Habitat Deterioration, Habitat Destruction, and Metapopulation Persistence in a Heterogenous Landscape

Levinsʹs unstructured metapopulation model predicts that the equilibrium fraction of empty habitat patches is a constant function of the fractionhof suitable patches in the landscape and that this constant equals the threshold value for metapopulation persistence. Levinsʹs model thus suggests that the minimum amount of suitable habitat necessary for metapopulation persistence can be estimated from the fraction of empty patches at steady state. In this paper we construct several more realistic structured metapopulation models that include variation in patch quality and the rescue effect. These models predict both positive and negative correlations between the fractions of suitable patches and empty patches. The type of correlation depends in an intricate manner on the strength of the rescue effect and on the quality distribution of the patches to be destroyed. Empty patches can be considered as the resource limiting metapopulation growth. Our results demonstrate that the correlation between the fractions of suitable patches and empty patches is positive if and only if the average value of the resource decreases as the number of patches increases.