Deciphering Interactions in Moving Animal Groups

Jacques Gautrais,Stéphane Blanco,Guy Theraulaz,Hugues Chaté,Marc Soria,Francesco Ginelli,Richard Fournier,Simon A Levin

doi:10.1371/journal.pcbi.1002678

Abstract

Collective motion phenomena in large groups of social organisms have long fascinated the observer, especially in cases, such as bird flocks or fish schools, where large-scale highly coordinated actions emerge in the absence of obvious leaders. However, the mechanisms involved in this self-organized behavior are still poorly understood, because the individual-level interactions underlying them remain elusive. Here, we demonstrate the power of a bottom-up methodology to build models for animal group motion from data gathered at the individual scale. Using video tracks of fish shoal in a tank, we show how a careful, incremental analysis at the local scale allows for the determination of the stimulus/response function governing an individual's moving decisions. We find in particular that both positional and orientational effects are present, act upon the fish turning speed, and depend on the swimming speed, yielding a novel schooling model whose parameters are all estimated from data. Our approach also leads to identify a density-dependent effect that results in a behavioral change for the largest groups considered. This suggests that, in confined environment, the behavioral state of fish and their reaction patterns change with group size. We debate the applicability, beyond the particular case studied here, of this novel framework for deciphering interactions in moving animal groups.

Highlights

Collective motion occurs across a variety of scales in nature, offering a wealth of fascinating phenomena which have attracted a lot of attention [1,2,3,4,5]
Fluctuations of speed can be allowed, some short-range repulsion can be added, even explicit alignment can be replaced by inelastic collisions, etc., all these changes will still produce the remarkable nonlinear high-density high-order bands emerging near onset of collective motion, and, deeper in the ordered moving phase, the anomalously strong number fluctuations which have become a landmark of the collective motion of polarly aligning self-propelled particles [16,17,18,19,20]
Schools of fish and flocks of birds display an impressive variety of collective patterns that emerge from local interactions among group members

Summary

Introduction

Collective motion occurs across a variety of scales in nature, offering a wealth of fascinating phenomena which have attracted a lot of attention [1,2,3,4,5]. The self-organized motion of social animals is intriguing because the behavioral rules the individuals follow and from which these remarkable collective phenomena emerge often remain largely unknown due to the tremendous difficulties to collect quality field data and/or perform controlled experiments in the laboratory This situation does not prevent a thriving modeling activity, thanks to the relative ease by which numerical simulations can be conducted. Recent studies within the physics community of simple, minimal models for collective motion have revealed an emerging picture of universality classes [11,12,13,14,15]: Take, for instance, the Vicsek model, arguably one of the simplest models exhibiting collective motion In this model, point particles move at constant speed and choose, at discrete time-steps, their new heading to be the average of that of their neighbors located within unit distance. Different models in this class merely differ in the numerical values of their parameters [21,22,23], very much like different fluids are commonly described by the Navier-Stokes equations and differ only in their viscosity and other constitutive parameters

Methods

Results

Discussion

Conclusion