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.     

Multiple adaptive substitutions during evolution in novel environments

We consider an asexual population under strong selection-weak mutation conditions evolving on rugged fitness landscapes with many local fitness peaks. Unlike the previous studies in which the initial fitness of the population is assumed to be high, here we start the adaptation process with a low fitness corresponding to a population in a stressful novel environment. For generic fitness distributions, using an analytic argument we find that the average number of steps to a local optimum varies logarithmically with the genotype sequence length and increases as the correlations among genotypic fitnesses increase. When the fitnesses are exponentially or uniformly distributed, using an evolution equation for the distribution of population fitness, we analytically calculate the fitness distribution of fixed beneficial mutations and the walk length distribution.     

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.     

The impact of population size on the evolution of asexual microbes on smooth versus rugged fitness landscapes

Background  

It is commonly thought that large asexual populations evolve more rapidly than smaller ones, due to their increased rate of beneficial mutations. Less clear is how population size influences the level of fitness an asexual population can attain. Here, we simulate the evolution of bacteria in repeated serial passage experiments to explore how features such as fitness landscape ruggedness, the size of the mutational target under selection, and the mutation supply rate, interact to affect the evolution of microbial populations of different sizes.     

Evolution of Fitness in Experimental Populations of Vesicular Stomatitis Virus

The evolution of fitness in experimental clonal populations of vesicular stomatitis virus (VSV) has been compared under different genetic (fitness of initial clone) and demographic (population dynamics) regimes. In spite of the high genetic heterogeneity among replicates within experiments, there is a clear effect of population dynamics on the evolution of fitness. Those populations that went through strong periodic bottlenecks showed a decreased fitness in competition experiments with wild type. Conversely, mutant populations that were transferred under the dynamics of continuous population expansions increased their fitness when compared with the same wild type. The magnitude of the observed effect depended on the fitness of the original viral clone. Thus, high fitness clones showed a larger reduction in fitness than low fitness clones under dynamics with included periodic bottleneck. In contrast, the gain in fitness was larger the lower the initial fitness of the viral clone. The quantitative genetic analysis of the trait ``fitness' in the resulting populations shows that genetic variation for the trait is positively correlated with the magnitude of the change in the same trait. The results are interpreted in terms of the operation of MULLER's ratchet and genetic drift as opposed to the appearance of beneficial mutations.     

Clonal interference and the periodic selection of new beneficial mutations in Escherichia coli

The conventional model of adaptation in asexual populations implies sequential fixation of new beneficial mutations via rare selective sweeps that purge all variation and preserve the clonal genotype. However, in large populations multiple beneficial mutations may co-occur, causing competition among them, a phenomenon called "clonal interference." Clonal interference is thus expected to lead to longer fixation times and larger fitness effects of mutations that ultimately become fixed, as well as to a genetically more diverse population. Here, we study the significance of clonal interference in populations consisting of mixtures of differently marked wild-type and mutator strains of Escherichia coli that adapt to a minimal-glucose environment for 400 generations. We monitored marker frequencies during evolution and measured the competitive fitness of random clones from each marker state after evolution. The results demonstrate the presence of multiple beneficial mutations in these populations and slower and more erratic invasion of mutants than expected by the conventional model, showing the signature of clonal interference. We found that a consequence of clonal interference is that fitness estimates derived from invasion trajectories were less than half the magnitude of direct estimates from competition experiments, thus revealing fundamental problems with this fitness measure. These results force a reevaluation of the conventional model of periodic selection for asexual microbes.     

