Migration-selection Balance Research Articles

The genetic architecture of polygenic local adaptation and its role in shaping barriers to gene flow.

We consider how the genetic architecture underlying locally adaptive traits determines the strength of a barrier to gene flow in a mainland-island model. Assuming a general life cycle, we derive an expression for the effective migration rate when local adaptation is due to genetic variation at many loci under directional selection on the island, allowing for arbitrary fitness and dominance effects across loci. We show how the effective migration rate can be combined with classical single-locus diffusion theory to accurately predict multilocus differentiation between the mainland and island at migration-selection-drift equilibrium and determine the migration rate beyond which local adaptation collapses, while accounting for genetic drift and weak linkage. Using our efficient numerical tools, we then present a detailed study of the effects of dominance on barriers to gene flow, showing that when total selection is sufficiently strong, more recessive local adaptation generates stronger barriers to gene flow. We then study how heterogeneous genetic architectures of local adaptation affect barriers to gene flow, characterizing adaptive differentiation at migration-selection balance for different distributions of fitness effects. We find that a more heterogeneous genetic architecture generally yields a stronger genome-wide barrier to gene flow and that the detailed genetic architecture underlying locally adaptive traits can have an important effect on observable differentiation when divergence is not too large. Lastly, we study the limits of our approach as loci become more tightly linked, showing that our predictions remain accurate over a large biologically relevant domain.

Allele frequencies and selection coefficients in locally adapted populations

Understanding the role of natural selection in driving evolutionary change requires accurate estimates of the strength of selection acting at the genetic level in the wild. This is challenging to achieve but may be easier in the case of populations in migration-selection balance. When two populations are at equilibrium under migration-selection balance, there exist loci whose alleles are selected different ways in the two populations. Such loci can be identified from genome sequencing by their high values of FST. This raises the question of what is the strength of selection on locally-adaptive alleles. To answer this question we analyse a 1-locus 2-allele model of a population distributed between two niches. We show by simulation of selected cases that the outputs from finite-population models are essentially the same as those from deterministic infinite-population models. We then derive theory for the infinite-population model showing the dependence of selection coefficients on equilibrium allele frequencies, migration rates, dominance and relative population sizes in the two niches. An Excel spreadsheet is provided for the calculation of selection coefficients and their approximate standard errors from observed values of population parameters. We illustrate our results with a worked example, with graphs showing the dependence of selection coefficients on equilibrium allele frequencies, and graphs showing how FST depends on the selection coefficients acting on the alleles at a locus. Given the extent of recent progress in ecological genomics, we hope our methods may help those studying migration-selection balance to quantify the advantages conferred by adaptive genes.

The best of both worlds: Combining population genetic and quantitative genetic models

Numerous traits under migration–selection balance are shown to exhibit complex patterns of genetic architecture with large variance in effect sizes. However, the conditions under which such genetic architectures are stable have yet to be investigated, because studying the influence of a large number of small allelic effects on the maintenance of spatial polymorphism is mathematically challenging, due to the high complexity of the systems that arise. In particular, in the most simple case of a haploid population in a two-patch environment, while it is known from population genetics that polymorphism at a single major-effect locus is stable in the symmetric case, there exist no analytical predictions on how this polymorphism holds when a polygenic background also contributes to the trait. Here we propose to answer this question by introducing a new eco-evo methodology that allows us to take into account the combined contributions of a major-effect locus and of a quantitative background resulting from small-effect loci, where inheritance is encoded according to an extension to the infinitesimal model. In a regime of small variance contributed by the quantitative loci, we justify that traits are concentrated around the major alleles, according to a normal distribution, using new convex analysis arguments. This allows a reduction in the complexity of the system using a separation of time scales approach. We predict an undocumented phenomenon of loss of polymorphism at the major-effect locus despite strong selection for local adaptation, because the quantitative background slowly disrupts the rapidly established polymorphism at the major-effect locus, which is confirmed by individual-based simulations. Our study highlights how segregation of a quantitative background can greatly impact the dynamics of major-effect loci by provoking migrational meltdowns. We also provide a comprehensive toolbox designed to describe how to apply our method to more complex population genetic models.

