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Using neuronal models to capture burst and glide motion and leadership in fish

While mathematical models, in particular self-propelled particle (SPP) models, capture many of the observed properties of large fish schools, they do not always capture the interactions of smaller shoals. Nor do these models tend to account for the observation that, when swimming alone or in smaller groups, many species of fish use intermittent locomotion, often referred to as burst and coast or burst and glide. Recent empirical studies have suggested that burst and glide movement is indeed pivotal to the social interactions of individual fish. In this paper, we propose a model of social burst and glide motion by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. We begin by showing that the model can capture the motion of a single fish swimming down a channel. By then extending to a two fish model, where visual stimuli of the position of the other fish affect the internal burst or glide state of the fish, we find that our model captures a rich set of swimming dynamics found in many species of fish. These include: leader-follower behaviour; periodic changes in leadership; apparently random (i.e. chaotic) leadership change; and pendulum-like tit-for-tat turn taking. Unlike SPP models, which assume that fish move at a constant speed, the model produces realistic motion of individual fish. Moreover, unlike previous studies where a random component is used for leadership switching to occur, we show that leadership switching, both periodic and chaotic, can be the result of a deterministic interaction. We give several empirically testable predictions on how fish interact and discuss our results in light of recently established correlations between fish locomotion and brain activity.

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