from individual to collective information processing in fish schools
TRANSCRIPT
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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
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What are the neighboring partners involved in the interaction?
Determining interactions rules
Determining interactions rulesWhat are the neighboring partners involved in the interaction?
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Determining interactions rulesWhat are the neighboring partners involved in the interaction?
Determining interactions rulesWhat are the neighboring partners involved in the interaction?
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i
How is the information combined?
Determining interactions rules
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
Weitz, S. et al., Plos One (2012)Gautrais, J. et al., Plos ComputationalBiology (2012)
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
Weitz, S. et al., Plos One (2012)Gautrais, J. et al., Plos ComputationalBiology (2012)
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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
Empirical investigation of fish schooling
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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
Empirical investigation of fish schooling
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
Gautrais, J. et al., J. Math. Biol., (2009)
Swimming speed(m/s)
Spontaneous fish movement
Modeling single fish behavior and wall avoidance
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A persistent turning walker model of fish movement
Gautrais, J. et al., J. Math. Biol., (2009)
Wall
Spontaneous swimming
: characteristic time of the (exponentially decaying)autocorrelation function of
Modeling single fish behavior and wall avoidance
A persistent turning walker model of fish movement
Gautrais, J. et al., J. Math. Biol., (2009)
Wall avoidance
1 m
Walldistance before collision
Spontaneous swimming
Modeling single fish behavior and wall avoidance
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ModelData
Wall avoidance
Mean squaredisplacement ( m 2 s -1 )
Time (s)
Data
Model
A persistent turning walker model of fish movement
Gautrais, J. et al., J. Math. Biol., (2009)
Modeling single fish behavior and wall avoidance
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
Empirical investigation of fish schooling
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
Empirical investigation of fish schooling
Gautrais, J. et al., Plos Computational Biology (2012)
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
Empirical investigation of fish schooling
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
Gautrais, J. et al., Plos Computational Biology (2012)
Modeling pair interactions
Positional effect (attraction): turn towards the neighbor
Large inter-distance
Characterizing interactions between pairs of fish in the model
Gautrais, J. et al., Plos Computational Biology (2012)
Modeling pair interactions
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Directional information (alignment): turn to align with the neighbor
Low swimming speed
Characterizing interactions between pairs of fish in the model
Gautrais, J. et al., Plos Computational Biology (2012)
Modeling pair interactions
Directional information (alignment): turn to align with the neighbor
High swimming speed
Characterizing interactions between pairs of fish in the model
Gautrais, J. et al., Plos Computational Biology (2012)
Modeling pair interactions
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Directionaleffect
Walleffect
Positionaleffect
Modeling pair interactions
Parameter estimation
Gautrais, J. et al., Plos Computational Biology (2012)
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
Gautrais, J. et al., Plos Computational Biology (2012)
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
Data-driven fish school model
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
Determining the number and position of influential neighbors
Data-driven fish school model
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
Determining the number and position of influential neighbors
Data-driven fish school model
Approximating "visible" neighbors with a greedy triangulation
Determining the number and position of influential neighbors
Gautrais, J. et al., Plos Computational Biology (2012)
Data-driven fish school model
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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
Gautrais, J. et al., Plos Computational Biology (2012)
Data-driven fish school model
2 Fish
5 Fish
10 Fish
15 Fish
30 Fish
Mean inter-individual distancePolarization
DataModelNo interaction
Comparison between model predictions and experimental data
Data-driven fish school model
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Gregarious locusts
Solitarious locust
Serotoninlevel
Anstey et coll.,Science (2009)
Quantification of group-size effect
Group size
Data-driven fish school model
2 Fish
5 Fish
10 Fish
15 Fish
30 Fish
Mean inter-individual distancePolarization
DataModelNo interaction
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
Mean inter-individual distancePolarization
DataModelNo interaction
Gautrais, J. et al., PLoS Computational Biology (2012)
Data-driven fish school model
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
Empirical investigation of fish schooling
Attraction Alignment
Neighbor behind
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Neighbors’ influence depends on their position
Empirical investigation of fish schooling
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
Exploring the parameter space
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
Exploring the parameter space
Calovi, D. et al., New Journal of Physics (2014)Attraction ( γ )
Alig
nmen
t ( β
)
Polarization
Milling
Nearestneighbor distance
Calovi, D. et al., New Journal of Physics (2014)Attraction ( γ )
Alig
nmen
t ( β
)
Region II: Milling
Time ( s)
Pol
ariz
atio
n &
Mill
ing
II
PolarizationMilling
Exploring the parameter space
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Region III: Winding zone (line configuration)
Time ( s)
Pol
ariz
atio
n &
Mill
ing
PolarizationMilling
III
Exploring the parameter space
Polarization
Milling
Nearestneighbor distance
Calovi, D. et al., New Journal of Physics (2014)Attraction ( γ )
Alig
nmen
t ( β
)
Region III: Winding zone (line configuration)
School of Atlantic herring(Clupea harengus)© P. Brehmer, IRD
Exploring the parameter space
III
Polarization
Milling
Nearestneighbor distance
Calovi, D. et al., New Journal of Physics (2014)Attraction ( γ )
Alig
nmen
t ( β
)
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Region I-II: Transition zone
Time ( s)
Pol
ariz
atio
n &
Mill
ing
PolarizationMilling
Exploring the parameter space
Polarization
Milling
Nearestneighbor distance
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