Natural selection and the distribution of chromosomal inversion lengths.

Chromosomal inversions contribute substantially to genome evolution, yet the processes governing their evolutionary dynamics remain poorly understood. Theory suggests that a readily measurable property of inversions-their length-can potentially affect their evolutionary fates. Emerging data on the lengths of polymorphic and fixed inversions may therefore provide clues to the evolutionary processes promoting inversion establishment. However, formal predictions for the distribution of inversion lengths remain incomplete, making empirical patterns difficult to interpret. We model the relation between inversion length and establishment probability for four inversion types: (1) neutral, (2) underdominant, (3) directly beneficial, and (4) indirectly beneficial, with selection favouring the latter because they capture locally adapted alleles at migration-selection balance and suppress recombination between them. We also consider how deleterious mutations affect the lengths of established inversions. We show that length distributions of common polymorphic and fixed inversions systematically differ among inversion types. Small rearrangements contribute the most to genome evolution under neutral and underdominant scenarios of selection, with the lengths of neutral inversion substitutions increasing, and those of underdominant substitutions decreasing, with effective population size. Among directly beneficial inversions, small rearrangements are preferentially fixed, whereas intermediate-to-large inversions are maintained as balanced polymorphisms via associative overdominance. Finally, inversions established under the local adaptation scenario are predominantly intermediate-to-large. Such inversions remain polymorphic or approach fixation within the local populations where they are favoured. Our models clarify how inversion length distributions relate to processes of inversion establishment, providing a platform for testing how natural selection shapes the evolution of genome structure.

Opportunities and challenges in assessing climate change vulnerability through genomics

By investigating how past selection has affected allele frequencies across space, genomic tools are providing new insights into adaptive evolutionary processes. Now researchers are considering how this genomic information can be used to predict the future vulnerability of species under climate change. Genomic vulnerability assessments show promise, but challenges remain.

Immigration counter-acts local micro-evolution of a major fitness component: Migration-selection balance in free-living song sparrows.

Ongoing adaptive evolution, and resulting “evolutionary rescue” of declining populations, requires additive genetic variation in fitness. Such variation can be increased by gene flow resulting from immigration, potentially facilitating evolution. But, gene flow could in fact constrain rather than facilitate local adaptive evolution if immigrants have low additive genetic values for local fitness. Local migration‐selection balance and micro‐evolutionary stasis could then result. However, key quantitative genetic effects of natural immigration, comprising the degrees to which gene flow increases the total local additive genetic variance yet counteracts local adaptive evolutionary change, have not been explicitly quantified in wild populations. Key implications of gene flow for population and evolutionary dynamics consequently remain unclear. Our quantitative genetic analyses of long‐term data from free‐living song sparrows (Melospiza melodia) show that mean breeding value for local juvenile survival to adulthood, a major component of fitness, increased across cohorts more than expected solely due to drift. Such micro‐evolutionary change should be expected given nonzero additive genetic variance and consistent directional selection. However, this evolutionary increase was counteracted by negative additive genetic effects of recent immigrants, which increased total additive genetic variance but prevented a net directional evolutionary increase in total additive genetic value. These analyses imply an approximate quantitative genetic migration‐selection balance in a major fitness component, and hence demonstrate a key mechanism by which substantial additive genetic variation can be maintained yet decoupled from local adaptive evolutionary change.

Microhabitat contributes to microgeographic divergence in threespine stickleback

Since the New Synthesis, most migration-selection balance theory has predicted that there should be negligible differentiation over small spatial scales (relative to dispersal), because gene flow should erode any effect of divergent selection. Nevertheless, there are classic examples of microgeographic divergence, which theory suggests can arise under specific conditions: exceptionally strong selection, phenotypic plasticity in philopatric individuals, or nonrandom dispersal. Here, we present evidence of microgeographic morphological variation within lake and stream populations of threespine stickleback (Gasterosteus aculeatus). It seems reasonable to assume that a given lake or stream population of fish is well-mixed. However, we found this assumption to be untenable. We examined trap-to-trap variation in 34 morphological traits measured on stickleback from 16 lakes and 16 streams. Most traits varied appreciably among traps within populations. Both between-trap distance and microhabitat characteristics such as depth and substrate explained some of the within-population morphological variance. Microhabitat was also associated with genotype at particular loci but there was no genetic isolation by distance, implying that heritable habitat preferences may contribute to microgeographic variation. Our study adds to growing evidence that microgeographic divergence can occur across small spatial scales within individuals' daily dispersal neighborhood where gene flow is expected to be strong.

