Age structure in predator-prey systems: intraspecific carnivore interaction, passive diffusion, and the paradox of...

An existing arthropod predator-prey model incorporating age structure in the carnivore through the use of the von Foerster equation is extended to include the effects of intraspecific carnivore interaction and passive diffusion or migration. A linear stability analysis of the community equilibrium point of that differential-integral equation system is performed and the resulting secular equation analyzed by the method of D-partitions. These stability results are then compared to those obtained by employing an analogous differential equation model without age structure, in particular as they relate to the so-called paradox of enrichment. In the absence of passive diffusion, it is shown that, unlike for a differential equation model, the paradox of enrichment can occur even with a carnivore which exhibits intraspecific competition. This destabilizing effect of age structure is seen to occur most dramatically when interspecific interactions are large, while the effect of passive diffusion is to offset that tendency and restabilize the system. These predictions are in accordance with relevant experimental evidence involving mites.