Coalescent Theory of Migration Network Motifs

Natural populations display a variety of spatial arrangements, each potentially with a distinctive impact on genetic diversity and genetic differentiation among subpopulations. Although the spatial arrangement of populations can lead to intricate migration networks, theoretical developments have focused mainly on a small subset of such networks, emphasizing the island-migration and stepping-stone models. In this study, we investigate all small network motifs: the set of all possible migration networks among populations subdivided into at most four subpopulations. For each motif, we use coalescent theory to derive expectations for three quantities that describe genetic variation: nucleotide diversity, F(ST), and half-time to equilibrium diversity. We describe the impact of network properties on these quantities, finding that motifs with a high mean node degree have the largest nucleotide diversity and the longest time to equilibrium, whereas motifs with low density have the largest F(ST). In addition, we show that the motifs whose pattern of variation is most strongly influenced by loss of a connection or a subpopulation are those that can be split easily into disconnected components. We illustrate our results using two example data sets—sky island birds of genus Sholicola and Indian tigers—identifying disturbance scenarios that produce the greatest reduction in genetic diversity; for tigers, we also compare the benefits of two assisted gene flow scenarios. Our results have consequences for understanding the effect of geography on genetic diversity, and they can assist in designing strategies to alter population migration networks toward maximizing genetic variation in the context of conservation of endangered species.