The effects of linkage and gene flow on local adaptation: a two-locus continent-island model

Coupling of Barriers to Gene Exchange: Causes and Consequences

Coupling has emerged as a concept to describe the transition from differentiated populations to newly evolved species through the strengthening of reproductive isolation. However, the term has been used in multiple ways, and relevant processes have sometimes not been clearly distinguished. Here, we synthesize existing uses of the concept of coupling and find three main perspectives: (1) coupling as the build-up of linkage disequilibrium among loci underlying barriers to gene exchange, (2) coupling as the build-up of genome-wide linkage disequilibrium, and (3) coupling as the process generating a coincidence of distinct barrier effects. We compare and contrast these views, show the diverse processes involved and the complexity of the relationships among recombination, linkage disequilibrium, and reproductive isolation, and, finally, we emphasize how each perspective can guide new directions in speciation research. Although the importance of coupling for evolutionary divergence and speciation is well established, many theoretical and empirical questions remain unanswered.

Locally adaptive inversions in structured populations

Inversions have been proposed to facilitate local adaptation, by linking together locally coadapted alleles at different loci. Prior work addressing this question theoretically has considered the spread of inversions in "continent-island" scenarios in which there is a unidirectional flow of maladapted migrants into the island population. In this setting, inversions capturing locally adaptive haplotypes are most likely to invade when selection is weak, because stronger local selection (i) more effectively purges maladaptive alleles and (ii) generates linkage disequilibrium between adaptive alleles, thus lessening the advantage of inversions. We show this finding only holds under limited conditions by studying the establishment of inversions in a more general two-deme model, which explicitly considers the dynamics of allele frequencies in both populations linked by bidirectional migration. In this model, the level of symmetry between demes can be varied from complete asymmetry (continent-island) to complete symmetry. For symmetric selection and migration, strong selection increases the allele frequency divergence between demes thereby increasing the frequency of maladaptive alleles in migrants, favoring inversions-the opposite of the pattern seen in the asymmetric continent-island scenario. We also account for the likelihood that a new inversion captures an adaptive haplotype in the first instance. When considering the combined process of capture and invasion in "continent island" and symmetric scenarios, relatively strong selection increases inversion establishment probability. Migration must also be low enough that the inversion is likely to capture an adaptive allele combination, but not so low as to eliminate the inversion's advantage. Overall, our analysis suggests that inversions are likely to harbor larger effect alleles that experience relatively strong selection.

Repeatability of adaptation in sunflowers reveals that genomic regions harbouring inversions also drive adaptation in species lacking an inversion

Local adaptation commonly involves alleles of large effect, which experience fitness advantages when in positive linkage disequilibrium (LD). Because segregating inversions suppress recombination and facilitate the maintenance of LD between locally adapted loci, they are also commonly found to be associated with adaptive divergence. However, it is unclear what fraction of an adaptive response can be attributed to inversions and alleles of large effect, and whether the loci within an inversion could still drive adaptation in the absence of its recombination-suppressing effect. Here, we use genome-wide association studies to explore patterns of local adaptation in three species of sunflower: Helianthus annuus, Helianthus argophyllus, and Helianthus petiolaris, which each harbour a large number of species-specific inversions. We find evidence of significant genome-wide repeatability in signatures of association to phenotypes and environments, which are particularly enriched within regions of the genome harbouring an inversion in one species. This shows that while inversions may facilitate local adaptation, at least some of the loci can still harbour mutations that make substantial contributions without the benefit of recombination suppression in species lacking a segregating inversion. While a large number of genomic regions show evidence of repeated adaptation, most of the strongest signatures of association still tend to be species-specific, indicating substantial genotypic redundancy for local adaptation in these species.

Inferring multi-locus selection in admixed populations

Admixture, the exchange of genetic information between distinct source populations, is thought to be a major source of adaptive genetic variation. Unlike mutation events, which periodically generate single alleles, admixture can introduce many selected alleles simultaneously. As such, the effects of linkage between selected alleles may be especially pronounced in admixed populations. However, existing tools for identifying selected mutations within admixed populations only account for selection at a single site, overlooking phenomena such as linkage among proximal selected alleles. Here, we develop and extensively validate a method for identifying and quantifying the individual effects of multiple linked selected sites on a chromosome in admixed populations. Our approach numerically calculates the expected local ancestry landscape in an admixed population for a given multi-locus selection model, and then maximizes the likelihood of the model. After applying this method to admixed populations of Drosophila melanogaster and Passer italiae, we found that the impacts between linked sites may be an important contributor to natural selection in admixed populations. Furthermore, for the situations we considered, the selection coefficients and number of selected sites are overestimated in analyses that do not consider the effects of linkage among selected sites. Our results imply that linkage among selected sites may be an important evolutionary force in admixed populations. This tool provides a powerful generalized method to investigate these crucial phenomena in diverse populations.

Comparative study highlights how gene flow shapes adaptive genomic architecture

Adaptation to environmental conditions, and the mechanisms underlying these adaptations, can vary greatly among species. This variation can be attributed to a variety of factors including the strength of evolutionary processes like selection, gene flow, time since divergence, and/or genetic drift, as well as the interactions between these processes. A number of simulation and theoretical studies have helped elucidate the role of these processes on the genomic basis of adaptation (Schaal et al., 2022; Yeaman et al., 2016). However, complementary empirical studies to test these theoretical expectations for within-species adaptation have been limited due to the challenging nature of evaluating these processes in a comparative framework. To do this effectively, it is necessary to have systems where the range of environmental variation is similar between species, but where one or more of these evolutionary processes vary. In a From the Cover article in this issue of Molecular Ecology, Shi et al. (2022) provide an excellent example of a freshwater system where rates of gene flow differ between populations of six riverine species due to variation in spawning strategies (i.e., broadcast spawners = high gene flow, nest spawners = low gene flow), but all experience the same variation in environmental conditions across their distributions. The authors take a multivariate approach to evaluate the genomic basis of adaptation by using a combination of differentiation-based and genotype-environment association (GEA) methods. By comparing the amount of gene flow between species and the resulting genomic basis of local adaptation, they are able to infer how genomic architecture may be shaped by rates of gene flow. Their results identify a general pattern of increased genomic clustering in species with increasing levels of gene flow. However, two of six species did not follow this pattern, which could be due to additional factors not assessed. Additionally, they provide convincing evidence that the underlying evolutionary mechanisms that formed genomic clusters within each species vary. These deviations from a general pattern highlight how difficult evaluating these processes in natural populations are, particularly because species-specific responses can vary dramatically. Taken together, their comparative framework for assessing the genomic architecture of adaptation is unique, sheds important light on how evolutionary processes can impact adaptation, and provides robust empirical support of foundational theoretical and simulation studies.

