Self-reorganization and information transfer in large-scale models of fish schools.

The remarkable cohesion and coordination of moving animal groups and their collective responsiveness to threats are often attributed to scale-free correlations, where behavioral changes in one animal influence others in the group, regardless of the distance between them. But are these features independent of group size? Here, we investigate group cohesiveness and collective responsiveness in computational models of massive schools of fish of up to 50,000 individuals. We show that as the number of swimmers increases, flow interactions destabilize the school, creating clusters that constantly fragment, disperse, and regroup, much like in natural animal groups. Importantly, while spatial correlations in cohesive and polarized clusters are indeed scale free, fragmentation events are preceded by a decrease in correlation length, weakening the group's collective responsiveness and leaving it more vulnerable to predation. We further show that information about directional changes propagates linearly in time among group members, thanks to the non-reciprocal nature of visual interactions between individuals. Merging events speed up this information transfer, while fragmentation slows it down. Our findings suggest that flow interactions may have played an important role in group size regulation, behavioral adaptations, and dispersion in living animal groups.