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.     

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.     

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.     

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 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 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.     

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.     

Adaptation,Clonal Interference,and Frequency-Dependent Interactions in a Long-Term Evolution Experiment with Escherichia coli

Twelve replicate populations of Escherichia coli have been evolving in the laboratory for >25 years and 60,000 generations. We analyzed bacteria from whole-population samples frozen every 500 generations through 20,000 generations for one well-studied population, called Ara−1. By tracking 42 known mutations in these samples, we reconstructed the history of this population’s genotypic evolution over this period. The evolutionary dynamics of Ara−1 show strong evidence of selective sweeps as well as clonal interference between competing lineages bearing different beneficial mutations. In some cases, sets of several mutations approached fixation simultaneously, often conveying no information about their order of origination; we present several possible explanations for the existence of these mutational cohorts. Against a backdrop of rapid selective sweeps both earlier and later, two genetically diverged clades coexisted for >6000 generations before one went extinct. In that time, many additional mutations arose in the clade that eventually prevailed. We show that the clades evolved a frequency-dependent interaction, which prevented the immediate competitive exclusion of either clade, but which collapsed as beneficial mutations accumulated in the clade that prevailed. Clonal interference and frequency dependence can occur even in the simplest microbial populations. Furthermore, frequency dependence may generate dynamics that extend the period of coexistence that would otherwise be sustained by clonal interference alone.     

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.     

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.     

Hypermutation and stress adaptation in bacteria

Hypermutability is a phenotype characterized by a moderate to high elevation of spontaneous mutation rates and could result from DNA replication errors, defects in error correction mechanisms and many other causes. The elevated mutation rates are helpful to organisms to adapt to sudden and unforeseen threats to survival. At the same time hypermutability also leads to the generation of many deleterious mutations which offset its adaptive value and therefore disadvantageous. Nevertheless, it is very common in nature, especially among clinical isolates of pathogens. Hypermutability is inherited by indirect (second order) selection along with the beneficial mutations generated. At large population sizes and high mutation rates many cells in the population could concurrently acquire beneficial mutations of varying adaptive (fitness) values. These lineages compete with the ancestral cells and also among themselves for fixation. The one with the ‘fittest’ mutation gets fixed ultimately while the others are lost. This has been called ‘clonal interference’ which puts a speed limit on adaptation. The original clonal interference hypothesis has been modified recently. Nonheritable (transient) hypermtability conferring significant adaptive benefits also occur during stress response although its molecular basis remains controversial. The adaptive benefits of heritable hypermutability are discussed with emphasis on host–pathogen interactions.     

Emergent neutrality in adaptive asexual evolution

In nonrecombining genomes, genetic linkage can be an important evolutionary force. Linkage generates interference interactions, by which simultaneously occurring mutations affect each other's chance of fixation. Here, we develop a comprehensive model of adaptive evolution in linked genomes, which integrates interference interactions between multiple beneficial and deleterious mutations into a unified framework. By an approximate analytical solution, we predict the fixation rates of these mutations, as well as the probabilities of beneficial and deleterious alleles at fixed genomic sites. We find that interference interactions generate a regime of emergent neutrality: all genomic sites with selection coefficients smaller in magnitude than a characteristic threshold have nearly random fixed alleles, and both beneficial and deleterious mutations at these sites have nearly neutral fixation rates. We show that this dynamic limits not only the speed of adaptation, but also a population's degree of adaptation in its current environment. We apply the model to different scenarios: stationary adaptation in a time-dependent environment and approach to equilibrium in a fixed environment. In both cases, the analytical predictions are in good agreement with numerical simulations. Our results suggest that interference can severely compromise biological functions in an adapting population, which sets viability limits on adaptive evolution under linkage.     

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 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.     

