The genetic basis of phenotypic adaptation I: fixation of beneficial mutations in the moving optimum model

The impacts of positive selection on genomic variation in Drosophila serrata: Insights from a deep learning approach

This study explores the impact of positive selection on the genetic composition of a Drosophila serrata population in eastern Australia through a comprehensive analysis of 110 whole genome sequences. Utilizing an advanced deep learning algorithm (partialS/HIC) and a range of inferred demographic histories, we identified that approximately 14% of the genome is directly affected by sweeps, with soft sweeps being more prevalent (10.6%) than hard sweeps (2.1%), and partial sweeps being uncommon (1.3%). The algorithm demonstrated robustness to demographic assumptions in classifying complete sweeps but faced challenges in distinguishing neutral regions from partial sweeps and linked regions under demographic misspecification. The findings reveal the indirect influence of sweeps on nearly two-thirds of the genome through linkage, with an over-representation of putatively deleterious variants suggesting that positive selection drags deleterious variants to higher frequency due to hitchhiking with beneficial loci. Gene ontology enrichment analysis further supported our confidence in the accuracy of sweep detection as several traits expected to be under positive selection due to evolutionary arms races (e.g. immunity) were detected in hard sweeps. This study provides valuable insights into the direct and indirect contributions of positive selection in shaping genomic variation in natural populations.

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.

Adaptation of a quantitative trait to a changing environment: New analytical insights on the asexual and infinitesimal sexual models

Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits subject to stabilizing selection around an optimal phenotype, whose value is shifted continuously through time. In this context, the population fate results from the equilibrium distribution of the trait, relative to the moving optimum. Such a distribution may vary with the shape of selection, the system of reproduction, the number of loci, the mutation kernel or their interactions. Here, we develop a methodology that provides quantitative measures of population maladaptation and potential of survival directly from the entire profile of the phenotypic distribution, without any a priori on its shape. We investigate two different systems of reproduction (asexual and infinitesimal sexual models of inheritance), with various forms of selection. In particular, we recover that fitness functions such that selection weakens away from the optimum lead to evolutionary tipping points, with an abrupt collapse of the population when the speed of environmental change is too high. Our unified framework allows deciphering the mechanisms that lead to this phenomenon. More generally, it allows discussing similarities and discrepancies between the two systems of reproduction, which are ultimately explained by different constraints on the evolution of the phenotypic variance. We demonstrate that the mean fitness in the population crucially depends on the shape of the selection function in the infinitesimal sexual model, in contrast with the asexual model. In the asexual model, we also investigate the effect of the mutation kernel and we show that kernels with higher kurtosis tend to reduce maladaptation and improve fitness, especially in fast changing environments.

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.

OPTIMAL CONTROL OF GENETIC DIVERSITY IN THE MORAN MODEL WITH POPULATION GROWTH

In the Moran model of drift and selection of a mutant allele with population growth, instead of examining the consequences of pre-specified selection and population growth, the coexistence of the wild allele and the mutant allele becomes the maximization of the expected sojourn time in a given set. The process is controlled by the additional mortality of the mutant and by population growth. This makes it possible to retroactively assign fitness values as functions of the constraints, thus guiding a conservation policy or the achievement of a wishful proportion of mutants. This also gives the optimal conditions that have allowed an observed coexistence.

Allen Orr and the genetics of adaptation

Over most of the 20th century, evolutionary biologists predominantly subscribed to a strong form of "micro-mutationism," in which adaptive phenotypic divergence arises from allele frequency changes at many loci, each with a small effect on the phenotype. To be sure, there were well-known examples of large-effect alleles contributing to adaptation, yet such cases were generally regarded as atypical and unrepresentative of evolutionary change in general. In 1998, Allen Orr published a landmark theoretical paper in Evolution, which showed that both small- and large-effect mutations are likely to contribute to "adaptive walks" of a population to an optimum. Coupled with a growing set of empirical examples of large-effect alleles contributing to divergence (e.g., from QTL studies), Orr's paper provided a mathematical formalism that converted many evolutionary biologists from micro-mutationism to a more pluralistic perspective on the genetic basis of evolutionary change. We revisit the theoretical insights emerging from Orr's paper within the historical context leading up to 1998, and track the influence of this paper on the field of evolutionary biology through an examination of its citations over the last two decades and an analysis of the extensive body of theoretical and empirical research that Orr's pioneering paper inspired.

Fitness maps to a large-effect locus in introduced stickleback populations

Mutations of small effect underlie most adaptation to new environments, but beneficial variants with large fitness effects are expected to contribute under certain conditions. Genes and genomic regions having large effects on phenotypic differences between populations are known from numerous taxa, but fitness effect sizes have rarely been estimated. We mapped fitness over a generation in an F2 intercross between a marine and a lake stickleback population introduced to a freshwater pond. A quantitative trait locus map of the number of surviving offspring per F2 female detected a single, large-effect locus near Ectodysplasin (Eda), a gene having an ancient freshwater allele causing reduced bony armor and other changes. F2 females homozygous for the freshwater allele had twice the number of surviving offspring as homozygotes for the marine allele, producing a large selection coefficient, s = 0.50 ± 0.09 SE. Correspondingly, the frequency of the freshwater allele increased from 0.50 in F2 mothers to 0.58 in surviving offspring. We compare these results to allele frequency changes at the Eda gene in an Alaskan lake population colonized by marine stickleback in the 1980s. The frequency of the freshwater Eda allele rose steadily over multiple generations and reached 95% within 20 y, yielding a similar estimate of selection, s = 0.49 ± 0.05, but a different degree of dominance. These findings are consistent with other studies suggesting strong selection on this gene (and/or linked genes) in fresh water. Selection on ancient genetic variants carried by colonizing ancestors is likely to increase the prevalence of large-effect fitness variants in adaptive evolution.

