The balance between mutators and nonmutators in asexual populations

Direct and indirect selection in a proofreading polymerase

The traits that affect evolvability are subject to indirect selection, as these traits affect the course of evolution over many generations rather than the direct replicative fitness of an individual. However, the evolution of evolvability-determining traits is often difficult to study because putative evolvability alleles often have confounding direct fitness effects of unknown origin and size. Here, we study theoretically and experimentally the evolution of mutation rates in proofreading polymerases with orthogonal control of direct and indirect selection. Mutagenic DNA polymerases enjoy a long-time fitness advantage by enhancing the rate of acquiring beneficial mutations. However, this is offset by a short-time fitness penalty, which we trace to a counterintuitive trade-off between mutation rates and activity in proofreading polymerases. Since these fitness effects act on different timescales, no one number characterizes the fitness of a mutator allele. We find unusual dynamic features in the resulting evolutionary dynamics, such as kinetic exclusion, selection by dynamic environments, and Rock-Paper-Scissors dynamics in the absence of ecology. Our work has implications for the evolution of mutation rates and more broadly, evolution in the context of an anti-correlation between mutation rates and short term fitness.

Phenotype switching of the mutation rate facilitates adaptive evolution

The mutation rate plays an important role in adaptive evolution. It can be modified by mutator and anti-mutator alleles. Recent empirical evidence hints that the mutation rate may vary among genetically identical individuals: evidence from bacteria suggests that the mutation rate can be affected by expression noise of a DNA repair protein and potentially also by translation errors in various proteins. Importantly, this non-genetic variation may be heritable via a transgenerational epigenetic mode of inheritance, giving rise to a mutator phenotype that is independent from mutator alleles. Here, we investigate mathematically how the rate of adaptive evolution is affected by the rate of mutation rate phenotype switching. We model an asexual population with two mutation rate phenotypes, non-mutator and mutator. An offspring may switch from its parental phenotype to the other phenotype. We find that switching rates that correspond to so-far empirically described non-genetic systems of inheritance of the mutation rate lead to higher rates of adaptation on both artificial and natural fitness landscapes. These switching rates can maintain within the same individuals both a mutator phenotype and intermediary mutations, a combination that facilitates adaptation. Moreover, non-genetic inheritance increases the proportion of mutators in the population, which in turn increases the probability of hitchhiking of the mutator phenotype with adaptive mutations. This in turns facilitates the acquisition of additional adaptive mutations. Our results rationalize recently observed noise in the expression of proteins that affect the mutation rate and suggest that non-genetic inheritance of this phenotype may facilitate evolutionary adaptive processes.

Evolutionary action of mutations reveals antimicrobial resistance genes in Escherichia coli

Since antibiotic development lags, we search for potential drug targets through directed evolution experiments. A challenge is that many resistance genes hide in a noisy mutational background as mutator clones emerge in the adaptive population. Here, to overcome this noise, we quantify the impact of mutations through evolutionary action (EA). After sequencing ciprofloxacin or colistin resistance strains grown under different mutational regimes, we find that an elevated sum of the evolutionary action of mutations in a gene identifies known resistance drivers. This EA integration approach also suggests new antibiotic resistance genes which are then shown to provide a fitness advantage in competition experiments. Moreover, EA integration analysis of clinical and environmental isolates of antibiotic resistant of E. coli identifies gene drivers of resistance where a standard approach fails. Together these results inform the genetic basis of de novo colistin resistance and support the robust discovery of phenotype-driving genes via the evolutionary action of genetic perturbations in fitness landscapes.

Evolutionary Significance of Fungal Hypermutators: Lessons Learned from Clinical Strains and Implications for Fungal Plant Pathogens

Rapid evolution of fungal pathogens poses a serious threat to medicine and agriculture. The mutation rate determines the pace of evolution of a fungal pathogen. Hypermutator fungal strains have an elevated mutation rate owing to certain defects such as those in the DNA mismatch repair system. Studies in Saccharomyces cerevisiae show that hypermutators expedite evolution by generating beneficial alleles at a faster pace than the wild-type strains. However, an accumulation of deleterious alleles in a hypermutator may reduce its fitness. The balance between fitness cost and mutation benefit determines the prevalence of hypermutators in a population. This balance is affected by a complex interaction of ploidy, mode of reproduction, population size, and recent population history. Studies in human fungal pathogens like Aspergillus fumigatus, Candida albicans, Candida glabrata, Cryptococcus deuterogattii, and Cryptococcus neoformans have highlighted the importance of hypermutators in host adaptation and development of antifungal resistance. However, a critical examination of hypermutator biology, experimental evolution studies, and epidemiological studies suggests that hypermutators may impact evolutionary investigations. This review aims to integrate the knowledge about biology, experimental evolution, and dynamics of fungal hypermutators to critically examine the evolutionary role of hypermutators in fungal pathogen populations and project implications of hypermutators in the evolution of fungal plant pathogen populations. Understanding the factors determining the emergence and evolution of fungal hypermutators can open a novel avenue of managing rapidly evolving fungal pathogens in medicine and agriculture.

Weak mixed phase in the mutator model

We consider the mutator model with unidirected transitions from the wild type to the mutator type, with different fitness functions for the wild types and mutator types. We calculate both the fraction of mutator types in the population and the surpluses, i.e., the mean number of mutations in the regular part of genomes for the wild type and mutator type, which have never been derived exactly. We identify the phase structure. Beside the mixed (ordinary evolution phase with finite fraction of wild types at large genome length) and the mutator phase (the absolute majority is mutators), we find another new phase as well-it has the mean fitness of the mixed phase but an exponentially small (in genome length) fraction of wild types. We identify the phase transition point and discuss its implications.

