From individual to collective information processing in fish schools ...

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From individual to collectiveinformation processing in fish schools

Crowd DynamicsInternational Conference on

Mathematical Modeling and ApplicationsMeiji University, Tokyo, January 11, 2015

Guy TheraulazCentre de Recherches sur la Cognition Animale

CNRS, UMR 5169, Toulouse, France

© Alex Mustard

From individual to collectiveinformation processing in fish schools

© Christopher Swann

Scomber scombrus

To coordinate their actions fishhave to exchange someinformation and perform somespecific actions (controllinglinear and turning velocities) inresponse to this information

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Collective motion in biological systems

Paenibacillus vortex

Sphyraena barracuda

Paenibacillus vortex

Sphyraena barracuda

© Eshel Ben Jacob© Eshel Ben Jacob

Sturnus vulgaris ( © C. Carrere )

Collective motion in bird flocks

Ballerini, M. et al., PNAS (2008); Cavagna, A. et al., PNAS (2010); Bialek, W. et al., PNAS (2012)

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Océans, (2010)Directed byJacques Perrin,Pathé Distribution

Collective motion in fish schools

Sphyraena barracuda

Collective motion in fish schoolsSchooling manoeuvres in response to predator attacks

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Collective motion in fish schoolsCollective patterns arising from interactions between fish

What are the interactions rules and behavioral mechanismsinvolved in the coordination of collective motion?

Determining interactions rulesWhat kind of information is collected?

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Determining interactions rulesWhat kind of information is collected?

ii

jposition

velocity

heading?

What kind of information is collected?

Determining interactions rules

6

What are the neighboring partners involved in the interaction?


Determining interactions rulesWhat are the neighboring partners involved in the interaction?

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8

i

How is the information combined?


Cavagna, A. et al., Proc. R. Soc. B (2013)

Quantification of behaviours atdifferent scales and in groupsof different sizes

Connecting micro-level tomacro-level: how do complexpatterns emerge out of localinteractions among individuals?

Trajectory analysis is used tobuild a model of spontaneousmovement

A methodology to build reliable modelsIndividual level

Trajectory analysis

Weitz, S. et al., Plos One (2012)Gautrais, J. et al., Plos ComputationalBiology (2012)

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Interactions between pairs ofindividuals are characterized

Computational models aredeveloped to test assumptionsabout the combination ofinformation sources at theindividual level and theresulting behavioural decision

The already-determinedparameters are keptunchanged and the stimulus-response function and thecorresponding parameters aredetermined from data

stimulus

Beh

avio

ral

resp

onse

S1

S2

S3

Behavioralresponse

Computationalmodel

Response functions

Pair interactions

A methodology to build reliable models


Collective level: combining manyinteractions

Dynamics of interaction network

To how many neighbors doindividuals respond, and what isthe relative weight given to each?

Quantitative predictions: is themodel able to accurately predictthe collective dynamics and theoutcome of novel situations?

The incremental analysis allows abetter understanding of the roleplayed by each behavioralcomponent in the observedcollective pattern

A methodology to build reliable models


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La Réunion

Saint-Leu

Coral Farm

Study site

Empirical investigation of fish schooling

10 cm

Khulia mugil

Study species: the barred flagtail


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5 Fish

30 Fish

4 m

Single fish and groups ofincreasing size (N = 2, 5,10, 15, 30) have beenrecorded in a 4-m wide and1-m depth tank

Two minutes wereextracted from digital videorecordings and the positionof the individual's head wastracked every 1/12 s (1440data-points per trajectory)

Experimental setup and video tracking


5 Fish

30 Fish

b

Time (s)

Alig

nmen

t

Group polarization

Empirical investigation of fish schoolingExperimental setup and video tracking

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The swimming speed ofeach fish is constant

Gautrais, J. et al., J. Math. Biol., (2009)

Time (s)S

(t)

Modeling single fish behavior and wall avoidance

Swimming speed(m/s)

Curvilinear distance

Spontaneous fish movement

Turning speed(rad/s)

The swimming speed ofeach fish is constant

The observed motionresults from a control of theturning speed

There is a significantautocorrelation of theturning speed

There is a spontaneoustendency of the fish torandomly change theturning speed


Swimming speed(m/s)

Spontaneous fish movement


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A persistent turning walker model of fish movement