Adapt or Perish: Evolutionary Rescue in a Gradually Deteriorating Environment

We investigate the evolutionary rescue of a microbial population in a gradually deteriorating environment, through a combination of analytical calculations and stochastic simulations. We consider a population destined for extinction in the absence of mutants, which can survive only if mutants sufficiently adapted to the new environment arise and fix. We show that mutants that appear later during the environment deterioration have a higher probability to fix. The rescue probability of the population increases with a sigmoidal shape when the product of the carrying capacity and of the mutation probability increases. Furthermore, we find that rescue becomes more likely for smaller population sizes and/or mutation probabilities if the environment degradation is slower, which illustrates the key impact of the rapidity of environment degradation on the fate of a population. We also show that our main conclusions are robust across various types of adaptive mutants, including specialist and generalist ones, as well as mutants modeling antimicrobial resistance evolution. We further express the average time of appearance of the mutants that do rescue the population and the average extinction time of those that do not. Our methods can be applied to other situations with continuously variable fitnesses and population sizes, and our analytical predictions are valid in the weak-to-moderate mutation regime.

Continuous Storage Root Formation and Bulking in Sweetpotato

This study investigated the phenotypic variation of continuous storage root formation and bulking (CSRFAB) growth patterns underlying the development of sweetpotato genotypes for identification of potential varieties adapted to piecemeal harvesting for small scale farmers. The research was conducted between September 2016 and August 2017 in Uganda. Genotypes from two distinct sweetpotato genepool populations (Population Uganda A and Population Uganda B) comprising 130 genotypes, previously separated using 31 simple sequence repeat (SSR) markers were used. Measurements (4 harvest times with 4 plants each) were repeated on genotypes in a randomized complete block design with 2 replications in 2 locations for 2 seasons. We developed a scoring scale of 1 to 9 and used it to compare growth changes between consecutive harvests. Data analysis was done using residual or restricted maximum likelihood (REML). Data showed a non-linear growth pattern within and between locations, seasons, and genotypes for most traits. Some genotypes displayed early initiation and increase of bulking, while others showed late initiation. Broad sense heritability of CSRFAB was low due to large GxE interactions but higher in other traits  probably due to high genetic influence and the effectiveness of the methodology. A high level of reproducibility (89%) was observed comparing 2016B and 2017A seasons (A and B are first and second season, respectively) at the National Crops Resources Research Institute (NaCRRI), Namulonge, Uganda. Choosing CSRFAB genotypes can more than double the sweetpotato production (average maximum yield of 13.1 t/ha for discontinuous storage root formation and bulking (DSRFAB) versus 28.6 t/ha for CSRFAB, demonstrating the importance of this underresearched component of storage root yield.

Why is cancer not more common? A changing microenvironment may help to explain why, and suggests strategies for anti-cancer therapy

One of the great unsolved puzzles in cancer biology is not why cancers occur, but rather explaining why so few cancers occur compared with the theoretical number that could occur, given the number of progenitor cells in the body and the normal mutation rate. We hypothesized that a contributory explanation is that the tumour microenvironment (TME) is not fixed due to factors such as immune cell infiltration, and that this could impair the ability of neoplastic cells to retain a high enough fitness to become a cancer. The TME has implicitly been assumed to be static in most cancer evolution models, and we therefore developed a mathematical model of spatial cancer evolution assuming that the TME, and thus the optimum cancer phenotype, changes over time. Based on simulations, we show how cancer cell populations adapt to diverse changing TME conditions and fitness landscapes. Compared with static TMEs, which generate neutral dynamics, changing TMEs lead to complex adaptations with characteristic spatio-temporal heterogeneity involving variable fitness effects of driver mutations, subclonal mixing, subclonal competition and phylogeny patterns. In many cases, cancer cell populations fail to grow or undergo spontaneous regression, and even extinction. Our analyses predict that cancer evolution in a changing TME is challenging, and can help to explain why cancer is neither inevitable nor as common as expected. Should cancer driver mutations with effects dependent of the TME exist, they are likely to be selected. Anti-cancer prevention and treatment strategies based on changing the TME are feasible and potentially effective.

The Linked Selection Signature of Rapid Adaptation in Temporal Genomic Data

The majority of empirical population genetic studies have tried to understand the evolutionary processes that have shaped genetic variation in a single sample taken from a present-day population. However, genomic data collected over tens of generations in both natural and laboratory populations are increasingly used to find selected loci underpinning adaptation over these short timescales. Although these studies have been quite successful in detecting selection on large-effect loci, the fitness differences between individuals are often polygenic, such that selection leads to allele frequency changes that are difficult to distinguish from genetic drift. However, one promising signal comes from polygenic selection's effect on neutral sites that become stochastically associated with the genetic backgrounds that lead to fitness differences between individuals. Previous theoretical work has established that the random associations between a neutral allele and heritable fitness backgrounds act to reduce the effective population size experienced by this neutral allele. These associations perturb neutral allele frequency trajectories, creating autocovariance in the allele frequency changes across generations. Here, we show how temporal genomic data allow us to measure the temporal autocovariance in allele frequency changes and characterize the genome-wide impact of polygenic selection. We develop expressions for these temporal autocovariances, showing that their magnitude is determined by the level of additive genetic variation, recombination, and linkage disequilibria in a region. Furthermore, by using analytic expressions for the temporal variances and autocovariances in allele frequency, we demonstrate that one can estimate the additive genetic variation for fitness and the drift-effective population size from temporal genomic data. We also show how the proportion of total variation in allele frequency change due to linked selection can be estimated from temporal data. Overall, we demonstrate that temporal genomic data offer opportunities to identify the role of linked selection on genome-wide diversity over short timescales, and can help bridge population genetic and quantitative genetic studies of adaptation.