Chromosomal inversion polymorphisms shape the genomic landscape of deer mice

Chromosomal inversions are an important form of structural variation that can affect recombination, chromosome structure and fitness. However, because inversions can be challenging to detect, the prevalence and hence the significance of inversions segregating within species remains largely unknown, especially in natural populations of mammals. Here, by combining population-genomic and long-read sequencing analyses in a single, widespread species of deer mouse (Peromyscus maniculatus), we identified 21 polymorphic inversions that are large (1.5-43.8 Mb) and cause near-complete suppression of recombination when heterozygous (0-0.03 cM Mb-1). We found that inversion breakpoints frequently occur in centromeric and telomeric regions and are often flanked by long inverted repeats (0.5-50 kb), suggesting that they probably arose via ectopic recombination. By genotyping inversions in populations across the species' range, we found that the inversions are often widespread and do not harbour deleterious mutational loads, and many are likely to be maintained as polymorphisms by divergent selection. Comparisons of forest and prairie ecotypes of deer mice revealed 13 inversions that contribute to differentiation between populations, of which five exhibit significant associations with traits implicated in local adaptation. Taken together, these results show that inversion polymorphisms have a significant impact on recombination, genome structure and genetic diversity in deer mice and likely facilitate local adaptation across the widespread range of this species.

Inference of Gene Flow between Species under Misspecified Models

Genomic sequence data provide a rich source of information about the history of species divergence and interspecific hybridization or introgression. Despite recent advances in genomics and statistical methods, it remains challenging to infer gene flow, and as a result, one may have to estimate introgression rates and times under misspecified models. Here we use mathematical analysis and computer simulation to examine estimation bias and issues of interpretation when the model of gene flow is misspecified in analysis of genomic datasets, for example, if introgression is assigned to the wrong lineages. In the case of two species, we establish a correspondence between the migration rate in the continuous migration model and the introgression probability in the introgression model. When gene flow occurs continuously through time but in the analysis is assumed to occur at a fixed time point, common evolutionary parameters such as species divergence times are surprisingly well estimated. However, the time of introgression tends to be estimated towards the recent end of the period of continuous gene flow. When introgression events are assigned incorrectly to the parental or daughter lineages, introgression times tend to collapse onto species divergence times, with introgression probabilities underestimated. Overall, our analyses suggest that the simple introgression model is useful for extracting information concerning between-specific gene flow and divergence even when the model may be misspecified. However, for reliable inference of gene flow it is important to include multiple samples per species, in particular, from hybridizing species.

Genetic architecture of repeated phenotypic divergence in Littorina saxatilis ecotype evolution

Chromosomal inversions have been shown to play a major role in a local adaptation by suppressing recombination between alternative arrangements and maintaining beneficial allele combinations. However, so far, their importance relative to the remaining genome remains largely unknown. Understanding the genetic architecture of adaptation requires better estimates of how loci of different effect sizes contribute to phenotypic variation. Here, we used three Swedish islands where the marine snail Littorina saxatilis has repeatedly evolved into two distinct ecotypes along a habitat transition. We estimated the contribution of inversion polymorphisms to phenotypic divergence while controlling for polygenic effects in the remaining genome using a quantitative genetics framework. We confirmed the importance of inversions but showed that contributions of loci outside inversions are of similar magnitude, with variable proportions dependent on the trait and the population. Some inversions showed consistent effects across all sites, whereas others exhibited site-specific effects, indicating that the genomic basis for replicated phenotypic divergence is only partly shared. The contributions of sexual dimorphism as well as environmental factors to phenotypic variation were significant but minor compared to inversions and polygenic background. Overall, this integrated approach provides insight into the multiple mechanisms contributing to parallel phenotypic divergence.

Reproductive isolation via polygenic local adaptation in sub-divided populations: Effect of linkage disequilibria and drift

This paper considers how polygenic local adaptation and reproductive isolation between hybridizing populations is influenced by linkage disequilibria (LD) between loci, in scenarios where both gene flow and genetic drift counteract selection. It shows that the combined effects of multi-locus LD and genetic drift on allele frequencies at selected loci and on heterozygosity at neutral loci are predicted accurately by incorporating (deterministic) effective migration rates into the diffusion approximation (for selected loci) and into the structured coalescent (for neutral loci). Theoretical approximations are tested against individual-based simulations and used to investigate conditions for the maintenance of local adaptation on an island subject to one-way migration from a differently adapted mainland, and in an infinite-island population with two habitats under divergent selection. The analysis clarifies the conditions under which LD between sets of locally deleterious alleles allows these to be collectively eliminated despite drift, causing sharper and (under certain conditions) shifted migration thresholds for loss of adaptation. Local adaptation also has counter-intuitive effects on neutral (relative) divergence: F_ST is highest for a pair of subpopulations belonging to the same (rare) habitat, despite the lack of reproductive isolation between them.

Environmental adaptation often involves spatially heterogeneous selection at many genetic loci. Thus, the evolutionary consequences of hybridisation between populations adapted to different environments depend on the coupled dynamics of multiple loci under selection, migration and genetic drift, making them challenging to predict. Here, I introduce theoretical approximations that accurately capture the effect of such coupling on allele frequencies at individual loci, while also accounting for the stochastic effects of genetic drift. I then use these approximations to study hybridisation in a metapopulation consisting of many interconnected subpopulations, where each subpopulation belongs to one of two habitats under divergent selection. The analysis clarifies how subpopulations belonging to a rare habitat can maintain local adaptation despite high levels of migration if net selection against multi-locus genotypes is stronger than a threshold which depends on the relative abundances of the two habitats. Further, local adaptation in a metapopulation can significantly elevate F_ST between subpopulations belonging to the same habitat, even though these are not reproductively isolated. These findings highlight the importance of carefully considering the genetic architecture and spatial context of divergence when interpreting patterns of genomic differentiation between speciating populations.

Association mapping of colour variation in a butterfly provides evidence that a supergene locks together a cluster of adaptive loci

Supergenes are genetic architectures associated with discrete and concerted variation in multiple traits. It has long been suggested that supergenes control these complex polymorphisms by suppressing recombination between sets of coadapted genes. However, because recombination suppression hinders the dissociation of the individual effects of genes within supergenes, there is still little evidence that supergenes evolve by tightening linkage between coadapted genes. Here, combining a landmark-free phenotyping algorithm with multivariate genome-wide association studies, we dissected the genetic basis of wing pattern variation in the butterfly Heliconius numata. We show that the supergene controlling the striking wing pattern polymorphism displayed by this species contains several independent loci associated with different features of wing patterns. The three chromosomal inversions of this supergene suppress recombination between these loci, supporting the hypothesis that they may have evolved because they captured beneficial combinations of alleles. Some of these loci are, however, associated with colour variations only in a subset of morphs where the phenotype is controlled by derived inversion forms, indicating that they were recruited after the formation of the inversions. Our study shows that supergenes and clusters of adaptive loci in general may form via the evolution of chromosomal rearrangements suppressing recombination between co-adapted loci but also via the subsequent recruitment of linked adaptive mutations. This article is part of the theme issue 'Genomic architecture of supergenes: causes and evolutionary consequences'.