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 Properties of Adaptive Walks in Evolving Populations of Fungus

The rarity of beneficial mutations has frustrated efforts to develop a quantitative theory of adaptation. Recent models of adaptive walks, the sequential substitution of beneficial mutations by selection, make two compelling predictions: adaptive walks should be short, and fitness increases should become exponentially smaller as successive mutations fix. We estimated the number and fitness effects of beneficial mutations in each of 118 replicate lineages of Aspergillus nidulans evolving for approximately 800 generations at two population sizes using a novel maximum likelihood framework, the results of which were confirmed experimentally using sexual crosses. We find that adaptive walks do indeed tend to be short, and fitness increases become smaller as successive mutations fix. Moreover, we show that these patterns are associated with a decreasing supply of beneficial mutations as the population adapts. We also provide empirical distributions of fitness effects among mutations fixed at each step. Our results provide a first glimpse into the properties of multiple steps in an adaptive walk in asexual populations and lend empirical support to models of adaptation involving selection towards a single optimum phenotype. In practical terms, our results suggest that the bulk of adaptation is likely to be accomplished within the first few steps.     

Genetic loads under fitness‐dependent mutation rates

Abstract Although much theory depends on the genome‐wide rate of deleterious mutations, good estimates of the mutation rate are scarce and remain controversial. Furthermore, mutation rate may not be constant, and a recent study suggests that mutation rates are higher in mildly stressful environments. If mutation rate is a function of condition, then individuals carrying more mutations will tend to be in worse condition and therefore produce more mutations. Here I examine the mean fitnesses of sexual and asexual populations evolving under such condition‐dependent mutation rates. The equilibrium mean fitness of a sexual population depends on the shape of the curve relating fitness to mutation rate. If mutation rate declines synergistically with increasing condition the mean fitness will be much lower than if mutation rate declines at a diminishing rate. In contrast, asexual populations are less affected by condition‐dependent mutation rates. The equilibrium mean fitness of an asexual population only depends on the mutation rate of the individuals in the least loaded class. Because such individuals have high fitness and therefore a low mutation rate, asexual populations experience less genetic load than sexual populations, thus increasing the twofold cost of sex.     

Lack of evolutionary stasis during alternating replication of an arbovirus in insect and mammalian cells

The evolution of vesicular stomatitis virus (VSV) in a constant environment, consisting of either mammalian or insect cells, has been compared to the evolution of the same viral population in changing environments consisting in alternating passages in mammalian and insect cells. Fitness increases were observed in all cases. An initial fitness loss of VSV passaged in insect cells was noted when fitness was measured in BHK-21 cells, but this effect could be attributed to a difference of temperature during VSV replication at 37 degrees C in BHK-21 cells. Sequencing of nucleotides 1-4717 at the 3' end of the VSV genome (N, P, M and G genes) showed that at passage 80 the number of mutations accumulated during alternated passages (seven mutations) is similar or larger than that observed in populations evolving in a constant environment (two to four mutations). Our results indicate that insect and mammalian cells can constitute similar environments for viral replication. Thus, the slow rates of evolution observed in natural populations of arboviruses are not necessarily due to the need for the virus to compromise between adaptation to both arthropod and vertebrate cell types.     

Genetic variation and the fate of beneficial mutations in asexual populations

The fate of a newly arising beneficial mutation depends on many factors, such as the population size and the availability and fitness effects of other mutations that accumulate in the population. It has proved difficult to understand how these factors influence the trajectories of particular mutations, since experiments have primarily focused on characterizing successful clones emerging from a small number of evolving populations. Here, we present the results of a massively parallel experiment designed to measure the full spectrum of possible fates of new beneficial mutations in hundreds of experimental yeast populations, whether these mutations are ultimately successful or not. Using strains in which a particular class of beneficial mutation is detectable by fluorescence, we followed the trajectories of these beneficial mutations across 592 independent populations for 1000 generations. We find that the fitness advantage provided by individual mutations plays a surprisingly small role. Rather, underlying "background" genetic variation is quickly generated in our initially clonal populations and plays a crucial role in determining the fate of each individual beneficial mutation in the evolving population.     