Selective Sweep at a QTL in a Randomly Fluctuating Environment

Adaptation is mediated by phenotypic traits that are often near continuous, and undergo selective pressures that may change with the environment. The dynamics of allelic frequencies at underlying quantitative trait loci (QTL) depend on their own phenotypic effects, but also possibly on other polymorphic loci affecting the same trait, and on environmental change driving phenotypic selection. Most environments include a substantial component of random noise, characterized both by its magnitude and its temporal autocorrelation, which sets the timescale of environmental predictability. I investigate the dynamics of a mutation affecting a quantitative trait in an autocorrelated stochastic environment that causes random fluctuations of an optimum phenotype. The trait under selection may also exhibit background polygenic variance caused by many polymorphic loci of small effects elsewhere in the genome. In addition, the mutation at the QTL may affect phenotypic plasticity, the phenotypic response of given genotype to its environment of development or expression. Stochastic environmental fluctuations increase the variance of the evolutionary process, with consequences for the probability of a complete sweep at the QTL. Background polygenic variation critically alters this process, by setting an upper limit to stochastic variance of population genetics at the QTL. For a plasticity QTL, stochastic fluctuations also influences the expected selection coefficient, and alleles with the same expected trajectory can have very different stochastic variances. Finally, a mutation may be favored through its effect on plasticity despite causing a systematic mismatch with optimum, which is compensated by evolution of the mean background phenotype.

Long-term evolutionary conflict, Sisyphean arms races, and power in Fisher's geometric model

Evolutionary conflict and arms races are important drivers of evolution in nature. During arms races, new abilities in one party select for counterabilities in the second party. This process can repeat and lead to successive fixations of novel mutations, without a long-term increase in fitness. Models of co-evolution rarely address successive fixations, and one of the main models that use successive fixations-Fisher's geometric model-does not address co-evolution. We address this gap by expanding Fisher's geometric model to the evolution of joint phenotypes that are affected by two parties, such as probability of infection of a host by a pathogen. The model confirms important intuitions and offers some new insights. Conflict can lead to long-term Sisyphean arms races, where parties continue to climb toward their fitness peaks, but are dragged back down by their opponents. This results in far more adaptive evolution compared to the standard geometric model. It also results in fixation of mutations of larger effect, with the important implication that the common modeling assumption of small mutations will apply less often under conflict. Even in comparison with random abiotic change of the same magnitude, evolution under conflict results in greater distances from the optimum, lower fitness, and more fixations, but surprisingly, not larger fixed mutations. We also show how asymmetries in selection strength, mutation size, and mutation input allow one party to win over another. However, winning abilities come with diminishing returns, helping to keep weaker parties in the game.

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.

Surfing on the seascape: Adaptation in a changing environment

The environment changes constantly at various time scales and, in order to survive, species need to keep adapting. Whether these species succeed in avoiding extinction is a major evolutionary question. Using a multilocus evolutionary model of a mutation-limited population adapting under strong selection, we investigate the effects of the frequency of environmental fluctuations on adaptation. Our results rely on an "adaptive-walk" approximation and use mathematical methods from evolutionary computation theory to investigate the interplay between fluctuation frequency, the similarity of environments, and the number of loci contributing to adaptation. First, we assume a linear additive fitness function, but later generalize our results to include several types of epistasis. We show that frequent environmental changes prevent populations from reaching a fitness peak, but they may also prevent the large fitness loss that occurs after a single environmental change. Thus, the population can survive, although not thrive, in a wide range of conditions. Furthermore, we show that in a frequently changing environment, the similarity of threats that a population faces affects the level of adaptation that it is able to achieve. We check and supplement our analytical results with simulations.

Evolutionary Dynamics in the RNA Bacteriophage Qβ Depends on the Pattern of Change in Selective Pressures

The rate of change in selective pressures is one of the main factors that determines the likelihood that populations can adapt to stress conditions. Generally, the reduction in the population size that accompanies abrupt environmental changes makes it difficult to generate and select adaptive mutations. However, in systems with high genetic diversity, as happens in RNA viruses, mutations with beneficial effects under new conditions can already be present in the population, facilitating adaptation. In this work, we have propagated an RNA bacteriophage (Qβ) at temperatures higher than the optimum, following different patterns of change. We have determined the fitness values and the consensus sequences of all lineages throughout the evolutionary process in order to establish correspondences between fitness variations and adaptive pathways. Our results show that populations subjected to a sudden temperature change gain fitness and fix mutations faster than those subjected to gradual changes, differing also in the particular selected mutations. The life-history of populations prior to the environmental change has great importance in the dynamics of adaptation. The conclusion is that in the bacteriophage Qβ, the standing genetic diversity together with the rate of temperature change determine both the rapidity of adaptation and the followed evolutionary pathways.

