Recombination Speeds Adaptation by Reducing Competition between Beneficial Mutations in Populations of Escherichia coli

Identification of the selective forces contributing to the origin and maintenance of sex is a fundamental problem in biology. The Fisher–Muller model proposes that sex is advantageous because it allows beneficial mutations that arise in different lineages to recombine, thereby reducing clonal interference and speeding adaptation. I used the F plasmid to mediate recombination in the bacterium Escherichia coli and measured its effect on adaptation at high and low mutation rates. Recombination increased the rate of adaptation ∼3-fold more in the high mutation rate treatment, where beneficial mutations had to compete for fixation. Sequencing of candidate loci revealed the presence of a beneficial mutation in six high mutation rate lines. In the absence of recombination, this mutation took longer to fix and, over the course of its substitution, conferred a reduced competitive advantage, indicating interference between competing beneficial mutations. Together, these results provide experimental support for the Fisher–Muller model and demonstrate that plasmid-mediated gene transfer can accelerate bacterial adaptation.     

Rate of Adaptation in Sexuals and Asexuals: A Solvable Model of the Fisher–Muller Effect

The adaptation of large asexual populations is hampered by the competition between independently arising beneficial mutations in different individuals, which is known as clonal interference. In classic work, Fisher and Muller proposed that recombination provides an evolutionary advantage in large populations by alleviating this competition. Based on recent progress in quantifying the speed of adaptation in asexual populations undergoing clonal interference, we present a detailed analysis of the Fisher–Muller mechanism for a model genome consisting of two loci with an infinite number of beneficial alleles each and multiplicative (nonepistatic) fitness effects. We solve the deterministic, infinite population dynamics exactly and show that, for a particular, natural mutation scheme, the speed of adaptation in sexuals is twice as large as in asexuals. This result is argued to hold for any nonzero value of the rate of recombination. Guided by the infinite population result and by previous work on asexual adaptation, we postulate an expression for the speed of adaptation in finite sexual populations that agrees with numerical simulations over a wide range of population sizes and recombination rates. The ratio of the sexual to asexual adaptation speed is a function of population size that increases in the clonal interference regime and approaches 2 for extremely large populations. The simulations also show that the imbalance between the numbers of accumulated mutations at the two loci is strongly suppressed even by a small amount of recombination. The generalization of the model to an arbitrary number L of loci is briefly discussed. If each offspring samples the alleles at each locus from the gene pool of the whole population rather than from two parents, the ratio of the sexual to asexual adaptation speed is approximately equal to L in large populations. A possible realization of this scenario is the reassortment of genetic material in RNA viruses with L genomic segments.     

Investigating the Consequences of Interference between Multiple CD8+ T Cell Escape Mutations in Early HIV Infection

During early human immunodeficiency virus (HIV) infection multiple CD8⁺ T cell responses are elicited almost simultaneously. These responses exert strong selective pressures on different parts of HIV’s genome, and select for mutations that escape recognition and are thus beneficial to the virus. Some studies reveal that the later these escape mutations emerge, the more slowly they go to fixation. This pattern of escape rate decrease(ERD) can arise by distinct mechanisms. In particular, in large populations with high beneficial mutation rates interference among different escape strains –an effect that can emerge in evolution with asexual reproduction and results in delayed fixation times of beneficial mutations compared to sexual reproduction– could significantly impact the escape rates of mutations. In this paper, we investigated how interference between these concurrent escape mutations affects their escape rates in systems with multiple epitopes, and whether it could be a source of the ERD pattern. To address these issues, we developed a multilocus Wright-Fisher model of HIV dynamics with selection, mutation and recombination, serving as a null-model for interference. We also derived an interference-free null model assuming initial neutral evolution before immune response elicitation. We found that interference between several equally selectively advantageous mutations can generate the observed ERD pattern. We also found that the number of loci, as well as recombination rates substantially affect ERD. These effects can be explained by the underexponential decline of escape rates over time. Lastly, we found that the observed ERD pattern in HIV infected individuals is consistent with both independent, interference-free mutations as well as interference effects. Our results confirm that interference effects should be considered when analyzing HIV escape mutations. The challenge in estimating escape rates and mutation-associated selective coefficients posed by interference effects cannot simply be overcome by improved sampling frequencies or sizes. This problem is a consequence of the fundamental shortcomings of current estimation techniques under interference regimes. Hence, accounting for the stochastic nature of competition between mutations demands novel estimation methodologies based on the analysis of HIV strains, rather than mutation frequencies.     