How does adaptation sweep through the genome? Insights from long-term selection experiments

A major goal in evolutionary biology is to understand the origins and fates of adaptive mutations. Natural selection may act to increase the frequency of de novo beneficial mutations, or those already present in the population as standing genetic variation. These beneficial mutations may ultimately reach fixation in a population, or they may stop increasing in frequency once a particular phenotypic state has been achieved. It is not yet well understood how different features of population biology, and/or different environmental circumstances affect these adaptive processes. Experimental evolution is a promising technique for studying the dynamics of beneficial alleles, as populations evolving in the laboratory experience natural selection in a replicated, controlled manner. Whole-genome sequencing, regularly obtained over the course of sustained laboratory selection, could potentially reveal insights into the mutational dynamics that most likely occur in natural populations under similar circumstances. To date, only a few evolution experiments for which whole-genome data are available exist. This review describes results from these resequenced laboratory-selected populations, in systems with and without sexual recombination. In asexual systems, adaptation from new mutations can be studied, and results to date suggest that the complete, unimpeded fixation of these mutations is not always observed. In sexual systems, adaptation from standing genetic variation can be studied, and in the admittedly few examples we have, the complete fixation of standing variants is not always observed. To date, the relative frequency of adaptation from new mutations versus standing variation has not been tested using a single experimental system, but recent studies using Caenorhabditis elegans and Saccharomyces cerevisiae suggest that this a realistic future goal.     

Rapid increase in viability due to new beneficial mutations in <Emphasis Type="Italic">Drosophila melanogaster</Emphasis>

It is usually assumed that new beneficial mutations are extremely rare. Yet, few experiments have been performed in multicellular organisms that measure the effect of new beneficial mutations on viability and other measures of fitness. In most experiments, it is difficult to clearly distinguish whether adaptations have occurred due to selection on new beneficial mutations or on preexisting genetic variation. Using a modification of a Dobzhansky and Spassky (Evolution 1:191–216, 1947) assay to study change in viability over generations, we have observed an increase in viability in lines homozygous for the second and third chromosomes of Drosophila melanogaster in 6–26 generations due to the occurrence of new beneficial mutations in population sizes of 20, 100 and 1,000. The lines with the lowest initial viability responded the fastest to new beneficial mutations. These results show that new beneficial mutations, along with selection, can quickly increase viability and fitness even in small populations. Hence, new advantageous mutations may play an important role in adaptive evolution in higher organisms.     

Estimation of the rate and effect of new beneficial mutations in asexual populations

The rate and effect of available beneficial mutations are key parameters in determining how a population adapts to a new environment. However, these parameters are poorly known, in large part because of the difficulty of designing and interpreting experiments to examine the rare and intrinsically stochastic process of mutation occurrence. We present a new approach to estimate the rate and selective advantage of beneficial mutations that underlie the adaptation of asexual populations. We base our approach on the analysis of experiments that track the effect of newly arising beneficial mutations on the dynamics of a neutral marker in evolving bacterial populations and develop efficient estimators of mutation rate and selective advantage. Using extensive simulations, we evaluate the accuracy of our estimators and conclude that they are quite robust to the use of relatively low experimental replication. To validate the predictions of our model, we compare theoretical and experimentally determined estimates of the selective advantage of the first beneficial mutation to fix in a series of ten replicate populations. We find that our theoretical predictions are not significantly different from experimentally determined selection coefficients. Application of our method to suitably designed experiments will allow estimation of how population evolvability depends on demographic and initial fitness parameters.     

ADAPTIVE WALKS AND DISTRIBUTION OF BENEFICIAL FITNESS EFFECTS

We study the adaptation dynamics of a maladapted asexual population on rugged fitness landscapes with many local fitness peaks. The distribution of beneficial fitness effects is assumed to belong to one of the three extreme value domains, viz. Weibull, Gumbel, and Fréchet. We work in the strong selection‐weak mutation regime in which beneficial mutations fix sequentially, and the population performs an uphill walk on the fitness landscape until a local fitness peak is reached. A striking prediction of our analysis is that the fitness difference between successive steps follows a pattern of diminishing returns in the Weibull domain and accelerating returns in the Fréchet domain, as the initial fitness of the population is increased. These trends are found to be robust with respect to fitness correlations. We believe that this result can be exploited in experiments to determine the extreme value domain of the distribution of beneficial fitness effects. Our work here differs significantly from the previous ones that assume the selection coefficient to be small. On taking large effect mutations into account, we find that the length of the walk shows different qualitative trends from those derived using small selection coefficient approximation.     

