Effects of successive predator attacks on prey aggregations

We study the cumulative effect of successive predator attacks on the disturbance of a prey aggregation using a modelling approach. Our model intends to represent fish schools attacked by both aerial and underwater predators. This individual-based model uses long-distance attraction and short-distance repulsion between prey, which leads to prey aggregation and swarming in the absence of predators. When intermediate-distance alignment is added to the model, the prey aggregation displays a cohesive displacement, i.e., schooling, instead of swarming. Including predators, i.e. with repulsion behaviour for prey to predators in the model, leads to flash expansion of the prey aggregation after a predator attack. When several predators attack successively, the prey aggregation dynamics is a succession of expanding-grouping-swarming/schooling phases. We quantify this dynamics by recording the changes in the simulated prey aggregation radius over time. This radius is computed as the longest distance of individual prey to the aggregation centroid, and it is assumed to increase along with prey disturbance. The prey aggregation radius generally increases during flash expansion, then decreases during grouping until reaching a constant lowest level during swarming/schooling. This general dynamics is modulated by several parameters: the frequency, direction (vertical vs. horizontal) and target (centroid of the prey aggregation vs. random prey) of predator attacks; the distance at which prey detect predators; the number of prey and predators. Our results suggest that both aerial and underwater predators are more efficient at disturbing fish schools by increasing their attack frequency at such level that the fish cannot return to swarming/schooling. We find that a mix between aerial and underwater predators is more efficient at disturbing a fish school than a single type of attack, suggesting that aerial and underwater foragers may gain mutual benefits in forming foraging groups.