Who ate whom: Population dynamics with age-structured predation

We study a population model in which there are two species, one of which has a juvenile and adult life stage. The adults of the first species prey on the second species, which in turn preys on the juveniles of the first. One version of the model represents systems where neither species can survive on its own, although we find that both can survive through mutual predation. To avoid extinction, the two types of predation must be of sufficient strength and in appropriate proportion to one another. Another version of the model represents systems where each species can survive without the other, and there we find that mutual predation is capable of increasing both of their equilibrium populations or creating stable limit cycles.