Collective phases and long-term dynamics in a fish school model with burst-and-coast swimming.

Intermittent and asynchronous burst-and-coast swimming is widely adopted by various species of fish as an energy-efficient mode of locomotion. This swimming mode significantly influences how fish integrate information and make decisions in a social context. Here, we introduce a simplified fish school model in which individuals have an asynchronous burst-and-coast swimming mode and selectively interact only with one or two neighbours that exert the largest influence on their behaviour over a limited spatial range. The interactions consist of a fish that is attracted to and aligned with these neighbours. We show that, by adjusting the interactions between individuals above a sufficiently high level, depending on the relative strength of attraction and alignment, the model can produce a cohesive fish school that replicates the main collective phases observed in nature: schooling, milling and swarming when each individual interacts with only one neighbour; and schooling and swarming when each individual interacts with two neighbours. Moreover, the model showed that these patterns can be maintained over long simulations. However, with the exception of swarming, these patterns do not persist indefinitely, and fish lose cohesion and progressively disperse. We further identified the mechanisms that lead to group dispersion.