Quantifying population substructure: extending the graph-theoretic approach.

Among the few universal themes in ecology is that resources, energy, and organisms themselves, are patchily distributed. This patchy distribution imposes a need for some level of dispersal or connectivity among spatially separate patches in order to allow organisms to acquire sufficient resources for survival. To date, general patterns of connectivity have not emerged. This is, in part, because different species respond to different scales of patchiness. I propose an extension of the graph-theoretic approach to control for such differences and reveal potential generalities about how natural populations are organized. Using statistical methods and simple applications of graph theory, continuum percolation, and metapopulation models, I demonstrate a pattern of hierarchical clustering among populations in both a plant-pathogen system at an extent of 1000 m and gene flow in a salamander species across a subcontinental range. Results suggest that some patches or populations have a disproportionately high importance to the maintenance of overall connectivity in the system within and across scales.

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