Prey gathering may act as a counterattack measure against predators.

Abstract

Two generalist predators not interfering with each other and hunting the same single prey that gathers in a herd are here considered. The system allows only two possible final outcomes, the prey-free state in which both predators thrive at their own carrying capacities, an equilibrium that is always present, and coexistence, which is not guaranteed to exist. When it arises, it does it in pair, of which one point is a saddle. As a result, the phase space is partitioned into two domains of attraction corresponding to these two equilibria. If the prey represents a pest, this result would provide a theoretical tool for its eradication, provided that it is coupled with some human external action, such as insecticide spraying, which however can be administered just in a mild way, sufficient to push the system trajectories into the prey-free point domain of attraction. If it is a species to be preserved instead, corresponding measures for enhancing its survival should be taken, such as increasing its reproductivity or lowering the predators’ pressure, so that the state of the system would fall into the attraction domain of the coexistence equilibrium.