Stability and response of polygenic traits to stabilizing selection and mutation

Polygenic dynamics underlying the response of quantitative traits to directional selection

We study the response of a quantitative trait to exponential directional selection in a finite haploid population, both at the genetic and the phenotypic level. We assume an infinite sites model, in which the number of new mutations per generation in the population follows a Poisson distribution (with mean Θ) and each mutation occurs at a new, previously monomorphic site. Mutation effects are beneficial and drawn from a distribution. Sites are unlinked and contribute additively to the trait. Assuming that selection is stronger than random genetic drift, we model the initial phase of the dynamics by a supercritical Galton-Watson process. This enables us to obtain time-dependent results. We show that the copy-number distribution of the mutant in generation n, conditioned on non-extinction until n, is described accurately by the deterministic increase from an initial distribution with mean 1. This distribution is related to the absolutely continuous part W+ of the random variable, typically denoted W, that characterizes the stochasticity accumulating during the mutant's sweep. A suitable transformation yields the approximate dynamics of the mutant frequency distribution in a Wright-Fisher population of size N. Our expression provides a very accurate approximation except when mutant frequencies are close to 1. On this basis, we derive explicitly the (approximate) time dependence of the expected mean and variance of the trait and of the expected number of segregating sites. Unexpectedly, we obtain highly accurate approximations for all times, even for the quasi-stationary phase when the expected per-generation response and the trait variance have equilibrated. The latter refine classical results. In addition, we find that Θ is the main determinant of the pattern of adaptation at the genetic level, i.e., whether the initial allele-frequency dynamics are best described by sweep-like patterns at few loci or small allele-frequency shifts at many. The number of segregating sites is an appropriate indicator for these patterns. The selection strength determines primarily the rate of adaptation. The accuracy of our results is tested by comprehensive simulations in a Wright-Fisher framework. We argue that our results apply to more complex forms of directional selection.

Polygenic selection to a changing optimum under self-fertilisation

Many traits are polygenic, affected by multiple genetic variants throughout the genome. Selection acting on these traits involves co-ordinated allele-frequency changes at these underlying variants, and this process has been extensively studied in random-mating populations. Yet many species self-fertilise to some degree, which incurs changes to genetic diversity, recombination and genome segregation. These factors cumulatively influence how polygenic selection is realised in nature. Here, we use analytical modelling and stochastic simulations to investigate to what extent self-fertilisation affects polygenic adaptation to a new environment. Our analytical solutions show that while selfing can increase adaptation to an optimum, it incurs linkage disequilibrium that can slow down the initial spread of favoured mutations due to selection interference, and favours the fixation of alleles with opposing trait effects. Simulations show that while selection interference is present, high levels of selfing (at least 90%) aids adaptation to a new optimum, showing a higher long-term fitness. If mutations are pleiotropic then only a few major-effect variants fix along with many neutral hitchhikers, with a transient increase in linkage disequilibrium. These results show potential advantages to self-fertilisation when adapting to a new environment, and how the mating system affects the genetic composition of polygenic selection.

A Path Integral Approach for Allele Frequency Dynamics Under Polygenic Selection

Many phenotypic traits have a polygenic genetic basis, making it challenging to learn their genetic architectures and predict individual phenotypes. One promising avenue to resolve the genetic basis of complex traits is through evolve-and-resequence experiments, in which laboratory populations are exposed to some selective pressure and trait-contributing loci are identified by extreme frequency changes over the course of the experiment. However, small laboratory populations will experience substantial random genetic drift, and it is difficult to determine whether selection played a roll in a given allele frequency change. Predicting how much allele frequencies change under drift and selection had remained an open problem well into the 21st century, even those contributing to simple, monogenic traits. Recently, there have been efforts to apply the path integral, a method borrowed from physics, to solve this problem. So far, this approach has been limited to genic selection, and is therefore inadequate to capture the complexity of quantitative, highly polygenic traits that are commonly studied. Here we extend one of these path integral methods, the perturbation approximation, to selection scenarios that are of interest to quantitative genetics. In particular, we derive analytic expressions for the transition probability (i.e., the probability that an allele will change in frequency from x , to y in time t ) of an allele contributing to a trait subject to stabilizing selection, as well as that of an allele contributing to a trait rapidly adapting to a new phenotypic optimum. We use these expressions to characterize the use of allele frequency change to test for selection, as well as explore optimal design choices for evolve-and-resequence experiments to uncover the genetic architecture of polygenic traits under selection.

A novel expectation-maximization approach to infer general diploid selection from time-series genetic data

Detecting and quantifying the strength of selection is a main objective in population genetics. Since selection acts over multiple generations, many approaches have been developed to detect and quantify selection using genetic data sampled at multiple points in time. Such time series genetic data is commonly analyzed using Hidden Markov Models, but in most cases, under the assumption of additive selection. However, many examples of genetic variation exhibiting non-additive mechanisms exist, making it critical to develop methods that can characterize selection in more general scenarios. Thus, we extend a previously introduced expectation-maximization algorithm for the inference of additive selection coefficients to the case of general diploid selection, in which heterozygote and homozygote fitnesses are parameterized independently. We furthermore introduce a framework to identify bespoke modes of diploid selection from given data, as well as a procedure for aggregating data across linked loci to increase power and robustness. Using extensive simulation studies, we find that our method accurately and efficiently estimates selection coefficients for different modes of diploid selection across a wide range of scenarios; however, power to classify the mode of selection is low unless selection is very strong. We apply our method to ancient DNA samples from Great Britain in the last 4,450 years, and detect evidence for selection in six genomic regions, including the well-characterized LCT locus. Our work is the first genome-wide scan characterizing signals of general diploid selection.

