Swarming, Schooling, Milling: Phase diagram of a data-driven fish school model

TL;DR

This study maps the phase diagram of a data-driven fish school model, revealing conditions for schooling and milling behaviors, and how group size and interaction rules influence these collective dynamics.

Contribution

It extends previous models by exploring parameter space beyond experimental values and introduces a frontal preference, analyzing behavioral transitions in fish schools.

Findings

Milling and schooling coexist in a transition region with multistability.

Large groups do not exhibit milling due to interaction distance and delays.

Behavioral transitions depend on social interactions and group size.

Abstract

We determine the basic phase diagram of the fish school model derived from data by Gautrais etal (PLoS Comp. Biol. 8, e1002678 (2012)), exploring its parameter space beyond the parameter values determined experimentally on groups of barred flagtails (Kuhlia mugil}) swimming in a shallow tank. A modified model is studied alongside the original one, in which an additional frontal preference is introduced in the stimulus/response function to account for the angular weighting of interactions. Our study, mostly limited to groups of moderate size (in the order of 100 individuals), focused not only on the transition to schooling induced by increasing the swimming speed, but also on the conditions under which a school can exhibit milling dynamics and the corresponding behavioral transitions. We show the existence of a transition region between milling and schooling, in which the school exhibits multistability and intermittency between schooling and milling for the same combination of individuals parameters. We also show that milling does not occur for arbitrarily large groups, mainly due to a distance dependence interaction of the model and information propagation delays in the school, which cause conflicting reactions for large groups. We finally discuss the biological significance of our findings, especially the dependence of behavioural transitions on social interactions, which were reported by Gautrais etal to be adaptive in the experimental conditions.