FIXATION OF MUTATORS IN ASEXUAL POPULATIONS: THE ROLE OF GENETIC DRIFT AND EPISTASIS

We study the evolutionary dynamics of an asexual population of nonmutators and mutators on a class of epistatic fitness landscapes. We consider the situation in which all mutations are deleterious and mutators are produced from nonmutators continually at a constant rate. We find that in an infinitely large population, a minimum nonmutator‐to‐mutator conversion rate is required to fix the mutators but an arbitrarily small conversion rate results in the fixation of mutators in a finite population. We calculate analytical expressions for the mutator fraction at mutation‐selection balance and fixation time for mutators in a finite population when the difference between the mutation rate for mutator and nonmutator is smaller (regime I) and larger (regime II) than the selection coefficient. Our main result is that in regime I, the mutator fraction and the fixation time are independent of epistasis but in regime II, mutators are rarer and take longer to fix when the decrease in fitness with the number of deleterious mutations occurs at an accelerating rate (synergistic epistasis) than at a diminishing rate (antagonistic epistasis). Our analytical results are compared with numerics and their implications 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.     

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.     

Fixation probability of rare nonmutator and evolution of mutation rates

Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of mutation rates, and we address this question in asexual populations at mutation‐selection equilibrium neglecting selective sweeps. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large asexual population of mutators and find that a nonmutator is more likely to fix when the deleterious mutation rate of the mutator population is high. Compensatory mutations in the mutator population are found to decrease the fixation probability of a nonmutator when the selection coefficient is large. But, surprisingly, the fixation probability changes nonmonotonically with increasing compensatory mutation rate when the selection is mild. Using these results for the fixation probability and a drift‐barrier argument, we find a novel relationship between the mutation rates and the population size. We also discuss the time to fix the nonmutator in an adapted population of asexual mutators, and compare our results with experiments.     

Experimental adaptation of Salmonella typhimurium to mice

Experimental evolution is a powerful approach to study the dynamics and mechanisms of bacterial niche specialization. By serial passage in mice, we evolved 18 independent lineages of Salmonella typhimurium LT2 and examined the rate and extent of adaptation to a mainly reticuloendothelial host environment. Bacterial mutation rates and population sizes were varied by using wild-type and DNA repair-defective mutator (mutS) strains with normal and high mutation rates, respectively, and by varying the number of bacteria intraperitoneally injected into mice. After <200 generations of adaptation all lineages showed an increased fitness as measured by a faster growth rate in mice (selection coefficients 0.11-0.58). Using a generally applicable mathematical model we calculated the adaptive mutation rate for the wild-type bacterium to be >10(-6)/cell/generation, suggesting that the majority of adaptive mutations are not simple point mutations. For the mutator lineages, adaptation to mice was associated with a loss of fitness in secondary environments as seen by a reduced metabolic capability. During adaptation there was no indication that a high mutation rate was counterselected. These data show that S. typhimurium can rapidly and extensively increase its fitness in mice but this niche specialization is, at least in mutators, associated with a cost.     

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.     

Evolution of mutation rates in bacteria

Evolutionary success of bacteria relies on the constant fine-tuning of their mutation rates, which optimizes their adaptability to constantly changing environmental conditions. When adaptation is limited by the mutation supply rate, under some conditions, natural selection favours increased mutation rates by acting on allelic variation of the genetic systems that control fidelity of DNA replication and repair. Mutator alleles are carried to high frequency through hitchhiking with the adaptive mutations they generate. However, when fitness gain no longer counterbalances the fitness loss due to continuous generation of deleterious mutations, natural selection favours reduction of mutation rates. Selection and counter-selection of high mutation rates depends on many factors: the number of mutations required for adaptation, the strength of mutator alleles, bacterial population size, competition with other strains, migration, and spatial and temporal environmental heterogeneity. Such modulations of mutation rates may also play a role in the evolution of antibiotic resistance.     

