Effect of movement frequency on global host–parasitoid spatial dynamics with unstable local dynamics

We present a spatial host–parasitoid model where individuals move on a square lattice of patches. Local interactions between hosts and parasitoids within patches are described by the Nicholson–Bailey model. Dispersal between patches is represented by a series of movement events from a patch to neighbouring patches. We study the effect of the number of movement events on the stability of the host–parasitoid system. The aim of this work is to determine conditions on this number for using a reduced model (called aggregated model) to predict the total host and parasitoid population dynamics. When the number of movement events is small, the system is usually persistent and spatial patterns are observed, such as spiral waves or chaotic dynamics. We show that when this number is larger than a critical value, spatial homogeneity is observed after some transient dynamics and the system does not persist; in that case the reduced model can be used. Our results show that the critical value is relatively small and that the reduced model can be used in realistic situations.