Demographic stochasticity reduces the synchronizing effect of dispersal in predator-prey metapopulations

Dispersal may affect predator-prey metapopulations by rescuing local sink populations from extinction or by synchronizing population dynamics across the metapopulation, increasing the risk of regional extinction. Dispersal is likely influenced by demographic stochasticity, however, particularly because dispersal rates are often very low in metapopulations. Yet the effects of demographic stochasticity on predator-prey metapopulations are not well known. To that end, I constructed three models of a two-patch predator-prey system. The models constitute a hierarchy of complexity, allowing direct comparisons. Two models included demographic stochasticity (pure jump process [PJP] and stochastic differential equations [SDE]), and the third was deterministic (ordinary differential equations [ODE]). One stochastic model (PJP) treated population sizes as discrete, while the other (SDE) allowed population sizes to change continuously. Both stochastic models only produced synchronized predator-prey dynamics when dispersal was high for both trophic levels. Frequent dispersal by only predators or prey in the PJP and SDE spatially decoupled the trophic interaction, reducing synchrony of the non-dispersive species. Conversely, the ODE generated synchronized predator-prey dynamics across all dispersal rates, except when initial conditions produced anti-phase transients. These results indicate that demographic stochasticity strongly reduces the synchronizing effect of dispersal, which is ironic because demographic stochasticity is often invoked post hoc as a driver of extinctions in synchronized metapopulations.