Evolution of collective predator evasion: Putting the criticality hypothesis to the test*

Complex systems theory predicts that collective information processing becomes optimal at the border between order and disorder, i.e. at a critical point. Thus, animal collectives have been suggested to be examples of self-organized critical systems. However, evolutionary adaptation towards a possible group-level optimum, implicitly assumes group-level selection in general not relevant for groups of non-related individuals. Furthermore, previous theories rely on abstract models, which ignore spatial self-organization effects. Using a generic, spatially explicit model of collective predator avoidance, we show that schooling prey performance is indeed optimal at criticality, but surprisingly not due to optimal collective response, as predicted by the criticality hypothesis, but due to dynamical group structure. More importantly, structural sensitivity makes the critical state evolutionary highly unstable, demonstrating the crucial importance of spatial self-organization when discussing evolutionary benefits of collective animal behavior.