Migration promotes mutator alleles in subdivided populations

Mutator alleles that elevate the genomic mutation rate may invade nonrecombining populations by hitchhiking with beneficial mutations. Mutators have been repeatedly observed to take over adapting laboratory populations and have been found at high frequencies in both microbial pathogen and cancer populations in nature. Recently, we have shown that mutators are only favored by selection in sufficiently large populations and transition to being disfavored as population size decreases. This population size‐dependent sign inversion in selective effect suggests that population structure may also be an important determinant of mutation rate evolution. Although large populations may favor mutators, subdividing such populations into sufficiently small subpopulations (demes) might effectively inhibit them. On the other hand, migration between small demes that otherwise inhibit hitchhiking may promote mutator fixation in the whole metapopulation. Here, we use stochastic, agent‐based simulations and evolution experiments with the yeast Saccharomyces cerevisiae to show that mutators can, indeed, be favored by selection in subdivided metapopulations composed of small demes connected by sufficient migration. In fact, we show that population structure plays a previously unsuspected role in promoting mutator success in subdivided metapopulations when migration is rare.     

Mutator dynamics in fluctuating environments

Populations with high mutation rates (mutator clones) are being found in increasing numbers of species, and a clear link is being established between the presence of mutator clones and drug resistance. Mutator clones exist despite the fact that in a constant environment most mutations are deleterious, with the spontaneous mutation rate generally held at a low value. This implies that mutator clones have an important role in the adaptation of organisms to changing environments. Our study examines how mutator dynamics vary according to the frequency of environmental fluctuations. Although recent studies have considered a single environmental switch, here we investigate mutator dynamics in a regularly varying environment, seeking to mimic conditions present, for example, under certain drug or pesticide regimes. Our model provides four significant new insights. First, the results demonstrate that mutators are most prevalent under intermediate rates of environmental change. When the environment oscillates more rapidly, mutators are unable to provide sufficient adaptability to keep pace with the frequent changes in selection pressure and, instead, a population of 'environmental generalists' dominates. Second, our findings reveal that mutator dynamics may be complex, exhibiting limit cycles and chaos. Third, we demonstrate that when each beneficial mutation provides a greater gain in fitness, mutators achieve higher densities in more rapidly fluctuating environments. Fourth, we find that mutators of intermediate strength reach higher densities than very weak or strong mutators.     

Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection

With a small effective population size, random genetic drift is more important than selection in determining the fate of new alleles. Small populations therefore accumulate deleterious mutations. Left unchecked, the effect of these fixed alleles is to reduce the reproductive capacity of a species, eventually to the point of extinction. New beneficial mutations, if fixed by selection, can restore some of this lost fitness. This paper derives the overall change in fitness due to fixation of new deleterious and beneficial alleles, as a function of the distribution of effects of new mutations and the effective population size. There is a critical effective size below which a population will on average decline in fitness, but above which beneficial mutations allow the population to persist. With reasonable estimates of the relevant parameters, this critical effective size is likely to be a few hundred. Furthermore, sexual selection can act to reduce the fixation probability of deleterious new mutations and increase the probability of fixing new beneficial mutations. Sexual selection can therefore reduce the risk of extinction of small populations.     

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.     

Enrichment and elimination of mutY mutators in Escherichia coli populations

The kinetics of mutator sweeps was followed in two independent populations of Escherichia coli grown for up to 350 generations in glucose-limited continuous culture. A rapid elevation of mutation rates was observed in both populations within 120-150 generations, as was apparent from major increases in the proportion of the populations with unselected mutations in fhuA. The increase in mutation rates was due to sweeps by mutY mutators. In both cultures, the enrichment of mutators resulted from hitchhiking with identified beneficial mutations increasing fitness under glucose limitation; mutY hitchhiked with mgl mutations in one culture and ptsG in the other. In both cases, mutators were enriched to constitute close to 100% of the population before a periodic selection event reduced the frequency of unselected mutations and mutators in the cultures. The high proportion of mutators persisted for 150 generations in one population but began to be eliminated within 50 generations in the other. The persistence of mutator, as well as experimental data showing that mutY bacteria were as fit as near-isogenic mutY(+) bacteria in competition experiments, suggest that mutator load by deleterious mutations did not explain the rapidly diminishing proportion of mutators in the populations. The nonmutators sweeping out mutators were also unlikely to have arisen by reversion or antimutator mutations; the mutY mutations were major deletions in each case and the bacteria sweeping out mutators contained intact mutY. By following mgl allele frequencies in one population, we discovered that mutators were outcompeted by bacteria that had rare mgl mutations previously as well as additional beneficial mutation(s). The pattern of appearance of mutY, but not its elimination, conforms to current models of mutator sweeps in bacterial populations. A mutator with a narrow mutational spectrum like mutY may be lost if the requirement for beneficial mutations is for changes other than GC --> TA transversions. Alternatively, epistatic interactions between mutator mutation and beneficial mutations need to be postulated to explain mutator elimination.     

