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 (SA) 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 nonrecombining 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: (i) intrinsically neutral, (ii) directly beneficial (i.e., due to breakpoint or positional effects), and (iii) those capturing SA loci. Our models indicate that inversions capturing an SA locus initially in linkage disequilibrium with the ancestral SLR exhibit a strong fixation bias toward small inversions, while neutral, beneficial, and inversions capturing a genetically unlinked SA locus tend to favor larger inversions and exhibit similar distributions of fixed inversion lengths. 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.