Collective response to perturbations in a data-driven fish school model

Abstract

Fish schools are able to display a rich variety of collective states and behavioural responses when they are confronted by threats. However, a school's response to perturbations may be different depending on the nature of its collective state. Here we use a previously developed data-driven fish school model to investigate how the school responds to perturbations depending on its different collective states, we measure its susceptibility to such perturbations, and exploit its relation with the intrinsic fluctuations in the school. In particular, we study how a single or a small number of perturbing individuals whose attraction and alignment parameters are different from those of the main population affect the long-term behaviour of a school. We find that the responsiveness of the school to the perturbations is maximum near the transition region between milling and schooling states where the school exhibits multistability and regularly shifts between these two states. It is also in this region that the susceptibility, and hence the fluctuations, of the polarization order parameter is maximal. We also find that a significant school's response to a perturbation only happens below a certain threshold of the noise to social interactions ratio.

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.…”

“…In contrast to the previous models mentioned in [8,33], we also provide a function f d which restricts the range of both the speed and turning response, defined as follows:…”

“…Its motion is driven by the same equations in (3), with speed U 0 (t), but where Ω 0 (t) = 0 and σ u dW (t) = 0, ∀t. A compatible interaction network between all agents is chosen based on a periodic equivalent to the non-metric Voronoi neighbourhood used in related models [8,13,33,45]. A more detailed description and a diagram of the construction of this topology is shown in Fig.…”

“…Effects of controlled external stimuli have also been studied, specifically the use of biomimetic robots (ethorobotics) to elicit responses both at the individual level [24][25][26] and in the collective behaviour of fish shoals [27][28][29][30]. Meanwhile, purely computational studies have explored the dynamic response of biologically inspired mobile agents in the presence of an informed agent or group of agents [31][32][33].…”