Persistence in Patchy Irregular Landscapes

This paper presents a simulation and three approximations designed to study the effects of spatial clumping of patches in a metapopulation linked by costly dispersal. Assuming that all patches are identical and that each experiences a simple regime of density-independent uncorrelated extinction, we demonstrate that clumping enhances persistence of the population. We find a persistence threshold which depends on the leading eigenvalue of the matrix describing dispersal success between each pair of patches and show that this eigenvalue exceeds the mean dispersal success. An averaged approximation that uses a single statistic to describe each path, rather than the full matrix, successfully predicts the regional population size produced by the simulation and predicts a simple linear relationship between this statistic and the patch immigration rate. An approximation which ignores the detailed spatial structure fails to accurately predict the simulation results.