Switching effect on the stability of the prey-predator system with three trophic levels

The effect of predator switching on the stability of two- and three-trophic level systems is analyzed. It is assumed that the predator has a switching property characterized by two parameters: a measure of bias in switching response and the intensity of switching. In the two-trophic level system which consists of two prey and one predator species, the following two qualitative conclusions are derived: (1) the stabilizing influence of switching requires heterogeneity in prey intrinsic growth rates, and (2) the stabilizing effect is enhanced if the bias in switching response is toward the prey with a lower intrinsic growth rate. In the three trophic level system in which the consumption of one prey by the other prey is allowed, the analysis leads to three conclusions: (1) Too much exploitation of one prey by the other precludes the coexistence of the three species. (2) If a coexisting steady state exists and the death rate of the middle species is not very large, the system has a locally stable equilibrium point or a stable limit cycle so that all three species persist together. (3) When the top predator prefers the lower prey species to the middle species, then switching enhances the stability of the coexisting steady state as the consumption rate of the lowest level by the middle species increases. Finally it is shown for both systems mentioned above that the evolutionarily stable state with respect to switching parameters is dynamically stable.