Fitness effects of fixed beneficial mutations in microbial populations

Beneficial mutations are intuitively relevant to understanding adaptation, yet not all beneficial mutations are of consequence to the long-term evolutionary outcome of adaptation. Many beneficial mutations-mostly those of small effect-are lost due either to (1) genetic drift or to (2) competition among clones carrying different beneficial mutations, a phenomenon called the "Hill-Robertson effect" for sexual populations and "clonal interference" for asexual populations. Competition among clones becomes more prevalent with increasing genetic linkage and increasing population size, and it is thus generally characteristic of microbial populations. Together, these two phenomena suggest that only those beneficial mutations of large fitness effect should achieve fixation, despite the fact that most beneficial mutations produced are predicted to have very small fitness effects. Here, we confirm this prediction-both empirically and theoretically-by showing that fitness effects of fixed beneficial mutations follow a distribution whose mode is positive.     

Contrasting dynamics of a mutator allele in asexual populations of differing size

Mutators have been shown to hitchhike in asexual populations when the anticipated beneficial mutation supply rate of the mutator subpopulation, NU(b) (for subpopulation of size N and beneficial mutation rate U(b)) exceeds that of the wild-type subpopulation. Here, we examine the effect of total population size on mutator dynamics in asexual experimental populations of Saccharomyces cerevisiae. Although mutators quickly hitchhike to fixation in smaller populations, mutator fixation requires more and more time as population size increases; this observed delay in mutator hitchhiking is consistent with the expected effect of clonal interference. Interestingly, despite their higher beneficial mutation supply rate, mutators are supplanted by the wild type in very large populations. We postulate that this striking reversal in mutator dynamics is caused by an interaction between clonal interference, the fitness cost of the mutator allele, and infrequent large-effect beneficial mutations in our experimental populations. Our work thus identifies a potential set of circumstances under which mutator hitchhiking can be inhibited in natural asexual populations, despite recent theoretical predictions that such populations should have a net tendency to evolve ever-higher genomic mutation rates.     

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.     

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.     

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.     

Mutational effects on the clonal interference phenomenon

We study the process of fixation of beneficial mutations in an asexual population by means of a theoretical model. Particularly, we wish to investigate how the supply of deleterious and beneficial mutations influences the dynamics of the adaptive process of an evolving population. It is well known that the deleterious mutations drastically affect the fate of beneficial mutations. In addition, an increasing supply of favorable mutations, to compensate the decay of the fitness due to the accumulation of deleterious mutations, produces the clonal interference phenomenon where advantageous mutations in distinct lineages compete to reach fixation. This competition imposes a limit to the speed of adaptation of the population. Intuitively, we would expect that the interplay of the two mechanisms would conspire to ensure fixation of only large-effect beneficial mutations. Our results, however, show that beneficial mutations of small effect have an increased probability of fixation when both beneficial and deleterious mutations rates are increased.     

THE EFFECTS OF POPULATION BOTTLENECKS ON CLONAL INTERFERENCE, AND THE ADAPTATION EFFECTIVE POPULATION SIZE

Clonal interference refers to the competition that arises in asexual populations when multiple beneficial mutations segregate simultaneously. A large body of theoretical and experimental work now addresses this issue. Although much of the experimental work is performed in populations that grow exponentially between periodic population bottlenecks, the theoretical work to date has addressed only populations of a constant size. We derive an analytical approximation for the rate of adaptation in the presence of both clonal interference and bottlenecks, and compare this prediction to the results of an individual-based simulation, showing excellent agreement in the parameter regime in which clonal interference prevails. We also derive an appropriate definition for the effective population size for adaptive evolution experiments in the presence of population bottlenecks. This "adaptation effective population size" allows for a good approximation of the expected rate of adaptation, either in the strong-selection weak-mutation regime, or when clonal interference comes into play. In the multiple mutation regime, when the product of the population size and mutation rate is extremely large, these results no longer hold.     

The influence of deleterious mutations on adaptation in asexual populations

We study the dynamics of adaptation in asexual populations that undergo both beneficial and deleterious mutations. In particular, how the deleterious mutations affect the fixation of beneficial mutations was investigated. Using extensive Monte Carlo simulations, we find that in the "strong-selection weak mutation (SSWM)" regime or in the "clonal interference (CI)" regime, deleterious mutations rarely influence the distribution of "selection coefficients of the fixed mutations (SCFM)"; while in the "multiple mutations" regime, the accumulation of deleterious mutations would lead to a decrease in fitness significantly. We conclude that the effects of deleterious mutations on adaptation depend largely on the supply of beneficial mutations. And interestingly, the lowest adaptation rate occurs for a moderate value of selection coefficient of deleterious mutations.     