Slower environmental change hinders adaptation from standing genetic variation

Evolutionary responses to environmental change depend on the time available for adaptation before environmental degradation leads to extinction. Explicit tests of this relationship are limited to microbes where adaptation usually depends on the sequential fixation of de novo mutations, excluding standing variation for genotype-by-environment fitness interactions that should be key for most natural species. For natural species evolving from standing genetic variation, adaptation at slower rates of environmental change may be impeded since the best genotypes at the most extreme environments can be lost during evolution due to genetic drift or founder effects. To address this hypothesis, we perform experimental evolution with self-fertilizing populations of the nematode Caenorhabditis elegans and develop an inference model to describe natural selection on extant genotypes under environmental change. Under a sudden environmental change, we find that selection rapidly increases the frequency of genotypes with high fitness in the most extreme environment. In contrast, under a gradual environmental change selection first favors genotypes that are worse at the most extreme environment. We demonstrate with a second set of evolution experiments that, as a consequence of slower environmental change and thus longer periods to reach the most extreme environments, genetic drift and founder effects can lead to the loss of the most beneficial genotypes. We further find that maintenance of standing genetic variation can retard the fixation of the best genotypes in the most extreme environment because of interference between them. Taken together, these results show that slower environmental change can hamper adaptation from standing genetic variation and they support theoretical models indicating that standing variation for genotype-by-environment fitness interactions critically alters the pace and outcome of adaptation under environmental change.

Phenotypic lag and population extinction in the moving-optimum model: insights from a small-jumps limit

Continuous environmental change-such as slowly rising temperatures-may create permanent maladaptation of natural populations: Even if a population adapts evolutionarily, its mean phenotype will usually lag behind the phenotype favored in the current environment, and if the resulting phenotypic lag becomes too large, the population risks extinction. We analyze this scenario using a moving-optimum model, in which one or more quantitative traits are under stabilizing selection towards an optimal value that increases at a constant rate. We have recently shown that, in the limit of infinitely small mutations and high mutation rate, the evolution of the phenotypic lag converges to an Ornstein-Uhlenbeck process around a long-term equilibrium value. Both the mean and the variance of this equilibrium lag have simple analytical formulas. Here, we study the properties of this limit and compare it to simulations of an evolving population with finite mutational effects. We find that the "small-jumps limit" provides a reasonable approximation, provided the mean lag is so large that the optimum cannot be reached by a single mutation. This is the case for fast environmental change and/or weak selection. Our analysis also provides insights into population extinction: Even if the mean lag is small enough to allow a positive growth rate, stochastic fluctuations of the lag will eventually cause extinction. We show that the time until this event follows an exponential distribution, whose mean depends strongly on a composite parameter that relates the speed of environmental change to the adaptive potential of the population.

Genomics of Adaptation Depends on the Rate of Environmental Change in Experimental Yeast Populations

The rate of directional environmental change may have profound consequences for evolutionary dynamics and outcomes. Yet, most evolution experiments impose a sudden large change in the environment, after which the environment is kept constant. We previously cultured replicate Saccharomyces cerevisiae populations for 500 generations in the presence of either gradually increasing or constant high concentrations of the heavy metals cadmium, nickel, and zinc. Here, we investigate how each of these treatments affected genomic evolution. Whole-genome sequencing of evolved clones revealed that adaptation occurred via a combination of SNPs, small indels, and whole-genome duplications and other large-scale structural changes. In contrast to some theoretical predictions, gradual and abrupt environmental change caused similar numbers of genomic changes. For cadmium, which is toxic already at comparatively low concentrations, mutations in the same genes were used for adaptation to both gradual and abrupt increase in concentration. Conversely, for nickel and zinc, which are toxic at high concentrations only, mutations in different genes were used for adaptation depending on the rate of change. Moreover, evolution was more repeatable following a sudden change in the environment, particularly for nickel and zinc. Our results show that the rate of environmental change and the nature of the selection pressure are important drivers of evolutionary dynamics and outcomes, which has implications for a better understanding of societal problems such as climate change and pollution.

On the large-time behaviour of the solution of a stochastic differential equation driven by a Poisson point process

We study a stochastic differential equation driven by a Poisson point process, which models the continuous change in a population's environment, as well as the stochastic fixation of beneficial mutations that might compensate for this change. The fixation probability of a given mutation increases as the phenotypic lag Xt between the population and the optimum grows larger, and successful mutations are assumed to fix instantaneously (leading to an adaptive jump). Our main result is that the process is transient (i.e. converges to -∞, so that continued adaptation is impossible) if the rate of environmental change v exceeds a parameter m, which can be interpreted as the rate of adaptation in case every beneficial mutation becomes fixed with probability 1. If v < m, the process is Harris recurrent and possesses a unique invariant probability measure, while in the limiting case m = v, Harris recurrence with an infinite invariant measure or transience depends upon additional technical conditions. We show how our results can be extended to a class of time varying rates of environmental change.

Dynamics of molecular evolution in RNA virus populations depend on sudden versus gradual environmental change

Understanding the dynamics of molecular adaptation is a fundamental goal of evolutionary biology. While adaptation to constant environments has been well characterized, the effects of environmental complexity remain seldom studied. One simple but understudied factor is the rate of environmental change. Here we used experimental evolution with RNA viruses to investigate whether evolutionary dynamics varied based on the rate of environmental turnover. We used whole-genome next-generation sequencing to characterize evolutionary dynamics in virus populations adapting to a sudden versus gradual shift onto a novel host cell type. In support of theoretical models, we found that when populations evolved in response to a sudden environmental change, mutations of large beneficial effect tended to fix early, followed by mutations of smaller beneficial effect; as predicted, this pattern broke down in response to a gradual environmental change. Early mutational steps were highly parallel across replicate populations in both treatments. The fixation of single mutations was less common than sweeps of associated "cohorts" of mutations, and this pattern intensified when the environment changed gradually. Additionally, clonal interference appeared stronger in response to a gradual change. Our results suggest that the rate of environmental change is an important determinant of evolutionary dynamics in asexual populations.

