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.     

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.     

Mutators, population size, adaptive landscape and the adaptation of asexual populations of bacteria.

Selection of mutator alleles, increasing the mutation rate up to 10, 000-fold, has been observed during in vitro experimental evolution. This spread is ascribed to the hitchhiking of mutator alleles with favorable mutations, as demonstrated by a theoretical model using selective parameters corresponding to such experiments. Observations of unexpectedly high frequencies of mutators in natural isolates suggest that the same phenomenon could occur in the wild. But it remains questionable whether realistic in natura parameter values could also result in selection of mutators. In particular, the main parameters of adaptation, the size of the adapting population and the height and steepness of the adaptive peak characterizing adaptation, are very variable in nature. By simulation approach, we studied the effect of these parameters on the selection of mutators in asexual populations, assuming additive fitness. We show that the larger the population size, the more likely the fixation of mutator alleles. At a large population size, at least four adaptive mutations are needed for mutator fixation; moreover, under stronger selection stronger mutators are selected. We propose a model based on multiple mutations to illustrate how second-order selection can optimize population fitness when few favorable mutations are required for adaptation.     

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.     

The evolution of mutator genes in bacterial populations: the roles of environmental change and timing

Recent studies have found high frequencies of bacteria with increased genomic rates of mutation in both clinical and laboratory populations. These observations may seem surprising in light of earlier experimental and theoretical studies. Mutator genes (genes that elevate the genomic mutation rate) are likely to induce deleterious mutations and thus suffer an indirect selective disadvantage; at the same time, bacteria carrying them can increase in frequency only by generating beneficial mutations at other loci. When clones carrying mutator genes are rare, however, these beneficial mutations are far more likely to arise in members of the much larger nonmutator population. How then can mutators become prevalent? To address this question, we develop a model of the population dynamics of bacteria confronted with ever-changing environments. Using analytical and simulation procedures, we explore the process by which initially rare mutator alleles can rise in frequency. We demonstrate that subsequent to a shift in environmental conditions, there will be relatively long periods of time during which the mutator subpopulation can produce a beneficial mutation before the ancestral subpopulations are eliminated. If the beneficial mutation arises early enough, the overall frequency of mutators will climb to a point higher than when the process began. The probability of producing a subsequent beneficial mutation will then also increase. In this manner, mutators can increase in frequency over successive selective sweeps. We discuss the implications and predictions of these theoretical results in relation to antibiotic resistance and the evolution of mutation rates.     

The Fixation Probability of Rare Mutators in Finite Asexual Populations

A mutator is an allele that increases the mutation rate throughout the genome by disrupting some aspect of DNA replication or repair. Mutators that increase the mutation rate by the order of 100-fold have been observed to spontaneously emerge and achieve high frequencies in natural populations and in long-term laboratory evolution experiments with Escherichia coli. In principle, the fixation of mutator alleles is limited by (i) competition with mutations in wild-type backgrounds, (ii) additional deleterious mutational load, and (iii) random genetic drift. Using a multiple-locus model and employing both simulation and analytic methods, we investigate the effects of these three factors on the fixation probability P_fix of an initially rare mutator as a function of population size N, beneficial and deleterious mutation rates, and the strength of mutations s. Our diffusion-based approximation for P_fix successfully captures effects ii and iii when selection is fast compared to mutation (). This enables us to predict the conditions under which mutators will be evolutionarily favored. Surprisingly, our simulations show that effect i is typically small for strong-effect mutators. Our results agree semiquantitatively with existing laboratory evolution experiments and suggest future experimental directions.     

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.     

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.     

Interplay between Pleiotropy and Secondary Selection Determines Rise and Fall of Mutators in Stress Response

Mutators are clones whose mutation rate is about two to three orders of magnitude higher than the rate of wild-type clones and their roles in adaptive evolution of asexual populations have been controversial. Here we address this problem by using an ab initio microscopic model of living cells, which combines population genetics with a physically realistic presentation of protein stability and protein-protein interactions. The genome of model organisms encodes replication controlling genes (RCGs) and genes modeling the mismatch repair (MMR) complexes. The genotype-phenotype relationship posits that the replication rate of an organism is proportional to protein copy numbers of RCGs in their functional form and there is a production cost penalty for protein overexpression. The mutation rate depends linearly on the concentration of homodimers of MMR proteins. By simulating multiple runs of evolution of populations under various environmental stresses—stationary phase, starvation or temperature-jump—we find that adaptation most often occurs through transient fixation of a mutator phenotype, regardless of the nature of stress. By contrast, the fixation mechanism does depend on the nature of stress. In temperature jump stress, mutators take over the population due to loss of stability of MMR complexes. In contrast, in starvation and stationary phase stresses, a small number of mutators are supplied to the population via epigenetic stochastic noise in production of MMR proteins (a pleiotropic effect), and their net supply is higher due to reduced genetic drift in slowly growing populations under stressful environments. Subsequently, mutators in stationary phase or starvation hitchhike to fixation with a beneficial mutation in the RCGs, (second order selection) and finally a mutation stabilizing the MMR complex arrives, returning the population to a non-mutator phenotype. Our results provide microscopic insights into the rise and fall of mutators in adapting finite asexual populations.     