A percolation model of natural selection

A new approach has been proposed and developed: the selection of optimal variants in the evolutionary mutation flow is considered as an analogue of a percolation filter. Interaction of mutations in a series of generations and random processes of drift determine the collective behavior of nodes (individuals - carriers and converters of mutations) and bonds (mutations) in the space of percolation lattice. It is shown that the choice of the development trajectory at the population level depends on the spectrum of supporting and prohibiting mutations under the influence of conjugate deterministic and random factors. From the point of view of the fluctuation-bifurcation process, new concepts of the lower and upper thresholds of the percolation selection grid are defined in the hierarchical structure of speciation. The upper threshold determines the state of self-organized criticality, which, when overcome, leads to irreversible self-organization processes in the population caused by the accumulation of mutations.

Epigenetic switching as a strategy for quick adaptation while attenuating biochemical noise

Epigenetic switches are bistable, molecular systems built from self-reinforcing feedback loops that can spontaneously switch between heritable phenotypes in the absence of DNA mutation. It has been hypothesized that epigenetic switches first evolved as a mechanism of bet-hedging and adaptation, but the evolutionary trajectories and conditions by which an epigenetic switch can outcompete adaptation through genetic mutation remain unknown. Here, we used computer simulations to evolve a mechanistic, biophysical model of a self-activating genetic circuit, which can both adapt genetically through mutation and exhibit epigenetic switching. We evolved these genetic circuits under a fluctuating environment that alternatively selected for low and high protein expression levels. In all tested conditions, the population first evolved by genetic mutation towards a region of genotypes where genetic adaptation can occur faster after each environmental transition. Once in this region, the self-activating genetic circuit can exhibit epigenetic switching, which starts competing with genetic adaptation. We show a trade-off between either minimizing the adaptation time or increasing the robustness of the phenotype to biochemical noise. Epigenetic switching was superior in a fast fluctuating environment because it adapted faster than genetic mutation after an environmental transition, while still attenuating the effect of biochemical noise on the phenotype. Conversely, genetic adaptation was favored in a slowly fluctuating environment because it maximized the phenotypic robustness to biochemical noise during the constant environment between transitions, even if this resulted in slower adaptation. This simple trade-off predicts the conditions and trajectories under which an epigenetic switch evolved to outcompete genetic adaptation, shedding light on possible mechanisms by which bet-hedging strategies might emerge and persist in natural populations.

Epigenetic switches regulate cell fate decisions during development in multicellular organisms, but their origin predates multicellularity because they are found in viruses, bacteria, and unicellular eukaryotes. It has been suggested that epigenetic switches first evolved as a mechanism of bet-hedging and adaptation to fluctuating environments. To discern the evolutionary pressures that select for epigenetic switches, we used computer simulations to evolve a mechanistic, biophysical model of a self-activating genetic circuit, which can both adapt genetically and exhibit epigenetic switching. Unlike laboratory evolution experiments, this in silico experiment was run many times over a range of evolutionary parameters (population size, selection pressure, mutation step-size, fluctuation frequency) and different model assumptions to uncover statistical regularities in the evolutionary trajectories. Using this computational approach, we could elucidate simple principles that predict the conditions that favor adaptation by epigenetic switching over genetic mutation in a fluctuating environment.

The fitness cost of mismatch repair mutators in Saccharomyces cerevisiae: partitioning the mutational load

Mutational load is the depression in a population's mean fitness that results from the continual influx of deleterious mutations. Here, we directly estimate the mutational load in a population of haploid Saccharomyces cerevisiae that are deficient for mismatch repair. We partition the load in haploids into two components. To estimate the load due to nonlethal mutations, we measure the competitive fitness of hundreds of randomly selected clones from both mismatch-repair-deficient and -proficient populations. Computation of the mean clone fitness for the mismatch-repair-deficient strain permits an estimation of the nonlethal load, and the histogram of fitness provides an interesting visualization of a loaded population. In a separate experiment, in order to estimate the load due to lethal mutations (i.e. the lethal mutation rate), we manipulate thousands of individual pairs of mother and daughter cells and track their fates. These two approaches yield point estimates for the two contributors to load, and the addition of these estimates is nearly equal to the separately measured short-term competitive fitness deficit for the mismatch-repair-deficient strain. This correspondence suggests that there is no need to invoke direct fitness effects to explain the fitness difference between mismatch-repair-deficient and -proficient strains. Assays in diploids are consistent with deleterious mutations in diploids tending towards recessivity. These results enhance our understanding of mutational load, a central population genetics concept, and we discuss their implications for the evolution of mutation rates.

Evolution of Stress-Induced Mutagenesis in the Presence of Horizontal Gene Transfer

Stress-induced mutagenesis has been observed in multiple species of bacteria and yeast. It has been suggested that in asexual populations, a mutator allele that increases the mutation rate during stress can sweep to fixation with the beneficial mutations it generates. However, even asexual microbes can undergo horizontal gene transfer and rare recombination, which typically interfere with the spread of mutator alleles. Here we examine the effect of horizontal gene transfer on the evolutionary advantage of stress-induced mutator alleles. Our results demonstrate that stress-induced mutator alleles are favored by selection even in the presence of horizontal gene transfer and more so when the mutator alleles also increase the rate of horizontal gene transfer. We suggest that when regulated by stress, mutation and horizontal gene transfer can be complementary rather than competing adaptive strategies and that stress-induced mutagenesis has important implications for evolutionary biology, ecology, and epidemiology, even in the presence of horizontal gene transfer and rare recombination.