Rate of novel host invasion affects adaptability of evolving RNA virus lineages

Although differing rates of environmental turnover should be consequential for the dynamics of adaptive change, this idea has been rarely examined outside of theory. In particular, the importance of RNA viruses in disease emergence warrants experiments testing how differing rates of novel host invasion may impact the ability of viruses to adaptively shift onto a novel host. To test whether the rate of environmental turnover influences adaptation, we experimentally evolved 144 Sindbis virus lineages in replicated tissue-culture environments, which transitioned from being dominated by a permissive host cell type to a novel host cell type. The rate at which the novel host 'invaded' the environment varied by treatment. The fitness (growth rate) of evolved virus populations was measured on each host type, and molecular substitutions were mapped via whole genome consensus sequencing. Results showed that virus populations more consistently reached high fitness levels on the novel host when the novel host 'invaded' the environment more gradually, and gradual invasion resulted in less variable genomic outcomes. Moreover, virus populations that experienced a rapid shift onto the novel host converged upon different genotypes than populations that experienced a gradual shift onto the novel host, suggesting a strong effect of historical contingency.

Factors influencing the effect size distribution of adaptive substitutions

The distribution of effect sizes of adaptive substitutions has been central to evolutionary biology since the modern synthesis. Early theory proposed that because large-effect mutations have negative pleiotropic consequences, only small-effect mutations contribute to adaptation. More recent theory suggested instead that large-effect mutations could be favoured when populations are far from their adaptive peak. Here we suggest that the distributions of effect sizes are expected to differ among study systems, reflecting the wide variation in evolutionary forces and ecological conditions experienced in nature. These include selection, mutation, genetic drift, gene flow, and other factors such as the degree of pleiotropy, the distance to the phenotypic optimum, whether the optimum is stable or moving, and whether new mutation or standing genetic variation provides the source of adaptive alleles. Our goal is to review how these factors might affect the distribution of effect sizes and to identify new research directions. Until more theory and empirical work is available, we feel that it is premature to make broad generalizations about the effect size distribution of adaptive substitutions important in nature.

Catch Me if You Can: Adaptation from Standing Genetic Variation to a Moving Phenotypic Optimum

Adaptation lies at the heart of Darwinian evolution. Accordingly, numerous studies have tried to provide a formal framework for the description of the adaptive process. Of these, two complementary modeling approaches have emerged: While so-called adaptive-walk models consider adaptation from the successive fixation of de novo mutations only, quantitative genetic models assume that adaptation proceeds exclusively from preexisting standing genetic variation. The latter approach, however, has focused on short-term evolution of population means and variances rather than on the statistical properties of adaptive substitutions. Our aim is to combine these two approaches by describing the ecological and genetic factors that determine the genetic basis of adaptation from standing genetic variation in terms of the effect-size distribution of individual alleles. Specifically, we consider the evolution of a quantitative trait to a gradually changing environment. By means of analytical approximations, we derive the distribution of adaptive substitutions from standing genetic variation, that is, the distribution of the phenotypic effects of those alleles from the standing variation that become fixed during adaptation. Our results are checked against individual-based simulations. We find that, compared to adaptation from de novo mutations, (i) adaptation from standing variation proceeds by the fixation of more alleles of small effect and (ii) populations that adapt from standing genetic variation can traverse larger distances in phenotype space and, thus, have a higher potential for adaptation if the rate of environmental change is fast rather than slow.

The Utility of Fisher's Geometric Model in Evolutionary Genetics

The accumulation of data on the genomic bases of adaptation has triggered renewed interest in theoretical models of adaptation. Among these models, Fisher Geometric Model (FGM) has received a lot of attention over the last two decades. FGM is based on a continuous multidimensional phenotypic landscape, but it is for the emerging properties of individual mutation effects that it is mostly used. Despite an apparent simplicity and a limited number of parameters, FGM integrates a full model of mutation and epistatic interactions that allows the study of both beneficial and deleterious mutations, and subsequently the fate of evolving populations. In this review, I present the different properties of FGM and the qualitative and quantitative support they have received from experimental evolution data. I later discuss how to estimate the different parameters of the model and outline some future directions to connect FGM and the molecular determinants of adaptation.

Modeling evolution using the probability of fixation: history and implications

Many models of evolution calculate the rate of evolution by multiplying the rate at which new mutations originate within a population by a probability of fixation. Here we review the historical origins, contemporary applications, and evolutionary implications of these "origin-fixation" models, which are widely used in evolutionary genetics, molecular evolution, and phylogenetics. Origin-fixation models were first introduced in 1969, in association with an emerging view of "molecular" evolution. Early origin-fixation models were used to calculate an instantaneous rate of evolution across a large number of independently evolving loci; in the 1980s and 1990s, a second wave of origin-fixation models emerged to address a sequence of fixation events at a single locus. Although origin fixation models have been applied to a broad array of problems in contemporary evolutionary research, their rise in popularity has not been accompanied by an increased appreciation of their restrictive assumptions or their distinctive implications. We argue that origin-fixation models constitute a coherent theory of mutation-limited evolution that contrasts sharply with theories of evolution that rely on the presence of standing genetic variation. A major unsolved question in evolutionary biology is the degree to which these models provide an accurate approximation of evolution in natural populations.