A chromosomal inversion contributes to divergence in multiple traits between deer mouse ecotypes

How locally adapted ecotypes are established and maintained within a species is a long-standing question in evolutionary biology. Using forest and prairie ecotypes of deer mice (Peromyscus maniculatus), we characterized the genetic basis of variation in two defining traits-tail length and coat color-and discovered a 41-megabase chromosomal inversion linked to both. The inversion frequency is 90% in the dark, long-tailed forest ecotype; decreases across a habitat transition; and is absent from the light, short-tailed prairie ecotype. We implicate divergent selection in maintaining the inversion at frequencies observed in the wild, despite high levels of gene flow, and explore fitness benefits that arise from suppressed recombination within the inversion. We uncover a key role for a large, previously uncharacterized inversion in the evolution and maintenance of classic mammalian ecotypes.

Genetic architecture of adaptive radiation across two trophic levels

Evolution of trophic diversity is a hallmark of adaptive radiation. Yet, transitions between carnivory and herbivory are rare in young adaptive radiations. Haplochromine cichlid fish of the African Great Lakes are exceptional in this regard. Lake Victoria was colonized by an insectivorous generalist and in less than 20 000 years, several clades of specialized herbivores evolved. Carnivorous versus herbivorous lifestyles in cichlids require many different adaptations in functional morphology, physiology and behaviour. Ecological transitions in either direction thus require many traits to change in a concerted fashion, which could be facilitated if genomic regions underlying these traits were physically linked or pleiotropic. However, linkage/pleiotropy could also constrain evolvability. To investigate components of the genetic architecture of a suite of traits that distinguish invertivores from algae scrapers, we performed quantitative trait locus (QTL) mapping using a second-generation hybrid cross. While we found indications of linkage/pleiotropy within trait complexes, QTLs for distinct traits were distributed across several unlinked genomic regions. Thus, a mixture of independently segregating variation and some pleiotropy may underpin the rapid trophic transitions. We argue that the emergence and maintenance of associations between the different genomic regions underpinning co-adapted traits that evolved and persist against some gene flow required reproductive isolation.

Evolutionary dynamics of complex traits in sexual populations in a heterogeneous environment: how normal?

When studying the dynamics of trait distribution of populations in a heterogeneous environment, classical models from quantitative genetics choose to look at its system of moments, specifically the first two ones. Additionally, in order to close the resulting system of equations, they often assume the local trait distributions are Gaussian [see for instance Ronce and Kirkpatrick (Evolution 55(8):1520-1531, 2001. https://doi.org/10.1111/j.0014-3820.2001.tb00672.x.37 )]. The aim of this paper is to introduce a mathematical framework that follows the whole trait distribution (without prior assumption) to study evolutionary dynamics of sexually reproducing populations. Specifically, it focuses on complex traits, whose inheritance can be encoded by the infinitesimal model of segregation (Fisher in Trans R Soc Edinb 52(2):399-433, 1919. https://doi.org/10.1017/S0080456800012163 ). We show that it allows us to derive a regime in which our model gives the same dynamics as when assuming Gaussian local trait distributions. To support that, we compare the stationary problems of the system of moments derived from our model with the one given in Ronce and Kirkpatrick (Evolution 55(8):1520-1531, 2001. https://doi.org/10.1111/j.0014-3820.2001.tb00672.x.37 ) and show that they are equivalent under this regime and do not need to be otherwise. Moreover, under this regime of equivalence, we show that a separation bewteen ecological and evolutionary time scales arises. A fast relaxation toward monomorphism allows us to reduce the complexity of the system of moments, using a slow-fast analysis. This reduction leads us to complete, still in this regime, the analytical description of the bistable asymmetrical equilibria numerically found in Ronce and Kirkpatrick (Evolution 55(8):1520-1531, 2001. https://doi.org/10.1111/j.0014-3820.2001.tb00672.x.37 ). More globally, we provide explicit modelling hypotheses that allow for such local adaptation patterns to occur.

Physical geography, isolation by distance and environmental variables shape genomic variation of wild barley (Hordeum vulgare L. ssp. spontaneum) in the Southern Levant

Determining the extent of genetic variation that reflects local adaptation in crop-wild relatives is of interest for the purpose of identifying useful genetic diversity for plant breeding. We investigated the association of genomic variation with geographical and environmental factors in wild barley (Hordeum vulgare L. ssp. spontaneum) populations of the Southern Levant using genotyping by sequencing (GBS) of 244 accessions in the Barley 1K+ collection. The inference of population structure resulted in four genetic clusters that corresponded to eco-geographical habitats and a significant association between lower gene flow rates and geographical barriers, e.g. the Judaean Mountains and the Sea of Galilee. Redundancy analysis (RDA) revealed that spatial autocorrelation explained 45% and environmental variables explained 15% of total genomic variation. Only 4.5% of genomic variation was solely attributed to environmental variation if the component confounded with spatial autocorrelation was excluded. A synthetic environmental variable combining latitude, solar radiation, and accumulated precipitation explained the highest proportion of genomic variation (3.9%). When conditioned on population structure, soil water capacity was the most important environmental variable explaining 1.18% of genomic variation. Genome scans with outlier analysis and genome-environment association studies were conducted to identify adaptation signatures. RDA and outlier methods jointly detected selection signatures in the pericentromeric regions, which have reduced recombination, of the chromosomes 3H, 4H, and 5H. However, selection signatures mostly disappeared after correction for population structure. In conclusion, adaptation to the highly diverse environments of the Southern Levant over short geographical ranges had a limited effect on the genomic diversity of wild barley. This highlighted the importance of nonselective forces in genetic differentiation.

Evolution of polygenic traits under global vs local adaptation

Observations about the number, frequency, effect size, and genomic distribution of alleles associated with complex traits must be interpreted in light of evolutionary process. These characteristics, which constitute a trait's genetic architecture, can dramatically affect evolutionary outcomes in applications from agriculture to medicine, and can provide a window into how evolution works. Here, I review theoretical predictions about the evolution of genetic architecture under spatially homogeneous, global adaptation as compared with spatially heterogeneous, local adaptation. Due to the tension between divergent selection and migration, local adaptation can favor "concentrated" genetic architectures that are enriched for alleles of larger effect, clustered in a smaller number of genomic regions, relative to expectations under global adaptation. However, the evolution of such architectures may be limited by many factors, including the genotypic redundancy of the trait, mutation rate, and temporal variability of environment. I review the circumstances in which predictions differ for global vs local adaptation and discuss where progress can be made in testing hypotheses using data from natural populations and lab experiments. As the field of comparative population genomics expands in scope, differences in architecture among traits and species will provide insights into how evolution works, and such differences must be interpreted in light of which kind of selection has been operating.

