Non-equilibria in Small Metapopulations: Comparing the Deterministic Levins Model with its Stochastic Counterpart

In this paper, we examine, for small metapopulations, the stochastic analog of the classical Levins metapopulation model. We study its basic model output, the expected time to metapopulation extinction, for systems which are brought out of equilibrium by imposing sudden changes in patch number and the colonization and extinction parameters. We find that the expected metapopulation extinction time shows different behavior from the relaxation time of the original, deterministic, Levins model. This relaxation time is therefore limited in value for predicting the behavior of the stochastic model. However, predictions about the extinction time for deterministically unviable cases remain qualitatively the same. Our results further suggest that, if we want to counteract the effects of habitat loss or increased dispersal resistance, the optimal conservation strategy is not to restore the original situation, that is, to create habitat or decrease resistance against dispersal. As long as the costs for different management options are not too dissimilar, it is better to improve the quality of the remaining habitat in order to decrease the local extinction rate.