The speed of evolution and maintenance of variation in asexual populations

BACKGROUND: The rate at which beneficial mutations accumulate determines how fast asexual populations evolve, but this is only partially understood. Some recent clonal-interference models suggest that evolution in large asexual populations is limited because smaller beneficial mutations are outcompeted by larger beneficial mutations that occur in different lineages within the same population. This analysis assumes that the important mutations fix one at a time; it ignores multiple beneficial mutations that occur in the lineage of an earlier beneficial mutation, before the first mutation in the series can fix. We focus on the effects of such multiple mutations. RESULTS: Our analysis predicts that the variation in fitness maintained by a continuously evolving population increases as the logarithm of the population size and logarithm of the mutation rate and thus yields a similar logarithmic increase in the speed of evolution. To test these predictions, we evolved asexual budding yeast in glucose-limited media at a range of population sizes and mutation rates. CONCLUSIONS: We find that their evolution is dominated by the accumulation of multiple mutations of moderate effect. Our results agree with our theoretical predictions and are inconsistent with the one-by-one fixation of mutants assumed by recent clonal-interference analysis.     

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.     

Clonal interference, multiple mutations and adaptation in large asexual populations

Two important problems affect the ability of asexual populations to accumulate beneficial mutations and hence to adapt. First, clonal interference causes some beneficial mutations to be outcompeted by more-fit mutations that occur in the same genetic background. Second, multiple mutations occur in some individuals, so even mutations of large effect can be outcompeted unless they occur in a good genetic background that contains other beneficial mutations. In this article, we use a Monte Carlo simulation to study how these two factors influence the adaptation of asexual populations. We find that the results depend qualitatively on the shape of the distribution of the fitness effects of possible beneficial mutations. When this distribution falls off slower than exponentially, clonal interference alone reasonably describes which mutations dominate the adaptation, although it gives a misleading picture of the evolutionary dynamics. When the distribution falls off faster than exponentially, an analysis based on multiple mutations is more appropriate. Using our simulations, we are able to explore the limits of validity of both of these approaches, and we explore the complex dynamics in the regimes where neither one is fully applicable.     

The First Steps of Adaptation of Escherichia coli to the Gut Are Dominated by Soft Sweeps

The accumulation of adaptive mutations is essential for survival in novel environments. However, in clonal populations with a high mutational supply, the power of natural selection is expected to be limited. This is due to clonal interference - the competition of clones carrying different beneficial mutations - which leads to the loss of many small effect mutations and fixation of large effect ones. If interference is abundant, then mechanisms for horizontal transfer of genes, which allow the immediate combination of beneficial alleles in a single background, are expected to evolve. However, the relevance of interference in natural complex environments, such as the gut, is poorly known. To address this issue, we have developed an experimental system which allows to uncover the nature of the adaptive process as Escherichia coli adapts to the mouse gut. This system shows the invasion of beneficial mutations in the bacterial populations and demonstrates the pervasiveness of clonal interference. The observed dynamics of change in frequency of beneficial mutations are consistent with soft sweeps, where different adaptive mutations with similar phenotypes, arise repeatedly on different haplotypes without reaching fixation. Despite the complexity of this ecosystem, the genetic basis of the adaptive mutations revealed a striking parallelism in independently evolving populations. This was mainly characterized by the insertion of transposable elements in both coding and regulatory regions of a few genes. Interestingly, in most populations we observed a complete phenotypic sweep without loss of genetic variation. The intense clonal interference during adaptation to the gut environment, here demonstrated, may be important for our understanding of the levels of strain diversity of E. coli inhabiting the human gut microbiota and of its recombination rate.     

The two-mutant problem: clonal interference in evolutionary graph theory

In large asexual populations, clonal interference, whereby different beneficial mutations compete to fix in the population simultaneously, may be the norm. Results extrapolated from the spread of individual mutations in homogeneous backgrounds are found to be misleading in such situations: clonal interference severely inhibits the spread of beneficial mutations. In contrast with results gained in systems with just one mutation striving for fixation at any one time, the spatial structure of the population is found to be an important factor in determining the fixation probability when there are two beneficial mutations.     

