Predicting barrier architecture and the genomic landscape of differentiation under polygenic divergent selection

We consider polygenic divergent selection in a mainland-island model, where our aim is to understand how patterns of genetic variation along the genome reflect the genetic architecture of postzygotic reproductive isolation. We derive a new expression for the effective migration rate () at both neutral and divergently selected loci (i.e. barrier loci), and develop a numerical approach to co-predict and allele frequencies at barrier loci. Using this , we predict neutral coalescence times along the genome, and show how our results for the mainland-island model can be used to obtain coalescence time predictions for nonequilibrium demographic models. We validate our approach extensively using forward-in-time individual-based simulations and show that our -based approximation remains accurate across a broad parameter range. We study both the case of a single barrier locus and a pair of barrier loci in detail to identify the conditions under which an -based approach performs well. We use our new predictions to examine how the genetic architecture of divergent selection shapes barriers to gene flow, quantifying hitchhiking effects along the genome and evaluating the effects of polygenicity on reproductive isolation. We discuss the implications for mapping barriers to gene flow using population genomic data, both for model-based inference and genome scan approaches based on summary statistics.