Deep attention networks reveal the rules of collective motion in zebrafish

Abstract

A variety of simple models has been proposed to understand the collective motion of animals. These models can be insightful but lack important elements necessary to predict the motion of each individual in the collective. Adding more detail increases predictability but can make models too complex to be insightful. Here we report that deep attention networks can obtain in a data-driven way a model of collective behavior that is simultaneously predictive and insightful thanks to an organization in modules. The model obtains that interactions between two zebrafish, Danio rerio, in a large groups of 60-100, can be approximately be described as repulsive, attractive or as alignment, but only when moving slowly. At high velocities, interactions correspond only to alignment or alignment mixed with repulsion at close distances. The model also shows that each zebrafish decides where to move by aggregating information from the group as a weighted average over neighbours. Weights are higher for neighbours that are close, in a collision path or moving faster in frontal and lateral locations. These weights effectively select 5 relevant neighbours on average, but this number is dynamical, changing between a single neighbour to up to 12, often in less than a second. Our results suggest that each animal in a group decides by dynamically selecting information from the group. Highlights• At 30 days postfertilization, zebrafish, Danio rerio, can move in very cohesive and predictable large groups• Deep attention networks obtain a predictive and understadable model of collective motion• When moving slowly, interations between pairs of zebrafish have clear components of repulsion, attraction and alignment• When moving fast, interactions correspond to alignment and a mixture of alignment and repulsion at close distances • Zebrafish turn left or right depending on a weighted average of interaction information with other fish, with weights higher for close fish, those in a collision path or those moving fast in front or to the sides • Aggregation is dynamical, oscillating between 1 and 12 neighbouring fish, with 5 on average

Genetic Control of Collective Behavior in Zebrafish

“…neighbors (Couzin et al, 2002;Calovi et al, 2018;Heras et al, 2018;Harpaz et al, 2017;Katz et al, 2011;. We use a model to ask if salient observed differences in collective motion (i.e., the scattered, huddled, and coherent collective motion patterns) can be explained by differences in how individuals turn in response to neighboring fish.…”

“…where s i is the speed of the focal individual, r j , φ j , and θ j are the neighbor distance, angular position, and relative heading, respectively (Fig 4A ), and N = 6 is the number of fish. Following Heras et al (2018), we formulate the model as a 'turn-classifier' and calculate P i , the probability of turning left after a specified time delay, using a logistic function with weight parameter w. Positive values of z i predict left-turns, and negative values predict right turns, with the magnitude setting the probability of the prediction. The terms on the right-hand side of Eq.…”

“…Because of the speed differences, we use different values of τ for each line. For WT, we set τ = 1 sec (this value was used in other modeling work that examined motion prediction of adult zebrafish (Heras et al, 2018)). For the other lines we use a scaled value τ S WT /S L , where S WT is the median speed for WT and S L is the median speed for line L. With this scaling, predictions are made after approximately the same distance traveled for lines that moved at different speed.…”

“…The combination of Eqs. 7-8 is a standard formulation for binary classification, and we fit using a soft-margin loss function (Heras et al, 2018) (Goodfellow et al, 2017) with additional normalization constraints on the interaction functions implemented via a Lagrange-multiplier approach. The loss function for line L is E = ln (1 + exp [−P i (t) sgn(γ i (t, τ S WT /S L ))]) i,t…”

The zebrafish subcortical social brain as a model for studying social behavior disorders

“…Researchers have modeled individual behavioral rules in response to the motion of a social stimulus fish using theoretical frameworks based on the Bayesian decision theory (Box 2) (Arganda et al, 2012) and transfer entropy (Box 2) (Porfiri and Ruiz Marín, 2017). Other studies first improved continuous tracking of individuals and then computationally modeled pairwise interactions using the optimal control theory (Laan et al, 2017), deep attention networks (Heras et al, 2018), transfer entropy (Butail et al, 2016) and other data-driven methods (Zienkiewicz et al, 2018) to reveal how pairs of individuals attract, repulse and align with each other.…”