Sweepstakes reproduction facilitates rapid adaptation in highly fecund populations

Adaptation enables natural populations to survive in a changing environment. Understanding the mechanics of adaptation is therefore crucial for learning about the evolution and ecology of natural populations. We focus on the impact of random sweepstakes on selection in highly fecund haploid and diploid populations partitioned into two genetic types, with one type conferring selective advantage. For the diploid populations, we incorporate various dominance mechanisms. We assume that the populations may experience recurrent bottlenecks. In random sweepstakes, the distribution of individual recruitment success is highly skewed, resulting in a huge variance in the number of offspring contributed by the individuals present in any given generation. Using computer simulations, we investigate the joint effects of random sweepstakes, recurrent bottlenecks and dominance mechanisms on selection. In our framework, bottlenecks allow random sweepstakes to have an effect on the time to fixation, and in diploid populations, the effect of random sweepstakes depends on the dominance mechanism. We describe selective sweepstakes that are approximated by recurrent sweeps of strongly beneficial allelic types arising by mutation. We demonstrate that both types of sweepstakes reproduction may facilitate rapid adaptation (as defined based on the average time to fixation of a type conferring selective advantage conditioned on fixation of the type). However, whether random sweepstakes cause rapid adaptation depends also on their interactions with bottlenecks and dominance mechanisms. Finally, we review a case study in which a model of recurrent sweeps is shown to essentially explain population genomic data from Atlantic cod.

Phenotypic stasis with genetic divergence

Whether or not genetic divergence in the short-term of tens to hundreds of generations is compatible with phenotypic stasis remains a relatively unexplored problem. We evolved predominantly outcrossing, genetically diverse populations of the nematode Caenorhabditis elegans under a constant and homogeneous environment for 240 generations and followed individual locomotion behavior. Although founders of lab populations show highly diverse locomotion behavior, during lab evolution, the component traits of locomotion behavior - defined as the transition rates in activity and direction - did not show divergence from the ancestral population. In contrast, transition rates' genetic (co)variance structure showed a marked divergence from the ancestral state and differentiation among replicate populations during the final 100 generations and after most adaptation had been achieved. We observe that genetic differentiation is a transient pattern during the loss of genetic variance along phenotypic dimensions under drift during the last 100 generations of lab evolution. These results suggest that short-term stasis of locomotion behavior is maintained because of stabilizing selection, while the genetic structuring of component traits is contingent upon drift history.

A theory of oligogenic adaptation of a quantitative trait

Rapid phenotypic adaptation is widespread in nature, but the underlying genetic dynamics remain controversial. Whereas population genetics envisages sequential beneficial substitutions, quantitative genetics assumes a collective response through subtle shifts in allele frequencies. This dichotomy of a monogenic and a highly polygenic view of adaptation raises the question of a middle ground, as well as the factors controlling the transition. Here, we consider an additive quantitative trait with equal locus effects under Gaussian stabilizing selection that adapts to a new trait optimum after an environmental change. We present an analytical framework based on Yule branching processes to describe how phenotypic adaptation is achieved by collective changes in allele frequencies at the underlying loci. In particular, we derive an approximation for the joint allele-frequency distribution conditioned on the trait mean as a comprehensive descriptor of the adaptive architecture. Depending on the model parameters, this architecture reproduces the well-known patterns of sequential, monogenic sweeps, or of subtle, polygenic frequency shifts. Between these endpoints, we observe oligogenic architecture types that exhibit characteristic patterns of partial sweeps. We find that a single compound parameter, the population-scaled background mutation rate Θbg, is the most important predictor of the type of adaptation, while selection strength, the number of loci in the genetic basis, and linkage only play a minor role.

Polygenic adaptation dynamics in large, finite populations

Although many phenotypic traits are determined by a large number of genetic variants, how a polygenic trait adapts in response to a change in the environment is not completely understood. In the framework of diffusion theory, we study the steady state and the adaptation dynamics of a large but finite population evolving under stabilizing selection and symmetric mutations when selection and mutation are moderately large. We find that in the stationary state, the allele frequency distribution at a locus is unimodal if its effect size is below a threshold effect and bimodal otherwise; these results are the stochastic analog of the deterministic ones where the stable allele frequency becomes bistable when the effect size exceeds a threshold. It is known that following a sudden shift in the phenotypic optimum, in an infinitely large population, selective sweeps at a large-effect locus are prevented and adaptation proceeds exclusively via subtle changes in the allele frequency; in contrast, we find that the chance of sweep is substantially enhanced in large, finite populations and the allele frequency at a large-effect locus can reach a high frequency at short times even for small shifts in the phenotypic optimum.

A novel cost framework reveals evidence for competitive selection in the evolution of complex traits during plant domestication

Most models of selection incorporate some notion of environmental degradation where the majority of the population becomes less fit concerning a character resulting in pressure to adapt. Such models have been variously associated with an adaptation cost, the substitution load. Conversely, adaptative mutations that represent an improvement in fitness in the absence of environmental change have generally been assumed to be associated with negligible cost. However, such adaptations could represent a competitive advantage that diminishes resource availability for others and so induces a cost. This type of adaptation in the form of seedling competition has been suggested as a mechanism for increases in seed sizes during domestication, a trait associated with the standard stabilizing selection model. We present a novel cost framework for competitive selection that demonstrates significant differences in behaviour to environmental-based selection in intensity, intensity over time and directly contrasts with the expectations of the standard model. Grain metrics of nine archaeological crops fit a mixed model in which episodes of competitive selection often emerge from shifting optimum episodes of stabilizing selection, highlighting the potential prevalence of the mechanism outlined here and providing fundamental insight into the factors driving domestication.

