Emergence of global behaviour in a host–parasitoid model with density-dependent dispersal in a chain of patches

We present a time discrete spatial host–parasitoid model. The environment is a chain of patches connected by dispersal events. Dispersal of parasitoids is host-density dependent. When the host density is small (resp. high), the proportion of migrant parasitoids is close to unity (resp. to zero). We assume fast patch to patch dispersal with respect to local interactions. Local host–parasitoid interactions are described by the classical Nicholson–Bailey model. By using time scales separation methods (or aggregation methods), we obtain a reduced model that governs the total host and parasitoid densities (obtained by addition over all patches). The aggregated model describes the time evolution of the total number of hosts and parasitoids of the system of patches. This global model is useful to make predictions of emerging behaviour regarding the dynamics of the complete system. We study the effects of number of patches and host density-dependent parasitoid dispersal on the overall stability of the host–parasitoid system. We finally compare our stability results with the CV2 > 1 rule.