Migration alone can produce persistence of host-parasitoid models

It has long been recognized that the unstable equilibrium of a single-patch predator-prey model cannot be stabilized by diffusive coupling with identical patches, since the coupled system acts exactly like the single-patch system if the patches are synchronized (Maynard Smith 1974; Allen 1975; Reeve 1988). Persistence of coupled locally unstable systems depends on the maintenance of asynchrony among the populations sufficient to buffer crashes (den Boer 1968; Allen 1975; Crowley 1981; Reeve 1988, 1990; Taylor 1988).