Impact of stochastic migration on species diversity in meta-food webs consisting of several patches

The structure of space has an appreciable influence on the diversity and stability of ecosystems. So far, there are only few theoretical studies investigating the population dynamics of food webs consisting of many species that can migrate between several patches, and in most of these models migration is a continuous, deterministic process. However, when migration events are rare (for instance because the patches are far apart), migration is a stochastic process and should be modeled accordingly. We present computer simulations of a food web model of many species on a spatial network of several patches, combining deterministic local population dynamics with stochastic migration. We evaluate the influence of the migration rate and other model parameters on local and regional species diversity and on stability. We find that migration increases the number of surviving and coexisting populations by two effects. These are the rescue effect, which restores local populations that have gone extinct, and dynamical coexistence, which sustains local populations that could not persist in the absence of immigration. Both effects occur even when migration events are rare. Species diversity increases on local and regional scales with the frequency of migration events. Furthermore, we investigate the adiabatic limit in which population dynamics always reaches an equilibrium before the next migration event, and we investigate the possible long-term scenarios. While the final state often contains the same food web on all patches, we also find instances where two slightly different food webs coexist on different patches, even when initially each patch contained the same food web.