MetaSMC: a coalescent-based shotgun sequence simulator for evolving microbial populations

MOTIVATION

High-throughput sequencing technology has revolutionized the study of metagenomics and cancer evolution. In a relatively simple environment, a metagenomics sequencing data is dominated by a few species. By analyzing the alignment of reads from microbial species, single nucleotide polymorphisms can be discovered and the evolutionary history of the populations can be reconstructed. The ever-increasing read length will allow more detailed analysis about the evolutionary history of microbial or tumor cell population. A simulator of shotgun sequences from such populations will be helpful in the development or evaluation of analysis algorithms.

RESULTS

Here, we described an efficient algorithm, MetaSMC, which simulates reads from evolving microbial populations. Based on the coalescent theory, our simulator supports all evolutionary scenarios supported by other coalescent simulators. In addition, the simulator supports various substitution models, including Jukes-Cantor, HKY85 and generalized time-reversible models. The simulator also supports mutator phenotypes by allowing different mutation rates and substitution models in different subpopulations. Our algorithm ignores unnecessary chromosomal segments and thus is more efficient than standard coalescent when recombination is frequent. We showed that the process behind our algorithm is equivalent to Sequentially Markov Coalescent with an incomplete sample. The accuracy of our algorithm was evaluated by summary statistics and likelihood curves derived from Monte Carlo integration over large number of random genealogies.

AVAILABILITY AND IMPLEMENTATION

MetaSMC is written in C. The source code is available at https://github.com/tarjxvf/metasmc.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

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.

Population size changes and selection drive patterns of parallel evolution in a host-virus system

Predicting the repeatability of evolution remains elusive. Theory and empirical studies suggest that strong selection and large population sizes increase the probability for parallel evolution at the phenotypic and genotypic levels. However, selection and population sizes are not constant, but rather change continuously and directly affect each other even on short time scales. Here, we examine the degree of parallel evolution shaped through eco-evolutionary dynamics in an algal host population coevolving with a virus. We find high degrees of parallelism at the level of population size changes (ecology) and at the phenotypic level between replicated populations. At the genomic level, we find evidence for parallelism, as the same large genomic region was duplicated in all replicated populations, but also substantial novel sequence divergence between replicates. These patterns of genome evolution can be explained by considering population size changes as an important driver of rapid evolution.

High mutation rates limit evolutionary adaptation in Escherichia coli

Mutation is fundamental to evolution, because it generates the genetic variation on which selection can act. In nature, genetic changes often increase the mutation rate in systems that range from viruses and bacteria to human tumors. Such an increase promotes the accumulation of frequent deleterious or neutral alleles, but it can also increase the chances that a population acquires rare beneficial alleles. Here, we study how up to 100-fold increases in Escherichia coli's genomic mutation rate affect adaptive evolution. To do so, we evolved multiple replicate populations of asexual E. coli strains engineered to have four different mutation rates for 3000 generations in the laboratory. We measured the ability of evolved populations to grow in their original environment and in more than 90 novel chemical environments. In addition, we subjected the populations to whole genome population sequencing. Although populations with higher mutation rates accumulated greater genetic diversity, this diversity conveyed benefits only for modestly increased mutation rates, where populations adapted faster and also thrived better than their ancestors in some novel environments. In contrast, some populations at the highest mutation rates showed reduced adaptation during evolution, and failed to thrive in all of the 90 alternative environments. In addition, they experienced a dramatic decrease in mutation rate. Our work demonstrates that the mutation rate changes the global balance between deleterious and beneficial mutational effects on fitness. In contrast to most theoretical models, our experiments suggest that this tipping point already occurs at the modest mutation rates that are found in the wild.

Beneficial mutation-selection dynamics in finite asexual populations: a free boundary approach

Using a free boundary approach based on an analogy with ice melting models, we propose a deterministic PDE framework to describe the dynamics of fitness distributions in the presence of beneficial mutations with non-epistatic effects on fitness. Contrarily to most approaches based on deterministic models, our framework does not rely on an infinite population size assumption, and successfully captures the transient as well as the long time dynamics of fitness distributions. In particular, consistently with stochastic individual-based approaches or stochastic PDE approaches, it leads to a constant asymptotic rate of adaptation at large times, that most deterministic approaches failed to describe. We derive analytic formulas for the asymptotic rate of adaptation and the full asymptotic distribution of fitness. These formulas depend explicitly on the population size, and are shown to be accurate for a wide range of population sizes and mutation rates, compared to individual-based simulations. Although we were not able to derive an analytic description for the transient dynamics, numerical computations lead to accurate predictions and are computationally efficient compared to stochastic simulations. These computations show that the fitness distribution converges towards a travelling wave with constant speed, and whose profile can be computed analytically.

