Positional choice and robust collective behavior in fish schools: biohybrid experiments and modeling
Abstract: Collective behavior of fish schools is usually modeled on the assumption that each individual follows specific rules of motion that depend on its position and velocity relative to its neighbors. Although these models reproduce many schooling patterns observed in nature, it remains unclear whether the assumed rules are realistic at the individual level. To address this question, we first analyzed a set of experiments in which a live fish interacted with four moving robotic fish in a tank, and measured the time it spent in each position relative to the robots. We then simulated this experiment, replacing the fish with an agent, and assessed the extent to which classical models agree with the experimental observations. An extensive exploration of the parameter space showed that these models closely matched the experimental observations, with a very specific choice of parameters. However, they were highly sensitive to the parameter values: a minor perturbation caused them to fail completely. To resolve this, we propose a new model that incorporates an additional exploratory term characterizing the agent's positional preference at every moment. This model proved robust to small errors in the parameters while successfully replicating the experiments. Furthermore, when generalised to multiple fish, the model reproduced schooling behaviour and common schooling patterns, while also exhibiting exploratory behaviour at both the individual and the school level. This shows that social cohesion coexists with individual exploratory behaviour, and that realistic models of collective behaviour should account for both social interactions and this exploratory component.