Genetic variation for adaptive traits is associated with polymorphic inversions in Littorina saxatilis

Chromosomal inversions have long been recognized for their role in local adaptation. By suppressing recombination in heterozygous individuals, they can maintain coadapted gene complexes and protect them from homogenizing effects of gene flow. However, to fully understand their importance for local adaptation we need to know their influence on phenotypes under divergent selection. For this, the marine snail Littorina saxatilis provides an ideal study system. Divergent ecotypes adapted to wave action and crab predation occur in close proximity on intertidal shores with gene flow between them. Here, we used F2 individuals obtained from crosses between the ecotypes to test for associations between genomic regions and traits distinguishing the Crab‐/Wave‐adapted ecotypes including size, shape, shell thickness, and behavior. We show that most of these traits are influenced by two previously detected inversion regions that are divergent between ecotypes. We thus gain a better understanding of one important underlying mechanism responsible for the rapid and repeated formation of ecotypes: divergent selection acting on inversions. We also found that some inversions contributed to more than one trait suggesting that they may contain several loci involved in adaptation, consistent with the hypothesis that suppression of recombination within inversions facilitates differentiation in the presence of gene flow.

The Effect of Habitat Choice on Evolutionary Rescue in Subdivided Populations

AbstractEvolutionary rescue is the process by which a population, in response to an environmental change, successfully avoids extinction through adaptation. In spatially structured environments, dispersal can affect the probability of rescue. Here, we model an environment consisting of patches that degrade one after another, and we investigate the probability of rescue by a mutant adapted to the degraded habitat. We focus on the effects of dispersal and of immigration biases. We identify up to three regions delimiting the effect of dispersal on the probability of evolutionary rescue: (i) starting from low dispersal rates, the probability of rescue increases with dispersal; (ii) at intermediate dispersal rates, it decreases; and (iii) at large dispersal rates, it increases again with dispersal, except if mutants are too counterselected in not-yet-degraded patches. The probability of rescue is generally highest when mutant and wild-type individuals preferentially immigrate into patches that have already undergone environmental change. Additionally, we find that mutants that will eventually rescue the population most likely first appear in nondegraded patches. Overall, our results show that habitat choice, compared with the often-studied unbiased immigration scheme, can substantially alter the dynamics of population survival and adaptation to new environments.

The effectiveness of pseudomagic traits in promoting divergence and enhancing local adaptation

"Magic traits," in which the same trait is both under divergent ecological selection and forms the basis of assortative mating, have been sought after due to their supposed unique ability to promote divergence with gene flow. Here, we ask how unique magic traits are, by exploring whether a tightly linked complex of a locus under divergent selection and a locus that acts as a mating cue can mimic a magic trait in its divergence. We find that these "pseudomagic traits" can be very effective in promoting divergence; with tight linkage they are essentially as effective as a magic trait and with loose linkage, and even no linkage, divergence can still be enhanced. Distinguishing between magic and pseudomagic traits in empirical cases may thus not be important when inferring their role in divergence. The ability of divergence in the mating trait to drive divergence in the ecological trait by lowering the effective migration rate, which occurs somewhat even without linkage, is particularly striking; magic traits are typically considered to have the other direction of causality. Our results thus suggest that divergence in a mating trait can at least modestly increase local adaption by allowing more ecological divergence, particularly with tighter linkage.

Consequences of Single-Locus and Tightly Linked Genomic Architectures for Evolutionary Responses to Environmental Change

Genetic and genomic architectures of traits under selection are key factors influencing evolutionary responses. Yet, knowledge of their impacts has been limited by a widespread assumption that most traits are controlled by unlinked polygenic architectures. Recent advances in genome sequencing and eco-evolutionary modeling are unlocking the potential for integrating genomic information into predictions of population responses to environmental change. Using eco-evolutionary simulations, we demonstrate that hypothetical single-locus control of a life history trait produces highly variable and unpredictable harvesting-induced evolution relative to the classically applied multilocus model. Single-locus control of complex traits is thought to be uncommon, yet blocks of linked genes, such as those associated with some types of structural genomic variation, have emerged as taxonomically widespread phenomena. Inheritance of linked architectures resembles that of single loci, thus enabling single-locus-like modeling of polygenic adaptation. Yet, the number of loci, their effect sizes, and the degree of linkage among them all occur along a continuum. We review how linked architectures are often associated, directly or indirectly, with traits expected to be under selection from anthropogenic stressors and are likely to play a large role in adaptation to environmental disturbance. We suggest using single-locus models to explore evolutionary extremes and uncertainties when the trait architecture is unknown, refining parameters as genomic information becomes available, and explicitly incorporating linkage among loci when possible. By overestimating the complexity (e.g., number of independent loci) of the genomic architecture of traits under selection, we risk underestimating the complexity (e.g., nonlinearity) of their evolutionary dynamics.

Genetic architecture of a key reproductive isolation trait differs between sympatric and non-sympatric sister species of Lake Victoria cichlids

One hallmark of the East African cichlid radiations is the rapid evolution of reproductive isolation that is robust to full sympatry of many closely related species. Theory predicts that species persistence and speciation in sympatry with gene flow are facilitated if loci of large effect or physical linkage (or pleiotropy) underlie traits involved in reproductive isolation. Here, we investigate the genetic architecture of a key trait involved in behavioural isolation, male nuptial coloration, by crossing two sister species pairs of Lake Victoria cichlids of the genus Pundamilia and mapping nuptial coloration in the F2 hybrids. One is a young sympatric species pair, representative of an axis of colour motif differentiation, red-dorsum versus blue, that is highly recurrent in closely related sympatric species. The other is a species pair representative of colour motifs, red-chest versus blue, that are common in allopatric but uncommon in sympatric closely related species. We find significant quantitative trait loci (QTLs) with moderate to large effects (some overlapping) for red and yellow in the sympatric red-dorsum × blue cross, whereas we find no significant QTLs in the non-sympatric red-chest × blue cross. These findings are consistent with theory predicting that large effect loci or linkage/pleiotropy underlying mating trait differentiation could facilitate speciation and species persistence with gene flow in sympatry.

