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

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

Jan 31, 2024 330 likes •693 views

Collective states and transitional behavior in schooling fish KOLBJRN TUNSTRM Collective Animal Behavior CouzinLab@ PrincetonUniversity Local rules and emergent behavior Couzin, I.D. et al., 2002. Collective memory and spatial sorting in

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Collective states and transitional behavior in schooling fish

Collective Animal Behavior CouzinLab@PrincetonUniversity

KOLBJØRN TUNSTRØM

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SLIDE 2
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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.
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SLIDE 4

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

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SLIDE 5

16x normal speed 30 fish 70 fish 30 fish 30 fish 150 fish 300 fish

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Collective states

Swarm (S)

Polarized (P) Milling (M)

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SLIDE 7

Low dimensional representation: Order parameters

Rotational order parameter: Polarization order parameter:

Swarm (S)

Milling (M) Polarized (P)

Or = 1 N

N

X

i=1

|ui × ncm,i| Op = 1 N

N

X

i=1

|ui|

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SLIDE 8

Time series of order parameters

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SLIDE 9

MODELS DATA

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SLIDE 10
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SLIDE 11 Relative heading Distance front-back Distance left-right

Force Velocity

Focal Focal Fish Fish

V e l

  • c

i t y

Neighboring Neighboring Fish Fish

Turning force Sspeeding force

Katz et al. PNAS 2011

A force model of social interactions

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SLIDE 12

? ? ?

Inferring interaction rules: revisited

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SLIDE 13

30 golden shiners

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SLIDE 14

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

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SLIDE 15 2 1 1 2 2 1 1 2 Distance Body length Distance Body length 21. 21.
  • Par. a ms2
0.0 0.5 1.0 1.5 2.0 2.5 20 10 10 20 Distance Body length Force parameter a ms2 Sector 1 0.0 0.5 1.0 1.5 2.0 2.5 20 10 10 20 Distance Body length Force parameter a ms2 Sector 2 0.0 0.5 1.0 1.5 2.0 2.5 20 10 10 20 Distance Body length Force parameter a ms2 Sector 3 0.0 0.5 1.0 1.5 2.0 2.5 20 10 10 20 Distance Body length Force parameter a ms2 Sector 4

Force matching example: attraction/repulsion

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SLIDE 16

30 fps

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Observational time scale: simulations

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 20 40 60 80 100 Radius Pairwise force 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 Pairwise force 1 2 3 4 5 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2 Radius Pairwise force

Original dt = 50 dt = 30 dt = 10 dt = 1

Lennard-Jones Quadratic Morse

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SLIDE 18

0.0 0.5 1.0 1.5 2.0 2.5 0.6 0.4 0.2 0.0 0.2 0.4 0.6 Distance Body length Force parameter c unitless sector 1 0.0 0.5 1.0 1.5 2.0 2.5 0.6 0.4 0.2 0.0 0.2 0.4 0.6 Distance Body length Force parameter c unitless sector 2 0.0 0.5 1.0 1.5 2.0 2.5 0.6 0.4 0.2 0.0 0.2 0.4 0.6 Distance Body length Force parameter c unitless sector 3 0.0 0.5 1.0 1.5 2.0 2.5 0.6 0.4 0.2 0.0 0.2 0.4 0.6 Distance Body length Force parameter c unitless sector 4 dt = 1 dt = 10 dt = 30 dt = 50

0.0 0.5 1.0 1.5 2.0 2.5 20 10 10 20 Distance Body length Force parameter a ms2 Sector 1 0.0 0.5 1.0 1.5 2.0 2.5 20 10 10 20 Distance Body length Force parameter a ms2 Sector 2 0.0 0.5 1.0 1.5 2.0 2.5 20 10 10 20 Distance Body length Force parameter a ms2 Sector 3 0.0 0.5 1.0 1.5 2.0 2.5 20 10 10 20 Distance Body length Force parameter a ms2 Sector 4

Observational time scale: experiments

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Effects of tracking difficulties

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Tracking accuracy per frame

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10 20 30 40 50 60 0.2 0.4 0.6 0.8 1 Statistics of individual track lengths Length of individual track [s] Fraction of tracks

Individual track lengths

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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 20 40 60 80 100 Radius Pairwise force 1 2 3 4 5 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2 Radius Pairwise force 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 Pairwise force

Lennard-Jones Quadratic Morse

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Observational time scale: simulations

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 20 40 60 80 100 Radius Pairwise force 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 Pairwise force 1 2 3 4 5 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2 Radius Pairwise force

Original dt = 50 dt = 30 dt = 10 dt = 1

Lennard-Jones Quadratic Morse

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SLIDE 24

0.0 0.5 1.0 1.5 2.0 2.5 2 1 1 2 Distance Body length Force parameter a ms2 Sector 1 0.0 0.5 1.0 1.5 2.0 2.5 2 1 1 2 Distance Body length Force parameter a ms2 Sector 2 0.0 0.5 1.0 1.5 2.0 2.5 2 1 1 2 Distance Body length Force parameter a ms2 Sector 3 0.0 0.5 1.0 1.5 2.0 2.5 2 1 1 2 Distance Body length Force parameter a ms2 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 10 20 Distance Body length Force parameter a ms2 Sector 1 0.0 0.5 1.0 1.5 2.0 2.5 20 10 10 20 Distance Body length Force parameter a ms2 Sector 2 0.0 0.5 1.0 1.5 2.0 2.5 20 10 10 20 Distance Body length Force parameter a ms2 Sector 3 0.0 0.5 1.0 1.5 2.0 2.5 20 10 10 20 Distance Body length Force parameter a ms2 Sector 4

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Force matching: three examples

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Attraction/repulsion Attraction/repulsion Alignment Attraction/repulsion Turning

Force matching: three examples

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Inspired by Daniel Strömbom

4 2 2 4 4 2 2 4 Distance Body length Distance Body length 6.9 6.9
  • Par. a ms2

Attraction/repulsion with blind angle

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SLIDE 28

Colin Twomey@CouzinLab

Interaction network: field of view

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Colin Twomey@CouzinLab

Interaction network: field of view

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Individual decision making

Colin Twomey@CouzinLab

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SLIDE 31

Individual decision making

Colin Twomey@CouzinLab

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Individual decision making

500 1000 1500
  • 300
  • 200
  • 100
100 200 300
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SLIDE 33 20 40 60 80 100 120 20 40 60 80 Scale free velocity correlations Square root of group area [cm] Correlation length [cm]

Physical properties

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Thanks.