Fisher's geometric model with a moving optimum

Fisher's geometric model has been widely used to study the effects of pleiotropy and organismic complexity on phenotypic adaptation. Here, we study a version of Fisher's model in which a population adapts to a gradually moving optimum. Key parameters are the rate of environmental change, the dimensionality of phenotype space, and the patterns of mutational and selectional correlations. We focus on the distribution of adaptive substitutions, that is, the multivariate distribution of the phenotypic effects of fixed beneficial mutations. Our main results are based on an “adaptive-walk approximation,” which is checked against individual-based simulations. We find that (1) the distribution of adaptive substitutions is strongly affected by the ecological dynamics and largely depends on a single composite parameter γ, which scales the rate of environmental change by the “adaptive potential” of the population; (2) the distribution of adaptive substitution reflects the shape of the fitness landscape if the environment changes slowly, whereas it mirrors the distribution of new mutations if the environment changes fast; (3) in contrast to classical models of adaptation assuming a constant optimum, with a moving optimum, more complex organisms evolve via larger adaptive steps.

Between migration load and evolutionary rescue: dispersal, adaptation and the response of spatially structured populations to environmental change

The evolutionary potential of populations is mainly determined by population size and available genetic variance. However, the adaptability of spatially structured populations may also be affected by dispersal: positively by spreading beneficial mutations across sub-populations, but negatively by moving locally adapted alleles between demes. We develop an individual-based, two-patch, allelic model to investigate the balance between these opposing effects on a population's evolutionary response to rapid climate change. Individual fitness is controlled by two polygenic traits coding for local adaptation either to the environment or to climate. Under conditions of selection that favour the evolution of a generalist phenotype (i.e. weak divergent selection between patches) dispersal has an overall positive effect on the persistence of the population. However, when selection favours locally adapted specialists, the beneficial effects of dispersal outweigh the associated increase in maladaptation for a narrow range of parameter space only (intermediate selection strength and low linkage among loci), where the spread of beneficial climate alleles is not strongly hampered by selection against non-specialists. Given that local selection across heterogeneous and fragmented landscapes is common, the complex effect of dispersal that we describe will play an important role in determining the evolutionary dynamics of many species under rapidly changing climate.

Rapid evolution of quantitative traits: theoretical perspectives

An increasing number of studies demonstrate phenotypic and genetic changes in natural populations that are subject to climate change, and there is hope that some of these changes will contribute to avoiding species extinctions ('evolutionary rescue'). Here, we review theoretical models of rapid evolution in quantitative traits that can shed light on the potential for adaptation to a changing climate. Our focus is on quantitative-genetic models with selection for a moving phenotypic optimum. We point out that there is no one-to-one relationship between the rate of adaptation and population survival, because the former depends on relative fitness and the latter on absolute fitness. Nevertheless, previous estimates that sustainable rates of genetically based change usually do not exceed 0.1 haldanes (i.e., phenotypic standard deviations per generation) are probably correct. Survival can be greatly facilitated by phenotypic plasticity, and heritable variation in plasticity can further speed up genetic evolution. Multivariate selection and genetic correlations are frequently assumed to constrain adaptation, but this is not necessarily the case and depends on the geometric relationship between the fitness landscape and the structure of genetic variation. Similar conclusions hold for adaptation to shifting spatial gradients. Recent models of adaptation in multispecies communities indicate that the potential for rapid evolution is strongly influenced by interspecific competition.

Fold or hold: experimental evolution in vitro

We introduce a system for experimental evolution consisting of populations of short oligonucleotides (Oli populations) evolving in a modified quantitative polymerase chain reaction (qPCR). It is tractable at the genetic, genomic, phenotypic and fitness levels. The Oli system uses DNA hairpins designed to form structures that self-prime under defined conditions. Selection acts on the phenotype of self-priming, after which differences in fitness are amplified and quantified using qPCR. We outline the methodological and bioinformatics tools for the Oli system here and demonstrate that it can be used as a conventional experimental evolution model system by test-driving it in an experiment investigating adaptive evolution under different rates of environmental change.

Genomic parasites or symbionts? Modeling the effects of environmental pressure on transposition activity in asexual populations

Transposable elements are DNA segments capable of persisting in host genomes by self-replication in spite of deleterious mutagenic effects. The theoretical dynamics of these elements within genomes has been studied extensively, and population genetic models predict that they can invade and maintain as a result of both intra-genomic and inter-individual selection in sexual species. In asexuals, the success of selfish DNA is more difficult to explain. However, most theoretical work assumes constant environment. Here, we analyze the impact of environmental change on the dynamics of transposition activity when horizontal DNA exchange is absent, based on a stochastic computational model of transposable element proliferation. We argue that repeated changes in the phenotypic optimum in a multidimensional fitness landscape may induce explosive bursts of transposition activity associated with faster adaptation. However, long-term maintenance of transposition activity is unlikely. This could contribute to the significant variation in the transposable element copy number among closely related species.

