Continuous-time models of host-parasitoid interactions.

Although there is a large literature about the effects of spatial heterogeneity and parasitoid aggregation on the population dynamics of model host-parasitoid systems, most studies deal only with hosts and parasitoids that have discrete, nonoverlapping generations. Here, I present three different models of host-parasitoid interactions in which hosts and parasitoids have overlapping generations. In two models, birth, death, and dispersal occur continuously within patches, and this makes it necessary to model population dynamics by explicitly following the internal dynamics of each patch. These models are similar in structure to metapopulation models of predator-prey systems, and their stability properties can be explained in terms of asynchrony in the population fluctuations of each of the constituent patches. In the third model, the global population dynamics depend on the instantaneous distributions of hosts and parasitoids among patches rather than on continuous dispersal. The stability properties of this model are very similar to those of corresponding models with nonoverlapping generations; stability arises from variability in the chance that a given host is parasitized. The influence of spatial heterogeneity and parasitoid aggregation on population dynamics is different for each model, which thus demonstrates the complexity of predicting population dynamics in continuous-time models of host-parasitoid systems.