Models of sex chromosome and autosome evolution yield key predictions about the genomic basis of adaptive divergence, and such models have been important in guiding empirical research in comparative genomics and studies of speciation. In addition to the adaptive differentiation that occurs between species over time, selection also favors genetic divergence across geographic space, with subpopulations of single species evolving conspicuous differences in traits involved in adaptation to local environmental conditions. The potential contribution of sex chromosomes (the or) to local adaptation remains unclear, as we currently lack theory that directly links spatial variation in selection to local adaptation of -linked and autosomal genes. Here, we develop population genetic models that explicitly consider the effects of genetic dominance, effective population size, and sex-specific migration and selection on the relative contributions of-linked and autosomal genes to local adaptation. We show that -linked genes should nearly always disproportionately contribute to local adaptation in the presence of gene flow. We also show that considerations of dominance and effective population size-which play pivotal roles in the theory of faster- adaptation between species-have surprisingly little influence on the relative contribution of the chromosome to local adaptation. Instead, sex-biased migration is the primary mediator of the strength of spatial large- effects. Our results yield novel predictions about the role of sex chromosomes in local adaptation. We outline empirical approaches in evolutionary quantitative genetics and genomics that could build upon this new theory.

Natural selection varies widely among locations of a species' range, favoring population divergence and adaptation to local environmental conditions. Selection also differs between females and males, favoring the evolution of sexual dimorphism. Both forms of within-species evolutionary diversification are widely studied, though largely in isolation, and it remains unclear whether environmental variability typically generates similar or distinct patterns of selection on each sex. Studies of sex-specific local adaptation are also challenging because they must account for genetic correlations between female and male traits, which may lead to correlated patterns of trait divergence between sexes, whether or not local selection patterns are aligned or differ between the sexes. We quantified sex-specific divergence in five clinally variable traits in Drosophila melanogaster that individually vary in their magnitude of cross-sex genetic correlation (i.e., from moderate to strongly positive). In all five traits, we observed parallel male and female clines, regardless of the magnitude of their genetic correlation. These patterns imply that parallel spatial divergence of female and male traits is a reflection of sexually concordant directional selection imposed by local environmental conditions. In such contexts, genetic correlations between the sexes promote, rather than constrain, local adaptation to a spatially variable environment.

Evolutionary potential for adaptation hinges upon the orientation of genetic variation for traits under selection, captured by the additive genetic variance‐covariance matrix (G), as well as the evolutionary stability of G. Yet studies that assess both the stability of G and its alignment with selection are extraordinarily rare. We evaluated the stability of G in three Drosophila melanogaster populations that have adapted to local climatic conditions along a latitudinal cline. We estimated population‐ and sex‐specific G matrices for wing size and three climatic stress‐resistance traits that diverge adaptively along the cline. To determine how G affects evolutionary potential within these populations, we used simulations to quantify how well G aligns with the direction of trait divergence along the cline (as a proxy for the direction of local selection) and how genetic covariances between traits and sexes influence this alignment. We found that G was stable across the cline, showing no significant divergence overall, or in sex‐specific subcomponents, among populations. G also aligned well with the direction of clinal divergence, with genetic covariances strongly elevating evolutionary potential for adaptation to climatic extremes. These results suggest that genetic covariances between both traits and sexes should significantly boost evolutionary responses to environmental change.

During local adaptation with gene flow, some regions of the genome are inherently more responsive to selection than others. Recent theory predicts that X‐linked genes should disproportionately contribute to local adaptation relative to other genomic regions, yet this prediction remains to be tested. We carried out a multigeneration crossing scheme, using two cline‐end populations of Drosophila melanogaster, to estimate the relative contributions of the X chromosome, autosomes, and mitochondrial genome to divergence in four traits involved in local adaptation (wing size, resistance to heat, desiccation, and starvation stresses). We found that the mitochondrial genome and autosomes contributed significantly to clinal divergence in three of the four traits. In contrast, the X made no significant contribution to divergence in these traits. Given the small size of the mitochondrial genome, our results indicate that it plays a surprisingly large role in clinal adaptation. In contrast, the X, which represents roughly 20% of the Drosophila genome, contributes negligibly—a pattern that conflicts with theoretical predictions. These patterns reinforce recent work implying a central role of mitochondria in climatic adaptation, and suggest that different genomic regions may play fundamentally different roles in processes of divergence with gene flow.

No abstract