Diminishing returns of population size in the rate of RNA virus adaptation

Whenever an asexual viral population evolves by adapting to new environmental conditions, beneficial mutations, the ultimate cause of adaptation, are randomly produced and then fixed in the population. The larger the population size and the higher the mutation rate, the more beneficial mutations can be produced per unit time. With the usually high mutation rate of RNA viruses and in a large enough population, several beneficial mutations could arise at the same time but in different genetic backgrounds, and if the virus is asexual, they will never be brought together through recombination. Thus, the best of these genotypes must outcompete each other on their way to fixation. This competition among beneficial mutations has the effect of slowing the overall rate of adaptation. This phenomenon is known as clonal interference. Clonal interference predicts a speed limit for adaptation as the population size increases. In the present report, by varying the size of evolving vesicular stomatitis virus populations, we found evidence clearly demonstrating this speed limit and thus indicating that clonal interference might be an important factor modulating the rate of adaptation to an in vitro cell system. Several evolutionary and epidemiological implications of the clonal interference model applied to RNA viruses are discussed.     

Interfering waves of adaptation promote spatial mixing

A fundamental problem of asexual adaptation is that beneficial substitutions are not efficiently accumulated in large populations: Beneficial mutations often go extinct because they compete with one another in going to fixation. It has been argued that such clonal interference may have led to the evolution of sex and recombination in well-mixed populations. Here, we study clonal interference, and mechanisms of its mitigation, in an evolutionary model of spatially structured populations with uniform selection pressure. Clonal interference is much more prevalent with spatial structure than without, due to the slow wave-like spread of beneficial mutations through space. We find that the adaptation speed of asexuals saturates when the linear habitat size exceeds a characteristic interference length, which becomes shorter with smaller migration and larger mutation rate. The limiting speed is proportional to μ(1/2) and μ(1/3) in linear and planar habitats, respectively, where the mutational supply μ is the product of mutation rate and local population density. This scaling and the existence of a speed limit should be amenable to experimental tests as they fall far below predicted adaptation speeds for well-mixed populations (that scale as the logarithm of population size). Finally, we show that not only recombination, but also long-range migration is a highly efficient mechanism of relaxing clonal competition in structured populations. Our conservative estimates of the interference length predict prevalent clonal interference in microbial colonies and biofilms, so clonal competition should be a strong driver of both genetic and spatial mixing in those contexts.     

Genetic linkage and natural selection

The prevalence of recombination in eukaryotes poses one of the most puzzling questions in biology. The most compelling general explanation is that recombination facilitates selection by breaking down the negative associations generated by random drift (i.e. Hill–Robertson interference, HRI). I classify the effects of HRI owing to: deleterious mutation, balancing selection and selective sweeps on: neutral diversity, rates of adaptation and the mutation load. These effects are mediated primarily by the density of deleterious mutations and of selective sweeps. Sequence polymorphism and divergence suggest that these rates may be high enough to cause significant interference even in genomic regions of high recombination. However, neither seems able to generate enough variance in fitness to select strongly for high rates of recombination. It is plausible that spatial and temporal fluctuations in selection generate much more fitness variance, and hence selection for recombination, than can be explained by uniformly deleterious mutations or species-wide selective sweeps.     

Adaptation in sexuals vs. asexuals: clonal interference and the Fisher-Muller model

Fisher and Muller's theory that recombination speeds adaptation by eliminating competition among beneficial mutations has proved a popular explanation for the advantage of sex. Recent theoretical studies have attempted to quantify the speed of adaptation under the Fisher-Muller model, partly in an attempt to understand the role of "clonal interference" in microbial experimental evolution. We reexamine adaptation in sexuals vs. asexuals, using a model of DNA sequence evolution. In this model, a modest number of sites can mutate to beneficial alleles and the fitness effects of these mutations are unequal. We study (1) transition probabilities to different beneficial mutations; (2) waiting times to the first and the last substitutions of beneficial mutations; and (3) trajectories of mean fitness through time. We find that some of these statistics are surprisingly similar between sexuals and asexuals. These results highlight the importance of the choice of substitution model in assessing the Fisher-Muller advantage of sex.     

