Spontaneous response of a self-organized fish school to a predator

While the collective movements of fish schools evading predators in nature are complex, they can be fundamentally represented by simplified mathematical models. Here we develop a numerical model, which considers self-propelled particles subject to phenomenological behavioural rules and the hydrodynamic interactions between individuals. We introduce a predator in this model, to study the spontaneous response of a group of simulated fish to the threat. A self-organized fish school with a milling pattern is considered, which was expected to be efficient to evade the threat of predators. Four different attack tactics are adopted by the predator. We find that the simulated fish form transiently smaller structures as some prey individuals split from the main group, but eventually they will re-organize, sometimes into sub groups when the simulated predator approaches the fish school unidirectionally or take a reciprocating action. As the predator is programmed to target the centroid, the school ends in a gradually enlarging circle. For the fourth tactic, as the predator chases its nearest prey, the fish school's response varies with the predator's delay factor. Moreover, the average speed of the group and the distance between individuals have also been studied, both demonstrating that the fish school is able to respond spontaneously to the predator's invasion. We demonstrate that the currently adopted model can predict prey-predator interactions.