Swarming, schooling, milling: phase diagram of a data-driven fish school model

Abstract

We determine the basic phase diagram of the fish school model derived from data by Gautrais et al (2012 PLoS Comput. Biol. 8 e1002678), 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 behavioural transitions. We show the existence of a transition region between milling and schooling, in which the school exhibits multistability and intermittence between schooling and milling for the same combination of 7

Leadership emergence in a data-driven model of zebrafish shoals with speed modulation

“…The turning interaction function is further supplemented by an additional prefactor (1 + cos θ ij ) which imparts an angular weighting on the turning interaction, maximised when the neighbour is directly in front with respect to the viewing angle of the focal fish. As described in [33,44], this extra position-dependence breaks the otherwise symmetric force response allowing for stable rotational (milling) and winding collective phases to emerge, producing qualitatively better fits to the group behaviour of small zebrafish shoals.…”

“…Our interaction model is adapted from the previous work of Gautrais et al [8] and subsequent modifications by Calovi and others in [33,44]. We derive a minimal model in which each contributing term, and associated parameters, are constrained by features observed directly from the experiment.…”

Collective dynamics of soft active particles

“…In fact, most of these systems display both types of behavior, e.g. fish switch between migration and rotation (milling) [2,15], and, depending on environmental conditions, slime molds [6,16,17] and bacteria [18][19][20] will migrate or rotate. For example, the slime mold Dictyostelium discoideum (or Dicty) will collectively migrate if food is scarce, but transitions to a vortex to form a fruiting body as a last resort [21].…”

Analysis of Pairwise Interactions in a Maximum Likelihood Sense to Identify Leaders in a Group

“…The instantaneous turn rate at time t is modeled by the mean reverting stochastic differential process (Gautrais et al, 2012;Calovi et al, 2014) …”

“…First, we demonstrate the ability to detect a leader in a synthetic dataset generated using a data-driven model (Gautrais et al, 2012;Calovi et al, 2014), in which the turn rate of each fish is described as a mean reverting diffusion process. Through our combined approach, we are successful in precisely isolating the leader from the rest of the group.…”