Critical density in collective escape waves in fish*

Living systems such as neural networks or animal groups process information about their environment via the dynamics of many interacting units and can transition between distinct macroscopic behaviors. While many studies focus on the idea that being close to such a transition optimally manages a trade-off between desired functions of the macroscopic behaviors, or yields optimal computation, little attention has been given to the fact that this ’optimality’ will depend on environmental context. Here, we combine experimental data and computer simulations to show that for escape waves in schooling fish the distance to a critical point is changed according to the environment’s perceived risk via a modulation of density. We find that even though dynamical range and sensitivity are maximized at the critical point, the fish schools remain subcritical, which we attribute to a trade-off between false and true positives.