Network theory and metapopulation persistence: incorporating node self-connections.

Network analysis is gaining increasing importance in conservation planning. However, which network metrics are the best predictors of metapopulation persistence is still unresolved. Here, we identify a critical limitation of graph theory-derived network metrics that have been proposed for this purpose: their omission of node self-connections. We resolve this by presenting modifications of existing network metrics, and developing entirely new metrics, that account for node self-connections. Then, we illustrate the performance of these new and modified metrics with an age-structured metapopulation model for a real-world marine reserve network case study, and we evaluate the robustness of our findings by systematically varying particular features of that network. Our new and modified metrics predict metapopulation persistence much better than existing metrics do, even when self-connections are weak. Existing metrics become good predictors of persistence only when self-connections are entirely absent, an unrealistic scenario in the overwhelming majority of metapopulation applications. Our study provides a set of novel tools that can substantially enhance the extent to which network metrics can be employed to understand, and manage for, metapopulation persistence.