Polygenic adaptation after a sudden change in environment

Polygenic adaptation is thought to be ubiquitous, yet remains poorly understood. Here, we model this process analytically, in the plausible setting of a highly polygenic, quantitative trait that experiences a sudden shift in the fitness optimum. We show how the mean phenotype changes over time, depending on the effect sizes of loci that contribute to variance in the trait, and characterize the allele dynamics at these loci. Notably, we describe the two phases of the allele dynamics: The first is a rapid phase, in which directional selection introduces small frequency differences between alleles whose effects are aligned with or opposed to the shift, ultimately leading to small differences in their probability of fixation during a second, longer phase, governed by stabilizing selection. As we discuss, key results should hold in more general settings and have important implications for efforts to identify the genetic basis of adaptation in humans and other species.

Using singleton densities to detect recent selection in Bos taurus

Many quantitative traits are subject to polygenic selection, where several genomic regions undergo small, simultaneous changes in allele frequency that collectively alter a phenotype. The widespread availability of genome data, along with novel statistical techniques, has made it easier to detect these changes. We apply one such method, the "Singleton Density Score" (SDS), to the Holstein breed of Bos taurus to detect recent selection (arising up to around 740 years ago). We identify several genes as candidates for targets of recent selection, including some relating to cell regulation, catabolic processes, neural-cell adhesion and immunity. We do not find strong evidence that three traits that are important to humans-milk protein content, milk fat content, and stature-have been subject to directional selection. Simulations demonstrate that because B. taurus recently experienced a population bottleneck, singletons are depleted so the power of SDS methods is reduced. These results inform on which genes underlie recent genetic change in B. taurus, while providing information on how polygenic selection can be best investigated in future studies.

Emerging evidence of plant domestication as a landscape-level process

The evidence from ancient crops over the past decade challenges some of our most basic assumptions about the process of domestication. The emergence of crops has been viewed as a technologically progressive process in which single or multiple localized populations adapt to human environments in response to cultivation. By contrast, new genetic and archaeological evidence reveals a slow process that involved large populations over wide areas with unexpectedly sustained cultural connections in deep time. We review evidence that calls for a new landscape framework of crop origins. Evolutionary processes operate across vast distances of landscape and time, and the origins of domesticates are complex. The domestication bottleneck is a redundant concept and the progressive nature of domestication is in doubt.

Rapid Evolutionary Adaptation in Response to Selection on Quantitative Traits

Evolutionary adaptation after sudden environmental changes can occur very rapidly. The mechanisms facilitating rapid adaptation range from strong positive directional selection leading to large shifts in the allele frequencies at a few loci (selective sweeps) to polygenic selection causing small changes in allele frequencies at many loci. In addition, combinations of these two extreme mechanisms may also result in fast evolution. In recent years, following reports of new case studies of rapid adaptation, population genetic models have been proposed to explain these observations. In these models, the role of the major selective forces (positive directional and stabilizing selection) is highlighted as well as the genetic architecture of quantitative traits. Furthermore, the factors limiting the speed of adaptation are analyzed, in particular, the effects of random genetic drift and demography due to finite population size.

The genetic architecture of temperature adaptation is shaped by population ancestry and not by selection regime

Background

Understanding the genetic architecture of temperature adaptation is key for characterizing and predicting the effect of climate change on natural populations. One particularly promising approach is Evolve and Resequence, which combines advantages of experimental evolution such as time series, replicate populations, and controlled environmental conditions, with whole genome sequencing. Recent analysis of replicate populations from two different Drosophila simulans founder populations, which were adapting to the same novel hot environment, uncovered very different architectures—either many selection targets with large heterogeneity among replicates or fewer selection targets with a consistent response among replicates.

Results

Here, we expose the founder population from Portugal to a cold temperature regime. Although almost no selection targets are shared between the hot and cold selection regime, the adaptive architecture was similar. We identify a moderate number of targets under strong selection (19 selection targets, mean selection coefficient = 0.072) and parallel responses in the cold evolved replicates. This similarity across different environments indicates that the adaptive architecture depends more on the ancestry of the founder population than the specific selection regime.

Conclusions

These observations will have broad implications for the correct interpretation of the genomic responses to a changing climate in natural populations.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13059-021-02425-9.

An Experimental Test of Adaptive Introgression in Locally Adapted Populations of Splash Pool Copepods

As species struggle to keep pace with the rapidly warming climate, adaptive introgression of beneficial alleles from closely related species or populations provides a possible avenue for rapid adaptation. We investigate the potential for adaptive introgression in the copepod, Tigriopus californicus, by hybridizing two populations with divergent heat tolerance limits. We subjected hybrids to strong heat selection for 15 generations followed by whole-genome resequencing. Utilizing a hybridize evolve and resequence (HER) technique, we can identify loci responding to heat selection via a change in allele frequency. We successfully increased the heat tolerance (measured as LT50) in selected lines, which was coupled with higher frequencies of alleles from the southern (heat tolerant) population. These repeatable changes in allele frequencies occurred on all 12 chromosomes across all independent selected lines, providing evidence that heat tolerance is polygenic. These loci contained genes with lower protein-coding sequence divergence than the genome-wide average, indicating that these loci are highly conserved between the two populations. In addition, these loci were enriched in genes that changed expression patterns between selected and control lines in response to a nonlethal heat shock. Therefore, we hypothesize that the mechanism of heat tolerance divergence is explained by differential gene expression of highly conserved genes. The HER approach offers a unique solution to identifying genetic variants contributing to polygenic traits, especially variants that might be missed through other population genomic approaches.