Fixation probability of a nonmutator in a large population of asexual mutators

In an adapted population of mutators in which most mutations are deleterious, a nonmutator that lowers the mutation rate is under indirect selection and can sweep to fixation. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large population of asexual mutators. We show that when beneficial mutations are absent, the fixation probability is a nonmonotonic function of the mutation rate of the mutator: it first increases sublinearly and then decreases exponentially. We also find that beneficial mutations can enhance the fixation probability of a nonmutator. Our analysis is relevant to an understanding of recent experiments in which a reduction in the mutation rates has been observed.

Adaptive tuning of mutation rates allows fast response to lethal stress in Escherichia coli

While specific mutations allow organisms to adapt to stressful environments, most changes in an organism's DNA negatively impact fitness. The mutation rate is therefore strictly regulated and often considered a slowly-evolving parameter. In contrast, we demonstrate an unexpected flexibility in cellular mutation rates as a response to changes in selective pressure. We show that hypermutation independently evolves when different Escherichia coli cultures adapt to high ethanol stress. Furthermore, hypermutator states are transitory and repeatedly alternate with decreases in mutation rate. Specifically, population mutation rates rise when cells experience higher stress and decline again once cells are adapted. Interestingly, we identified cellular mortality as the major force driving the quick evolution of mutation rates. Together, these findings show how organisms balance robustness and evolvability and help explain the prevalence of hypermutation in various settings, ranging from emergence of antibiotic resistance in microbes to cancer relapses upon chemotherapy.

Population Heterogeneity in Mutation Rate Increases the Frequency of Higher-Order Mutants and Reduces Long-Term Mutational Load

Mutation rate is a crucial evolutionary parameter that has typically been treated as a constant in population genetic analyses. However, the propensity to mutate is likely to vary among co-existing individuals within a population, due to genetic polymorphisms, heterogeneous environmental influences, and random physiological fluctuations. We review the evidence for mutation rate heterogeneity and explore its consequences by extending classic population genetic models to allow an arbitrary distribution of mutation rate among individuals, either with or without inheritance. With this general new framework, we rigorously establish the effects of heterogeneity at various evolutionary timescales. In a single generation, variation of mutation rate about the mean increases the probability of producing zero or many simultaneous mutations on a genome. Over multiple generations of mutation and selection, heterogeneity accelerates the appearance of both deleterious and beneficial multi-point mutants. At mutation-selection balance, higher-order mutant frequencies are likewise boosted, while lower-order mutants exhibit subtler effects; nonetheless, population mean fitness is always enhanced. We quantify the dependencies on moments of the mutation rate distribution and selection coefficients, and clarify the role of mutation rate inheritance. While typical methods of estimating mutation rate will recover only the population mean, analyses assuming mutation rate is fixed to this mean could underestimate the potential for multi-locus adaptation, including medically relevant evolution in pathogenic and cancerous populations. We discuss the potential to empirically parameterize mutation rate distributions, which have to date hardly been quantified.

Limiting fitness distributions in evolutionary dynamics

Natural selection works on variation in fitness, but how should we measure "variation" to predict the rate of future evolution? Fisher's fundamental theorem of natural selection provides the short-run answer: the instantaneous rate of growth of a population's mean fitness is its variance in fitness. This identity captures an important feature of the evolutionary process, but, because it does not specify how the variance itself evolves in time, it cannot be used to predict evolutionary dynamics in the long run. In this paper we reconsider the problem of computing evolutionary trajectories from limited statistical information. We identify the feature of fitness distributions which controls their late-time evolution: their (suitably defined) tail indices. We show that the location, scale and shape of the fitness distribution can be predicted far into the future from the measurement of this tail index at some initial time. Unlike the "fitness waves" studied in the literature, this pattern encompasses both positive and negative selection and is not restricted to rapidly adapting populations. Our results are well supported by numerical simulations, both from the Wright-Fisher model and from a less structured genetic algorithm.

The Nonstationary Dynamics of Fitness Distributions: Asexual Model with Epistasis and Standing Variation

Various models describe asexual evolution by mutation, selection, and drift. Some focus directly on fitness, typically modeling drift but ignoring or simplifying both epistasis and the distribution of mutation effects (traveling wave models). Others follow the dynamics of quantitative traits determining fitness (Fisher's geometric model), imposing a complex but fixed form of mutation effects and epistasis, and often ignoring drift. In all cases, predictions are typically obtained in high or low mutation rate limits and for long-term stationary regimes, thus losing information on transient behaviors and the effect of initial conditions. Here, we connect fitness-based and trait-based models into a single framework, and seek explicit solutions even away from stationarity. The expected fitness distribution is followed over time via its cumulant generating function, using a deterministic approximation that neglects drift. In several cases, explicit trajectories for the full fitness distribution are obtained for arbitrary mutation rates and standing variance. For nonepistatic mutations, especially with beneficial mutations, this approximation fails over the long term but captures the early dynamics, thus complementing stationary stochastic predictions. The approximation also handles several diminishing returns epistasis models (e.g., with an optimal genotype); it can be applied at and away from equilibrium. General results arise at equilibrium, where fitness distributions display a "phase transition" with mutation rate. Beyond this phase transition, in Fisher's geometric model, the full trajectory of fitness and trait distributions takes a simple form; robust to the details of the mutant phenotype distribution. Analytical arguments are explored regarding why and when the deterministic approximation applies.