A Few Stickleback Suffice for the Transport of Alleles to New Lakes.

Threespine stickleback populations provide a striking example of local adaptation to divergent habitats in populations that are connected by recurrent gene flow. These small fish occur in marine and freshwater habitats throughout the Northern Hemisphere, and in numerous cases the smaller freshwater populations have been established “de novo” from marine colonists. Independently evolved freshwater populations exhibit similar phenotypes that have been shown to derive largely from the same standing genetic variants. Geographic isolation prevents direct migration between the freshwater populations, strongly suggesting that these shared locally adaptive alleles are transported through the marine population. However it is still largely unknown how gene flow, recombination, and selection jointly impact the standing variation that might fuel this adaptation. Here we use individual-based, spatially explicit simulations to determine the levels of gene flow that best match observed patterns of allele sharing among habitats in stickleback. We aim to better understand how gene flow and local adaptation in large metapopulations determine the speed of adaptation and re-use of standing genetic variation. In our simulations we find that repeated adaptation uses a shared set of alleles that are maintained at low frequency by migration-selection balance in oceanic populations. This process occurs over a realistic range of intermediate levels of gene flow that match previous empirical population genomic studies in stickleback. Examining these simulations more deeply reveals how lower levels of gene flow leads to slow, independent adaptation to different habitats, whereas higher levels of gene flow leads to significant mutation load – but an increased probability of successful population genomic scans for locally adapted alleles. Surprisingly, we find that the genealogical origins of most freshwater adapted alleles can be traced back to the original generation of marine individuals that colonized the lakes, as opposed to subsequent migrants. These simulations provide deeper context for existing studies of stickleback evolutionary genomics, and guidance for future empirical studies in this model. More broadly, our results support existing theory of local adaptation but extend it by more completely documenting the genealogical history of adaptive alleles in a metapopulation.

Spatial analyses of two color polymorphisms in an alpine grasshopper reveal a role of small-scale heterogeneity.

Discrete color polymorphisms represent a fascinating aspect of intraspecific diversity. Color morph ratios often vary clinally, but in some cases, there are no marked clines and mixes of different morphs occur at appreciable frequencies in most populations. This poses the questions of how polymorphisms are maintained. We here study the spatial and temporal distribution of a very conspicuous color polymorphism in the club‐legged grasshopper Gomphocerus sibiricus. The species occurs in a green and a nongreen (predominately brown) morph, a green–brown polymorphism that is common among Orthopteran insects. We sampled color morph ratios at 42 sites across the alpine range of the species and related color morph ratios to local habitat parameters and climatic conditions. Green morphs occurred in both sexes, and their morph ratios were highly correlated among sites, suggesting shared control of the polymorphism in females and males. We found that in at least 40 of 42 sites green and brown morphs co‐occurred with proportions of green ranging from 0% to 70% with significant spatial heterogeneity. The proportion of green individuals tended to increase with decreasing summer and winter precipitations. Nongreen individuals can be further distinguished into brown and pied individuals, and again, this polymorphism is shared with other grasshopper species. We found pied individuals at all sites with proportions ranging from 3% to 75%, with slight, but significant variation between years. Pied morphs show a clinal increase in frequency from east to west and decreased with altitude and lower temperatures and were more common on grazed sites. The results suggest that both small‐scale and large‐scale spatial heterogeneity affects color morph ratios. The almost universal co‐occurrence of all three color morphs argues against strong effects of genetic drift. Instead, the data suggest that small‐scale migration–selection balance and/or local balancing selection maintain populations polymorphic.

Migration-Selection Balance Drives Genetic Differentiation in Genes Associated with High-Altitude Function in the Speckled Teal (Anas flavirostris) in the Andes.

