Influence of predation on species coexistence in Volterra models

The possibility of predator-mediated coexistence of all species in model ecosystems of the Volterra type is discussed, that is, asymptotic behaviors of systems of two competing species are analyzed when one or two predators are added. All species in the communities can coexist in two distinct ways mathematically, that is, the species may coexist at equilibrium or may coexist in persistent oscillations. The stability of all species at equilibrium increases when one or two predators are added. The conditions for oscillatory coexistence in limit cycles or in chaotic behaviors of two-predator systems are more complicated than in those of one-predator systems. It is concluded that predator-mediated coexistence can be promoted by an intimate relationship between the competitive ability of the prey and the diet preference of the predators.