THE ADAPTATION RATE OF ASEXUALS: DELETERIOUS MUTATIONS,CLONAL INTERFERENCE AND POPULATION BOTTLENECKS

The rate at which a population adapts to its environment is a cornerstone of evolutionary theory, and recent experimental advances in microbial populations have renewed interest in predicting and testing this rate. Efforts to understand the adaptation rate theoretically are complicated by high mutation rates, to both beneficial and deleterious mutations, and by the fact that beneficial mutations compete with each other in asexual populations (clonal interference). Testable predictions must also include the effects of population bottlenecks, repeated reductions in population size imposed by the experimental protocol. In this contribution, we integrate previous work that addresses each of these issues, developing an overall prediction for the adaptation rate that includes: beneficial mutations with probabilistically distributed effects, deleterious mutations of arbitrary effect, population bottlenecks, and clonal interference.     

Deleterious Passengers in Adapting Populations

Most new mutations are deleterious and are eventually eliminated by natural selection. But in an adapting population, the rapid amplification of beneficial mutations can hinder the removal of deleterious variants in nearby regions of the genome, altering the patterns of sequence evolution. Here, we analyze the interactions between beneficial “driver” mutations and linked deleterious “passengers” during the course of adaptation. We derive analytical expressions for the substitution rate of a deleterious mutation as a function of its fitness cost, as well as the reduction in the beneficial substitution rate due to the genetic load of the passengers. We find that the fate of each deleterious mutation varies dramatically with the rate and spectrum of beneficial mutations and the deleterious substitution rate depends nonmonotonically on the population size and the rate of adaptation. By quantifying this dependence, our results allow us to estimate which deleterious mutations will be likely to fix and how many of these mutations must arise before the progress of adaptation is significantly reduced.     

Frequent beneficial mutations during single-colony serial transfer of Streptococcus pneumoniae

The appearance of new mutations within a population provides the raw material for evolution. The consistent decline in fitness observed in classical mutation accumulation studies has provided support for the long-held view that deleterious mutations are more common than beneficial mutations. Here we present results of a study using a mutation accumulation design with the bacterium Streptococcus pneumoniae in which the fitness of the derived populations increased. This rise in fitness was associated specifically with adaptation to survival during brief stationary phase periods between single-colony population bottlenecks. To understand better the population dynamics behind this unanticipated adaptation, we developed a maximum likelihood model describing the processes of mutation and stationary-phase selection in the context of frequent population bottlenecks. Using this model, we estimate that the rate of beneficial mutations may be as high as 4.8×10(-4) events per genome for each time interval corresponding to the pneumococcal generation time. This rate is several orders of magnitude higher than earlier estimates of beneficial mutation rates in bacteria but supports recent results obtained through the propagation of small populations of Escherichia coli. Our findings indicate that beneficial mutations may be relatively frequent in bacteria and suggest that in S. pneumoniae, which develops natural competence for transformation, a steady supply of such mutations may be available for sampling by recombination.     

The Effect of Linkage on Establishment and Survival of Locally Beneficial Mutations

We study invasion and survival of weakly beneficial mutations arising in linkage to an established migration–selection polymorphism. Our focus is on a continent–island model of migration, with selection at two biallelic loci for adaptation to the island environment. Combining branching and diffusion processes, we provide the theoretical basis for understanding the evolution of islands of divergence, the genetic architecture of locally adaptive traits, and the importance of so-called “divergence hitchhiking” relative to other mechanisms, such as “genomic hitchhiking”, chromosomal inversions, or translocations. We derive approximations to the invasion probability and the extinction time of a de novo mutation. Interestingly, the invasion probability is maximized at a nonzero recombination rate if the focal mutation is sufficiently beneficial. If a proportion of migrants carries a beneficial background allele, the mutation is less likely to become established. Linked selection may increase the survival time by several orders of magnitude. By altering the timescale of stochastic loss, it can therefore affect the dynamics at the focal site to an extent that is of evolutionary importance, especially in small populations. We derive an effective migration rate experienced by the weakly beneficial mutation, which accounts for the reduction in gene flow imposed by linked selection. Using the concept of the effective migration rate, we also quantify the long-term effects on neutral variation embedded in a genome with arbitrarily many sites under selection. Patterns of neutral diversity change qualitatively and quantitatively as the position of the neutral locus is moved along the chromosome. This will be useful for population-genomic inference. Our results strengthen the emerging view that physically linked selection is biologically relevant if linkage is tight or if selection at the background locus is strong.     

