The effect of dispersal between patches on the stability of large trophic food webs

Using computer simulations for the population dynamics of systems with many species, we investigate the stability of food webs distributed over several patches that are connected by migration. We evaluate the proportion of persisting species (robustness) and the probability that dynamics reach a fixed point in dependence of food-web complexity, patch arrangement, and migration rule. We find that migration in general increases robustness. This increase is strongest for intermediate migration rates and for star-like patch arrangements. The probability of reaching a fixed point decreases for intermediate migration rate, and has a large peak at larger migration rate for the star topology. We explain these various observations by the rescue effect, by dynamical coexistence of species, and by the buildup of biomass reservoirs in highly connected patches. As the species number becomes larger, differences between different patch arrangements become smaller, and the decrease in the probability of reaching a fixed point vanishes. This means that complex food webs are in some sense dynamically simpler than food webs consisting of less species.