Wall

Spontaneous swimming

: characteristic time of the (exponentially decaying)autocorrelation function of




Wall avoidance

1 m

Walldistance before collision

Spontaneous swimming


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ModelData

Wall avoidance

Mean squaredisplacement ( m 2 s -1 )

Time (s)

Data

Model




Deciphering interactions between pairs of fish

Mea

n sp

eed

Experiments

E1 E2 E3 E4 E5 E6

Tracking the movementpatterns in groups of 2 fish

Fish n°1

Fish n°2


Gautrais, J. et al., Plos Computational Biology (2012)

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_

+

Speed

Time

Pola

rizat

ion

Influence of swimming speed on coordination and alignment

Synchronization increaseswith swimming speed

Directional information is arequired component toachieve synchronization

Positional information islikely to play a key role inthe cohesion of the school



Influence of swimming speed on coordination and alignment

The degree ofsynchronization increasesas a result of an increaseof swimming speed

Directional information is arequired component toachieve synchronization

Positional information islikely to play a key role inthe cohesion of the school


Kowalko, J.E. et al., Current Biology (2013)

Light Dark

Pro

porti

on o

f tim

eS

pent

sch

oolin

g

Astyanax mexicanus

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Positional effect (attraction): turn towards the neighbor

Characterizing interactions between pairs of fish in the model

Fish i

Fish j

Short inter-distance


Modeling pair interactions

Positional effect (attraction): turn towards the neighbor

Large inter-distance




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Directional information (alignment): turn to align with the neighbor

Low swimming speed




Directional information (alignment): turn to align with the neighbor

High swimming speed




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Directionaleffect

Walleffect

Positionaleffect


Parameter estimation


Data-driven fish school model

Directionaleffect

Walleffect

Positionaleffect

ModelData2 Fish

Speed Speed

PolarizationData

Model

Mean inter-individual distance

0.024 m 28.9 m-1 s-1/2

0.94 0.41 m-1 s-1 2.7 m-1


Data-driven fish school modelModeling pair interactions

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rc

Metric interactions

Determining the number and position of influential neighbors

To how many neighbors doindividuals respond, andwhat is the relative weightgiven to each?

In starling flocks each birdinteracts with a fixednumber of neighbors (6-7)irrespective of theirdistance


Ballerini, M. et al., PNAS (2008)Raynaud, F. 3D Collective Behavior Models.

Ph.D. thesis, Université Paris 7 (2009)

Topological interactions To how many neighbors do

individuals respond, andwhat is the relative weightgiven to each?

In starling flocks each birdinteracts with a fixednumber of neighbors (6-7)irrespective of theirdistance



Ballerini, M. et al., PNAS (2008)Raynaud, F. 3D Collective Behavior Models.

Ph.D. thesis, Université Paris 7 (2009)

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K Nearest Neighbors?

KNN = 7



Approximating "visible" neighbors with a greedy triangulation




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Weighting all influential neighborsModelData

5 Fish Simplest assumption:averaging the influence ofall "visible" neighbors

DataModel

Speed Speed

Mean inter-individual distance Polarization

0.024 m 28.9 m-1 s-1/2

0.94 0.41 m-1 s-1 2.7 m-1



2 Fish

5 Fish

10 Fish

15 Fish

30 Fish

Mean inter-individual distancePolarization

DataModelNo interaction

Comparison between model predictions and experimental data


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Gregarious locusts

Solitarious locust

Serotoninlevel

Anstey et coll.,Science (2009)

Quantification of group-size effect

Group size


2 Fish

5 Fish

10 Fish

15 Fish

30 Fish



Data-driven fish school modelComparison between model predictions and experimental data

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Comparison between model predictions and experimental data

30 Fish

ModelData



Gautrais, J. et al., PLoS Computational Biology (2012)


Speed

What are the the modelpredictions for larger groups inunbounded space?

Speed = 0.2 m/s

Speed = 0.9 m/s

Speed-induced transition to schooling100 Fish

Swarming

Schooling

Model properties

Polarization

Calovi, D. et al., New Journal of Physics (2014)

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Speed

What are the the modelpredictions for large groups inunbounded space?

