A simple cognitive model explains movement decisions during schooling in zebrafish
While moving, animals must frequently make decisions about their future travel direction, whether they are alone or in a group. Here we investigate this process for zebrafish (Danio rerio), which naturally move in cohesive groups. Employing state-of-the-art virtual reality, we study how real fish follow one or several moving, virtual conspecifics. These data are used to inform, and test, a model of social response that includes a process of explicit decision-making, whereby the fish can decide which of the virtual conspecifics to follow, or to follow some average direction. This approach is in contrast with previous models where the direction of motion was based on a continuous computation, such as directional averaging. Building upon a simplified version of this model [Sridhar et al., 2021], which has been shown to exhibit a spontaneous symmetry-breaking transition from moving along a "compromise" (average) direction, to deciding on following one of the virtual fish. This previously published simplified version was limited to a one-dimensional projection of the fish motion, while here we present a model that describes the motion of the real fish as it swims freely in two-dimensions. Here, we extend our proposed Ising-like model, which inherently describes a spontaneous symmetry-breaking transition from moving along a "compromise" (average) direction, to deciding on following one of the virtual fish. Motivated by experimental observations, the swim speed of the fish in this model uses a burst-and-coast swimming pattern, with the burst frequency being dependent on the distance of the fish from the followed conspecific(s). We demonstrate that this model is able to explain the observed spatial distribution of the real fish behind the virtual conspecifics in the experiments, as a function of their average speed and number. In particular, the model naturally explains the observed critical bifurcations for a freely swimming fish, which appear in the spatial distributions whenever the fish makes a decision to follow only one of the virtual conspecifics, instead of following them as an averaged group. This model can provide the foundation for modeling a cohesive shoal of swimming fish, while explicitly describing their directional decision-making process at the individual level.