Fitness evolution and the rise of mutator alleles in experimental Escherichia coli populations

We studied the evolution of high mutation rates and the evolution of fitness in three experimental populations of Escherichia coli adapting to a glucose-limited environment. We identified the mutations responsible for the high mutation rates and show that their rate of substitution in all three populations was too rapid to be accounted for simply by genetic drift. In two of the populations, large gains in fitness relative to the ancestor occurred as the mutator alleles rose to fixation, strongly supporting the conclusion that mutator alleles fixed by hitchhiking with beneficial mutations at other loci. In one population, no significant gain in fitness relative to the ancestor occurred in the population as a whole while the mutator allele rose to fixation, but a substantial and significant gain in fitness occurred in the mutator subpopulation as the mutator neared fixation. The spread of the mutator allele from rarity to fixation took >1000 generations in each population. We show that simultaneous adaptive gains in both the mutator and wild-type subpopulations (clonal interference) retarded the mutator fixation in at least one of the populations. We found little evidence that the evolution of high mutation rates accelerated adaptation in these populations.     

A comparison of directed evolution approaches using the beta-glucuronidase model system

Protein engineers can alter the properties of enzymes by directing their evolution in vitro. Many methods to generate molecular diversity and to identify improved clones have been developed, but experimental evolution remains as much an art as a science. We previously used DNA shuffling (sexual recombination) and a histochemical screen to direct the evolution of Escherichia coli beta-glucuronidase (GUS) variants with improved beta-galactosidase (BGAL) activity. Here, we employ the same model evolutionary system to test the efficiencies of several other techniques: recursive random mutagenesis (asexual), combinatorial cassette mutagenesis (high-frequency recombination) and a versatile high-throughput microplate screen. GUS variants with altered specificity evolved in each trial, but different combinations of mutagenesis and screening techniques effected the fixation of different beneficial mutations. The new microplate screen identified a broader set of mutations than the previously employed X-gal colony screen. Recursive random mutagenesis produced essentially asexual populations, within which beneficial mutations drove each other into extinction (clonal interference); DNA shuffling and combinatorial cassette mutagenesis led instead to the accumulation of beneficial mutations within a single allele. These results explain why recombinational approaches generally increase the efficiency of laboratory evolution.     

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.     

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.     

Beneficial mutation selection balance and the effect of linkage on positive selection

When beneficial mutations are rare, they accumulate by a series of selective sweeps. But when they are common, many beneficial mutations will occur before any can fix, so there will be many different mutant lineages in the population concurrently. In an asexual population, these different mutant lineages interfere and not all can fix simultaneously. In addition, further beneficial mutations can accumulate in mutant lineages while these are still a minority of the population. In this article, we analyze the dynamics of such multiple mutations and the interplay between multiple mutations and interference between clones. These result in substantial variation in fitness accumulating within a single asexual population. The amount of variation is determined by a balance between selection, which destroys variation, and beneficial mutations, which create more. The behavior depends in a subtle way on the population parameters: the population size, the beneficial mutation rate, and the distribution of the fitness increments of the potential beneficial mutations. The mutation-selection balance leads to a continually evolving population with a steady-state fitness variation. This variation increases logarithmically with both population size and mutation rate and sets the rate at which the population accumulates beneficial mutations, which thus also grows only logarithmically with population size and mutation rate. These results imply that mutator phenotypes are less effective in larger asexual populations. They also have consequences for the advantages (or disadvantages) of sex via the Fisher-Muller effect; these are discussed briefly.     

The effect of population bottlenecks on mutation rate evolution in asexual populations

In the absence of recombination, a mutator allele can spread through a population by hitchhiking with beneficial mutations that appear in its genetic background. Theoretical studies over the past decade have shown that the survival and fixation probability of beneficial mutations can be severely reduced by population size bottlenecks. Here, we use computational modelling and evolution experiments with the yeast S. cerevisiae to examine whether population bottlenecks can affect mutator dynamics in adapting asexual populations. In simulation, we show that population bottlenecks can inhibit mutator hitchhiking with beneficial mutations and are most effective at lower beneficial mutation supply rates. We then subjected experimental populations of yeast propagated at the same effective population size to three different bottleneck regimes and observed that the speed of mutator hitchhiking was significantly slower at smaller bottlenecks, consistent with our theoretical expectations. Our results, thus, suggest that bottlenecks can be an important factor in mutation rate evolution and can in certain circumstances act to stabilize or, at least, delay the progressive elevation of mutation rates in asexual populations. Additionally, our findings provide the first experimental support for the theoretically postulated effect of population bottlenecks on beneficial mutations and demonstrate the usefulness of studying mutator frequency dynamics for understanding the underlying dynamics of fitness‐affecting mutations.     

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.