Adaptation In Asexual Populations Research Articles

Larger Numbers Can Impede Adaptation in Asexual Populations despite Entailing Greater Genetic Variation

Periodic bottlenecks play a major role in shaping the adaptive dynamics of natural and laboratory populations of asexual microbes. Here we study how they affect the ‘Extent of Adaptation’ (EoA), in such populations. EoA, the average fitness gain relative to the ancestor, is the quantity of interest in a large number of microbial experimental-evolution studies which assume that for any given bottleneck size (N0) and number of generations between bottlenecks (g), the harmonic mean size (HM = N0g) will predict the ensuing evolutionary dynamics. However, there are no theoretical or empirical validations for HM being a good predictor of EoA. Using experimental-evolution with Escherichia coli and individual-based simulations, we show that HM fails to predict EoA (i.e., higher N0g does not lead to higher EoA). This is because although higher g allows populations to arrive at superior benefits by entailing increased variation, it also reduces the efficacy of selection, which lowers EoA. We show that EoA can be maximized in evolution experiments by either maximizing N0 and/or minimizing g. We also conjecture that N0/g is a better predictor of EoA than N0g. Our results call for a re-evaluation of the role of population size in predicting fitness trajectories. They also aid in predicting adaptation in asexual populations, which has important evolutionary, epidemiological and economic implications.

Hitchhiking and epistasis give rise to cohort dynamics in adapting populations

Beneficial mutations are the driving force of adaptive evolution. In asexual populations, the identification of beneficial alleles is confounded by the presence of genetically linked hitchhiker mutations. Parallel evolution experiments enable the recognition of common targets of selection; yet these targets are inherently enriched for genes of large target size and mutations of large effect. A comprehensive study of individual mutations is necessary to create a realistic picture of the evolutionarily significant spectrum of beneficial mutations. Here we use a bulk-segregant approach to identify the beneficial mutations across 11 lineages of experimentally evolved yeast populations. We report that nearly 80% of detected mutations have no discernible effects on fitness and less than 1% are deleterious. We determine the distribution of driver and hitchhiker mutations in 31 mutational cohorts, groups of mutations that arise synchronously from low frequency and track tightly with one another. Surprisingly, we find that one-third of cohorts lack identifiable driver mutations. In addition, we identify intracohort synergistic epistasis between alleles of hsl7 and kel1, which arose together in a low-frequency lineage.

The interplay of two mutations in a population of varying size: A stochastic eco-evolutionary model for clonal interference

Clonal interference, competition between multiple beneficial mutations, has a major role in adaptation of asexual populations. We provide a simple stochastic model of clonal interference taking into account a wide variety of competitive interactions. The population evolves as a three-type birth-and-death process with type dependent competitions. This allows us to relax the classical assumption of transitivity between mutations, and to predict genetic patterns, such as coexistence of several mutants or emergence of Rock–Paper–Scissors cycles, which were not explained by existing models. In addition, we call into questions some classical preconceived ideas about fixation time and fixation probability of competing mutations.

Exploiting the Adaptation Dynamics to Predict the Distribution of Beneficial Fitness Effects.

Adaptation of asexual populations is driven by beneficial mutations and therefore the dynamics of this process, besides other factors, depends on the distribution of beneficial fitness effects. It is known that on uncorrelated fitness landscapes, this distribution can only be of three types: truncated, exponential and power law. We performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects. The first quantity studied here is the fitness difference between successive mutations that spread in the population, which is found to decrease in the case of truncated distributions, remains nearly a constant for exponentially decaying distributions and increases when the fitness distribution decays as a power law. The second quantity of interest, namely, the rate of change of fitness with time also shows quantitatively different behaviour for different beneficial fitness distributions. The patterns displayed by the two aforementioned quantities are found to hold good for both low and high mutation rates. We discuss how these patterns can be exploited to determine the distribution of beneficial fitness effects in microbial experiments.

Long-Term Dynamics of Adaptation in Asexual Populations

Experimental studies of evolution have increased greatly in number in recent years, stimulated by the growing power of genomic tools. However, organismal fitness remains the ultimate metric for interpreting these experiments, and the dynamics of fitness remain poorly understood over long time scales. Here, we examine fitness trajectories for 12 Escherichia coli populations during 50,000 generations. Mean fitness appears to increase without bound, consistent with a power law. We also derive this power-law relation theoretically by incorporating clonal interference and diminishing-returns epistasis into a dynamical model of changes in mean fitness over time.