Role of epistasis on the fixation probability of a non-mutator in an adapted asexual population

The mutation rate of a well adapted population is prone to reduction so as to have a lower mutational load. We aim to understand the role of epistatic interactions between the fitness affecting mutations in this process. Using a multitype branching process, the fixation probability of a single non-mutator emerging in a large asexual mutator population is analytically calculated here. The mutator population undergoes deleterious mutations at constant, but at a much higher rate than that of the non-mutator. We find that antagonistic epistasis lowers the chances of mutation rate reduction, while synergistic epistasis enhances it. Below a critical value of epistasis, the fixation probability behaves non-monotonically with variation in the mutation rate of the background population. Moreover, the variation of this critical value of the epistasis parameter with the strength of the mutator is discussed in the appendix. For synergistic epistasis, when selection is varied, the fixation probability reduces overall, with damped oscillations.

The rich phase structure of a mutator model

We propose a modification of the Crow-Kimura and Eigen models of biological molecular evolution to include a mutator gene that causes both an increase in the mutation rate and a change in the fitness landscape. This mutator effect relates to a wide range of biomedical problems. There are three possible phases: mutator phase, mixed phase and non-selective phase. We calculate the phase structure, the mean fitness and the fraction of the mutator allele in the population, which can be applied to describe cancer development and RNA viruses. We find that depending on the genome length, either the normal or the mutator allele dominates in the mixed phase. We analytically solve the model for a general fitness function. We conclude that the random fitness landscape is an appropriate choice for describing the observed mutator phenomenon in the case of a small fraction of mutators. It is shown that the increase in the mutation rates in the regular and the mutator parts of the genome should be set independently; only some combinations of these increases can push the complex biomedical system to the non-selective phase, potentially related to the eradication of tumors.

Evolution of Mutation Rates in Rapidly Adapting Asexual Populations

Mutator and antimutator alleles often arise and spread in both natural microbial populations and laboratory evolution experiments. The evolutionary dynamics of these mutation rate modifiers are determined by indirect selection on linked beneficial and deleterious mutations. These indirect selection pressures have been the focus of much earlier theoretical and empirical work, but we still have a limited analytical understanding of how the interplay between hitchhiking and deleterious load influences the fates of modifier alleles. Our understanding is particularly limited when clonal interference is common, which is the regime of primary interest in laboratory microbial evolution experiments. Here, we calculate the fixation probability of a mutator or antimutator allele in a rapidly adapting asexual population, and we show how this quantity depends on the population size, the beneficial and deleterious mutation rates, and the strength of a typical driver mutation. In the absence of deleterious mutations, we find that clonal interference enhances the fixation probability of mutators, even as they provide a diminishing benefit to the overall rate of adaptation. When deleterious mutations are included, natural selection pushes the population toward a stable mutation rate that can be suboptimal for the adaptation of the population as a whole. The approach to this stable mutation rate is not necessarily monotonic: even in the absence of epistasis, selection can favor mutator and antimutator alleles that "overshoot" the stable mutation rate by substantial amounts.

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.

DNA Repair Is Associated with Information Content in Bacteria, Archaea, and DNA Viruses

The concept of a "proteomic constraint" proposes that DNA repair capacity is positively correlated with the information content of a genome, which can be approximated to the size of the proteome (P). This in turn implies that DNA repair genes are more likely to be present in genomes with larger values of P. This stands in contrast to the common assumption that informational genes have a core function and so are evenly distributed across organisms. We examined the presence/absence of 18 DNA repair genes in bacterial genomes. A positive relationship between gene presence and P was observed for 17 genes in the total dataset, and 16 genes when only nonintracellular bacteria were examined. A marked reduction of DNA repair genes was observed in intracellular bacteria, consistent with their reduced value of P. We also examined archaeal and DNA virus genomes, and show that the presence of DNA repair genes is likewise related to a larger value of P. In addition, the products of the bacterial genes mutY, vsr, and ndk, involved in the correction of GC/AT mutations, are strongly associated with reduced genome GC content. We therefore propose that a reduction in information content leads to a loss of DNA repair genes and indirectly to a reduction in genome GC content in bacteria by exposure to the underlying AT mutation bias. The reduction in P may also indirectly lead to the increase in substitution rates observed in intracellular bacteria via loss of DNA repair genes.

Molecular Clock of Neutral Mutations in a Fitness-Increasing Evolutionary Process

The molecular clock of neutral mutations, which represents linear mutation fixation over generations, is theoretically explained by genetic drift in fitness-steady evolution or hitchhiking in adaptive evolution. The present study is the first experimental demonstration for the molecular clock of neutral mutations in a fitness-increasing evolutionary process. The dynamics of genome mutation fixation in the thermal adaptive evolution of Escherichia coli were evaluated in a prolonged evolution experiment in duplicated lineages. The cells from the continuously fitness-increasing evolutionary process were subjected to genome sequencing and analyzed at both the population and single-colony levels. Although the dynamics of genome mutation fixation were complicated by the combination of the stochastic appearance of adaptive mutations and clonal interference, the mutation fixation in the population was simply linear over generations. Each genome in the population accumulated 1.6 synonymous and 3.1 non-synonymous neutral mutations, on average, by the spontaneous mutation accumulation rate, while only a single genome in the population occasionally acquired an adaptive mutation. The neutral mutations that preexisted on the single genome hitchhiked on the domination of the adaptive mutation. The successive fixation processes of the 128 mutations demonstrated that hitchhiking and not genetic drift were responsible for the coincidence of the spontaneous mutation accumulation rate in the genome with the fixation rate of neutral mutations in the population. The molecular clock of neutral mutations to the fitness-increasing evolution suggests that the numerous neutral mutations observed in molecular phylogenetic trees may not always have been fixed in fitness-steady evolution but in adaptive evolution.