The Evolution of Recombination: Removing the Limits to Natural Selection

One of the oldest hypotheses for the advantage of recombination is that recombination allows beneficial mutations that arise in different individuals to be placed together on the same chromosome. Unless recombination occurs, one of the beneficial alleles is doomed to extinction, slowing the rate at which adaptive mutations are incorporated within a population. We model the effects of a modifier of recombination on the fixation probability of beneficial mutations when beneficial alleles are segregating at other loci. We find that modifier alleles that increase recombination do increase the fixation probability of beneficial mutants and subsequently hitchhike along as the mutants rise in frequency. The strength of selection favoring a modifier that increases recombination is proportional to λ(2)Sδr/r when linkage is tight and λ(2)S(3)δ r/N when linkage is loose, where λ is the beneficial mutation rate per genome per generation throughout a population of size N, S is the average mutant effect, r is the average recombination rate, and δr is the amount that recombination is modified. We conclude that selection for recombination will be substantial only if there is tight linkage within the genome or if many loci are subject to directional selection as during periods of rapid evolutionary change.     

Fisher’s Geometrical Model Emerges as a Property of Complex Integrated Phenotypic Networks

Models relating phenotype space to fitness (phenotype–fitness landscapes) have seen important developments recently. They can roughly be divided into mechanistic models (e.g., metabolic networks) and more heuristic models like Fisher’s geometrical model. Each has its own drawbacks, but both yield testable predictions on how the context (genomic background or environment) affects the distribution of mutation effects on fitness and thus adaptation. Both have received some empirical validation. This article aims at bridging the gap between these approaches. A derivation of the Fisher model “from first principles” is proposed, where the basic assumptions emerge from a more general model, inspired by mechanistic networks. I start from a general phenotypic network relating unspecified phenotypic traits and fitness. A limited set of qualitative assumptions is then imposed, mostly corresponding to known features of phenotypic networks: a large set of traits is pleiotropically affected by mutations and determines a much smaller set of traits under optimizing selection. Otherwise, the model remains fairly general regarding the phenotypic processes involved or the distribution of mutation effects affecting the network. A statistical treatment and a local approximation close to a fitness optimum yield a landscape that is effectively the isotropic Fisher model or its extension with a single dominant phenotypic direction. The fit of the resulting alternative distributions is illustrated in an empirical data set. These results bear implications on the validity of Fisher’s model’s assumptions and on which features of mutation fitness effects may vary (or not) across genomic or environmental contexts.     

The Dynamics of Genetic Draft in Rapidly Adapting Populations

The accumulation of beneficial mutations on competing genetic backgrounds in rapidly adapting populations has a striking impact on evolutionary dynamics. This effect, known as clonal interference, causes erratic fluctuations in the frequencies of observed mutations, randomizes the fixation times of successful mutations, and leaves distinct signatures on patterns of genetic variation. Here, we show how this form of “genetic draft” affects the forward-time dynamics of site frequencies in rapidly adapting asexual populations. We calculate the probability that mutations at individual sites shift in frequency over a characteristic timescale, extending Gillespie’s original model of draft to the case where many strongly selected beneficial mutations segregate simultaneously. We then derive the sojourn time of mutant alleles, the expected fixation time of successful mutants, and the site frequency spectrum of beneficial and neutral mutations. Finally, we show how this form of draft affects inferences in the McDonald–Kreitman test and how it relates to recent observations that some aspects of genetic diversity are described by the Bolthausen–Sznitman coalescent in the limit of very rapid adaptation.     