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.

Competing islands limit the rate of adaptation in structured populations

Beneficial mutations can co-occur when population structure slows down adaptation. Here, we consider the process of adaptation in asexual populations distributed over several locations (“islands”). New beneficial mutations arise at constant rate ub, and each mutation has the same selective advantage s>0. We assume that populations evolve within islands according to the successional mutations regime of Desai and Fisher (2007), that is, the time to local fixation of a mutation is short compared to the expected waiting time until the next mutation occurs. To study the rate of adaptation, we introduce an approximate model, the successional mutations (SM) model, which can be simulated efficiently and yields accurate results for a wide range of parameters. In the SM model, mutations fix instantly within islands, and migrants can take over the destination island if they are fitter than the residents. For the special case of a population distributed equally across two islands with population size N, we approximate the model further for small and large migration rates in comparison to the mutation rate. These approximations lead to explicit formulas for the rate of adaptation which fit the original model for a large range of parameter values. For the d island case we provide some heuristics on how to extend the explicit formulas and check these with computer simulations. We conclude that the SM model is a good approximation of the adaptation process in a structured population, at least if mutation or migration is limited.

An ABC Method for Estimating the Rate and Distribution of Effects of Beneficial Mutations

Determining the distribution of adaptive mutations available to natural selection is a difficult task. These are rare events and most of them are lost by chance. Some theoretical works propose that the distribution of newly arising beneficial mutations should be close to exponential. Empirical data are scarce and do not always support an exponential distribution. Analysis of the dynamics of adaptation in asexual populations of microorganisms has revealed that these can be summarized by two effective parameters, the effective mutation rate, Ue, and the effective selection coefficient of a beneficial mutation, Se. Here, we show that these effective parameters will not always reflect the rate and mean effect of beneficial mutations, especially when the distribution of arising mutations has high variance, and the mutation rate is high. We propose a method to estimate the distribution of arising beneficial mutations, which is motivated by a common experimental setup. The method, which we call One Biallelic Marker Approximate Bayesian Computation, makes use of experimental data consisting of periodic measures of neutral marker frequencies and mean population fitness. Using simulations, we find that this method allows the discrimination of the shape of the distribution of arising mutations and that it provides reasonable estimates of their rates and mean effects in ranges of the parameter space that may be of biological relevance.

Genealogies of rapidly adapting populations

The genetic diversity of a species is shaped by its recent evolutionary history and can be used to infer demographic events or selective sweeps. Most inference methods are based on the null hypothesis that natural selection is a weak or infrequent evolutionary force. However, many species, particularly pathogens, are under continuous pressure to adapt in response to changing environments. A statistical framework for inference from diversity data of such populations is currently lacking. Towards this goal, we explore the properties of genealogies in a model of continual adaptation in asexual populations. We show that lineages trace back to a small pool of highly fit ancestors, in which almost simultaneous coalescence of more than two lineages frequently occurs. Whereas such multiple mergers are unlikely under the neutral coalescent, they create a unique genetic footprint in adapting populations. The site frequency spectrum of derived neutral alleles, for example, is nonmonotonic and has a peak at high frequencies, whereas Tajima's D becomes more and more negative with increasing sample size. Because multiple merger coalescents emerge in many models of rapid adaptation, we argue that they should be considered as a null model for adapting populations.

Distribution of fixed beneficial mutations and the rate of adaptation in asexual populations

When large asexual populations adapt, competition between simultaneously segregating mutations slows the rate of adaptation and restricts the set of mutations that eventually fix. This phenomenon of interference arises from competition between mutations of different strengths as well as competition between mutations that arise on different fitness backgrounds. Previous work has explored each of these effects in isolation, but the way they combine to influence the dynamics of adaptation remains largely unknown. Here, we describe a theoretical model to treat both aspects of interference in large populations. We calculate the rate of adaptation and the distribution of fixed mutational effects accumulated by the population. We focus particular attention on the case when the effects of beneficial mutations are exponentially distributed, as well as on a more general class of exponential-like distributions. In both cases, we show that the rate of adaptation and the influence of genetic background on the fixation of new mutants is equivalent to an effective model with a single selection coefficient and rescaled mutation rate, and we explicitly calculate these effective parameters. We find that the effective selection coefficient exactly coincides with the most common fixed mutational effect. This equivalence leads to an intuitive picture of the relative importance of different types of interference effects, which can shift dramatically as a function of the population size, mutation rate, and the underlying distribution of fitness effects.