The evolution of group differences in changing environments

The selection pressures that have shaped the evolution of complex traits in humans remain largely unknown, and in some contexts highly contentious, perhaps above all where they concern mean trait differences among groups. To date, the discussion has focused on whether such group differences have any genetic basis, and if so, whether they are without fitness consequences and arose via random genetic drift, or whether they were driven by selection for different trait optima in different environments. Here, we highlight a plausible alternative: that many complex traits evolve under stabilizing selection in the face of shifting environmental effects. Under this scenario, there will be rapid evolution at the loci that contribute to trait variation, even when the trait optimum remains the same. These considerations underscore the strong assumptions about environmental effects that are required in ascribing trait differences among groups to genetic differences.

Polygenic Adaptation in a Population of Finite Size

Polygenic adaptation in response to selection on quantitative traits has become an important topic in evolutionary biology. Here we review the recent literature on models of polygenic adaptation. In particular, we focus on a model that includes mutation and both directional and stabilizing selection on a highly polygenic trait in a population of finite size (thus experiencing random genetic drift). Assuming that a sudden environmental shift of the fitness optimum occurs while the population is in a stochastic equilibrium, we analyze the adaptation of the trait to the new optimum. When the shift is not too large relative to the equilibrium genetic variance and this variance is determined by loci with mostly small effects, the approach of the mean phenotype to the optimum can be approximated by a rapid exponential process (whose rate is proportional to the genetic variance). During this rapid phase the underlying changes to allele frequencies, however, may depend strongly on genetic drift. While trait-increasing alleles with intermediate equilibrium frequencies are dominated by selection and contribute positively to changes of the trait mean (i.e., are aligned with the direction of the optimum shift), alleles with low or high equilibrium frequencies show more of a random dynamics, which is expected when drift is dominating. A strong effect of drift is also predicted for population size bottlenecks. Our simulations show that the presence of a bottleneck results in a larger deviation of the population mean of the trait from the fitness optimum, which suggests that more loci experience the influence of drift.

Low Additive Genetic Variation in a Trait Under Selection in Domesticated Rice

Quantitative traits are important targets of both natural and artificial selection. The genetic architecture of these traits and its change during the adaptive process is thus of fundamental interest. The fate of the additive effects of variants underlying a trait receives particular attention because they constitute the genetic variation component that is transferred from parents to offspring and thus governs the response to selection. While estimation of this component of phenotypic variation is challenging, the increasing availability of dense molecular markers puts it within reach. Inbred plant species offer an additional advantage because phenotypes of genetically identical individuals can be measured in replicate. This makes it possible to estimate marker effects separately from the contribution of the genetic background not captured by genotyped loci. We focused on root growth in domesticated rice, Oryza sativa, under normal and aluminum (Al) stress conditions, a trait under recent selection because it correlates with survival under drought. A dense single nucleotide polymorphism (SNP) map is available for all accessions studied. Taking advantage of this map and a set of Bayesian models, we assessed additive marker effects. While total genetic variation accounted for a large proportion of phenotypic variance, marker effects contributed little information, particularly in the Al-tolerant tropical japonica population of rice. We were unable to identify any loci associated with root growth in this population. Models estimating the aggregate effects of all measured genotypes likewise produced low estimates of marker heritability and were unable to predict total genetic values accurately. Our results support the long-standing conjecture that additive genetic variation is depleted in traits under selection. We further provide evidence that this depletion is due to the prevalence of low-frequency alleles that underlie the trait.

Important role of genetic drift in rapid polygenic adaptation

We analyzed a model to determine the factors that facilitate or limit rapid polygenic adaptation. This model includes population genetic terms of mutation and both directional and stabilizing selection on a highly polygenic trait in a diploid population of finite size. First, we derived the equilibrium distribution of the allele frequencies of the multilocus model by diffusion approximation. This formula describing the equilibrium allele frequencies as a mutation-selection-drift balance was examined by computer simulation using parameter values inferred for human height, a well-studied polygenic trait. Second, assuming that a sudden environmental shift of the fitness optimum occurs while the population is in equilibrium, we analyzed the adaptation of the trait to the new optimum. The speed at which the trait mean approaches the new optimum increases with the equilibrium genetic variance. Thus, large population size and/or large mutation rate may facilitate rapid adaptation. Third, the contribution of an individual locus i to polygenic adaptation depends on the compound parameterγ i p i 0 q i 0 , where γ i is the effect size,p i 0 the equilibrium frequency of the trait-increasing allele of this locus, andq i 0 = 1 - p i 0 . Thus, only loci with large values of this parameter contribute coherently to polygenic adaptation. Given that mutation rates are relatively small, this is more likely in large populations, in which the effects of drift are limited.

