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 favoured when it couples male‐beneficial alleles to the proto‐Y chromosome, and female‐beneficial alleles to the proto‐X. This article is part of the theme issue ‘Genomic architecture of supergenes: causes and evolutionary consequences’. Thus, although sexually antagonistic selection is a key hypothesis for the formation of supergenes on sex chromosomes, it remains challenging to detect. We are unable, however, to rule out the alternative hypothesis that the peaks of divergence result from demographic effects. We identify four windows with elevated divergence between the X and Y in the recombining region, all in or very near genes associated with phenotypes potentially under sexually antagonistic selection in humans. Phasing allows us to date the suppression of recombination on the sex chromosome and provides unprecedented resolution to identify sexually antagonistic selection in the recombining region of the chromosome. Here we perform an analysis of phased young sex chromosomes to look for signals of sexually antagonistic selection in the Japan Sea stickleback ( Gasterosteus nipponicus ). This form of selection is thought to be key to the evolution of sex chromosomes but is hard to detect. Intralocus sexually antagonistic selection occurs when an allele is beneficial to one sex but detrimental to the other. Here, we model a simple and testable hypothesis explaining the stepwise extensions of recombination suppression on sex chromosomes, mating-type chromosomes, and supergenes in general. This may explain why sex chromosomes remain homomorphic in some organisms but are highly divergent in others. However, inversions capturing a permanently heterozygous allele were found to be less likely to spread when the mutation load segregating in populations was lower (e.g., under large effective population sizes or low mutation rates). Similar results were obtained with models assuming recombination-suppressing mechanisms other than chromosomal inversions and for supergenes other than sex chromosomes, including those without XY-like asymmetry, such as fungal mating-type chromosomes. Permanently heterozygous alleles, such as the male-determining allele in XY systems, protect linked chromosomal inversions against the expression of their recessive mutation load, leading to the successive accumulation of inversions around these alleles without antagonistic selection. We show here, by mathematical modeling and stochastic simulation, that recombination suppression on sex chromosomes and around supergenes can expand under a wide range of parameter values simply because it shelters recessive deleterious mutations, which are ubiquitous in genomes. However, it has proved difficult to obtain empirical evidence of a role for sexually antagonistic selection in extending recombination suppression, and antagonistic selection has been shown to be unlikely to account for the evolutionary strata observed on fungal mating-type chromosomes. The reasons for this remain poorly understood, but the principal hypotheses proposed to date are based on antagonistic selection due to differences between sexes. Many organisms have sex chromosomes with large nonrecombining regions that have expanded stepwise, generating "evolutionary strata" of differentiation.
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