The rate of adaptation in asexuals

I study the population genetics of adaptation in asexuals. I show that the rate of adaptive substitution in an asexual species or nonrecombining chromosome region is a bell-shaped function of the mutation rate: at some point, increasing the mutation rate decreases the rate of substitution. Curiously, the mutation rate that maximizes the rate of adaptation depends solely on the strength of selection against deleterious mutations. In particular, adaptation is fastest when the genomic rate of mutation, U, equals the harmonic mean of selection coefficients against deleterious mutations, where we assume that selection for favorable alleles is milder than that against deleterious ones. This simple result is independent of the shape of the distribution of effects among favorable and deleterious mutations, population size, and the action of clonal interference. In the course of this work, I derive an approximation to the probability of fixation of a favorable mutation in an asexual genome or nonrecombining chromosome region in which both favorable and deleterious mutations occur.     

Bypass of genetic constraints during mutator evolution to antibiotic resistance

Genetic constraints can block many mutational pathways to optimal genotypes in real fitness landscapes, yet the extent to which this can limit evolution remains to be determined. Interestingly, mutator bacteria elevate only specific types of mutations, and therefore could be very sensitive to genetic constraints. Testing this possibility is not only clinically relevant, but can also inform about the general impact of genetic constraints in adaptation. Here, we evolved 576 populations of two mutator and one wild-type Escherichia coli to doubling concentrations of the antibiotic cefotaxime. All strains carried TEM-1, a β-lactamase enzyme well known by its low availability of mutational pathways. Crucially, one of the mutators does not elevate any of the relevant first-step mutations known to improve cefatoximase activity. Despite this, both mutators displayed a similar ability to evolve more than 1000-fold resistance. Initial adaptation proceeded in parallel through general multi-drug resistance mechanisms. High-level resistance, in contrast, was achieved through divergent paths; with the a priori inferior mutator exploiting alternative mutational pathways in PBP3, the target of the antibiotic. These results have implications for mutator management in clinical infections and, more generally, illustrate that limits to natural selection in real organisms are alleviated by the existence of multiple loci contributing to fitness.     

Detection of mutator subpopulations in Salmonella typhimurium LT2 by reversion of his alleles

Defects in the methyl-directed mismatch repair lead to both the hypermutability phenotype and removal of a barrier to genetic exchange between species. Mutator bacteria carrying such defects occur frequently among bacterial pathogens, suggesting that subpopulations of mutators are contained within pathogen clones and give rise to the genetic variants that are acted upon by selective forces to allow survival or successful infection. We report here on the detection of the mutator subpopulation in Salmonella typhimurium and determination of its frequency in laboratory cultures. The analysis involved screening for mutators among revertants of S. typhimurium histidine auxotrophs selected for the His⁺ phenotype, since the frequency of mutators is expected to be increased in the selected mutant population they helped to spawn. The increases in spontaneous reversion of histidine mutations were first measured in isogenic strains carrying mismatch repair-defective mutH, mutL, mutS, or uvrD alleles, relative to their mismatch repair-proficient counterparts. Screening for the mutator phenotype in nearly 12,000 revertants of repair-proficient strains carrying his mutations highly stimulated for reversion in mutator backgrounds, the base substitution in hisG428 and frameshift in hisC3076, yielded five mutator strains (0.04%). the his⁺ reversion mutations contained within the newly-arisen mutator strains were characteristic of the predominant nucleotide changes expected in such mutators, as assessed by comparison with the spectra for reversion events in wild-type and mismatch correction-defective backgrounds. The results show that subpopulations of mutators, residing in normal populations at a finite frequency, can be culled from the culture by strong selection for a required phenotype. We calculate that the frequency of mutators in the unselected population of S. typhimurium is 1–4×10⁻⁶, an incidence of 10-fold lower than that expected based on studies of laboratory cultures of Escherichia coli.     