Polygenic Adaptation to an Environmental Shift: Temporal Dynamics of Variation Under Gaussian Stabilizing Selection and Additive Effects on a Single Trait

Predictions about the effect of natural selection on patterns of linked neutral variation are largely based on models involving the rapid fixation of unconditionally beneficial mutations. However, when phenotypes adapt to a new optimum trait value, the strength of selection on individual mutations decreases as the population adapts. Here, I use explicit forward simulations of a single trait with additive-effect mutations adapting to an "optimum shift." Detectable "hitchhiking" patterns are only apparent if (i) the optimum shifts are large with respect to equilibrium variation for the trait, (ii) mutation rates to large-effect mutations are low, and (iii) large-effect mutations rapidly increase in frequency and eventually reach fixation, which typically occurs after the population reaches the new optimum. For the parameters simulated here, partial sweeps do not appreciably affect patterns of linked variation, even when the mutations are strongly selected. The contribution of new mutations vs. standing variation to fixation depends on the mutation rate affecting trait values. Given the fixation of a strongly selected variant, patterns of hitchhiking are similar on average for the two classes of sweeps because sweeps from standing variation involving large-effect mutations are rare when the optimum shifts. The distribution of effect sizes of new mutations has little effect on the time to reach the new optimum, but reducing the mutational variance increases the magnitude of hitchhiking patterns. In general, populations reach the new optimum prior to the completion of any sweeps, and the times to fixation are longer for this model than for standard models of directional selection. The long fixation times are due to a combination of declining selection pressures during adaptation and the possibility of interference among weakly selected sites for traits with high mutation rates.

Thinking About the Evolution of Complex Traits in the Era of Genome-Wide Association Studies

Many traits of interest are highly heritable and genetically complex, meaning that much of the variation they exhibit arises from differences at numerous loci in the genome. Complex traits and their evolution have been studied for more than a century, but only in the last decade have genome-wide association studies (GWASs) in humans begun to reveal their genetic basis. Here, we bring these threads of research together to ask how findings from GWASs can further our understanding of the processes that give rise to heritable variation in complex traits and of the genetic basis of complex trait evolution in response to changing selection pressures (i.e., of polygenic adaptation). Conversely, we ask how evolutionary thinking helps us to interpret findings from GWASs and informs related efforts of practical importance.

Polygenic adaptation: From sweeps to subtle frequency shifts

Evolutionary theory has produced two conflicting paradigms for the adaptation of a polygenic trait. While population genetics views adaptation as a sequence of selective sweeps at single loci underlying the trait, quantitative genetics posits a collective response, where phenotypic adaptation results from subtle allele frequency shifts at many loci. Yet, a synthesis of these views is largely missing and the population genetic factors that favor each scenario are not well understood. Here, we study the architecture of adaptation of a binary polygenic trait (such as resistance) with negative epistasis among the loci of its basis. The genetic structure of this trait allows for a full range of potential architectures of adaptation, ranging from sweeps to small frequency shifts. By combining computer simulations and a newly devised analytical framework based on Yule branching processes, we gain a detailed understanding of the adaptation dynamics for this trait. Our key analytical result is an expression for the joint distribution of mutant alleles at the end of the adaptive phase. This distribution characterizes the polygenic pattern of adaptation at the underlying genotype when phenotypic adaptation has been accomplished. We find that a single compound parameter, the population-scaled background mutation rate Θ_bg, explains the main differences among these patterns. For a focal locus, Θ_bg measures the mutation rate at all redundant loci in its genetic background that offer alternative ways for adaptation. For adaptation starting from mutation-selection-drift balance, we observe different patterns in three parameter regions. Adaptation proceeds by sweeps for small Θ_bg ≲ 0.1, while small polygenic allele frequency shifts require large Θ_bg ≳ 100. In the large intermediate regime, we observe a heterogeneous pattern of partial sweeps at several interacting loci.

It is still an open question how complex traits adapt to new selection pressures. While population genetics champions the search for selective sweeps, quantitative genetics proclaims adaptation via small concerted frequency shifts. To date the empirical evidence of clear sweep signals is more scarce than expected, while subtle shifts remain notoriously hard to detect. In the current study we develop a theoretical framework to predict the expected adaptive architecture of a simple polygenic trait, depending on parameters such as mutation rate, effective population size, size of the trait basis, and the available genetic variability at the onset of selection. For a population in mutation-selection-drift balance we find that adaptation proceeds via complete or partial sweeps for a large set of parameter values. We predict adaptation by small frequency shifts for two main cases. First, for traits with a large mutational target size and high levels of genetic redundancy among loci, and second if the starting frequencies of mutant alleles are more homogeneous than expected in mutation-selection-drift equilibrium, e.g. due to population structure or balancing selection.

Genetic redundancy fuels polygenic adaptation in Drosophila

The genetic architecture of adaptive traits is of key importance to predict evolutionary responses. Most adaptive traits are polygenic-i.e., result from selection on a large number of genetic loci-but most molecularly characterized traits have a simple genetic basis. This discrepancy is best explained by the difficulty in detecting small allele frequency changes (AFCs) across many contributing loci. To resolve this, we use laboratory natural selection to detect signatures for selective sweeps and polygenic adaptation. We exposed 10 replicates of a Drosophila simulans population to a new temperature regime and uncovered a polygenic architecture of an adaptive trait with high genetic redundancy among beneficial alleles. We observed convergent responses for several phenotypes-e.g., fitness, metabolic rate, and fat content-and a strong polygenic response (99 selected alleles; mean s = 0.059). However, each of these selected alleles increased in frequency only in a subset of the evolving replicates. We discerned different evolutionary paradigms based on the heterogeneous genomic patterns among replicates. Redundancy and quantitative trait (QT) paradigms fitted the experimental data better than simulations assuming independent selective sweeps. Our results show that natural D. simulans populations harbor a vast reservoir of adaptive variation facilitating rapid evolutionary responses using multiple alternative genetic pathways converging at a new phenotypic optimum. This key property of beneficial alleles requires the modification of testing strategies in natural populations beyond the search for convergence on the molecular level.

