The effects of connectivity on metapopulation persistence: network symmetry and degree correlations

A spatial metapopulation is a mosaic of interconnected patch populations. The complex routes of colonization between the patches are governed by the metapopulation's dispersal network. Over the past two decades, there has been considerable interest in uncovering the effects of dispersal network topology and its symmetry on metapopulation persistence. While most studies find that the level of symmetry in dispersal pattern enhances persistence, some have reached the conclusion that symmetry has at most a minor effect. In this work, we present a new perspective on the debate. We study properties of the in- and out-degree distribution of patches in the metapopulation which define the number of dispersal routes into and out of a particular patch, respectively. By analysing the spectral radius of the dispersal matrices, we confirm that a higher level of symmetry has only a marginal impact on persistence. We continue to analyse different properties of the in-out degree distribution, namely the 'in-out degree correlation' (IODC) and degree heterogeneity, and find their relationship to metapopulation persistence. Our analysis shows that, in contrast to symmetry, the in-out degree distribution and particularly, the IODC are dominant factors controlling persistence.