The evolution of suppressed recombination between sex chromosomes and the lengths of evolutionary strata

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 sexually antagonistic selection drives the evolution of recombination arrest remains equivocal and alternative hypotheses underdeveloped. Here, we investigate whether the length of "evolutionary strata" formed by chromosomal inversions (or other large-effect recombination modifiers) expanding the non-recombining sex-linked region (SLR) on sex chromosomes can be informative of how selection influenced their fixation. We develop population genetic models to show how the length of an SLR-expanding inversion, and the presence of partially recessive deleterious mutational variation, affect the fixation probability of three different classes of inversions: (1) intrinsically neutral, (2) directly beneficial (i.e., due to breakpoint or positional effects), and (3) those capturing sexually antagonistic (SA) loci. Our models indicate that neutral inversions, and those capturing an SA locus in linkage disequilibrium with the ancestral SLR, will exhibit a strong fixation bias toward small inversions; while unconditionally beneficial inversions, and those capturing a genetically unlinked SA locus, will favor fixation of larger inversions. The footprint of evolutionary stratum size left behind by different selection regimes is strongly influenced by parameters affecting the deleterious mutation load, the physical position of the ancestral SLR, and the distribution of new inversion lengths.