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

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. Despite limited empirical evidence, the SA selection hypothesis overshadows several alternatives, including an incomplete but often-repeated "sheltering hypothesis" that suggests that expansion of the sex-linked region (SLR) reduces homozygous expression of partially recessive deleterious mutations at selected loci. Here, we use population genetic models to evaluate the consequences of deleterious mutational variation for the evolution of neutral chromosomal inversions expanding the SLR on proto-Y chromosomes. We find that SLR-expanding inversions face a race against time: lightly loaded inversions are initially beneficial, but eventually become deleterious as they accumulate new mutations, and must fix before this window of opportunity closes. The outcome of this race is strongly influenced by inversion size, the mutation rate, and the dominance coefficient of deleterious mutations. Yet, small inversions have elevated fixation probabilities relative to neutral expectations for biologically plausible parameter values. Our results demonstrate that deleterious genetic variation can plausibly drive recombination suppression in small steps and would be most consistent with empirical patterns of small evolutionary strata or gradual recombination arrest.