Print PageDispersal is crucial for species persistence in fragmented landscapes, as dispersers colonize empty habitat patches and provide rescue effects to “sink” populations. But these benefits may come with a downside: metapopulation models predict that between-patch dispersal can synchronize subpopulation dynamics and increase the risk of regional extinctions. However, empirical studies tend to show a weaker increase in synchrony with dispersal than theory predicts. One possible explanation for this discrepancy is that metapopulation models typically formulate dispersal as a continuous process, where fractions of individuals are always moving between patches. In reality organisms are particulate and dispersal can only occur when a whole individual moves between patches. As a result, previous metapopulation models may have inflated the synchronizing effect of dispersal.
To explore the effect of the continuous-dispersal assumption on metapopulation synchrony, I constructed parallel models describing a two-patch predator-prey system: a deterministic ordinary differential equation (ODE) model and a stochastic process-based model (Stochastic Simulation Algorithm; SSA). In the ODE, population processes (birth, death, dispersal) happen continuously through time and population sizes can take non-integer values. Conversely, the SSA recognizes the particulate nature of organisms: population sizes are constrained to integer values and can only change in discrete units. The ODE model is the mean-field approximation of the SSA model, making them directly comparable. I ran simulations with both models under a wide range of prey and predator dispersal rates using two initial conditions. For each simulation, I determined the between-patch synchrony of both trophic levels.
Results/Conclusions
The two models diverged quantitatively and qualitatively in their predictions. The ODE resulted in very high between-patch synchrony of both trophic levels for most dispersal rates and was sensitive to initial conditions. In contrast, the SSA only produced synchrony when dispersal was very high, and was generally insensitive to initial conditions. Frequent dispersal by only one trophic level in the SSA decoupled the local trophic interaction and did not synchronize the less-dispersive species. Conversely, dispersal by only one species synchronized both trophic levels in the ODE. Finally, dispersal rates were not useful predictors of metapopulation extinction probabilities. These results suggest that dispersal may not be as strong a synchronizing force as previously thought, shedding light on the mismatch between metapopulation theory and data.