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.

Adaptation of asexual populations in correlated environments

We introduce two computational models of subdivided populations of asexual organisms which present variability in selection pressure. In both models one can handle the level of environmental correlation among the subpopulations (demes), which is dependent on the length of the shortest path between the demes. This work mainly addresses how environmental heterogeneity can affect the rate at beneficial mutations fixes in a structured population, and the conditions under which clonal interference becomes significant. Although the fixation probability of beneficial mutations is roughly the same as in a panmitic population and so does not depend on the level of correlation among the demes, the simulation results show that fixation rates may be strongly influenced by environmental variability. Based on our simulations we conclude that an increased variability in selection leads to a smaller fixation rate. The effect of environmental heterogeneity on the adaptive process is enhanced as the flow of organisms between subpopulations is reduced. In extreme scenarios, the fixation rate decreases as the rate of beneficial mutations rises.

Beneficial mutations and the dynamics of adaptation in asexual populations

We discuss the dynamics of adaptive evolution in asexual (clonal) populations. The classical 'periodic selection' model of clonal evolution assumed that beneficial mutations are very rare and therefore substitute unfettered into populations as occasional, isolated events. Newer models allow for the possibility that beneficial mutations are sufficiently common to coexist and compete for fixation within populations. Experimental evolution studies in microbes provide empirical support for stochastic models in which both selection and mutation are strong effects and clones compete for fixation; however, the relative importance of competition among clones bearing mutations of different selective effects versus competition among clones bearing multiple mutations remains unresolved. We provide some new theoretical results, moreover, suggesting that population dynamics consistent with the periodic selection model can arise even in a deterministic model that can accommodate a very high beneficial mutation rate.

Mitotic recombination counteracts the benefits of genetic segregation

The ubiquity of sexual reproduction despite its cost has lead to an extensive body of research on the evolution and maintenance of sexual reproduction. Previous work has suggested that sexual reproduction can substantially speed up the rate of adaptation in diploid populations, because sexual populations are able to produce the fittest homozygous genotype by segregation and mating of heterozygous individuals. In contrast, asexual populations must wait for two rare mutational events, one producing a heterozygous carrier and the second converting a heterozygous to a homozygous carrier, before a beneficial mutation can become fixed. By avoiding this additional waiting time, it was shown that the benefits of segregation could overcome a twofold cost of sex. This previous result ignores mitotic recombination (MR), however. Here, we show that MR significantly hastens the spread of beneficial mutations in asexual populations. Indeed, given empirical data on MR, we find that adaptation in asexual populations proceeds as fast as that in sexual populations, especially when beneficial alleles are partially recessive. We conclude that asexual populations can gain most of the benefit of segregation through MR while avoiding the costs associated with sexual reproduction.

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.

Limits to adaptation in asexual populations

In asexual populations, the rate of adaptation is basically limited by the frequency and properties of spontaneous beneficial mutations. Hence, knowledge of these mutational properties and how they are affected by particular evolutionary conditions is a precondition for understanding the process of adaptation. Here, we address how the rate of adaptation of asexual populations is limited by its population size and mutation rate, as well as by two factors affecting the fraction of mutations that confer a benefit, i.e. the initial adaptedness of the population and the variability of the environment. These factors both influence which mutations are likely to occur, as well as the probability that they will ultimately contribute to adaptation. We attempt to separate the consequences of these basic population features in terms of their effect on the rate of adaptation by using results from evolution experiments with microorganisms.

The effect of deleterious alleles on adaptation in asexual populations.

We calculate the fixation probability of a beneficial allele that arises as the result of a unique mutation in an asexual population that is subject to recurrent deleterious mutation at rate U. Our analysis is an extension of previous works, which make a biologically restrictive assumption that selection against deleterious alleles is stronger than that on the beneficial allele of interest. We show that when selection against deleterious alleles is weak, beneficial alleles that confer a selective advantage that is small relative to U have greatly reduced probabilities of fixation. We discuss the consequences of this effect for the distribution of effects of alleles fixed during adaptation. We show that a selective sweep will increase the fixation probabilities of other beneficial mutations arising during some short interval afterward. We use the calculated fixation probabilities to estimate the expected rate of fitness improvement in an asexual population when beneficial alleles arise continually at some low rate proportional to U. We estimate the rate of mutation that is optimal in the sense that it maximizes this rate of fitness improvement. Again, this analysis relaxes the assumption made previously that selection against deleterious alleles is stronger than on beneficial alleles.