Time

Spe

ed

Group polarizationincreases with velocity

Polarization

Speed-induced transition to schooling

Model properties

Neighbor ahead

Neighbors’ influence depends on their position


Attraction Alignment

Neighbor behind

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Neighbors’ influence depends on their position


Attraction Alignment

In a confined environmentthe influence of the spatialmodulation of interactionson collective motionpatterns cannot bedetected (reaction to thewall and to the density offish)

Neighborahead

Neighborbehind

Angular weighting of fish interactions

Model properties

Calovi, D. et al., New Journal of Physics (2014)

i

j

i

j

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Parameter space effect on polarization (schooling)

Exploring the parameter space

Polarization

Transition to schooling isindependent of the attraction

Transition to schoolingdepends on the attraction

Polarisation (Schooling) : Orderparameter that tends to unity as fishare aligned, and zero when swarming

Attraction ( γ ) = 0.8 m/s(N = 100 fish)

Attraction ( γ )

Alig

nmen

t ( β

)

Parameter space effect on angular momentum (Milling)

Milling

No milling region detected A large milling region isobserved

Angular momentum (Milling) : Orderparameter that tends to unity as fishare swimming in a perfect circle


Alig

nmen

t ( β

)

Attraction ( γ ) Attraction ( γ ) = 0.8 m/s(N = 100 fish)

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Region I: Schooling

Polarization

Milling

Nearestneighbor distance

Time ( s)

Pol

ariz

atio

n &

Mill

ing

I

PolarizationMilling


Calovi, D. et al., New Journal of Physics (2014)Attraction ( γ )

Alig

nmen

t ( β

)

Polarization

Milling



Alig

nmen

t ( β

)

Region II: Milling

Time ( s)

Pol

ariz

atio

n &

Mill

ing

II

PolarizationMilling


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Region III: Winding zone (line configuration)

Time ( s)

Pol

ariz

atio

n &

Mill

ing

PolarizationMilling

III


Polarization

Milling



Alig

nmen

t ( β

)

Region III: Winding zone (line configuration)

School of Atlantic herring(Clupea harengus)© P. Brehmer, IRD


III

Polarization

Milling



Alig

nmen

t ( β

)

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Region I-II: Transition zone

Time ( s)

Pol

ariz

atio

n &

Mill

ing

PolarizationMilling


Polarization

Milling


Tunstrøm, K. et al., PLoS Computational Biology (2013)Attraction ( γ )

Alig

nmen

t ( β

)

I-II

Enhanced collective response to perturbationsin the transition zone

Model properties

Attraction ( γ )

Alig

nmen

t ( β

)

Calovi, D. et al., Journal of the Royal Society Interface (2015)

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Enhanced collective response to perturbationsin the transition zone close to criticality

Model properties

Attraction ( γ )

Alig

nmen

t ( β

)

Difference in averagepolarization

III

II

IN = 100 fish4.102 simulation runsAverage over 1039 s

I-II

The maximumresponse of theschool toperturbations isreached In thetransition zonebetweenschooling andmilling

Calovi, D. et al., Journal of the Royal Society Interface (2015)

Wrap-up: main findings

An incremental methodologywas used to build a fishbehavior model completelybased on interactions with thephysical environment andneighboring fish

There is a continuous balancingbetween attraction andalignment behavior as afunction of the distancebetween fish

Emergent coordination in fish schools

Khulia mugil

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© Octavio Aburto© Octavio Aburto

Conclusions

Emergent coordination in fish schools

Caranx sexfasciatum

© Octavio Aburto© Octavio Aburto

The modulation of strength of thealignment and attraction behaviorsplays a key role in the kind ofcollective motion pattern thatemerge at the school level

By providing a high responsivenessto perturbations the transition regionbetween milling and schooling is ahighly desired state that optimizesthe ability of the fish to reactcollectively (e.g. to a predatorattack) thus increasing the survivalof fish

Acknowledgements

Centre de Recherches sur la CognitionAnimale, CNRS, Université Paul SabatierToulouse, France

UMR EME, Institut de Recherchepour le Développement (IRD)La Réunion, France

Service de Physique de l’EtatCondensé, CEAGif-sur-Yvette, France

Laboratoire Plasma et Conversiond’Energie, CNRS, Université PaulSabatier, Toulouse, France

J. Gautrais R. FournierM. Soria H. Chaté F. Ginelli S. BlancoD.S. Calovi

From individual to collective information processing in fish schools ...

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