Mutations that have little influence on biological function are referred to as neutral mutations and frequently appear in molecular phylogenetic analyses. The fixation of neutral mutations in populations has been attributed to genetic drift in fitness-steady evolutionary processes or hitchhiking in adaptive evolution. We examined the fitness-increasing evolution of Escherichia coli for thermal adaptation to observe the fixation dynamics of genome-wide mutations. In the adaptive evolution, all genomes in the population equally accumulated neutral mutations by replication errors. The infrequent occurrence of an adaptive mutation on one of the genomes by chance resulted in the fixation of the neutral mutations that had pre-accumulated in the same genome by hitchhiking. Via successive hitchhiking events, the neutral mutations were fixed in the population linearly over generations at the same rate as the spontaneous mutation accumulation rate in the genome. The molecular clock of neutral mutations thus functions even in adaptive evolution. The evolutionary period characterized by the accumulation of numerous neutral mutations observed in molecular phylogenetic trees may not be specific to neutral evolution but may occur in adaptive evolution as well.

Non-equilibrium physics and evolution--adaptation, extinction, and ecology: a key issues review

Evolutionary dynamics in nature constitute an immensely complex non-equilibrium process. We review the application of physical models of evolution, by focusing on adaptation, extinction, and ecology. In each case, we examine key concepts by working through examples. Adaptation is discussed in the context of bacterial evolution, with a view toward the relationship between growth rates, mutation rates, selection strength, and environmental changes. Extinction dynamics for an isolated population are reviewed, with emphasis on the relation between timescales of extinction, population size, and temporally correlated noise. Ecological models are discussed by focusing on the effect of spatial interspecies interactions on diversity. Connections between physical processes--such as diffusion, turbulence, and localization--and evolutionary phenomena are highlighted.

Deleterious passengers in adapting populations

Most new mutations are deleterious and are eventually eliminated by natural selection. But in an adapting population, the rapid amplification of beneficial mutations can hinder the removal of deleterious variants in nearby regions of the genome, altering the patterns of sequence evolution. Here, we analyze the interactions between beneficial "driver" mutations and linked deleterious "passengers" during the course of adaptation. We derive analytical expressions for the substitution rate of a deleterious mutation as a function of its fitness cost, as well as the reduction in the beneficial substitution rate due to the genetic load of the passengers. We find that the fate of each deleterious mutation varies dramatically with the rate and spectrum of beneficial mutations and the deleterious substitution rate depends nonmonotonically on the population size and the rate of adaptation. By quantifying this dependence, our results allow us to estimate which deleterious mutations will be likely to fix and how many of these mutations must arise before the progress of adaptation is significantly reduced.

Ex uno plures: clonal reinforcement drives evolution of a simple microbial community

A major goal of genetics is to define the relationship between phenotype and genotype, while a major goal of ecology is to identify the rules that govern community assembly. Achieving these goals by analyzing natural systems can be difficult, as selective pressures create dynamic fitness landscapes that vary in both space and time. Laboratory experimental evolution offers the benefit of controlling variables that shape fitness landscapes, helping to achieve both goals. We previously showed that a clonal population of E. coli experimentally evolved under continuous glucose limitation gives rise to a genetically diverse community consisting of one clone, CV103, that best scavenges but incompletely utilizes the limiting resource, and others, CV101 and CV116, that consume its overflow metabolites. Because this community can be disassembled and reassembled, and involves cooperative interactions that are stable over time, its genetic diversity is sustained by clonal reinforcement rather than by clonal interference. To understand the genetic factors that produce this outcome, and to illuminate the community's underlying physiology, we sequenced the genomes of ancestral and evolved clones. We identified ancestral mutations in intermediary metabolism that may have predisposed the evolution of metabolic interdependence. Phylogenetic reconstruction indicates that the lineages that gave rise to this community diverged early, as CV103 shares only one Single Nucleotide Polymorphism with the other evolved clones. Underlying CV103's phenotype we identified a set of mutations that likely enhance glucose scavenging and maintain redox balance, but may do so at the expense of carbon excreted in overflow metabolites. Because these overflow metabolites serve as growth substrates that are differentially accessible to the other community members, and because the scavenging lineage shares only one SNP with these other clones, we conclude that this lineage likely served as an “engine” generating diversity by creating new metabolic niches, but not the occupants themselves.

The variability of natural systems makes it difficult to deduce how organisms' genotypes manifest as phenotypes, and how communities of interacting organisms arise. Using laboratory experimental evolution we can control this variation. We previously showed that a population of E. coli that originated from a single clone and was cultured in the presence of a single limiting resource, evolves into a stable, three-membered community, wherein one clone excretes metabolites that the others utilize as carbon sources. To discern the genetic factors at work in producing this outcome and to illuminate the community's physiology, we sequenced the genomes of the ancestral and evolved clones. We identified in the ancestor mutations that may have predisposed evolution of cross-feeding. We found that the lineages which gave rise to the community diverged early on, and that the numerically dominant lineage that best scavenges limiting glucose does so as a result of adaptive mutations that enhance glucose uptake but favor fermentative over respiratory pathways, resulting in overflow metabolites. Because this clone produces secondary resources that sustain other community members, and because it shares with them only one mutation, we conclude that it is an “engine” generating diversity by creating new niches, but not the occupants themselves.