Local adaptation frequently occurs across populations as a result of migration-selection balance between divergent selective pressures and gene flow associated with life in heterogeneous landscapes. Studying the effects of selection and gene flow on the adaptation process can be achieved in systems that have recently colonized extreme environments. This study utilizes an endemic South American duck species, the speckled teal (Anas flavirostris), which has both high- and low-altitude populations. High-altitude speckled teal (A. f. oxyptera) are locally adapted to the Andean environment and mostly allopatric from low-altitude birds (A. f. flavirostris); however, there is occasional gene flow across altitudinal gradients. In this study, we used next-generation sequencing to explore genetic patterns associated with high-altitude adaptation in speckled teal populations, as well as the extent to which the balance between selection and migration have affected genetic architecture. We identified a set of loci with allele frequencies strongly correlated with altitude, including those involved in the insulin-like signaling pathway, bone morphogenesis, oxidative phosphorylation, responders to hypoxia-induced DNA damage, and feedback loops to the hypoxia-inducible factor pathway. These same outlier loci were found to have depressed gene flow estimates, as well as being highly concentrated on the Z-chromosome. Our results suggest a multifactorial response to life at high altitudes through an array of interconnected pathways that are likely under positive selection and whose genetic components seem to be providing an effective genomic barrier to interbreeding, potentially functioning as an avenue for population divergence and speciation.

Sensory trait variation contributes to biased dispersal of threespine stickleback in flowing water.

Gene flow is widely thought to homogenize spatially separate populations, eroding effects of divergent selection. The resulting theory of 'migration-selection balance' is predicated on a common assumption that all genotypes are equally prone to dispersal. If instead certain genotypes are disproportionately likely to disperse, then migration can actually promote population divergence. For example, previous work has shown that threespine stickleback (Gasterosteus aculeatus) differ in their propensity to move up- or downstream ('rheotactic response'), which may facilitate genetic divergence between adjoining lake and stream populations of stickleback. Here, we demonstrate that intraspecific variation in a sensory system (superficial neuromast lines) contributes to this variation in swimming behaviour in stickleback. First, we show that intact neuromasts are necessary for a typical rheotactic response. Next, we showed that there is heritable variation in the number of neuromasts and that stickleback with more neuromasts are more likely to move downstream. Variation in pectoral fin shape contributes to additional variation in rheotactic response. These results illustrate how within-population quantitative variation in sensory and locomotor traits can influence dispersal behaviour, thereby biasing dispersal between habitats and favouring population divergence.

Spatiotemporal environmental heterogeneity and the maintenance of the tailspot polymorphism in the variable platyfish (Xiphophorus variatus).

Genetic variation is critical for adaptive evolution. Despite its importance, there is still limited evidence in support of some prominent theoretical models explaining the maintenance of genetic polymorphism within populations. We examined 84 populations of Xiphophorus variatus, a livebearing fish with a genetic polymorphism associated with physiological performance, to test: (1) whether niche differentiation explains broad-scale maintenance of polymorphism, (2) whether polymorphism is maintained among populations by local adaptation and migration, or (3) whether heterogeneity in explicit environmental variables could be linked to levels of polymorphism within populations. We found no evidence of climatic niche differentiation that could generate or maintain broad geographic variation in polymorphism. Subsequently, hierarchical partitioning of genetic richness and partial mantel tests revealed that 76% of the observed genetic richness was partitioned within populations with no effect of geographic distance on polymorphism. These results strongly suggest a lack of migration-selection balance in the maintenance of polymorphism, and model selection confirmed a significant relationship between environmental heterogeneity and genetic richness within populations. Few studies have demonstrated such effects at this scale, and additional studies in other taxa should examine the generality of gene-by-environment interactions across populations to better understand the dynamics and scale of balancing selection.

Molecular mechanisms of dominance evolution in Müllerian mimicry.

