Persistence of spatial populations depends on returning home.

There is a need for better description and heuristic understanding of the sustainability of populations connected over space by a dispersing stage, both for management purposes and to increase our basic knowledge of the dynamics of these populations. We show that persistence of such a population of connected subpopulations depends on whether the sum of the reproductive gains through all possible closed, between-patch reproductive paths through multiple generations, relative to the shortfall in self-persistence in each path, exceeds unity plus extra terms, which only appear if there are four or more patches. These extra terms have the heuristic explanation that they avoid double counting of reproductive paths that arise with four or more patches because there can be nonoverlapping subnetworks. Thus only those patterns of reproduction and connectivity which eventually lead to descendants returning to the patch from which they originate contribute to persistence. This result provides the basis for evaluating connectivity and habitat heterogeneity to understand reserve design, the effects of human fragmentation, the collapse of marine fisheries, and other conservation issues.