 � 20 1 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 Distance � Body length � Distance � Body length � 0 0 Sector 3 Sector 4 Force parameter a � m � s 2 � Force parameter a � m � s 2 � 20 20 � 1 10 10 � 2 0 0 � 21. � 2 � 1 0 1 2 � 10 � 10 Distance � Body length � � 20 � 20 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 Distance � Body length � Distance � Body length �
30 fps
Observational time scale: simulations 100 Lennard-Jones Quadratic 1.0 dt = 1 80 dt = 10 0.8 dt = 30 Pairwise force Pairwise force 60 0.6 dt = 50 Original 0.4 40 0.2 20 0.0 0 � 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Radius Radius 0.2 Morse 0.1 0.0 Pairwise force � 0.1 � 0.2 � 0.3 � 0.4 � 0.5 0 1 2 3 4 5 Radius
Observational time scale: experiments dt = 1 dt = 30 dt = 10 dt = 50 Force parameter c � unitless � Force parameter c � unitless � sector 1 sector 2 Sector 1 Sector 2 Force parameter a � m � s 2 � Force parameter a � m � s 2 � 20 0.6 20 0.6 0.4 0.4 10 10 0.2 0.2 0.0 0.0 0 0 � 0.2 � 0.2 � 10 � 0.4 � 10 � 0.4 � 0.6 � 0.6 � 20 � 20 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 Distance � Body length � Distance � Body length � Distance � Body length � Distance � Body length � Force parameter c � unitless � Force parameter c � unitless � sector 3 sector 4 Sector 3 Sector 4 Force parameter a � m � s 2 � Force parameter a � m � s 2 � 0.6 0.6 20 20 0.4 0.4 10 0.2 10 0.2 0.0 0.0 0 0 � 0.2 � 0.2 � 0.4 � 0.4 � 10 � 10 � 0.6 � 0.6 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 � 20 � 20 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 Distance � Body length � Distance � Body length � Distance � Body length � Distance � Body length �
Effects of tracking difficulties
Tracking accuracy per frame
Individual track lengths Statistics of individual track lengths 1 0.8 Fraction of tracks 0.6 0.4 0.2 0 0 10 20 30 40 50 60 Length of individual track [s]
Tracking accuracy: Simulations 100 Lennard-Jones Quadratic 1.0 dt = 1 80 dt = 10 0.8 dt = 30 Pairwise force Pairwise force 60 0.6 dt = 50 Original 0.4 40 0.2 20 0.0 0 � 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Radius Radius 0.2 Morse 0.1 0.0 Pairwise force � 0.1 � 0.2 � 0.3 � 0.4 � 0.5 0 1 2 3 4 5 Radius
Observational time scale: simulations 100 Lennard-Jones Quadratic 1.0 dt = 1 80 dt = 10 0.8 dt = 30 Pairwise force Pairwise force 60 0.6 dt = 50 Original 0.4 40 0.2 20 0.0 0 � 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Radius Radius 0.2 Morse 0.1 0.0 Pairwise force � 0.1 � 0.2 � 0.3 � 0.4 � 0.5 0 1 2 3 4 5 Radius
Test: short interaction length (2.5 BL) > 24 fish > 26 fish > 28 fish > 25 fish > 27 fish > 29 fish Sector 1 Sector 2 Sector 1 Sector 2 Force parameter a � m � s 2 � Force parameter a � m � s 2 � Force parameter a � m � s 2 � Force parameter a � m � s 2 � 2 2 20 20 1 1 10 10 0 0 0 0 � 1 � 1 � 10 � 10 � 2 � 2 � 20 � 20 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 Distance � Body length � Distance � Body length � Distance � Body length � Distance � Body length � Sector 3 Sector 4 Sector 3 Sector 4 Force parameter a � m � s 2 � Force parameter a � m � s 2 � Force parameter a � m � s 2 � Force parameter a � m � s 2 � 20 2 20 2 10 1 10 1 0 0 0 0 � 10 � 1 � 10 � 1 � 20 � 2 � 20 � 2 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 Distance � Body length � Distance � Body length � Distance � Body length � Distance � Body length �
Force matching: three examples
Force matching: three examples Attraction/repulsion Attraction/repulsion Attraction/repulsion Turning Alignment
Inspired by Daniel Strömbom Par. a � m � s 2 � 6.9 4 Distance � Body length � 2 0 0 � 2 � 4 � 6.9 � 4 � 2 0 2 4 Distance � Body length � Attraction/repulsion with blind angle
Interaction network: field of view Colin Twomey@CouzinLab
Interaction network: field of view Colin Twomey@CouzinLab
Individual decision making Colin Twomey@CouzinLab
Individual decision making Colin Twomey@CouzinLab
Individual decision making 300 200 100 0 - 100 - 200 - 300 0 500 1000 1500
Physical properties Scale free velocity correlations 80 Correlation length [cm] 60 40 20 0 0 20 40 60 80 100 120 Square root of group area [cm]
Thanks.
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