Adaptive evolution of asexual populations under Muller's ratchet

We study the population genetics of adaptation in nonequilibrium haploid asexual populations. We find that the accumulation of deleterious mutations, due to the operation of Muller's ratchet, can considerably reduce the rate of fixation of advantageous alleles. Such reduction can be approximated reasonably well by a reduction in the effective population size. In the absence of Muller's ratchet, a beneficial mutation can only become fixed if it creates the best possible genotype; if Muller's ratchet operates, however, mutations initially arising in a nonoptimal genotype can also become fixed in the population, since the loss of the least-loaded class implies that an initially nonoptimal background can become optimal. We show that, while the rate at which adaptive mutations become fixed is reduced, the rate of fixation of deleterious mutations due to the ratchet is not changed by the presence of beneficial mutations as long as the rate of their occurrence is low and the deleterious effects of mutations (s(d)) are higher than the beneficial effects (s(a)). When s(a) > s(d), the advantage of a beneficial mutation can outweigh the deleterious effects of associated mutations. Under these conditions, a beneficial allele can drag to fixation deleterious mutations initially associated with it at a higher rate than in the absence of advantageous alleles. We propose analytical approximations for the rates of accumulation of deleterious and beneficial mutations. Furthermore, when allowing for the possible occurrence of interference between beneficial alleles, we find that the presence of deleterious mutations of either very weak or very strong effect can marginally increase the rate of accumulation of beneficial mutations over that observed in the absence of such deleterious mutations.     

The balance between mutators and nonmutators in asexual populations

Mutator alleles, which elevate an individual's mutation rate from 10 to 10,000-fold, have been found at high frequencies in many natural and experimental populations. Mutators are continually produced from nonmutators, often due to mutations in mismatch-repair genes. These mutators gradually accumulate deleterious mutations, limiting their spread. However, they can occasionally hitchhike to high frequencies with beneficial mutations. We study the interplay between these effects. We first analyze the dynamics of the balance between the production of mutator alleles and their elimination due to deleterious mutations. We find that when deleterious mutation rates are high in mutators, there will often be many "young," recently produced mutators in the population, and the fact that deleterious mutations only gradually eliminate individuals from a population is important. We then consider how this mutator-nonmutator balance can be disrupted by beneficial mutations and analyze the circumstances in which fixation of mutator alleles is likely. We find that dynamics is crucial: even in situations where selection on average acts against mutators, so they cannot stably invade, the mutators can still occasionally generate beneficial mutations and hence be important to the evolution of the population.     

The dynamics of HIV-1 adaptation in early infection

Human immunodeficiency virus type 1 (HIV-1) undergoes a severe population bottleneck during sexual transmission and yet adapts extremely rapidly to the earliest immune responses. The bottleneck has been inferred to typically consist of a single genome, and typically eight amino acid mutations in viral proteins spread to fixation by the end of the early chronic phase of infection in response to selection by CD8(+) T cells. Stochastic simulation was used to examine the effects of the transmission bottleneck and of potential interference among spreading immune-escape mutations on the adaptive dynamics of the virus in early infection. If major viral population genetic parameters are assigned realistic values that permit rapid adaptive evolution, then a bottleneck of a single genome is not inconsistent with the observed pattern of adaptive fixations. One requirement is strong selection by CD8(+) T cells that decreases over time. Such selection may reduce effective population sizes at linked loci through genetic hitchhiking. However, this effect is predicted to be minor in early infection because the transmission bottleneck reduces the effective population size to such an extent that the resulting strong selection and weak mutation cause beneficial mutations to fix sequentially and thus avoid interference.     

The Probability of Fixation in Populations of Changing Size

The rate of adaptive evolution of a population ultimately depends on the rate of incorporation of beneficial mutations. Even beneficial mutations may, however, be lost from a population since mutant individuals may, by chance, fail to reproduce. In this paper, we calculate the probability of fixation of beneficial mutations that occur in populations of changing size. We examine a number of demographic models, including a population whose size changes once, a population experiencing exponential growth or decline, one that is experiencing logistic growth or decline, and a population that fluctuates in size. The results are based on a branching process model but are shown to be approximate solutions to the diffusion equation describing changes in the probability of fixation over time. Using the diffusion equation, the probability of fixation of deleterious alleles can also be determined for populations that are changing in size. The results developed in this paper can be used to estimate the fixation flux, defined as the rate at which beneficial alleles fix within a population. The fixation flux measures the rate of adaptive evolution of a population and, as we shall see, depends strongly on changes that occur in population size.     

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.