Frequency, Origins, and Evolutionary Role of Chromosomal Inversions in Plants

Chromosomal inversions have the potential to play an important role in evolution by reducing recombination between favorable combinations of alleles. Until recently, however, most evidence for their likely importance derived from dipteran flies, whose giant larval salivary chromosomes aided early cytogenetic studies. The widespread application of new genomic technologies has revealed that inversions are ubiquitous across much of the plant and animal kingdoms. Here we review the rapidly accumulating literature on inversions in the plant kingdom and discuss what we have learned about their establishment and likely evolutionary role. We show that inversions are prevalent across a wide range of plant groups. We find that inversions are often associated with locally favored traits, as well as with traits that contribute to assortative mating, suggesting that they may be key to adaptation and speciation in the face of gene flow. We also discuss the role of inversions in sex chromosome formation, and explore possible parallels with inversion establishment on autosomes. The identification of inversion origins, as well as the causal variants within them, will advance our understanding of chromosomal evolution in plants.

Frequency, Origins, and Evolutionary Role of Chromosomal Inversions in Plants

Chromosomal inversions have the potential to play an important role in evolution by reducing recombination between favorable combinations of alleles. Until recently, however, most evidence for their likely importance derived from dipteran flies, whose giant larval salivary chromosomes aided early cytogenetic studies. The widespread application of new genomic technologies has revealed that inversions are ubiquitous across much of the plant and animal kingdoms. Here we review the rapidly accumulating literature on inversions in the plant kingdom and discuss what we have learned about their establishment and likely evolutionary role. We show that inversions are prevalent across a wide range of plant groups. We find that inversions are often associated with locally favored traits, as well as with traits that contribute to assortative mating, suggesting that they may be key to adaptation and speciation in the face of gene flow. We also discuss the role of inversions in sex chromosome formation, and explore possible parallels with inversion establishment on autosomes. The identification of inversion origins, as well as the causal variants within them, will advance our understanding of chromosomal evolution in plants.

Genomic Resources for Darters (Percidae: Etheostominae) Provide Insight into Postzygotic Barriers Implicated in Speciation

Comparative genomic approaches are increasingly being used to study the evolution of reproductive barriers in nonmodel species. Although numerous studies have examined prezygotic isolation in darters (Percidae), investigations into postzygotic barriers have remained rare due to long generation times and a lack of genomic resources. Orangethroat and rainbow darters naturally hybridize and provide a remarkable example of male-driven speciation via character displacement. Backcross hybrids suffer from high mortality, which appears to promote behavioral isolation in sympatry. To investigate the genomic architecture of postzygotic isolation, we used Illumina and PacBio sequencing to generate a chromosome-level, annotated assembly of the orangethroat darter genome and high-density linkage maps for orangethroat and rainbow darters. We also analyzed genome-wide RADseq data from wild-caught adults of both species and laboratory-generated backcrosses to identify genomic regions associated with hybrid incompatibles. Several putative chromosomal translocations and inversions were observed between orangethroat and rainbow darters, suggesting structural rearrangements may underlie postzygotic isolation. We also found evidence of selection against recombinant haplotypes and transmission ratio distortion in backcross hybrid genomes, providing further insight into the genomic architecture of genetic incompatibilities. Notably, regions with high levels of genetic divergence between species were enriched for genes associated with developmental and meiotic processes, providing strong candidates for postzygotic isolating barriers. These findings mark significant contributions to our understanding of the genetic basis of reproductive isolation between species undergoing character displacement. Furthermore, the genomic resources presented here will be instrumental for studying speciation in darters, the most diverse vertebrate group in North America.

Whole-chromosome hitchhiking driven by a male-killing endosymbiont

Neo-sex chromosomes are found in many taxa, but the forces driving their emergence and spread are poorly understood. The female-specific neo-W chromosome of the African monarch (or queen) butterfly Danaus chrysippus presents an intriguing case study because it is restricted to a single 'contact zone' population, involves a putative colour patterning supergene, and co-occurs with infection by the male-killing endosymbiont Spiroplasma. We investigated the origin and evolution of this system using whole genome sequencing. We first identify the 'BC supergene', a broad region of suppressed recombination across nearly half a chromosome, which links two colour patterning loci. Association analysis suggests that the genes yellow and arrow in this region control the forewing colour pattern differences between D. chrysippus subspecies. We then show that the same chromosome has recently formed a neo-W that has spread through the contact zone within approximately 2,200 years. We also assembled the genome of the male-killing Spiroplasma, and find that it shows perfect genealogical congruence with the neo-W, suggesting that the neo-W has hitchhiked to high frequency as the male-killer has spread through the population. The complete absence of female crossing-over in the Lepidoptera causes whole-chromosome hitchhiking of a single neo-W haplotype, carrying a single allele of the BC supergene and dragging multiple non-synonymous mutations to high frequency. This has created a population of infected females that all carry the same recessive colour patterning allele, making the phenotypes of each successive generation highly dependent on uninfected male immigrants. Our findings show how hitchhiking can occur between the physically unlinked genomes of host and endosymbiont, with dramatic consequences.

Evolutionary potential for genomic islands of sexual divergence on recombining sex chromosomes

Differentiated sex chromosomes are thought to develop through the accumulation of polymorphisms at loci subject to opposing selection between males and females, and/or between haploids and diploids. As sex chromosomes differentiate, reduced recombination becomes favored between selected loci and the sex-determining region, strengthening genetic associations between alleles favored in a sex and the corresponding sex chromosome. Here a model is analyzed to explore whether polymorphism at one sexually or ploidally antagonistic locus facilitates the spread of rare alleles at other loci experiencing antagonistic selection, promoting further differentiation of the sex chromosomes. It is found that antagonistic polymorphisms can spread and capture other such loci, building 'genomic islands' of differentiation on sex chromosomes, but the conditions are very restrictive, requiring the loci to be strongly selected, tightly linked and distant from the sex-determining region. Epistatic interactions can facilitate the promotion of polymorphism among selected loci, but only if preferentially favoring heterozygotes. Although these results apply to any taxa, plants provide a fertile ground for testing these and related theories given the recurrent evolutionary transitions to dioecy, which provide multiple opportunities to track the early evolution of sex chromosomes.

Mating system impacts the genetic architecture of adaptation to heterogeneous environments

Self-fertilisation has consequences for variation across the genome as it reduces effective population size, effect recombination rates and pollen flow, with implications for local adaptation. We conducted simulations of divergent stabilising selection on a quantitative trait with drift, pollen flow, mutation, recombination and different outcrossing rates. We quantified trait divergence and the genetic architecture of adaptation. We conducted an F_ST outlier analysis to identify candidate loci and quantified the impact of mating system on detectability. Selfing promoted trait divergence mainly through reductions in pollen flow. Moreover, trait architecture became more diffuse with selfing. Average effect size of trait loci was lower, while the number of loci, and their clustering distance increased. The genetic architecture of selfers was also more diffuse than outcrossers for equivalent migration rates. However, when deleterious alleles were included, architectures became more concentrated in selfers, likely to be because of reductions in population size caused by mutational meltdown and impacts of background selection on N_e . Our simulations demonstrate that mating system has important impacts on adaptive divergence of traits and the genetic landscape underlying that divergence. Selfing has a significant effect on detectability of regions of the genome important for adaptation because of neutral divergence and diffuse trait architecture.

