Predation on schooling fish is shaped by encounters between prey during school formation using an Ideal Gas Model of animal movement

Fish schools reduce their predators' encounter rates not only by performing evasive maneuvers but also by increasing distances between prey patches. However, a similar challenge applies to isolated prey fish seeking refuge during periods of diel school formation. We demonstrate with an Ideal Gas movement model that as the stock sizes of a fish who forms schools daily decreases, school densities do not change, yet their average sizes become smaller and the numbers of isolated prey increases dramatically. In this scenario, predator encounter rates remain remarkably equivalent across a few orders of magnitude in stock sizes, with a marginal peak at intermediate prey densities. However, even slight benefits from predator evasion maneuvers would decrease predation rates on larger schools substantially. In support we found empirically that higher proportions of prey fish fail to join schools at low stock sizes and that predator consumption rates decline as prey stock size increases.