Consequences of partially recessive deleterious genetic variation for the evolution of inversions suppressing recombination between sex chromosomes1.

The evolution of suppressed recombination between sex chromosomes is widely hypothesized to be driven by sexually antagonistic selection (SA), where tighter linkage between the sex-determining gene(s) and nearby SA loci is favored when it couples male-beneficial alleles to the proto-Y chromosome, and female-beneficial alleles to the proto-X. Although difficult to test empirically, the SA selection hypothesis overshadows several alternatives, including an incomplete but often-repeated "sheltering" hypothesis which suggests that expansion of the sex-linked region (SLR) reduces the homozygous expression of deleterious mutations at selected loci. Here, we use population genetic models to evaluate the consequences of partially recessive deleterious mutational variation for the evolution of otherwise neutral chromosomal inversions expanding the SLR on proto-Y chromosomes. Both autosomal and SLR-expanding inversions face a race against time: lightly-loaded inversions are initially beneficial, but eventually become deleterious as they accumulate new mutations, after which their chances of fixing become negligible. In contrast, initially unloaded inversions eventually become neutral as their deleterious load reaches the same equilibrium as non-inverted haplotypes. Despite the differences in inheritance and indirect selection, SLR-expanding inversions exhibit similar evolutionary dynamics to autosomal inversions over many biologically plausible parameter conditions. Differences emerge when the population average mutation load is quite high; in this case large autosomal inversions that are lucky enough to be mutation-free can rise to intermediate to high frequencies where selection in homozygotes becomes important (Y-linked inversions never appear as homozygous karyotypes); conditions requiring either high mutation rates, highly recessive deleterious mutations, weak selection, or a combination thereof.