Experimental evolution and the dynamics of genomic mutation rate modifiers

Because genes that affect mutation rates are themselves subject to mutation, mutation rates can be influenced by natural selection and other evolutionary forces. The population genetics of mutation rate modifier alleles has been a subject of theoretical interest for many decades. Here, we review experimental contributions to our understanding of mutation rate modifier dynamics. Numerous evolution experiments have shown that mutator alleles (modifiers that elevate the genomic mutation rate) can readily rise to high frequencies via genetic hitchhiking in non-recombining microbial populations. Whereas these results certainly provide an explanatory framework for observations of sporadically high mutation rates in pathogenic microbes and in cancer lineages, it is nonetheless true that most natural populations have very low mutation rates. This raises the interesting question of how mutator hitchhiking is suppressed or its phenotypic effect reversed in natural populations. Very little experimental work has addressed this question; with this in mind, we identify some promising areas for future experimental investigation.

Frequency-dependent selection can lead to evolution of high mutation rates

Theoretical and experimental studies have shown that high mutation rates can be advantageous, especially in novel or fluctuating environments. Here we examine how frequency-dependent competition may lead to fluctuations in trait frequencies that exert upward selective pressure on mutation rates. We use a mathematical model to show that cyclical trait dynamics generated by "rock-paper-scissors" competition can cause the mutation rate in a population to converge to a high evolutionarily stable mutation rate, reflecting a trade-off between generating novelty and reproducing past success. Introducing recombination lowers the evolutionarily stable mutation rate but allows stable coexistence between mutation rates above and below the evolutionarily stable rate. Even considering strong mutational load and ignoring the costs of faithful replication, evolution favors positive mutation rates if the selective advantage of prevailing in competition exceeds the ratio of recombining to nonrecombining offspring. We discuss a number of genomic mechanisms that may meet our theoretical requirements for the adaptive evolution of mutation. Overall, our results suggest that local mutation rates may be higher on genes influencing cyclical competition and that global mutation rates in asexual species may be higher in populations subject to strong cyclical competition.

The advantage of arriving first: characteristic times in finite size populations of error-prone replicators

We study the evolution of a finite size population formed by mutationally isolated lineages of error-prone replicators in a two-peak fitness landscape. Computer simulations are performed to gain a stochastic description of the system dynamics. More specifically, for different population sizes, we compute the probability of each lineage being selected in terms of their mutation rates and the amplification factors of the fittest phenotypes. We interpret the results as the compromise between the characteristic time a lineage takes to reach its fittest phenotype by crossing the neutral valley and the selective value of the sequences that form the lineages. A main conclusion is drawn: for finite population sizes, the survival probability of the lineage that arrives first to the fittest phenotype rises significantly.

The evolution of bacterial mutation rates under simultaneous selection by interspecific and social parasitism

Many bacterial populations harbour substantial numbers of hypermutable bacteria, in spite of hypermutation being associated with deleterious mutations. One reason for the persistence of hypermutators is the provision of novel mutations, enabling rapid adaptation to continually changing environments, for example coevolving virulent parasites. However, hypermutation also increases the rate at which intraspecific parasites (social cheats) are generated. Interspecific and intraspecific parasitism are therefore likely to impose conflicting selection pressure on mutation rate. Here, we combine theory and experiments to investigate how simultaneous selection from inter- and intraspecific parasitism affects the evolution of bacterial mutation rates in the plant-colonizing bacterium Pseudomonas fluorescens. Both our theoretical and experimental results suggest that phage presence increases and selection for public goods cooperation (the production of iron-scavenging siderophores) decreases selection for mutator bacteria. Moreover, phages imposed a much greater growth cost than social cheating, and when both selection pressures were imposed simultaneously, selection for cooperation did not affect mutation rate evolution. Given the ubiquity of infectious phages in the natural environment and clinical infections, our results suggest that phages are likely to be more important than social interactions in determining mutation rate evolution.

Genome dynamics during experimental evolution

Evolutionary changes in organismal traits may occur either gradually or suddenly. However, until recently, there has been little direct information about how phenotypic changes are related to the rate and the nature of the underlying genotypic changes. Technological advances that facilitate whole-genome and whole-population sequencing, coupled with experiments that 'watch' evolution in action, have brought new precision to and insights into studies of mutation rates and genome evolution. In this Review, we discuss the evolutionary forces and ecological processes that govern genome dynamics in various laboratory systems in the context of relevant population genetic theory, and we relate these findings to evolution in natural populations.

Normal mutation rate variants arise in a Mutator (Mut S) Escherichia coli population

The rate at which mutations are generated is central to the pace of evolution. Although this rate is remarkably similar amongst all cellular organisms, bacterial strains with mutation rates 100 fold greater than the modal rates of their species are commonly isolated from natural sources and emerge in experimental populations. Theoretical studies postulate and empirical studies teort the hypotheses that these “mutator” strains evolved in response to selection for elevated rates of generation of inherited variation that enable bacteria to adapt to novel and/or rapidly changing environments. Less clear are the conditions under which selection will favor reductions in mutation rates. Declines in rates of mutation for established populations of mutator bacteria are not anticipated if such changes are attributed to the costs of augmented rates of generation of deleterious mutations. Here we report experimental evidence of evolution towards reduced mutation rates in a clinical isolate of Escherichia coli with an hyper-mutable phenotype due a deletion in a mismatch repair gene, (ΔmutS). The emergence in a ΔmutS background of variants with mutation rates approaching those of the normal rates of strains carrying wild-type MutS was associated with increase in fitness with respect to ancestral strain. We postulate that such an increase in fitness could be attributed to the emergence of mechanisms driving a permanent “aerobic style of life”, the negative consequence of this behavior being regulated by the evolution of mechanisms protecting the cell against increased endogenous oxidative radicals involved in DNA damage, and thus reducing mutation rate. Gene expression assays and full sequencing of evolved mutator and normo-mutable variants supports the hypothesis. In conclusion, we postulate that the observed reductions in mutation rate are coincidental to, rather than, the selective force responsible for this evolution.