The effects of stochastic and episodic movement of the optimum on the evolution of the G-matrix and the response of the trait mean to selection

Theoretical and empirical results demonstrate that the G-matrix, which summarizes additive genetic variances and covariances of quantitative traits, changes over time. Such evolution and fluctuation of the G-matrix could potentially have wide-ranging effects on phenotypic evolution. Nevertheless, no studies have yet addressed G-matrix stability and evolution when movement of an intermediate optimum includes large, episodic jumps or stochasticity. Here, we investigate such scenarios by using simulation-based models of G-matrix evolution. These analyses yield four important insights regarding the evolution and stability of the G-matrix. (i) Regardless of the model of peak movement, a moving optimum causes the G-matrix to orient towards the direction of net peak movement, so that genetic variance is enhanced in that direction (the variance enhancement effect). (ii) Peak movement skews the distribution of breeding values in the direction of movement, which impedes the response to selection. (iii) The stability of the G-matrix is affected by the overall magnitude and direction of peak movement, but modes and rates of peak movement have surprisingly small effects (the invariance principle). (iv) Both episodic and stochastic peak movement increase the probability that a population will fall below its carrying capacity and go extinct. We also present novel equations for the response of the trait mean to multivariate selection, which take into account the higher moments of the distribution of breeding values.

Patterns of neutral diversity under general models of selective sweeps

Two major sources of stochasticity in the dynamics of neutral alleles result from resampling of finite populations (genetic drift) and the random genetic background of nearby selected alleles on which the neutral alleles are found (linked selection). There is now good evidence that linked selection plays an important role in shaping polymorphism levels in a number of species. One of the best-investigated models of linked selection is the recurrent full-sweep model, in which newly arisen selected alleles fix rapidly. However, the bulk of selected alleles that sweep into the population may not be destined for rapid fixation. Here we develop a general model of recurrent selective sweeps in a coalescent framework, one that generalizes the recurrent full-sweep model to the case where selected alleles do not sweep to fixation. We show that in a large population, only the initial rapid increase of a selected allele affects the genealogy at partially linked sites, which under fairly general assumptions are unaffected by the subsequent fate of the selected allele. We also apply the theory to a simple model to investigate the impact of recurrent partial sweeps on levels of neutral diversity and find that for a given reduction in diversity, the impact of recurrent partial sweeps on the frequency spectrum at neutral sites is determined primarily by the frequencies rapidly achieved by the selected alleles. Consequently, recurrent sweeps of selected alleles to low frequencies can have a profound effect on levels of diversity but can leave the frequency spectrum relatively unperturbed. In fact, the limiting coalescent model under a high rate of sweeps to low frequency is identical to the standard neutral model. The general model of selective sweeps we describe goes some way toward providing a more flexible framework to describe genomic patterns of diversity than is currently available.

Mutations and binding sites of human transcription factors

Mutations in any genome may lead to phenotype characteristics that determine ability of an individual to cope with adaptation to environmental challenges. In studies of human biology, among the most interesting ones are phenotype characteristics that determine responses to drug treatments, response to infections, or predisposition to specific inherited diseases. Most of the research in this field has been focused on the studies of mutation effects on the final gene products, peptides, and their alterations. Considerably less attention was given to the mutations that may affect regulatory mechanism(s) of gene expression, although these may also affect the phenotype characteristics. In this study we make a pilot analysis of mutations observed in the regulatory regions of 24,667 human RefSeq genes. Our study reveals that out of eight studied mutation types, "insertions" are the only one that in a statistically significant manner alters predicted transcription factor binding sites (TFBSs). We also find that 25 families of TFBSs have been altered by mutations in a statistically significant manner in the promoter regions we considered. Moreover, we find that the related transcription factors are, for example, prominent in processes related to intracellular signaling; cell fate; morphogenesis of organs and epithelium; development of urogenital system, epithelium, and tube; neuron fate commitment. Our study highlights the significance of studying mutations within the genes regulatory regions and opens way for further detailed investigations on this topic, particularly on the downstream affected pathways.

The QTN program and the alleles that matter for evolution: all that's gold does not glitter

The search for the alleles that matter, the quantitative trait nucleotides (QTNs) that underlie heritable variation within populations and divergence among them, is a popular pursuit. But what is the question to which QTNs are the answer? Although their pursuit is often invoked as a means of addressing the molecular basis of phenotypic evolution or of estimating the roles of evolutionary forces, the QTNs that are accessible to experimentalists, QTNs of relatively large effect, may be uninformative about these issues if large-effect variants are unrepresentative of the alleles that matter. Although 20th century evolutionary biology generally viewed large-effect variants as atypical, the field has recently undergone a quiet realignment toward a view of readily discoverable large-effect alleles as the primary molecular substrates for evolution. I argue that neither theory nor data justify this realignment. Models and experimental findings covering broad swaths of evolutionary phenomena suggest that evolution often acts via large numbers of small-effect polygenes, individually undetectable. Moreover, these small-effect variants are different in kind, at the molecular level, from the large-effect alleles accessible to experimentalists. Although discoverable QTNs address some fundamental evolutionary questions, they are essentially misleading about many others.

On the fixation process of a beneficial mutation in a variable environment

A population that adapts to gradual environmental change will typically experience temporal variation in its population size and the selection pressure. On the basis of the mathematical theory of inhomogeneous branching processes, we present a framework to describe the fixation process of a single beneficial allele under these conditions. The approach allows for arbitrary time-dependence of the selection coefficient s(t) and the population size N(t), as may result from an underlying ecological model. We derive compact analytical approximations for the fixation probability and the distribution of passage times for the beneficial allele to reach a given intermediate frequency. We apply the formalism to several biologically relevant scenarios, such as linear or cyclic changes in the selection coefficient, and logistic population growth. Comparison with computer simulations shows that the analytical results are accurate for a large parameter range, as long as selection is not very weak.

