Population outbreaks in a discrete world

We present and analyze a simple three-patch host-parasitoid model where pop ulation growth is discrete. The model gives solutions that are qualitativel y similar to the stable large-amplitude patterns in space found in reaction -diffusion theory. In the context of host-parasitoid interactions, the larg e-amplitude portions of the solution can be thought of as spatially localiz ed host population outbreaks. Here, we show that the biological requirement s for localized population outbreaks in a discrete world are identical to t hose found in reaction-diffusion theory. Furthermore, the model convenientl y allows investigation into the robustness of these population outbreaks un der the influence of density-dependent dispersal behavior. We find that loc alized population outbreaks in space can still occur with modest amounts of pursuit and aggregative behavior by parasitoids. We end by showing that ev idence from a real host-parasitoid system is consistent with the prediction s of the model. (C) 2000 Academic Press.