Metapopulation persistence with age-dependent disturbance or succession

Simple metapopulation models with random disturbances are used in species conservation or management, relying on the condition for persistence that the per-patch colonization rate be greater than the per-patch extinction rate. For a general model incorporating the role of succession or patch age-dependent extinction, I show that persistence requires the per-patch colonization rate to be greater than the inverse of mean patch age, where age is the time since the patch became available for colonization. Because mean patch age can be arbitrarily large relative to the extinction rate, currently persisting metapopulations may be persisting despite small colonization rates, and management approaches that do not consider the role of mean patch age may unnecessarily doom populations to extinction.