Spatial and Temporal Heterogeneity of Host-Parasitoid Interactions in Lupine Habitat

The inhabitants of the bush lupine in coastal California have been the subject of scientific scrutiny in recent years. Observations of a host-parasitoid interaction in the shrub's foliage, in which victims are significantly less motile than their exploiters, record stable spatial patterns in a fairly homogeneous environment. Though such pattern formation has been found in reaction-diffusion models, the correspondence of these models to continuous-time predator-prey interactions does not reflect the reality of the system being studied. Near the root of the lupine, another host-parasitoid interaction is also of considerable interest. In some cases this interaction, which promotes the health of the lupine, has been observed to be much more persistent than suggested by mathematical models. In this work a discrete-time spatial model of the first host-parasitoid system is introduced. We analyze the model, describing its transient behavior and finding the conditions under which spatial patterns occur, as well as an estimate of outbreak size under those conditions. We consider the feasibility of the necessary conditions in the natural system by modeling the mechanisms responsible for them, and discuss the effects of variable habitat on pattern formation. We also explore one possible explanation for the persistence of the second host-parasitoid system -- the existence of an alternate host. Under certain surprising conditions and by means quite different from previous models of similar situations, an alternate host can greatly enhance persistence of the nematode parasitoid.