Natural selection acting on dominance between adaptive alleles at polymorphic loci can be sufficiently strong for dominance to evolve. However, the molecular mechanisms underlying such evolution are generally unknown. Here, using Müllerian mimicry as a case-study for adaptive morphological variation, we present a theoretical analysis of the invasion of dominance modifiers altering gene expression through different molecular mechanisms. Toxic species involved in Müllerian mimicry exhibit warning coloration, and converge morphologically with other toxic species of the local community, due to positive frequency-dependent selection acting on these colorations. Polymorphism in warning coloration may be maintained by migration-selection balance with fine scale spatial heterogeneity. We modeled a dominance modifier locus altering the expression of the warning coloration locus, targeting one or several alleles, acting in cis or trans, and either enhancing or repressing expression. We confirmed that dominance could evolve when balanced polymorphism was maintained at the color locus. Dominance evolution could result from modifiers enhancing one allele specifically, irrespective of their linkage with the targeted locus. Nonspecific enhancers could also persist in populations, at frequencies tightly depending on their linkage with the targeted locus. Altogether, our results identify which mechanisms of expression alteration could lead to dominance evolution in polymorphic mimicry.

The effects of sexual selection on trait divergence in a peripheral population with gene flow.

The unique aspects of speciation and divergence in peripheral populations have long sparked much research. Unidirectional migration, received by some peripheral populations, can hinder the evolution of distinct differences from their founding populations. Here, we explore the effects that sexual selection, long hypothesized to drive the divergence of distinct traits used in mate choice, can play in the evolution of such traits in a partially isolated peripheral population. Using population genetic continent-island models, we show that with phenotype matching, sexual selection increases the frequency of an island-specific mating trait only when female preferences are of intermediate strength. We identify regions of preference strength for which sexual selection can instead cause an island-specific trait to be lost, even when it would have otherwise been maintained at migration-selection balance. When there are instead separate preference and trait loci, we find that sexual selection can lead to low trait frequencies or trait loss when female preferences are weak to intermediate, but that sexual selection can increase trait frequencies when preferences are strong. We also show that novel preference strengths almost universally cannot increase, under either mating mechanism, precluding the evolution of premating isolation in peripheral populations at the early stages of species divergence.

Evolution of Quantitative Traits under a Migration-Selection Balance: When Does Skew Matter?

Quantitative-genetic models of differentiation under migration-selection balance often rely on the assumption of normally distributed genotypic and phenotypic values. When a population is subdivided into demes with selection toward different local optima, migration between demes may result in asymmetric, or skewed, local distributions. Using a simplified two-habitat model, we derive formulas without a priori assuming a Gaussian distribution of genotypic values, and we find expressions that naturally incorporate higher moments, such as skew. These formulas yield predictions of the expected divergence under migration-selection balance that are more accurate than models assuming Gaussian distributions, which illustrates the importance of incorporating these higher moments to assess the response to selection in heterogeneous environments. We further show with simulations that traits with loci of large effect display the largest skew in their distribution at migration-selection balance.

A genomic selection component analysis characterizes migration-selection balance.

The genetic differentiation of populations in response to local selection pressures has long been studied by evolutionary biologists, but key details about the process remain obscure. How rapidly can local adaptation evolve, how extensive is the process across the genome, and how strong are the opposing forces of natural selection and gene flow? Here, we combine direct measurement of survival and reproduction with whole-genome genotyping of a plant species (Mimulus guttatus) that has recently invaded a novel habitat (the Quarry population). We renovate the classic selection component method to accommodate genomic data and observe selection at SNPs throughout the genome. SNPs showing viability selection in Quarry exhibit elevated divergence from neighboring populations relative to neutral SNPs. We also find that nonsignificant SNPs exhibit a subtle, but still significant, change in allele frequency toward neighboring populations, a predicted effect of gene flow. Given that the Quarry population is most probably only 30-40 generations old, the alleles conferring local advantage are almost certainly older than the population itself. Thus, local adaptation owes to the recruitment of standing genetic variation.