Key role of recombination in evolutionary processes with migration between two habitats

Recombination is one of the leading forces of evolutionary dynamics. Although the importance of both recombination and migration in evolution is well recognized, there is currently no exact theory of evolutionary dynamics for large genome models that incorporates recombination, mutation, selection (quasispecies model with recombination), and spatial dynamics. To address this problem, we analyze the simplest spatial evolutionary process, namely, evolution of haploid populations with mutation, selection, recombination, and unidirectional migration, in its exact analytical form. This model is based on the quasispecies theory with recombination, but with replicators migrating from one habitat to another. In standard evolutionary models involving one habitat, the evolutionary processes depend on the ratios of fitness for different sequences. In the case of migration, we consider the absolute fitness values because there is no competition for resources between the population of different habitats. In the standard model without epistasis, recombination does not affect the mean fitness of the population. When migration is introduced, the situation changes drastically such that recombination can affect the mean fitness as strongly as mutation, as has been observed by Li and Nei for a few loci model without mutations. We have solved our model in the limit of large genome size for the fitness landscapes having different peaks in the first and second habitats and obtained the total population sizes for both habitats as well as the proportion of the population around two peak sequences in the second habitat. We identify four phases in the model and present the exact solutions for three of them.

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

Ecological factors and morphological traits are associated with repeated genomic differentiation between lake and stream stickleback

The repeated evolution of similar phenotypes in independent populations (i.e. parallel or convergent evolution) provides an opportunity to identify genetic and ecological factors that influence the process of adaptation. Threespine stickleback fish ( Gasterosteus aculeatus) are an excellent model for such studies, as they have repeatedly adapted to divergent habitats across the Northern hemisphere. Here, we use genomic, ecological and morphological data from 16 independent pairs of stickleback populations adapted to divergent lake and stream habitats. We combine a population genomic approach to identify regions of the genome that are likely under selection in these divergent habitats with an association mapping approach to identify regions of the genome that underlie variation in ecological factors and morphological traits. Over 37% of genomic windows are repeatedly differentiated across lake-stream pairs. Similarly, many genomic windows are associated with variation in abiotic factors, diet items and morphological phenotypes. Both the highly differentiated windows and candidate trait windows are non-randomly distributed across the genome and show some overlap. However, the overlap is not significant on a genome-wide scale. Together, our data suggest that adaptation to divergent food resources and predation regimes are drivers of differentiation in lake-stream stickleback, but that additional ecological factors are also important. This article is part of the theme issue 'Convergent evolution in the genomics era: new insights and directions'.

Genomic Patterns of Local Adaptation under Gene Flow in Arabidopsis lyrata

Short-scale local adaptation is a complex process involving selection, migration, and drift. The expected effects on the genome are well grounded in theory but examining these on an empirical level has proven difficult, as it requires information about local selection, demographic history, and recombination rate variation. Here, we use locally adapted and phenotypically differentiated Arabidopsis lyrata populations from two altitudinal gradients in Norway to test these expectations at the whole-genome level. Demography modeling indicates that populations within the gradients diverged <2 kya and that the sites are connected by gene flow. The gene flow estimates are, however, highly asymmetric with migration from high to low altitudes being several times more frequent than vice versa. To detect signatures of selection for local adaptation, we estimate patterns of lineage-specific differentiation among these populations. Theory predicts that gene flow leads to concentration of adaptive loci in areas of low recombination; a pattern we observe in both lowland-alpine comparisons. Although most selected loci display patterns of conditional neutrality, we found indications of genetic trade-offs, with one locus particularly showing high differentiation and signs of selection in both populations. Our results further suggest that resistance to solar radiation is an important adaptation to alpine environments, while vegetative growth and bacterial defense are indicated as selected traits in the lowland habitats. These results provide insights into genetic architectures and evolutionary processes driving local adaptation under gene flow. We also contribute to understanding of traits and biological processes underlying alpine adaptation in northern latitudes.

Ecological Genetic Conflict: Genetic Architecture Can Shift the Balance between Local Adaptation and Plasticity

Genetic polymorphism can contribute to local adaptation in heterogeneous habitats, for instance, as a single locus with alleles adapted to different habitats. Phenotypic plasticity can also contribute to trait variation across habitats, through developmental responses to habitat-specific cues. We show that the genetic architecture of genetically polymorphic and plasticity loci may influence the balance between local adaptation and phenotypic plasticity. These effects of genetic architecture are instances of ecological genetic conflict. A reduced effective migration rate for genes tightly linked to a genetic polymorphism provides an explanation for the effects, and they can occur both for a single trait and for a syndrome of coadapted traits. Using individual-based simulations and numerical analysis, we investigate how among-habitat genetic polymorphism and phenotypic plasticity depend on genetic architecture. We also study the evolution of genetic architecture itself, in the form of rates of recombination between genetically polymorphic loci and plasticity loci. Our main result is that for plasticity genes that are unlinked to loci with between-habitat genetic polymorphism, the slope of a reaction norm is steeper in comparison with the slope favored by plasticity genes that are tightly linked to genes for local adaptation.

Modularity of genes involved in local adaptation to climate despite physical linkage

BACKGROUND

Linkage among genes experiencing different selection pressures can make natural selection less efficient. Theory predicts that when local adaptation is driven by complex and non-covarying stresses, increased linkage is favored for alleles with similar pleiotropic effects, with increased recombination favored among alleles with contrasting pleiotropic effects. Here, we introduce a framework to test these predictions with a co-association network analysis, which clusters loci based on differing associations. We use this framework to study the genetic architecture of local adaptation to climate in lodgepole pine, Pinus contorta, based on associations with environments.

RESULTS

We identify many clusters of candidate genes and SNPs associated with distinct environments, including aspects of aridity and freezing, and discover low recombination rates among some candidate genes in different clusters. Only a few genes contain SNPs with effects on more than one distinct aspect of climate. There is limited correspondence between co-association networks and gene regulatory networks. We further show how associations with environmental principal components can lead to misinterpretation. Finally, simulations illustrate both benefits and caveats of co-association networks.

CONCLUSIONS

Our results support the prediction that different selection pressures favor the evolution of distinct groups of genes, each associating with a different aspect of climate. But our results went against the prediction that loci experiencing different sources of selection would have high recombination among them. These results give new insight into evolutionary debates about the extent of modularity, pleiotropy, and linkage in the evolution of genetic architectures.

