During speciation-with-gene-flow, a transition from single-locus to multi-locus processes can occur, as strong coupling of multiple loci creates a barrier to gene flow. Testing predictions about such transitions with empirical data requires building upon past theoretical work and the continued development of quantitative approaches. We simulated genomes under several evolutionary scenarios of gene flow and divergent selection, extending previous work with the additions of neutral sites and coupling statistics. We used these simulations to investigate, in a preliminary way, if and how selected and neutral sites differ in the conditions they require for transitions during speciation. For the parameter combinations we explored, as the per-locus strength of selection grew and/or migration decreased, it became easier for selected sites to show divergence-and thus to rise in linkage disequilibrium (LD) with each other as a statistical consequence-farther in advance of the conditions under which neutral sites could diverge. Indeed, even very low rates of effective gene flow were sufficient to prevent differentiation at neutral sites. However, once strong enough, coupling among selected sites eventually reduced gene flow at neutral sites as well. To explore whether similar transitions might be detectable in empirical data, we used published genome resequencing data from three taxa of Heliconius butterflies. We found that fixation index ( F S T ) outliers and allele-frequency outliers exhibited stronger patterns of within-deme LD than the genomic background, as expected. The statistical characteristics of within-deme LD-likely indicative of the strength of coupling of barrier loci-varied between chromosomes and taxonomic comparisons. Qualitatively, the patterns we observed in the empirical data and in our simulations suggest that selection drives rapid genome-wide transitions to multi-locus coupling, illustrating how divergence and gene flow interact along the speciation continuum.
Keywords: Heliconius; coupling; gene flow; nonlinear transitions; parapatry; population genomics; simulation model; sympatry.