Clonal interference is alleviated by high mutation rates in large populations

When a beneficial mutation is fixed in a population that lacks recombination, the genetic background linked to that mutation is fixed. As a result, beneficial mutations on different backgrounds experience competition, or "clonal interference," that can cause asexual populations to evolve more slowly than their sexual counterparts. Factors such as a large population size (N) and high mutation rates (mu) increase the number of competing beneficial mutations, and hence are expected to increase the intensity of clonal interference. However, recent theory suggests that, with very large values of Nmu, the severity of clonal interference may instead decline. The reason is that, with large Nmu, genomes including both beneficial mutations are rapidly created by recurrent mutation, obviating the need for recombination. Here, we analyze data from experimentally evolved asexual populations of a bacteriophage and find that, in these nonrecombining populations with very large Nmu, recurrent mutation does appear to ameliorate this cost of asexuality.     

Genomewide Patterns of Substitution in Adaptively Evolving Populations of the RNA Bacteriophage MS2

Experimental evolution of bacteriophage provides a powerful means of studying the genetics of adaptation, as every substitution contributing to adaptation can be identified and characterized. Here, I use experimental evolution of MS2, an RNA bacteriophage, to study its adaptive response to a novel environment. To this end, three lines of MS2 were adapted to rapid growth and lysis at cold temperature for a minimum of 50 phage generations and subjected to whole-genome sequencing. Using this system, I identified adaptive substitutions, monitored changes in frequency of adaptive mutations through the course of the experiment, and measured the effect on phage growth rate of each substitution. All three lines showed a substantial increase in fitness (a two- to threefold increase in growth rate) due to a modest number of substitutions (three to four). The data show some evidence that the substitutions occurring early in the experiment have larger beneficial effects than later ones, in accordance with the expected diminishing returns relationship between the fitness effects of a mutation and its order of substitution. Patterns of molecular evolution seen here—primarily a paucity of hitchhiking mutations—suggest an abundant supply of beneficial mutations in this system. Nevertheless, some beneficial mutations appear to have been lost, possibly due to accumulation of beneficial mutations on other genetic backgrounds, clonal interference, and negatively epistatic interactions with other beneficial mutations.     