Ploidy controls the success of mutators and nature of mutations during budding yeast evolution

BACKGROUND: We used the budding yeast Saccharomyces cerevisiae to ask how elevated mutation rates affect the evolution of asexual eukaryotic populations. Mismatch repair defective and nonmutator strains were competed during adaptation to four laboratory environments (rich medium, low glucose, high salt, and a nonfermentable carbon source). RESULTS: In diploids, mutators have an advantage over nonmutators in all conditions, and mutators that win competitions are on average fitter than nonmutator winners. In contrast, haploid mutators have no advantage when competed against haploid nonmutators, and haploid mutator winners are less fit than nonmutator winners. The diploid mutator winners were all superior to their ancestors both in the condition they had adapted to, and in two of the other conditions. This phenotype was due to a mutation or class of mutations that confers a large growth advantage during the respiratory phase of yeast cultures that precedes stationary phase. This generalist mutation(s) was not selected in diploid nonmutator strains or in haploid strains, which adapt primarily by fixing specialist (condition-specific) mutations. In diploid mutators, such mutations also occur, and the majority accumulates after the fixation of the generalist mutation. CONCLUSIONS: We conclude that the advantage of mutators depends on ploidy and that diploid mutators can give rise to beneficial mutations that are inaccessible to nonmutators and haploid mutators.     

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.     

The population genetics of adaptation: the adaptation of DNA sequences

I describe several patterns characterizing the genetics of adaptation at the DNA level. Following Gillespie (1983, 1984, 1991), I consider a population presently fixed for the ith best allele at a locus and study the sequential substitution of favorable mutations that results in fixation of the fittest DNA sequence locally available. Given a wild type sequence that is less than optimal, I derive the fitness rank of the next allele typically fixed by natural selection as well as the mean and variance of the jump in fitness that results when natural selection drives a substitution. Looking over the whole series of substitutions required to reach the best allele, I show that the mean fitness jumps occurring throughout an adaptive walk are constrained to a twofold window of values, assuming only that adaptation begins from a reasonably fit allele. I also show that the first substitution and the substitution of largest effect account for a large share of the total fitness increase during adaptation. I further show that the distribution of selection coefficients fixed throughout such an adaptive walk is exponential (ignoring mutations of small effect), a finding reminiscent of that seen in Fisher's geometric model of adaptation. Last, I show that adaptation by natural selection behaves in several respects as the average of two idealized forms of adaptation, perfect and random.     

Dynamics of Adaptation During Three Years of Evolution Under Long-Term Stationary Phase

Many bacterial species that cannot sporulate, such as the model bacterium Escherichia coli, can nevertheless survive for years, following exhaustion of external resources, in a state termed long-term stationary phase (LTSP). Here we describe the dynamics of E. coli adaptation during the first three years spent under LTSP. We show that during this time, E. coli continuously adapts genetically through the accumulation of mutations. For nonmutator clones, the majority of mutations accumulated appear to be adaptive under LTSP, reflected in an extremely convergent pattern of mutation accumulation. Despite the rapid and convergent manner in which populations adapt under LTSP, they continue to harbor extensive genetic variation. The dynamics of evolution of mutation rates under LTSP are particularly interesting. The emergence of mutators affects overall mutation accumulation rates as well as the mutational spectra and the ultimate spectrum of adaptive alleles acquired under LTSP. With time, mutators can evolve even higher mutation rates through the acquisition of additional mutation rate–enhancing mutations. Different mutator and nonmutator clones within a single population and time point can display extreme variation in their mutation rates, resulting in differences in both the dynamics of adaptation and their associated deleterious burdens. Despite these differences, clones that vary greatly in their mutation rates tend to coexist within their populations for many years, under LTSP.