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

Abstract

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.This article is part of the theme issue 'Linking local adaptation with the evolution of sex differences'.

Keywords: adaptation with gene flow; deleterious mutations; fast-X evolution; genome evolution; sex-biased migration.

Figure 1.

The spread of an inversion that captures a high-fitness genetic background. The cartoon illustrates the consequences of two forms of genetic variation on the evolution of inversions. The left and right panels each represent a sample of chromosomes from a population at two different points in time. Two loci (locus 1 and locus 2) segregate for locally adaptive alleles (marked as triangles) evolving at migration–selection balance. The remaining sites within the region segregate for deleterious alleles evolving at mutation–selection balance (red circles). The left-hand panel represents a population primarily comprising wild-type chromosomes, with rare inversions that each capture a random set of locally adaptive and/or deleterious alleles. Inversions marked in red are eventually purged from the population because they capture a deleterious mutation (the inversion labelled ‘a’), or fail to capture both locally adaptive alleles (the inversion labelled ‘b’). Such inversions suppress recombination with wild-type chromosomes and are, therefore, forever burdened by the suboptimal genotypes that they initially capture. The blue inversion (labelled ‘c’) is favoured by natural selection because it is mutation-free and it binds together the locally adaptive alleles by suppressing recombination between them. In the right-hand panel, the beneficial inversion has spread, while the deleterious inversions have been removed from the population.

Figure 2.

Effects of dominance and recombination on the establishment of inversions that capture two locally adapted alleles. (a) Effects of dominance on selection for rare inversions. Solid lines show the ratio of X and autosome approximations, based on equations (3.1a) and (3.1b), for three idealized scenarios of sex-specific migration: male-limited migration (blue), equal migration (black) and female-limited migration (red); open circles show numerical evaluation of exact equations (2.1) and (2.2), with (s_f + s_m)/2 = 0.1, and (m_f + m_m)/2 = 0.01, and a dominance coefficient of h = h_i at both loci. (b) A representative comparison between analytical approximations for X and autosome establishment probabilities (broken line, based on equations (3.1a) and (3.1b), with m_f = m_m) and stochastic simulations of inversion establishment in a Wright-Fisher population of size N = 500 000, with s = s_f = s_m = 0.005, m_f = m_m = 0.0002, and sex-specific recombination rates of r = r_f = r_m with no X-linked recombination in males; j refers to the mode of inheritance (j = {A, X}). Each circle shows the fraction of 10⁶ single-copy inversions that eventually become established in the population. Analytical, numerical and simulation results are based on the two-locus model of local adaptation in which inversions capture locally adaptive alleles at both loci. For additional simulation results, see electronic supplementary material, figures S1 and S2.

Figure 3.

Establishment probabilities of autosomal and X-linked inversions that span many loci with small effects on local adaptation. Curves show the special cases of equation (3.2) (see text following equation (3.2)), which assume that dominance of locally adaptive alleles is constant across the set of loci captured by the inversion (h = h_i), and distributions of selection coefficients among loci are the same for the X and autosomes . Values greater than one correspond to higher establishment probabilities for autosomal inversions; values less than one correspond to greater X-linked establishment probabilities.

Figure 4.

Deleterious mutations dampen establishment probabilities of autosomal inversions. The y-axis shows how deleterious mutations reduce the establishment probability of autosomal inversions relative to those on the X. Results are based on equation (3.3), with α = u_im/u_if, β = s_d,im/s_d,if, U_f = 0.01, m_A(n – 1) = m_X(n – 1) = 0.01.

Figure 5.

The X chromosome contains more inversions than expected relative to its size when considering fixed between-species differences. However, it contains fewer within-species polymorphic inversions. Each bar represents the ratio of the proportion of X-linked inversions to the proportion of autosomal inversions (i.e. fold enrichment on the X), scaled by the corresponding chromosome size for each species, or species pair (for polymorphic and fixed inversions, respectively). Data can be found in electronic supplementary material, tables S1 and S2. We have excluded species where fewer than 10 inversions are known.