Rate of Adaptation in Large Sexual Populations

Adaptation often involves the acquisition of a large number of genomic changes that arise as mutations in single individuals. In asexual populations, combinations of mutations can fix only when they arise in the same lineage, but for populations in which genetic information is exchanged, beneficial mutations can arise in different individuals and be combined later. In large populations, when the product of the population size N and the total beneficial mutation rate U_b is large, many new beneficial alleles can be segregating in the population simultaneously. We calculate the rate of adaptation, v, in several models of such sexual populations and show that v is linear in NU_b only in sufficiently small populations. In large populations, v increases much more slowly as log NU_b. The prefactor of this logarithm, however, increases as the square of the recombination rate. This acceleration of adaptation by recombination implies a strong evolutionary advantage of sex.IN asexual populations, beneficial mutations arising on different genotypes compete against each other and in large populations most of the beneficial mutations are lost because they arise on mediocre genetic backgrounds or acquire further beneficial mutations less rapidly than their peers—the combined effects of clonal interference and multiple mutations (Gerrish and Lenski 1998; Desai and Fisher 2007). Exchange of genetic material between individuals allows the combination of beneficial variants that arose in different lineages and can thereby speed up the process of adaptation (Fisher 1930; Muller 1932). Indeed, most life forms engage in some form of recombination, e.g., lateral gene transfer or competence for picking up DNA in bacteria, facultative sexual reproduction in yeast and plants, or obligate sexual reproduction in most animals. Some benefits of recombination for the rate of adaptation have recently been demonstrated experimentally in Caenorhabditis reinhardtii (Colegrave 2002), Escherichia coli (Cooper 2007), and Saccharomyces cerevisiae (Goddard et al. 2005); for a review of older experiments, see Rice (2002).Yet the benefits of sex become less obvious when one considers its disadvantageous effects: recombination can separate well-adapted combinations of alleles and sexual reproduction is more costly than asexual reproduction due to resources spent for mating and, in some cases, the necessity of males. The latter—in animals often termed the twofold cost of sex—implies that sexual populations can be unstable to the invasion of asexual variants. As a result, the pros and cons of sex have been the subject of many decades of debate in the theoretical literature (Crow and Kimura 1965; Maynard Smith 1968; Felsenstein 1974; Barton 1995a; Barton and Charlesworth 1998), and several different potentially beneficial aspects of sex have been identified, including the pruning of detrimental mutations (Peck 1994; Rice 1998) and host–parasite coevolution or otherwise changing environments (Charlesworth 1993; Ladle et al. 1993; Bürger 1999; Waxman and Peck 1999; Gandon and Otto 2007; Callahan et al. 2009). In the opposite situation of relatively static populations, it has been proposed that recombination is favored in the presence of negative epistasis (Feldman et al. 1980; Kondrashov 1984, 1988)—a situation when the combined detrimental effect of two unfavorable alleles is greater than the sum of the individual effects. While this may sometimes be a significant effect, most populations, especially microbes, are likely to be under continuing selection and the benefits of sex for speeding up adaptation are likely to dominate.The Fisher–Muller hypothesis is that sex speeds up adaptation by combining beneficial variants. Moreover, it has been demonstrated by Hill and Robertson (1966) that linkage decreases the efficacy of selection. This detrimental effect of linkage, known as the “Hill–Robertson effect,” causes selection for higher recombination rates, which has been shown by analyzing recombination modifier alleles at a locus linked to two competing segregating loci (Otto and Barton 1997; Iles et al. 2003; Barton and Otto 2005; Roze and Barton 2006; Martin et al. 2006). Hitchhiking of the allele that increases the recombination rates with the sweeping linked loci results in effective selection for increased recombination.Experiments and simulation studies suggest that the Hill–Roberston effect is more pronounced and selection for recombination modifiers is stronger in large populations with many sweeping loci (Felsenstein 1974; Colegrave 2002; Iles et al. 2003). However, the quantitative understanding of the effect of recombination in large populations is limited. Rouzine and Coffin have studied the role of recombination in the context of evolution of drug resistance in human immunodeficiency virus, finding that recombination of standing variation speeds up adaptation by producing anomalously fit individuals at the high fitness edge of the distribution (Rouzine and Coffin 2005; Gheorghiu-Svirschevski et al. 2007). The effects of epistatic interactions between polymorphisms and recombination on the dynamics of selection have recently been analyzed by Neher and Shraiman (2009). Yet none of these works consider the effects of new beneficial mutations. In the absence of new mutations (and in the absence of heterozygous advantage that can maintain polymorphisms) the fitness soon saturates as most alleles become extinct and standing variation disappears. Thus the crucial point that must be addressed is the balance between selection and recombination of existing variation and the injection of additional variation by new mutations.Here, we study the dynamics of continual evolution via new mutations, selection, and recombination using several models of recombination. Our primary models most naturally apply when periods of asexual reproduction occur between matings, so that they approximate the life style of facultatively outcrossing species such as S. cerevisiae, some plants, and C. elegans, which reproduce asexually most of the time but undergo extensive recombination when outcrossing. The models enable us to study analytically the explicit dependence of the rate of adaptation and of the dynamics of the beneficial alleles on the important parameters such as the outcrossing rate and population size. In an independent study N. H. Barton and J. Coe (personal communication) calculate the rate of adaptation for obligate sexual organisms using several different multilocus models of recombination, including the free recombination model studied here. The relation of our work to theirs, as well as to that of Cohen et al. (2005, 2006) who have also studied the effects of recombination with multiple new mutations, is commented on in the discussion.When deleterious mutations can be neglected, the rate of adaptation is the product of the rate of production of favorable mutations NU_b (N being the population size and U_b the genomewide beneficial mutation rate), the magnitude of their effect, and their fixation probability. The fixation probability is dominated by the probability that the allele becomes established, i.e., that it rises to high enough numbers in the population that it is very unlikely to die out by further stochastic fluctuations. In a homogeneous population a single beneficial mutation with selective advantage s has a probability of establishment and eventual fixation of (in discrete generation models, P_e≈2s) (Moran 1959). In a heterogeneous population, however, a novel beneficial mutation can arise on different genetic backgrounds and its establishment probability will thus vary, being greater if it arises in a well-adapted individual. But even well-adapted genotypes soon fall behind due to sweeps of other beneficial mutations and combinations. To avoid extinction, descendants of the novel mutation thus have to move to fitter genetic backgrounds via recombination in outcrossing events (Rice 2002). As a result the establishment probability decreases as the rate of average fitness gain, v, in the population increases. But the rate of average fitness gain or, equivalently, the rate of adaptation itself depends on the establishment probability. These two quantities therefore have to be determined self-consistently.In this article we analyze several models via self-consistent calculations of the fixation probability of new mutations. For a given production rate of beneficial mutations NU_b, we find that interference between mutations is of minor importance if the recombination rate r exceeds . In this regime, the rate of adaption is v ≈ NU_bs² as found for sequential mutations or in the absence of linkage. At recombination rates below , however, v grows only logarithmically with log NU_b. We find this behavior in all our models and argue that it obtains more generally. The prefactor of the log NU_b increases with the square of the recombination rate, implying a strong benefit of recombination in large populations.     