Contrasting patterns of neutral and functional genetic diversity in stable and disturbed environments

Genetic structure among and diversity within natural populations is influenced by a combination of ecological and evolutionary processes. These processes can differently influence neutral and functional genetic diversity and also vary according to environmental settings. To investigate the roles of interacting processes as drivers of population-level genetic diversity in the wild, we compared neutral and functional structure and diversity between 20 Tetrix undulata pygmy grasshopper populations in disturbed and stable habitats. Genetic differentiation was evident among the different populations, but there was no genetic separation between stable and disturbed environments. The incidence of long-winged phenotypes was higher in disturbed habitats, indicating that these populations were recently established by flight-capable colonizers. Color morph diversity and dispersion of outlier genetic diversity, estimated using AFLP markers, were higher in disturbed than in stable environments, likely reflecting that color polymorphism and variation in other functionally important traits increase establishment success. Neutral genetic diversity estimated using AFLP markers was lower in disturbed habitats, indicating stronger eroding effects on neutral diversity of genetic drift associated with founding events in disturbed compared to stable habitats. Functional diversity and neutral diversity were negatively correlated across populations, highlighting the utility of outlier loci in genetics studies and reinforcing that estimates of genetic diversity based on neutral markers do not infer evolutionary potential and the ability of populations and species to cope with environmental change.

Genetic architecture and selective sweeps after polygenic adaptation to distant trait optima

Understanding the genetic basis of phenotypic adaptation to changing environments is an essential goal of population and quantitative genetics. While technological advances now allow interrogation of genome-wide genotyping data in large panels, our understanding of the process of polygenic adaptation is still limited. To address this limitation, we use extensive forward-time simulation to explore the impacts of variation in demography, trait genetics, and selection on the rate and mode of adaptation and the resulting genetic architecture. We simulate a population adapting to an optimum shift, modeling sequence variation for 20 QTL for each of 12 different demographies for 100 different traits varying in the effect size distribution of new mutations, the strength of stabilizing selection, and the contribution of the genomic background. We then use random forest regression approaches to learn the relative importance of input parameters in determining a number of aspects of the process of adaptation, including the speed of adaptation, the relative frequency of hard sweeps and sweeps from standing variation, or the final genetic architecture of the trait. We find that selective sweeps occur even for traits under relatively weak selection and where the genetic background explains most of the variation. Though most sweeps occur from variation segregating in the ancestral population, new mutations can be important for traits under strong stabilizing selection that undergo a large optimum shift. We also show that population bottlenecks and expansion impact overall genetic variation as well as the relative importance of sweeps from standing variation and the speed with which adaptation can occur. We then compare our results to two traits under selection during maize domestication, showing that our simulations qualitatively recapitulate differences between them. Overall, our results underscore the complex population genetics of individual loci in even relatively simple quantitative trait models, but provide a glimpse into the factors that drive this complexity and the potential of these approaches for understanding polygenic adaptation.

A population genetic interpretation of GWAS findings for human quantitative traits

Human genome-wide association studies (GWASs) are revealing the genetic architecture of anthropomorphic and biomedical traits, i.e., the frequencies and effect sizes of variants that contribute to heritable variation in a trait. To interpret these findings, we need to understand how genetic architecture is shaped by basic population genetics processes-notably, by mutation, natural selection, and genetic drift. Because many quantitative traits are subject to stabilizing selection and because genetic variation that affects one trait often affects many others, we model the genetic architecture of a focal trait that arises under stabilizing selection in a multidimensional trait space. We solve the model for the phenotypic distribution and allelic dynamics at steady state and derive robust, closed-form solutions for summary statistics of the genetic architecture. Our results provide a simple interpretation for missing heritability and why it varies among traits. They predict that the distribution of variances contributed by loci identified in GWASs is well approximated by a simple functional form that depends on a single parameter: the expected contribution to genetic variance of a strongly selected site affecting the trait. We test this prediction against the results of GWASs for height and body mass index (BMI) and find that it fits the data well, allowing us to make inferences about the degree of pleiotropy and mutational target size for these traits. Our findings help to explain why the GWAS for height explains more of the heritable variance than the similarly sized GWAS for BMI and to predict the increase in explained heritability with study sample size. Considering the demographic history of European populations, in which these GWASs were performed, we further find that most of the associations they identified likely involve mutations that arose shortly before or during the Out-of-Africa bottleneck at sites with selection coefficients around s = 10-3.

Detecting gene subnetworks under selection in biological pathways

Advances in high throughput sequencing technologies have created a gap between data production and functional data analysis. Indeed, phenotypes result from interactions between numerous genes, but traditional methods treat loci independently, missing important knowledge brought by network-level emerging properties. Therefore, detecting selection acting on multiple genes affecting the evolution of complex traits remains challenging. In this context, gene network analysis provides a powerful framework to study the evolution of adaptive traits and facilitates the interpretation of genome-wide data. We developed a method to analyse gene networks that is suitable to evidence polygenic selection. The general idea is to search biological pathways for subnetworks of genes that directly interact with each other and that present unusual evolutionary features. Subnetwork search is a typical combinatorial optimization problem that we solve using a simulated annealing approach. We have applied our methodology to find signals of adaptation to high-altitude in human populations. We show that this adaptation has a clear polygenic basis and is influenced by many genetic components. Our approach, implemented in the R package signet, improves on gene-level classical tests for selection by identifying both new candidate genes and new biological processes involved in adaptation to altitude.

