Local adaptation and the evolution of inversions on sex chromosomes and autosomes

Spatially varying selection with gene flow can favour the evolution of inversions that bind locally adapted alleles together, facilitate local adaptation and ultimately drive genomic divergence between species. Several studies have shown that the rates of spread and establishment of new inversions capturing locally adaptive alleles depend on a suite of evolutionary factors, including the strength of selection for local adaptation, rates of gene flow and recombination, and the deleterious mutation load carried by inversions. Because the balance of these factors is expected to differ between X (or Z) chromosomes and autosomes, opportunities for inversion evolution are likely to systematically differ between these genomic regions, though such scenarios have not been formally modelled. Here, we consider the evolutionary dynamics of X-linked and autosomal inversions in populations evolving at a balance between migration and local selection. We identify three factors that lead to asymmetric rates of X-linked and autosome inversion establishment: (1) sex-biased migration, (2) dominance of locally adapted alleles and (3) chromosome-specific deleterious mutation loads. This theory predicts an elevated rate of fixation, and depressed opportunities for polymorphism, for X-linked inversions. Our survey of data on the genomic distribution of polymorphic and fixed inversions supports both theoretical predictions.