Extinction thresholds and metapopulation persistence in dynamic landscapes

Models of metapopulations have focused on the effects of extinction and colonization rate upon metapopulation persistence and dynamics, assuming static landscapes wherein patches are neither created nor go extinct. However, for species living in ephemeral (patchy) habitats, landscapes are highly dynamic rather than static. In this article, we develop a lattice metapopulation model, of the patch occupancy type, based on interacting particle systems that incorporate explicitly both metapopulation and patch dynamics. Under this scenario, we study the effects of different regimes of patch dynamics upon metapopulation persistence. We analyze the lattice behavior by numerical simulations and a mean field approximation (MF). We show that metapopulation persistence and extinction are strongly influenced by the rate at which the landscape changes, in addition to the amount of habitat destroyed. We derive MF analytical expressions for extinction thresholds related to landscape properties such as habitat suitability and patch average lifetime. Using numerical simulations, we also show how these thresholds are quantitatively overestimated by the MF equations, although the qualitative behavior of the spatial model is well explained by the MF when the array of habitat patches is dynamic or static but connected in space and time. The implications for conservation are also discussed.