The Genomic Architecture of a Rapid Island Radiation: Recombination Rate Variation, Chromosome Structure, and Genome Assembly of the Hawaiian Cricket Laupala

Phenotypic evolution and speciation depend on recombination in many ways. Within populations, recombination can promote adaptation by bringing together favorable mutations and decoupling beneficial and deleterious alleles. As populations diverge, crossing over can give rise to maladapted recombinants and impede or reverse diversification. Suppressed recombination due to genomic rearrangements, modifier alleles, and intrinsic chromosomal properties may offer a shield against maladaptive gene flow eroding coadapted gene complexes. Both theoretical and empirical results support this relationship. However, little is known about this relationship in the context of behavioral isolation, where coevolving signals and preferences are the major hybridization barrier. Here we examine the genomic architecture of recently diverged, sexually isolated Hawaiian swordtail crickets (Laupala). We assemble a de novo genome and generate three dense linkage maps from interspecies crosses. In line with expectations based on the species' recent divergence and successful interbreeding in the laboratory, the linkage maps are highly collinear and show no evidence for large-scale chromosomal rearrangements. Next, the maps were used to anchor the assembly to pseudomolecules and estimate recombination rates across the genome to test the hypothesis that loci involved in behavioral isolation (song and preference divergence) are in regions of low interspecific recombination. Contrary to our expectations, the genomic region where a male song and female preference QTL colocalize is not associated with particularly low recombination rates. This study provides important novel genomic resources for an emerging evolutionary genetics model system and suggests that trait-preference coevolution is not necessarily facilitated by locally suppressed recombination.

Varied Genomic Responses to Maladaptive Gene Flow and Their Evidence

Adaptation to a local environment often occurs in the face of maladaptive gene flow. In this perspective, I discuss several ideas on how a genome may respond to maladaptive gene flow during adaptation. On the one hand, selection can build clusters of locally adaptive alleles at fortuitously co-localized loci within a genome, thereby facilitating local adaptation with gene flow ('allele-only clustering'). On the other hand, the selective pressure to link adaptive alleles may drive co-localization of the actual loci relevant for local adaptation within a genome through structural genome changes or an evolving intra-genomic crossover rate ('locus clustering'). While the expected outcome is, in both cases, a higher frequency of locally adaptive alleles in some genome regions than others, the molecular units evolving in response to gene flow differ (i.e., alleles versus loci). I argue that, although making this distinction is important, we commonly lack the critical empirical evidence to do so. This is mainly because many current approaches are biased towards detecting local adaptation in genome regions with low crossover rates. The importance of low-crossover genome regions for adaptation with gene flow, such as in co-localizing relevant loci within a genome, thus remains unclear. Future empirical investigations should address these questions by making use of comparative genomics, where multiple de novo genome assemblies from species evolved under different degrees of genetic exchange are compared. This research promises to advance our understanding of how a genome adapts to maladaptive gene flow, thereby promoting adaptive divergence and reproductive isolation.

Transitions from Single- to Multi-Locus Processes during Speciation with Gene Flow

During speciation-with-gene-flow, a transition from single-locus to multi-locus processes can occur, as strong coupling of multiple loci creates a barrier to gene flow. Testing predictions about such transitions with empirical data requires building upon past theoretical work and the continued development of quantitative approaches. We simulated genomes under several evolutionary scenarios of gene flow and divergent selection, extending previous work with the additions of neutral sites and coupling statistics. We used these simulations to investigate, in a preliminary way, if and how selected and neutral sites differ in the conditions they require for transitions during speciation. For the parameter combinations we explored, as the per-locus strength of selection grew and/or migration decreased, it became easier for selected sites to show divergence-and thus to rise in linkage disequilibrium (LD) with each other as a statistical consequence-farther in advance of the conditions under which neutral sites could diverge. Indeed, even very low rates of effective gene flow were sufficient to prevent differentiation at neutral sites. However, once strong enough, coupling among selected sites eventually reduced gene flow at neutral sites as well. To explore whether similar transitions might be detectable in empirical data, we used published genome resequencing data from three taxa of Heliconius butterflies. We found that fixation index ( F S T ) outliers and allele-frequency outliers exhibited stronger patterns of within-deme LD than the genomic background, as expected. The statistical characteristics of within-deme LD-likely indicative of the strength of coupling of barrier loci-varied between chromosomes and taxonomic comparisons. Qualitatively, the patterns we observed in the empirical data and in our simulations suggest that selection drives rapid genome-wide transitions to multi-locus coupling, illustrating how divergence and gene flow interact along the speciation continuum.

The Limits to Parapatric Speciation II: Strengthening a Preexisting Genetic Barrier to Gene Flow in Parapatry

By encompassing the whole continuum between allopatric and sympatric scenarios, parapatric speciation includes many potential scenarios for the evolution of new species. Here, we investigate how a genetic barrier to gene flow, that relies on a single postzygotic genetic incompatibility, may further evolve under ongoing migration. We consider a continent island model with three loci involved in pairwise Dobzhansky–Muller incompatibilities (DMIs). Using an analytic approach, we derive the conditions for invasion of a new mutation and its consequences for the strength and stability of the initial genetic barrier. Our results show that the accumulation of genetic incompatibilities in the presence of gene flow is under strong selective constraints. In particular, preexisting incompatibilities do not always facilitate the invasion of further barrier genes. If new mutations do invade, they will often weaken or destroy the barrier rather than strengthening it. We conclude that migration is highly effective at disrupting the so-called “snowball effect”, the accelerated accumulation of DMIs that has been described for allopatric populations en route to reproductive isolation.

Adaptive Genetic Divergence Despite Significant Isolation-by-Distance in Populations of Taiwan Cow-Tail Fir (Keteleeria davidiana var. formosana)

Double digest restriction site-associated DNA sequencing (ddRADseq) is a tool for delivering genome-wide single nucleotide polymorphism (SNP) markers for non-model organisms useful in resolving fine-scale population structure and detecting signatures of selection. This study performs population genetic analysis, based on ddRADseq data, of a coniferous species, Keteleeria davidiana var. formosana, disjunctly distributed in northern and southern Taiwan, for investigation of population adaptive divergence in response to environmental heterogeneity. A total of 13,914 SNPs were detected and used to assess genetic diversity, FST outlier detection, population genetic structure, and individual assignments of five populations (62 individuals) of K. davidiana var. formosana. Principal component analysis (PCA), individual assignments, and the neighbor-joining tree were successful in differentiating individuals between northern and southern populations of K. davidiana var. formosana, but apparent gene flow between the southern DW30 population and northern populations was also revealed. Fifteen of 23 highly differentiated SNPs identified were found to be strongly associated with environmental variables, suggesting isolation-by-environment (IBE). However, multiple matrix regression with randomization analysis revealed strong IBE as well as significant isolation-by-distance. Environmental impacts on divergence were found between populations of the North and South regions and also between the two southern neighboring populations. BLASTN annotation of the sequences flanking outlier SNPs gave significant hits for three of 23 markers that might have biological relevance to mitochondrial homeostasis involved in the survival of locally adapted lineages. Species delimitation between K. davidiana var. formosana and its ancestor, K. davidiana, was also examined (72 individuals). This study has produced highly informative population genomic data for the understanding of population attributes, such as diversity, connectivity, and adaptive divergence associated with large- and small-scale environmental heterogeneity in K. davidiana var. formosana.