A method to infer positive selection from marker dynamics in an asexual population

MOTIVATION: The observation of positive selection acting on a mutant indicates that the corresponding mutation has some form of functional relevance. Determining the fitness effects of mutations thus has relevance to many interesting biological questions. One means of identifying beneficial mutations in an asexual population is to observe changes in the frequency of marked subsets of the population. We here describe a method to estimate the establishment times and fitnesses of beneficial mutations from neutral marker frequency data. RESULTS: The method accurately reproduces complex marker frequency trajectories. In simulations for which positive selection is close to 5% per generation, we obtain correlations upwards of 0.91 between correct and inferred haplotype establishment times. Where mutation selection coefficients are exponentially distributed, the inferred distribution of haplotype fitnesses is close to being correct. Applied to data from a bacterial evolution experiment, our method reproduces an observed correlation between evolvability and initial fitness defect.     

Environmental heterogeneity enhances clonal interference

Clonal interference (CI) is a phenomenon that may be important in several asexual microbes. It occurs when population sizes are large and mutation rates to new beneficial alleles are of significant magnitude. Here we explore the role of gene flow and spatial heterogeneity in selection strength in the adaptation of asexuals. We consider a subdivided population of individuals that are adapting, through new beneficial mutations, and that migrate between different patches. The fitness effect of each mutation depends on the patch and all mutations considered are assumed to be unconditionally beneficial. We find that spatial variation in selection pressure affects the rate of adaptive evolution and its qualitative effects depend on the level of gene flow. In particular, we find that both low migration and high levels of heterogeneity lead to enhanced CI. In contrast, for high levels of migration the rate of fixation of adaptive mutations is higher when environmental heterogeneity is present. In addition, we observe that the level of fitness variation is higher and simultaneous fixation of multiple mutations tends to occur in the regime of low migration rates and high heterogeneity.     

Dynamic mutation-selection balance as an evolutionary attractor

The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller's ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller's ratchet can lead to a rapid degradation of population fitness. Evidently, the long-term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Hence any stable evolutionary state of a population in a static environment must involve a dynamic mutation-selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that such a state can exist for any population size N and mutation rate U and calculate the fraction of beneficial mutations, ε, that maintains the balanced state. We find that a surprisingly low ε suffices to achieve stability, even in small populations in the face of high mutation rates and weak selection, maintaining a well-adapted population in spite of Muller's ratchet. This may explain the maintenance of mitochondria and other asexual genomes.     

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.     

Mutations of intermediate effect are responsible for adaptation in evolving Pseudomonas fluorescens populations

The fixation of a beneficial mutation represents the first step in adaptation, and the average effect of such mutations is therefore a fundamental property of evolving populations. It is nevertheless poorly characterized because the rarity of beneficial mutations makes it difficult to obtain reliable estimates of fitness. We obtained 68 genotypes each containing a single fixed beneficial mutation from experimental populations of Pseudomonas fluorescens, evolving in medium with serine as the sole carbon source and estimated the selective advantage of each by competition with the ancestor. The distribution of selection coefficients is modal and closely resembles the Weibull distribution. The average selection coefficient (2.1) and beneficial mutation rate (3.8x10(-8)) are high relative to previous studies, possibly because the ancestral population grows poorly in serine-limited medium. Our experiment suggests that the initial stages of adaptation to stressful environments will involve the substitution of mutations with large effect on fitness.