A Stage Structured Predator-Prey model and its Dependence on Through-Stage Delay and Death Rate

The work of Aiello and Freedman on a single species growth with stage structure has received much attention in the literature in recent years. Their model predicts a positive steady state as the global attractor and thus suggests that stage structure does not generate the sustained oscillations frequently observed in nature. This work inevitably stirred some controversy. Subsequent works by other authors suggest that the time delay to adulthood should be state dependent and careful formulation of such state dependent time delay can lead to models that produce periodic solutions. We review this work from a fresh biological angle: growth is a combined result of birth and death processes, both of which are closely linked to the resource supply which is dynamic in nature. From this basic standpoint, we formulate a general and robust predator-prey model with stage structure with constant maturation time delay (through-stage time delay) and perform a systematic mathematical and computational study. Our work indicates that if the juvenile death rate (through-stage death rate) is nonzero, then for small and large values of maturation time delays, the population dynamics takes the simple form of a globally attractive steady state. Our linear stability work shows that if the resource is dynamic, as in nature, there is a window in maturation time delay parameter that generates sustainable oscillatory