The evolution of recombination rates in finite populations during ecological speciation

Recombination can impede ecological speciation with gene flow by mixing locally adapted genotypes with maladapted migrant genotypes from a divergent population. In such a scenario, suppression of recombination can be selectively favoured. However, in finite populations evolving under the influence of random genetic drift, recombination can also facilitate adaptation by reducing Hill-Robertson interference between loci under selection. In this case, increased recombination rates can be favoured. Although these two major effects on recombination have been studied individually, their joint effect on ecological speciation with gene flow remains unexplored. Using a mathematical model, we investigated the evolution of recombination rates in two finite populations that exchange migrants while adapting to contrasting environments. Our results indicate a two-step dynamic where increased recombination is first favoured (in response to the Hill-Robertson effect), and then disfavoured, as the cost of recombining locally with maladapted migrant genotypes increases over time (the maladaptive gene flow effect). In larger populations, a stronger initial benefit for recombination was observed, whereas high migration rates intensify the long-term cost of recombination. These dynamics may have important implications for our understanding of the conditions that facilitate incipient speciation with gene flow and the evolution of recombination in finite populations.

The Spread of an Inversion with Migration and Selection

We re-examine the model of Kirkpatrick and Barton for the spread of an inversion into a local population. This model assumes that local selection maintains alleles at two or more loci, despite immigration of alternative alleles at these loci from another population. We show that an inversion is favored because it prevents the breakdown of linkage disequilibrium generated by migration; the selective advantage of an inversion is dependent on the amount of recombination between the loci involved, as in other cases where inversions are selected for as a result of their effects on recombination. We derive expressions for the rate of spread of an inversion; when the loci covered by the inversion are tightly linked, these conditions deviate substantially from those proposed previously, and imply that an inversion can then have only a small advantage.

Two-locus clines on the real line with a step environment

The shape of allele-frequency clines maintained by migration-selection balance depends not only on the properties of migration and selection, but also on the dominance relations among alleles and on linkage to other loci under selection. We investigate a two-locus model in which two diallelic, recombining loci are subject to selection caused by an abrupt environmental change. The habitat is one-dimensional and unbounded, selection at each locus is modeled by step functions such that in one region one allele at each locus is advantageous and in the other deleterious. We admit an environmentally independent, intermediate degree of dominance at both loci, including complete dominance. First, we derive an explicit expression for the single-locus cline with dominance, thus generalizing classical results by Haldane (1948). We show that the slope of the cline in the center (at the step) or, equivalently, the width of the cline, is independent of the degree of dominance. Second, under the assumption of strong recombination relative to selection and migration, the first-order approximations of the allele-frequency clines at each of the loci and of the linkage disequilibrium are derived. This may be interpreted as the quasi-linkage-equilibrium approximation of the two-locus cline. Explicit asymptotic expressions for the clines are deduced as x→±∞. For equivalent loci, explicit expressions for the whole clines are derived. The influence of dominance and of linkage on the slope of the cline in the center and on a global measure of steepness are investigated. This global measure reflects the influence of dominance. Finally, the accuracy of the approximations and the dependence of the shape of the two-locus cline on the full range of recombination rates is explored by numerical integration of the underlying system of partial differential equations.

Population-genomic inference of the strength and timing of selection against gene flow

The interplay of divergent selection and gene flow is key to understanding how populations adapt to local environments and how new species form. Here, we use DNA polymorphism data and genome-wide variation in recombination rate to jointly infer the strength and timing of selection, as well as the baseline level of gene flow under various demographic scenarios. We model how divergent selection leads to a genome-wide negative correlation between recombination rate and genetic differentiation among populations. Our theory shows that the selection density (i.e., the selection coefficient per base pair) is a key parameter underlying this relationship. We then develop a procedure for parameter estimation that accounts for the confounding effect of background selection. Applying this method to two datasets from Mimulus guttatus, we infer a strong signal of adaptive divergence in the face of gene flow between populations growing on and off phytotoxic serpentine soils. However, the genome-wide intensity of this selection is not exceptional compared with what M. guttatus populations may typically experience when adapting to local conditions. We also find that selection against genome-wide introgression from the selfing sister species M. nasutus has acted to maintain a barrier between these two species over at least the last 250 ky. Our study provides a theoretical framework for linking genome-wide patterns of divergence and recombination with the underlying evolutionary mechanisms that drive this differentiation.

Bounds to parapatric speciation: A Dobzhansky-Muller incompatibility model involving autosomes, X chromosomes, and mitochondria

We investigate the conditions for the origin and maintenance of postzygotic isolation barriers, so called (Bateson-)Dobzhansky-Muller incompatibilities or DMIs, among populations that are connected by gene flow. Specifically, we compare the relative stability of pairwise DMIs among autosomes, X chromosomes, and mitochondrial genes. In an analytical approach based on a continent-island framework, we determine how the maximum permissible migration rates depend on the genomic architecture of the DMI, on sex bias in migration rates, and on sex-dependence of allelic and epistatic effects, such as dosage compensation. Our results show that X-linkage of DMIs can enlarge the migration bounds relative to autosomal DMIs or autosome-mitochondrial DMIs, in particular in the presence of dosage compensation. The effect is further strengthened with male-biased migration. This mechanism might contribute to a higher density of DMIs on the X chromosome (large X-effect) that has been observed in several species clades. Furthermore, our results agree with empirical findings of higher introgression rates of autosomal compared to X-linked loci.

Chromosome inversions and ecological plasticity in the main African malaria mosquitoes

Chromosome inversions have fascinated the scientific community, mainly because of their role in the rapid adaption of different taxa to changing environments. However, the ecological traits linked to chromosome inversions have been poorly studied. Here, we investigated the roles played by 23 chromosome inversions in the adaptation of the four major African malaria mosquitoes to local environments in Africa. We studied their distribution patterns by using spatially explicit modeling and characterized the ecogeographical determinants of each inversion range. We then performed hierarchical clustering and constrained ordination analyses to assess the spatial and ecological similarities among inversions. Our results show that most inversions are environmentally structured, suggesting that they are actively involved in processes of local adaptation. Some inversions exhibited similar geographical patterns and ecological requirements among the four mosquito species, providing evidence for parallel evolution. Conversely, common inversion polymorphisms between sibling species displayed divergent ecological patterns, suggesting that they might have a different adaptive role in each species. These results are in agreement with the finding that chromosomal inversions play a role in Anopheles ecotypic adaptation. This study establishes a strong ecological basis for future genome-based analyses to elucidate the genetic mechanisms of local adaptation in these four mosquitoes.