What can genome-wide association studies tell us about the evolutionary forces maintaining genetic variation for quantitative traits?

Contents 21 I. 21 II. 22 III. 24 IV. 25 V. 29 30 References 30 SUMMARY: Understanding the evolutionary forces that shape genetic variation within species has long been a goal of evolutionary biology. Integrating data for the genetic architecture of traits from genome-wide association mapping studies (GWAS) along with the development of new population genetic methods for identifying selection in sequence data may allow us to evaluate the roles of mutation-selection balance and balancing selection in shaping genetic variation at various scales. Here, we review the theoretical predictions for genetic architecture and additional signals of selection on genomic sequence for the loci that affect traits. Next, we review how plant GWAS have tested for the signatures of various selective scenarios. Limited evidence to date suggests that within-population variation is maintained primarily by mutation-selection balance while variation across the landscape is the result of local adaptation. However, there are a number of inherent biases in these interpretations. We highlight these challenges and suggest ways forward to further understanding of the maintenance of variation.

Rapid Adaptation of a Polygenic Trait After a Sudden Environmental Shift

Although a number of studies have shown that natural and laboratory populations initially well adapted to their environment can evolve rapidly when conditions suddenly change, the dynamics of rapid adaptation are not well understood. Here a population genetic model of polygenic selection is analyzed to describe the short-term response of a quantitative trait after a sudden shift of the phenotypic optimum. We provide explicit analytical expressions for the timescales over which the trait mean approaches the new optimum. We find that when the effect sizes are small relative to a scaled mutation rate, small to moderate allele frequency changes occur in the short-term phase in a synergistic fashion. In contrast, selective sweeps, i.e., dramatic changes in the allele frequency, may occur provided the size of the effect is sufficiently large. Applications of our theoretical results to the relationship between QTL and selective sweep mapping and to tests of fast polygenic adaptation are discussed.

How does epistasis influence the response to selection?

Much of quantitative genetics is based on the 'infinitesimal model', under which selection has a negligible effect on the genetic variance. This is typically justified by assuming a very large number of loci with additive effects. However, it applies even when genes interact, provided that the number of loci is large enough that selection on each of them is weak relative to random drift. In the long term, directional selection will change allele frequencies, but even then, the effects of epistasis on the ultimate change in trait mean due to selection may be modest. Stabilising selection can maintain many traits close to their optima, even when the underlying alleles are weakly selected. However, the number of traits that can be optimised is apparently limited to ~4Ne by the 'drift load', and this is hard to reconcile with the apparent complexity of many organisms. Just as for the mutation load, this limit can be evaded by a particular form of negative epistasis. A more robust limit is set by the variance in reproductive success. This suggests that selection accumulates information most efficiently in the infinitesimal regime, when selection on individual alleles is weak, and comparable with random drift. A review of evidence on selection strength suggests that although most variance in fitness may be because of alleles with large Nes, substantial amounts of adaptation may be because of alleles in the infinitesimal regime, in which epistasis has modest effects.

Understanding the coevolutionary dynamics of mutualism with population genomics

Decades of research on the evolution of mutualism has generated a wealth of possible ways whereby mutually beneficial interactions between species persist in spite of the apparent advantages to individuals that accept the benefits of mutualism without reciprocating - but identifying how any particular empirical system is stabilized against cheating remains challenging. Different hypothesized models of mutualism stability predict different forms of coevolutionary selection, and emerging high-throughput sequencing methods allow examination of the selective histories of mutualism genes and, thereby, the form of selection acting on those genes. Here, I review the evolutionary theory of mutualism stability and identify how differing models make contrasting predictions for the population genomic diversity and geographic differentiation of mutualism-related genes. As an example of the possibilities offered by genomic data, I analyze genes with roles in the symbiosis of Medicago truncatula and nitrogen-fixing rhizobial bacteria, the first classic mutualism in which extensive genomic resources have been developed for both partners. Medicago truncatula symbiosis genes, as a group, differ from the rest of the genome, but they vary in the form of selection indicated by their diversity and differentiation - some show signs of selection expected from roles in sanctioning noncooperative symbionts, while others show evidence of balancing selection expected from coevolution with symbiont signaling factors. I then assess the current state of development for similar resources in other mutualistic interactions and look ahead to identify ways in which modern sequencing technology can best inform our understanding of mutualists and mutualism.

A Genomic Map of the Effects of Linked Selection in Drosophila

Natural selection at one site shapes patterns of genetic variation at linked sites. Quantifying the effects of "linked selection" on levels of genetic diversity is key to making reliable inference about demography, building a null model in scans for targets of adaptation, and learning about the dynamics of natural selection. Here, we introduce the first method that jointly infers parameters of distinct modes of linked selection, notably background selection and selective sweeps, from genome-wide diversity data, functional annotations and genetic maps. The central idea is to calculate the probability that a neutral site is polymorphic given local annotations, substitution patterns, and recombination rates. Information is then combined across sites and samples using composite likelihood in order to estimate genome-wide parameters of distinct modes of selection. In addition to parameter estimation, this approach yields a map of the expected neutral diversity levels along the genome. To illustrate the utility of our approach, we apply it to genome-wide resequencing data from 125 lines in Drosophila melanogaster and reliably predict diversity levels at the 1Mb scale. Our results corroborate estimates of a high fraction of beneficial substitutions in proteins and untranslated regions (UTR). They allow us to distinguish between the contribution of sweeps and other modes of selection around amino acid substitutions and to uncover evidence for pervasive sweeps in untranslated regions (UTRs). Our inference further suggests a substantial effect of other modes of linked selection and of adaptation in particular. More generally, we demonstrate that linked selection has had a larger effect in reducing diversity levels and increasing their variance in D. melanogaster than previously appreciated.