The evolution of mutation rates: separating causes from consequences

Natural selection can adjust the rate of mutation in a population by acting on allelic variation affecting processes of DNA replication and repair. Because mutation is the ultimate source of the genetic variation required for adaptation, it can be appealing to suppose that the genomic mutation rate is adjusted to a level that best promotes adaptation. Most mutations with phenotypic effects are harmful, however, and thus there is relentless selection within populations for lower genomic mutation rates. Selection on beneficial mutations can counter this effect by favoring alleles that raise the mutation rate, but the effect of beneficial mutations on the genomic mutation rate is extremely sensitive to recombination and is unlikely to be important in sexual populations. In contrast, high genomic mutation rates can evolve in asexual populations under the influence of beneficial mutations, but this phenomenon is probably of limited adaptive significance and represents, at best, a temporary reprieve from the continual selection pressure to reduce mutation. The physiological cost of reducing mutation below the low level observed in most populations may be the most important factor in setting the genomic mutation rate in sexual and asexual systems, regardless of the benefits of mutation in producing new adaptive variation. Maintenance of mutation rates higher than the minimum set by this "cost of fidelity" is likely only under special circumstances.     

Recombination enhances protein adaptation in Drosophila melanogaster

Evolutionary theory predicts that the rate and level of adaptation will be enhanced in sexual relative to asexual genomes because sexual recombination facilitates the elimination of deleterious mutations and the fixation of beneficial ones by natural selection. To date, the most compelling evidence for this prediction comes from experimental evolution studies and from loci completely lacking recombination, such as those on Y chromosomes, which often show reduced adaptation and even degeneration. Here, by analyzing replacement and silent DNA polymorphism and divergence at 98 loci, I show that recombination increases the efficacy of protein adaptation throughout the genome of the fruit fly Drosophila melanogaster. Genes residing in genomic regions with reduced recombination rates suffer a greater load of segregating, mildly deleterious mutations and fix fewer beneficial mutations than genes residing in regions with higher recombination rates. These findings suggest that the capacity to respond to natural selection varies with recombination rate across the genome, consistent with theory on the evolutionary advantages of sex and recombination.     

Drift increases the advantage of sex in RNA bacteriophage Phi6

The pervasiveness of sex and recombination remains one of the most enigmatic problems in evolutionary biology. According to many theoretical models, recombination can increase the rate of adaptation by restoring genetic variation. However, the potential for genetic drift to generate conditions that produce this outcome has yet to be studied experimentally. We have designed and performed an experiment that reveals the effects of drift on existing genetic variation by minimizing the influence of variation on beneficial mutation rate. Our experiment was conducted in populations of RNA bacteriophage Phi6 initiated from a common source population at varying bottleneck sizes. The segmented genome of this virus results in genetic exchange between viruses that co-infect the same host cell. In response to selection for growth in a high-temperature environment, sexual lines outperformed their asexual counterparts on average. The advantage of sex attenuated with increasing effective population size, implying that the rate of adaptation was limited by clonal interference among segments caused by drift. This is the first empirical evidence that the advantage of sex during adaptation increases with the intensity of drift.