Extinction threshold in metapopulation models

The term extinction threshold refers to a critical value of some attribute, such as the amount of habitat in the landscape, below which a population, a metapopulation, or a species does not persist. In this paper we discuss the existence and behavior of extinction thresholds in the context of metapopulation models. We review and extend recent developments in the theory and application of patch occupancy models, which have been developed for assessing the dynamics of species inhabiting highly fragmented landscapes. We discuss the relationship between deterministic and stochastic models, the possibility of alternative equilibria, transient dynamics following perturbations from the equilibrium state, and the effect of spatially correlated and temporally varying environmental conditions. We illustrate the theory with an empirical example based on the Glanville fritillary butterfl y (Melitaea cinxia) metapopulation in the Åland Islands in southwest Finland.