A Stage-structured Predator-prey Model

This chapter, originally intended for inclusion in [4], focuses on modeling issues by way of an example of a predator-prey model where the predator has a juvenile stage. A careful derivation of the model is given starting from an age-structured model for the predator population. The method of characteristics is used to reduce the partial differential equations to a system of integro-differential equations which represent delay equations with unbounded delays. The modeling assumptions of fixed maturation period and exponentially distributed death rates reduces the model to a system of familiar discrete delay equations. However, the appropriate initial data for the resulting delay equation is not what is usually assumed in the literature. Rather than analyzing the system using analytical tools, we rely on numerical simulations to suggest that the new initial conditions are superior to those commonly employed. A mathematical analysis of the equations would be quite similar to that in Chapter 8 of [4].