Top-down control in a patchy environment: revisiting the stabilizing role of food-dependent predator dispersal

In this paper, we revisit the stabilizing role that predator dispersal and aggregation have in the top-down regulation of predator-prey systems in a heterogeneous environment. We consider an environment consisting of sites interconnected by dispersal, and propose a novel mechanism of stabilization for the case with a non-sigmoid functional response of predators. We assume that the carrying capacity of the prey is infinitely large in each site, and show that successful top-down regulation of this otherwise globally unstable system is made possible through an interplay between the unevenness of prey fitness across the sites and the rapid food-dependent migration of predators. We argue that this mechanism of stabilization is different from those previously reported in the literature: in particular, it requires a high degree of synchronicity in local oscillations of species densities across the sites. Prey outbreaks take place synchronously, but the unevenness of prey growth rates across the sites results in a pronounced difference in the species densities, and so the predator quickly disperses to the sites with the highest prey abundances. For this reason, the consumption of prey mostly takes place in the sites with high densities of prey, which assures an efficient suppression of outbreaks. Furthermore, when the total size of prey population is low, the distribution of both species among the sites becomes more even, and this prevents overconsumption of the prey by the predator. Finally, we put forward the hypothesis that this mechanism, when considered in a tri-trophic plankton community in the water column, can explain the stability of the nutrient-rich low-chlorophyll open ocean regions.