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The evolution of suppressed recombination between sex chromosomes by chromosomal inversions

The idea that sex-differences in selection drive the evolution of suppressed recombination between sex chromosomes is well-developed in population genetics. Yet, despite a now classic body of theory, empirical evidence that sexual antagonism drives the evolution of recombination suppression remains meagre and alternative hypotheses underdeveloped. We investigate whether the length of ‘evolutionary strata’ formed by chromosomal inversions that expand the non-recombining sex determining region (SDR) on recombining sex chromosomes can offer an informative signature of whether, and how, selection influenced their fixation. We develop population genetic models that determine how the length of a chromosomal inversion that expands the SDR affects its fixation probability for three categories of inversions: (i) neutral, (ii) directly beneficial (i.e., due to breakpoint or position effects), and (iii) indirectly beneficial (especially those capturing sexually antagonistic loci). Our models predict that neutral inversions should leave behind a unique signature of large evolutionary strata, and that it will often be difficult or impossible to distinguish between smaller strata created by directly or indirectly beneficial inversions. An interesting and unexpected prediction of our models is that the physical location of the ancestral SDR on the sex chromosomes is the most important factor influencing the relation between inversion size and the probability of expanding the SDR. Our findings raise a suite of new questions about how physical as well as selective processes influence the evolution of recombination suppression between sex chromosomes.