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.     

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

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

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.     

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.     

Competition between high- and higher-mutating strains of Escherichia coli

Experimental studies have shown that a mutator allele can readily hitchhike to fixation with beneficial mutations in an asexual population having a low, wild-type mutation rate. Here, we show that a genotype bearing two mutator alleles can supplant a population already fixed for one mutator allele. Our results provide experimental support for recent theory predicting that mutator alleles will tend to accumulate in asexual populations by hitchhiking with beneficial mutations, causing an ever-higher genomic mutation rate.     

The evolution of low mutation rates in experimental mutator populations of Saccharomyces cerevisiae

Mutation is the source of both beneficial adaptive variation and deleterious genetic load, fueling the opposing selective forces than shape mutation rate evolution. This dichotomy is well illustrated by the evolution of the mutator phenotype, a genome-wide 10- to 100-fold increase in mutation rate. This phenotype has often been observed in clonally expanding populations exposed to novel or frequently changing conditions. Although studies of both experimental and natural populations have shed light on the evolutionary forces that lead to the spread of the mutator allele through a population, significant gaps in our understanding of mutator evolution remain. Here we use an experimental evolution approach to investigate the conditions required for the evolution of a reduction in mutation rate and the mechanisms by which populations tolerate the accumulation of deleterious mutations. We find that after ～6,700 generations, four out of eight experimental mutator lines had evolved a decreased mutation rate. We provide evidence that the accumulation of deleterious mutations leads to selection for reduced mutation rate clones in populations of mutators. Finally, we test the long-term consequences of the mutator phenotype, finding that mutator lines follow different evolutionary trajectories, some of which lead to drug resistance.     

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.     

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.     

Rates of DNA sequence evolution in experimental populations of Escherichia coli during 20,000 generations

We examined rates of DNA sequence evolution in 12 populations of Escherichia coli propagated in a glucose minimal medium for 20,000 generations. Previous work saw mutations mediated by mobile elements in these populations, but the extent of other genomic changes was not investigated. Four of the populations evolved defects in DNA repair and became mutators. Some 500 bp was sequenced in each of 36 genes for 50 clones, including 2 ancestral variants, 2 clones from each population at generation 10,000, and 2 from each at generation 20,000. Ten mutations were found in total, all point mutations including mostly synonymous substitutions and nonsynonymous polymorphisms; all 10 were found in mutator populations. We compared the observed sequence evolution to predictions based on different scenarios. The number of synonymous substitutions is lower than predicted from measured mutation rates in E. coli, but the number is higher than rates based on comparing E. coli and Salmonella genomes. Extrapolating to the entire genome, these data predict about 250 synonymous substitutions on average per mutator population, but only about 3 synonymous substitutions per nonmutator population, during 20,000 generations. These data illustrate the challenge of finding sequence variation among bacterial isolates that share such a recent ancestor. However, this limited variation also provides a useful baseline for research aimed at finding the beneficial substitutions in these populations.     

Horizontal acquisition of divergent chromosomal DNA in bacteria: effects of mutator phenotypes

We examine the potential beneficial effects of the expanded access to environmental DNA offered by mutators on the adaptive potential of bacterial populations. Using parameters from published studies of recombination in E. coli, we find that the presence of mutators has the potential to greatly enhance bacterial population adaptation when compared to populations without mutators. In one specific example, for which three specific amino acid substitutions are required for adaptation to occur in a 300-amino-acid protein, we found a 3500-fold increase in the rate of adaptation. The probability of a beneficial acquisition decreased if more amino acid changes, or integration of longer DNA fragments, were required for adaptation. The model also predicts that mutators are more likely than nonmutator phenotypes to acquire genetic variability from a more diverged set of donor bacteria. Bacterial populations harboring mutators in a sequence heterogeneous environment are predicted to acquire most of their DNA conferring adaptation in the range of 13-30% divergence, whereas nonmutator phenotypes become adapted after recombining with more homogeneous sequences of 7-21% divergence. We conclude that mutators can accelerate bacterial adaptation when desired genetic variability is present within DNA fragments of up to approximately 30% divergence.