Collective states and transitional behavior in schooling fish - PowerPoint PPT Presentation

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.