Coevolution with phages does not influence the evolution of bacterial mutation rates in soil

Coevolution with phages drive the evolution of high bacterial mutation rates in vitro, but the relevance of this finding to natural populations is unclear. Here, we investigated how coevolution affects mutation rate evolution in soil, in the presence and absence of the rest of the natural microbial community. Although mutation rate on average increased threefold, neither coevolving phages nor the rest of natural community significantly affected mutation rates. Our results suggest that features of the soil over and above directly interacting organisms constrain the evolution of strong mutators, helping to explain their relatively low frequency compared with some laboratory and clinical settings.

Evolution in microbes

This review presents a broad survey of experimental microbial evolution, covering diverse topics including trade-offs, epistasis, fluctuating conditions, spatial dynamics, cooperation, aging, and stochastic switching. Emphasis is placed on examples that highlight key conceptual points or address theoretical predictions. Experimental evolution is discussed from two points of view. First, population trajectories are described as adaptive walks on a fitness landscape, whose genetic structure can be probed by experiments. Second, populations are viewed from a physiological perspective, and their nongenetic heterogeneity is examined. Bringing together these two viewpoints remains a major challenge for the future.

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.

Genomic background and generation time influence deleterious mutation rates in Daphnia

Understanding how genetic variation is generated and how selection shapes mutation rates over evolutionary time requires knowledge of the factors influencing mutation and its effects on quantitative traits. We explore the impact of two factors, genomic background and generation time, on deleterious mutation in Daphnia pulicaria, a cyclically parthenogenic aquatic microcrustacean, using parallel mutation-accumulation experiments. The deleterious mutational properties of life-history characters for individuals from two different populations, and for individuals maintained at two different generation times, were quantified and compared. Mutational properties varied between populations, especially for clutch size, suggesting that genomic background influences mutational properties for some characters. Generation time was found to have a greater effect on mutational properties, with higher per-generation deleterious mutation rates in lines with longer generation times. These results suggest that differences in genetic architecture among populations and species may be explained in part by demographic features that significantly influence generation time and therefore the rate of mutation.

Fluctuations in fitness distributions and the effects of weak linked selection on sequence evolution

Evolutionary dynamics and patterns of molecular evolution are strongly influenced by selection on linked regions of the genome, but our quantitative understanding of these effects remains incomplete. Recent work has focused on predicting the distribution of fitness within an evolving population, and this forms the basis for several methods that leverage the fitness distribution to predict the patterns of genetic diversity when selection is strong. However, in weakly selected populations random fluctuations due to genetic drift are more severe, and neither the distribution of fitness nor the sequence diversity within the population are well understood. Here, we briefly review the motivations behind the fitness-distribution picture, and summarize the general approaches that have been used to analyze this distribution in the strong-selection regime. We then extend these approaches to the case of weak selection, by outlining a perturbative treatment of selection at a large number of linked sites. This allows us to quantify the stochastic behavior of the fitness distribution and yields exact analytical predictions for the sequence diversity and substitution rate in the limit that selection is weak.

Mechanisms and selection of evolvability: experimental evidence

The vast number of species we see around us today, all stemming from a common ancestor, clearly demonstrates the capacity of organisms to adapt to new environments. Understanding the underlying basis of differences in the capacity of genotypes to adapt - that is, their evolvability - has become a major research field. Several mechanisms have been demonstrated to influence evolvability, including differences in mutation rate, mutational robustness, and some kinds of gene interactions. However, the benefits of increased evolvability are indirect, so that the conditions required for selection of evolvability traits are expected to be more limited than for traits that confer immediately beneficial phenotypes. Moreover, just because a trait can affect evolvability does not mean that it actually does so in a particular environment. Instead, some other function of the trait may better explain its success. Nevertheless, there is accumulating experimental evidence that some traits can increase the evolvability of a genotype and that these traits do influence evolutionary outcomes. We discuss recent theory and experiments that demonstrate the potential for traits that influence evolvability to arise and be selected.

Cancer in light of experimental evolution

Cancer initiation, progression, and the emergence of therapeutic resistance are evolutionary phenomena of clonal somatic cell populations. Studies in microbial experimental evolution and the theoretical work inspired by such studies are yielding deep insights into the evolutionary dynamics of clonal populations, yet there has been little explicit consideration of the relevance of this rapidly growing field to cancer biology. Here, we examine how the understanding of mutation, selection, and spatial structure in clonal populations that is emerging from experimental evolution may be applicable to cancer. Along the way, we discuss some significant ways in which cancer differs from the model systems used in experimental evolution. Despite these differences, we argue that enhanced prediction and control of cancer may be possible using ideas developed in the context of experimental evolution, and we point out some prospects for future research at the interface between these traditionally separate areas.

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.