Migration-Selection Balance at Multiple Loci and Selection on Dominance and Recombination

A steady influx of a single deleterious multilocus genotype will impose genetic load on the resident population and leave multiple descendants carrying various numbers of the foreign alleles. Provided that the foreign types are rare at equilibrium, and all immigrant genes are eventually eliminated by selection, the population structure can be inferred explicitly from the branching process taking place within a single immigrant lineage. Unless the migration and recombination rates were high, this novel method gives a close approximation to the simulation with all possible multilocus genotypes considered. Once the load and the foreign genotypes frequencies are known, it becomes possible to estimate selection acting on the invading modifiers of (i) dominance and (ii) recombination rate on the foreign gene block. We found that the modifiers of the (i) type are able to invade faster than the type (ii) modifier, however, this result only applies in the strong selection/low migration/low recombination scenario. Varying the number of genes in the immigrant genotype can have a non-monotonic effect on the migration load and the modifier’s invasion rate: although blocks carrying more genes can give rise to longer lineages, they also experience stronger selection pressure. The heaviest load is therefore imposed by the genotypes carrying moderate numbers of genes.

GENETIC REGULATORY NETWORK MOTIFS CONSTRAIN ADAPTATION THROUGH CURVATURE IN THE LANDSCAPE OF MUTATIONAL (CO)VARIANCE

Systems biology is accumulating a wealth of understanding about the structure of genetic regulatory networks, leading to a more complete picture of the complex genotype-phenotype relationship. However, models of multivariate phenotypic evolution based on quantitative genetics have largely not incorporated a network-based view of genetic variation. Here we model a set of two-node, two-phenotype genetic network motifs, covering a full range of regulatory interactions. We find that network interactions result in different patterns of mutational (co)variance at the phenotypic level (the M-matrix), not only across network motifs but also across phenotypic space within single motifs. This effect is due almost entirely to mutational input of additive genetic (co)variance. Variation in M has the effect of stretching and bending phenotypic space with respect to evolvability, analogous to the curvature of space-time under general relativity, and similar mathematical tools may apply in each case. We explored the consequences of curvature in mutational variation by simulating adaptation under divergent selection with gene flow. Both standing genetic variation (the G-matrix) and rate of adaptation are constrained by M, so that G and adaptive trajectories are curved across phenotypic space. Under weak selection the phenotypic mean at migration-selection balance also depends on M.

The consequences of gene flow for local adaptation and differentiation: a two-locus two-deme model

We consider a population subdivided into two demes connected by migration in which selection acts in opposite direction. We explore the effects of recombination and migration on the maintenance of multilocus polymorphism, on local adaptation, and on differentiation by employing a deterministic model with genic selection on two linked diallelic loci (i.e., no dominance or epistasis). For the following cases, we characterize explicitly the possible equilibrium configurations: weak, strong, highly asymmetric, and super-symmetric migration, no or weak recombination, and independent or strongly recombining loci. For independent loci (linkage equilibrium) and for completely linked loci, we derive the possible bifurcation patterns as functions of the total migration rate, assuming all other parameters are fixed but arbitrary. For these and other cases, we determine analytically the maximum migration rate below which a stable fully polymorphic equilibrium exists. In this case, differentiation and local adaptation are maintained. Their degree is quantified by a new multilocus version of F_mathrm{ST} and by the migration load, respectively. In addition, we investigate the invasion conditions of locally beneficial mutants and show that linkage to a locus that is already in migration-selection balance facilitates invasion. Hence, loci of much smaller effect can invade than predicted by one-locus theory if linkage is sufficiently tight. We study how this minimum amount of linkage admitting invasion depends on the migration pattern. This suggests the emergence of clusters of locally beneficial mutations, which may form ‘genomic islands of divergence’. Finally, the influence of linkage and two-way migration on the effective migration rate at a linked neutral locus is explored. Numerical work complements our analytical results.

ESTABLISHMENT AND MAINTENANCE OF ADAPTIVE GENETIC DIVERGENCE UNDER MIGRATION, SELECTION, AND DRIFT

There is a long tradition in population genetics of exploring the maintenance of variation under migration-selection balance using deterministic models that assume infinite population size. With finite population size, stochastic dynamics can greatly reduce the potential for the maintenance of polymorphism, but this has yet to be explored in detail. Here, classical two-patch models are extended to predict: (1) the probability of a locally beneficial mutation rising in frequency in the patch where it is favored and (2) the critical threshold migration rate above which the maintenance of polymorphism is much less likely. Individual-based simulations show that these approximations provide accurate predictions across a wide range of parameter space.