Sex linkage, sex-specific selection, and the role of recombination in the evolution of sexually dimorphic gene expression

Abstract

Sex-biased genes--genes that are differentially expressed within males and females--are nonrandomly distributed across animal genomes, with sex chromosomes and autosomes often carrying markedly different concentrations of male- and female-biased genes. These linkage patterns are often gene- and lineage-dependent, differing between functional genetic categories and between species. Although sex-specific selection is often hypothesized to shape the evolution of sex-linked and autosomal gene content, population genetics theory has yet to account for many of the gene- and lineage-specific idiosyncrasies emerging from the empirical literature. With the goal of improving the connection between evolutionary theory and a rapidly growing body of genome-wide empirical studies, we extend previous population genetics theory of sex-specific selection by developing and analyzing a biologically informed model that incorporates sex linkage, pleiotropy, recombination, and epistasis, factors that are likely to vary between genes and between species. Our results demonstrate that sex-specific selection and sex-specific recombination rates can generate, and are compatible with, the gene- and species-specific linkage patterns reported in the genomics literature. The theory suggests that sexual selection may strongly influence the architectures of animal genomes, as well as the chromosomal distribution of fixed substitutions underlying sexually dimorphic traits.

Figure 1. Divergent expression-fitness landscapes generate conflicting selection over gene expression

The vertical gray lines represent the wild-type gene expression at the time point when the fitness landscapes diverge between the sexes. Arrows indicate the net direction of selection: stabilizing selection in the top panels, and selection for increased expression in the bottom panels. (A) Sex-specific selection without pleiotropy: selection favors a different level of gene expression in males and females. (B) Sex-specific selection with pleiotropy. A gene is expressed in multiple tissues or during multiple time periods during development. Expression-fitness functions overlap between the sexes within some contexts (context 1), and are divergent in others (context 2). Note that although we display symmetrical fitness landscapes (i.e., deviations above and below expression optima are equally costly), this need not necessarily be the case. The theory presented here permits asymmetries within or between male and female fitness landscapes.

Figure 2. Conceptual relationships between gene expression variation and dominance along a concave fitness surface

The solid line represents a hypothetical expression-fitness function with the expression optimum occurring at the filled circle. Mutations alter expression by Δx when heterozygous and 2Δx when homozygous. The fitness effects of heterozygous and homozygous mutations depend upon the position along the fitness surface. For a population that is fixed for alleles expressing at level b (at the optimum), mutations decrease fitness and the dominance coefficient for a deleterious mutation is h_d = α₁/(α₁ + α₂) < 1/2. For a population at position a or c on the fitness surface, beneficial mutations approaching position b will have dominance coefficients h_b = α₂/(α₁ + α₂) > 1/2.

Figure 3. Sequential invasion conditions and waiting times until tissue-specific gene expression divergence under antagonistic pleiotropy

Pleiotropically-expressed alleles (A₁ and A₂) follow the fitness parameterization from Table 3. Opportunities for invasion are described by the shaded bar at the base of each panel. The curves represent the mean time until derived alleles invade at the pleiotropic and modifier loci, with the uniform curve representing the X-linked scenario and the circle-bearing curve representing autosomal linkage. Results were obtained using the SSWM approximations presented in the text. Results are shown for k = 2 (h_d = ¼), t = 0.01, and utilize the permissive left hand term of eqs. (7a-7b); mutation rates per locus and per sex are u = v = 10⁻⁸; X and autosome effective sizes are N_A = 10⁶ = 4N_X/3. Results use dimorphic recombination parameters r_f = 0.001 and r_m = 0, yet sexually monomorphic recombination yields a nearly identical pattern.

Figure 4. Sequential invasion conditions and waiting times until sex-specific gene expression divergence under sexual antagonism

Opportunities for invasion are described by the shaded bar at the base of each panel. The curves represent the mean time until derived alleles invade at the sexually antagonistic and modifier loci, with the uniform curve representing the X-linked scenario and the circle-bearing curve representing autosomal linkage. Results were obtained using the SSWM approximations presented in the text. Sexually antagonistic alleles (A₁ and A₂) follow the fitness parameterization from Table 4. Results are shown for k = 2 (h_d = ¼), s_f = 0.01 for the case of directional selection in males, and s_m = 0.01 for directional selection in females; mutation rates per locus and per sex are u = v = 10⁻⁸; X and autosome effective sizes are N_A = 10⁶ = 4N_X/3. Results use dimorphic recombination parameters r_f = 0.001 and r_m = 0, yet sexually monomorphic recombination yields a nearly identical pattern.

Figure 5. Simultaneous invasion conditions and waiting times for epistatically beneficial haplotypes when males do not recombine

Opportunities for invasion are described by the shaded bar at the base of each panel. The curves represent the mean time until double-mutant haplotypes invade, with the uniform curve representing the X-linked scenario and the circle-bearing curve representing autosomal linkage. The net autosomal purifying selection against A₂B₁ or A₁B₂ haplotypes is ω_A = 0.001, with results for two ω_X/ω_A ratios shown. Results are shown for k = 2 (h_d = ¼), s_f = 0.01 for the case of directional selection in males, and s_m = 0.01 for directional selection in females; mutation rates per locus and per sex are u = v = 10⁻⁷; X and autosome effective sizes are N_A = 10⁶ = 4N_X/3. Results were obtained using the SSWM approximations presented in the text.

Figure 6. Simultaneous invasion conditions and waiting times for epistatically beneficial haplotypes when both sexes recombine

Opportunities for invasion are described by the shaded bar at the base of each panel. The curves represent the mean time until double-mutant haplotypes invade, with the uniform curve representing the X-linked scenario and the circle-bearing curve representing autosomal linkage. The results follow the same parameterization as presented in Figure 5, with r_m = r_f, and were obtained using the SSWM approximations presented in the text.