Interactions between egg-eating predator and prey: The effect of the functional response and of age structure

In this paper we analyse an age-structured predator-prey model in which predators eat only very young prey. The model can be formulated as a system of three Volterra integral equations with an implicitly defined non-linearity. An interpretation of the implicit relation is given. The linearized stability of the steady states is investigated. It turns out that concentration of the predator on very young individuals is a stabilizing mechanism. Furthermore, it is seen that a compound parameter which is a measure for the efficiency of the predator has a major influence on the stability of the steady states. If the efficiency of the predator decreases the steady state can become unstable and oscillations will arise. Furthermore it is seen from the model that the destabilizing effect of a juvenile period is stronger when it concerns the predator than when it concerns the prey species. In an appendix it is shown that an egg-eating predator and an indiscriminately eating predator can coexist in a stable steady state while feeding on only one prey species.