Fish in a ring: spatio-temporal pattern formation in one-dimensional animal groups.

In this work, we study the collective behaviour of fish shoals in annular domains. Shoal mates are modelled as self-propelled particles moving on a discrete lattice. Collective decision-making is determined by information exchange among neighbours. Neighbourhoods are specified using the perceptual limit and numerosity of fish. Fish self-propulsion and obedience to group decisions are described through random variables. Spatio-temporal schooling patterns are measured using coarse observables adapted from the literature on coupled oscillator networks and features of the time-varying network describing the fish-to-fish information exchange. Experiments on zebrafish schooling in an annular tank are used to validate the model. Effects of group size and obedience parameter on coarse observables and network features are explored to understand the implications of perceptual numerosity and spatial density on fish schooling. The proposed model is also compared with a more traditional metric model, in which the numerosity constraint is released and fish interactions depend only on physical configurations. Comparison shows that the topological regime on which the proposed model is constructed allows for interpreting characteristic behaviours observed in the experimental study that are not captured by the metric model.