The rate of multi-step evolution in Moran and Wright-Fisher populations

Several groups have recently modeled evolutionary transitions from an ancestral allele to a beneficial allele separated by one or more intervening mutants. The beneficial allele can become fixed if a succession of intermediate mutants are fixed or alternatively if successive mutants arise while the previous intermediate mutant is still segregating. This latter process has been termed stochastic tunneling. Previous work has focused on the Moran model of population genetics. I use elementary methods of analyzing stochastic processes to derive the probability of tunneling in the limit of large population size for both Moran and Wright-Fisher populations. I also show how to efficiently obtain numerical results for finite populations. These results show that the probability of stochastic tunneling is twice as large under the Wright-Fisher model as it is under the Moran model.

Information content in genome-wide scans: concordance between patterns of genetic differentiation and linkage mapping associations

BACKGROUND

Scanning the genome with high density SNP markers has become a standard approach for identifying regions of the genome showing substantial between-population genetic differentiation, and thus evidence of diversifying selection. Such regions may contain genes of large phenotypic effect. However, few studies have attempted to address the power or efficacy of such an approach.

RESULTS

In this study, the patterns of allele frequency differences between two cattle breeds based on the Bovine HapMap study were compared with statistical evidence for QTL based on a linkage mapping study of an experimental population formed by a cross between the same breeds. Concordance between the two datasets was seen for chromosomes carrying QTL with strong statistical support, such as BTA5 and BTA18, which carry genes associated with coat color. For these chromosomes, there was a correspondence between the strength of the QTL signal along the chromosome and the degree of genetic differentiation between breeds. However, such an association was not seen in a broader comparison that also included chromosomes carrying QTL with lower significance levels. In addition, other chromosomal regions with substantial QTL effects did not include markers showing extreme between-breed genetic differentiation. Furthermore, the overall consistency between the two studies was weak, with low genome-wide correlation between the statistical values obtained in the linkage mapping study and between-breed genetic differentiation from the HapMap study.

CONCLUSIONS

These results suggest that genomic diversity scans are capable of detecting regions associated with qualitative traits but may be limited in their power to detect regions associated with quantitative phenotypic differences between populations, which may depend on the marker resolution of the study and the level of LD in the populations under investigation.

Towards identifying genes underlying ecologically relevant traits in Arabidopsis thaliana

A major challenge in evolutionary biology and plant breeding is to identify the genetic basis of complex quantitative traits, including those that contribute to adaptive variation. Here we review the development of new methods and resources to fine-map intraspecific genetic variation that underlies natural phenotypic variation in plants. In particular, the analysis of 107 quantitative traits reported in the first genome-wide association mapping study in Arabidopsis thaliana sets the stage for an exciting time in our understanding of plant adaptation. We also argue for the need to place phenotype-genotype association studies in an ecological context if one is to predict the evolutionary trajectories of plant species.

The statistical mechanics of a polygenic character under stabilizing selection, mutation and drift

By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enough to accurately describe the dynamics of the trait mean and of its genetic variance (and in principle of any other quantity). Unlike previous approaches that were based on an infinite series of moments or cumulants, which had to be truncated arbitrarily, our calculations provide a well-defined approximation procedure. We apply the framework to abrupt and gradual changes in the optimum, as well as to changes in the strength of stabilizing selection. Our approximations are surprisingly accurate, even for systems with as few as five loci. We find that when the effects of drift are included, the expected genetic variance is hardly altered by directional selection, even though it fluctuates in any particular instance. We also find hysteresis, showing that even after averaging over the microscopic variables, the macroscopic trajectories retain a memory of the underlying genetic states.

Next-generation sequencing as a tool to study microbial evolution

Thanks to their short generation times and large population sizes, microbes evolve rapidly. Evolutionary biologists have exploited this to observe evolution in real time. The falling costs of whole-genome sequencing using next-generation technologies now mean that it is realistic to use this as a tool to study this rapid microbial evolution both in the laboratory and in the wild. Such experiments are being used to accurately estimate the rates of mutation, reveal the genetic targets and dynamics of natural selection, uncover the correlation (or lack thereof) between genetic and phenotypic change, and provide data to test long-standing evolutionary hypotheses. These advances have important implications for our understanding of the within- and between-host evolution of microbial pathogens.

The genetic basis of phenotypic adaptation II: the distribution of adaptive substitutions in the moving optimum model

We consider a population that adapts to a gradually changing environment. Our aim is to describe how ecological and genetic factors combine to determine the genetic basis of adaptation. Specifically, we consider the evolution of a polygenic trait that is under stabilizing selection with a moving optimum. The ecological dynamics are defined by the strength of selection, sigma, and the speed of the optimum, v; the key genetic parameters are the mutation rate Theta and the variance of the effects of new mutations, omega. We develop analytical approximations within an "adaptive-walk" framework and describe how selection acts as a sieve that transforms a given distribution of new mutations into the distribution of adaptive substitutions. Our analytical results are complemented by individual-based simulations. We find that (i) the ecological dynamics have a strong effect on the distribution of adaptive substitutions and their impact depends largely on a single composite measure gamma=v/(sigmaThetaomega(3)), which combines the ecological and genetic parameters; (ii) depending on gamma, we can distinguish two distinct adaptive regimes: for large gamma the adaptive process is mutation limited and dominated by genetic constraints, whereas for small gamma it is environmentally limited and dominated by the external ecological dynamics; (iii) deviations from the adaptive-walk approximation occur for large mutation rates, when different mutant alleles interact via linkage or epistasis; and (iv) in contrast to predictions from previous models assuming constant selection, the distribution of adaptive substitutions is generally not exponential.