Population genetic evidence for cold adaptation in European Drosophila melanogaster populations

We studied Drosophila melanogaster populations from Europe (the Netherlands and France) and Africa (Rwanda and Zambia) to uncover genetic evidence of adaptation to cold. We present here four lines of evidence for genes involved in cold adaptation from four perspectives: (i) the frequency of SNPs at genes previously known to be associated with chill-coma recovery time (CCRT), startle reflex (SR) and resistance to starvation stress (RSS) vary along environmental gradients and therefore among populations; (ii) SNPs of genes that correlate significantly with latitude and altitude in African and European populations overlap with SNPs that correlate with a latitudinal cline from North America; (iii) at the genomewide level, the top candidate genes are enriched in gene ontology (GO) terms that are related to cold tolerance; (iv) GO enriched terms from North American clinal genes overlap significantly with those from Africa and Europe. Each SNP was tested in 10 independent runs of Bayenv2, using the median Bayes factors to ascertain candidate genes. None of the candidate genes were found close to the breakpoints of cosmopolitan inversions, and only four candidate genes were linked to QTLs related to CCRT. To overcome the limitation that we used only four populations to test correlations with environmental gradients, we performed simulations to estimate the power of our approach for detecting selection. Based on our results, we propose a novel network of genes that is involved in cold adaptation.

Signatures of positive selection: from selective sweeps at individual loci to subtle allele frequency changes in polygenic adaptation

In the past 15 years, numerous methods have been developed to detect selective sweeps underlying adaptations. These methods are based on relatively simple population genetic models, including one or two loci at which positive directional selection occurs, and one or two marker loci at which the impact of selection on linked neutral variation is quantified. Information about the phenotype under selection is not included in these models (except for fitness). In contrast, in the quantitative genetic models of adaptation, selection acts on one or more phenotypic traits, such that a genotype-phenotype map is required to bridge the gap to population genetics theory. Here I describe the range of population genetic models from selective sweeps in a panmictic population of constant size to evolutionary traffic when simultaneous sweeps at multiple loci interfere, and I also consider the case of polygenic selection characterized by subtle allele frequency shifts at many loci. Furthermore, I present an overview of the statistical tests that have been proposed based on these population genetics models to detect evidence for positive selection in the genome.

Response of Polygenic Traits Under Stabilizing Selection and Mutation When Loci Have Unequal Effects

We consider an infinitely large population under stabilizing selection and mutation in which the allelic effects determining a polygenic trait vary between loci. We obtain analytical expressions for the stationary genetic variance as a function of the distribution of effects, mutation rate, and selection coefficient. We also study the dynamics of the allele frequencies, focusing on short-term evolution of the phenotypic mean as it approaches the optimum after an environmental change. We find that when most effects are small, the genetic variance does not change appreciably during adaptation, and the time until the phenotypic mean reaches the optimum is short if the number of loci is large. However, when most effects are large, the change of the variance during the adaptive process cannot be neglected. In this case, the short-term dynamics may be described by those of a few loci of large effect. Our results may be used to understand polygenic selection driving rapid adaptation.

Evolutionary meandering of intermolecular interactions along the drift barrier

Many cellular functions depend on highly specific intermolecular interactions, for example transcription factors and their DNA binding sites, microRNAs and their RNA binding sites, the interfaces between heterodimeric protein molecules, the stems in RNA molecules, and kinases and their response regulators in signal-transduction systems. Despite the need for complementarity between interacting partners, such pairwise systems seem to be capable of high levels of evolutionary divergence, even when subject to strong selection. Such behavior is a consequence of the diminishing advantages of increasing binding affinity between partners, the multiplicity of evolutionary pathways between selectively equivalent alternatives, and the stochastic nature of evolutionary processes. Because mutation pressure toward reduced affinity conflicts with selective pressure for greater interaction, situations can arise in which the expected distribution of the degree of matching between interacting partners is bimodal, even in the face of constant selection. Although biomolecules with larger numbers of interacting partners are subject to increased levels of evolutionary conservation, their more numerous partners need not converge on a single sequence motif or be increasingly constrained in more complex systems. These results suggest that most phylogenetic differences in the sequences of binding interfaces are not the result of adaptive fine tuning but a simple consequence of random genetic drift.

Adaptive fixation in two-locus models of stabilizing selection and genetic drift

The relationship between quantitative genetics and population genetics has been studied for nearly a century, almost since the existence of these two disciplines. Here we ask to what extent quantitative genetic models in which selection is assumed to operate on a polygenic trait predict adaptive fixations that may lead to footprints in the genome (selective sweeps). We study two-locus models of stabilizing selection (with and without genetic drift) by simulations and analytically. For symmetric viability selection we find that ∼16% of the trajectories may lead to fixation if the initial allele frequencies are sampled from the neutral site-frequency spectrum and the effect sizes are uniformly distributed. However, if the population is preadapted when it undergoes an environmental change (i.e., sits in one of the equilibria of the model), the fixation probability decreases dramatically. In other two-locus models with general viabilities or an optimum shift, the proportion of adaptive fixations may increase to >24%. Similarly, genetic drift leads to a higher probability of fixation. The predictions of alternative quantitative genetics models, initial conditions, and effect-size distributions are also discussed.