Mutational Spectrum Drives the Rise of Mutator Bacteria

Understanding how mutator strains emerge in bacterial populations is relevant both to evolutionary theory and to reduce the threat they pose in clinical settings. The rise of mutator alleles is understood as a result of their hitchhiking with linked beneficial mutations, although the factors that govern this process remain unclear. A prominent but underappreciated fact is that each mutator allele increases only a specific spectrum of mutational changes. This spectrum has been speculated to alter the distribution of fitness effects of beneficial mutations, potentially affecting hitchhiking. To study this possibility, we analyzed the fitness distribution of beneficial mutations generated from different mutator and wild-type Escherichia coli strains. Using antibiotic resistance as a model system, we show that mutational spectra can alter these distributions substantially, ultimately determining the competitive ability of each strain across environments. Computer simulation showed that the effect of mutational spectrum on hitchhiking dynamics follows a non-linear function, implying that even slight spectrum-dependent fitness differences are sufficient to alter mutator success frequency by several orders of magnitude. These results indicate an unanticipated central role for the mutational spectrum in the evolution of bacterial mutation rates. At a practical level, this study indicates that knowledge of the molecular details of resistance determinants is crucial for minimizing mutator evolution during antibiotic therapy.     

A method to infer positive selection from marker dynamics in an asexual population

MOTIVATION: The observation of positive selection acting on a mutant indicates that the corresponding mutation has some form of functional relevance. Determining the fitness effects of mutations thus has relevance to many interesting biological questions. One means of identifying beneficial mutations in an asexual population is to observe changes in the frequency of marked subsets of the population. We here describe a method to estimate the establishment times and fitnesses of beneficial mutations from neutral marker frequency data. RESULTS: The method accurately reproduces complex marker frequency trajectories. In simulations for which positive selection is close to 5% per generation, we obtain correlations upwards of 0.91 between correct and inferred haplotype establishment times. Where mutation selection coefficients are exponentially distributed, the inferred distribution of haplotype fitnesses is close to being correct. Applied to data from a bacterial evolution experiment, our method reproduces an observed correlation between evolvability and initial fitness defect.     

Distributions of beneficial fitness effects in RNA

Beneficial mutations are the driving force of evolution by natural selection. Yet, relatively little is known about the distribution of the fitness effects of beneficial mutations in populations. Recent work of Gillespie and Orr suggested some of the first generalizations for the distributions of beneficial fitness effects and, surprisingly, they depend only weakly on biological details. In particular, the theory suggests that beneficial mutations obey an exponential distribution of fitness effects, with the same exponential parameter across different regions of genotype space, provided only that few possible beneficial mutations are available to that genotype. Here we tested this hypothesis with a quasi-empirical model of RNA evolution in which fitness is based on the secondary structures of molecules and their thermodynamic stabilities. The fitnesses of randomly selected genotypes appeared to follow a Gumbel-type distribution and thus conform to a basic assumption of adaptation theory. However, the observed distributions of beneficial fitness effects conflict with specific predictions of the theory. In particular, the distributions of beneficial fitness effects appeared exponential only when the vast majority of small-effect beneficial mutations were ignored. Additionally, the distribution of beneficial fitness effects varied with the fitness of the parent genotype. We believe that correlation of the fitness values among similar genotypes is likely the cause of the departure from the predictions of recent adaptation theory. Although in conflict with the current theory, these results suggest that more complex statistical generalizations about beneficial mutations may be possible.     

Beneficial fitness effects are not exponential for two viruses

The distribution of fitness effects for beneficial mutations is of paramount importance in determining the outcome of adaptation. It is generally assumed that fitness effects of beneficial mutations follow an exponential distribution, for example, in theoretical treatments of quantitative genetics, clonal interference, experimental evolution, and the adaptation of DNA sequences. This assumption has been justified by the statistical theory of extreme values, because the fitnesses conferred by beneficial mutations should represent samples from the extreme right tail of the fitness distribution. Yet in extreme value theory, there are three different limiting forms for right tails of distributions, and the exponential describes only those of distributions in the Gumbel domain of attraction. Using beneficial mutations from two viruses, we show for the first time that the Gumbel domain can be rejected in favor of a distribution with a right-truncated tail, thus providing evidence for an upper bound on fitness effects. Our data also violate the common assumption that small-effect beneficial mutations greatly outnumber those of large effect, as they are consistent with a uniform distribution of beneficial effects.     

ANTIBIOTIC RESISTANCE AND STRESS IN THE LIGHT OF FISHER'S MODEL

The role of mutations in evolution depends upon the distribution of their effects on fitness. This distribution is likely to depend on the environment. Indeed genotype‐by‐environment interactions are key for the process of local adaptation and ecological specialization. An important trait in bacterial evolution is antibiotic resistance, which presents a clear case of change in the direction of selection between environments with and without antibiotics. Here, we study the distribution of fitness effects of mutations, conferring antibiotic resistance to Escherichia coli, in benign and stressful environments without drugs. We interpret the distributions in the light of a fitness landscape model that assumes a single fitness peak. We find that mutation effects (s) are well described by a shifted gamma distribution, with a shift parameter that reflects the distance to the fitness peak and varies across environments. Consistent with the theoretical predictions of Fisher's geometrical model, with a Gaussian relationship between phenotype and fitness, we find that the main effect of stress is to increase the variance in s. Our findings are in agreement with the results of a recent meta‐analysis, which suggest that a simple fitness landscape model may capture the variation of mutation effects across species and environments.     

Effects of genotype on rates of substitution during experimental evolution

Rates of molecular evolution may vary widely between populations, yet the causes of this variation are still incompletely understood. Genetic differences between populations may make an important contribution to variation in rates of evolution, owing to differences in fitness, population size, mutation rates, or in the distribution of fitness effects (DFEs) of available beneficial mutations. By whole genome sequencing of Escherichia coli populations experimentally evolved in the presence of a quinolone antibiotic, we found that rates of substitution varied by genotype, with evidence for a contribution from a genotype's starting fitness. Subsequent targeted sequencing showed that genotypes with high average substitution rates were more likely to undergo the simultaneous fixation of several mutations, consistent with theoretical models of multiple mutation dynamics. Moreover, patterns of substitution were indicative of epistatic relationships between known resistance mutations.     

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

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

Frequent beneficial mutations during single-colony serial transfer of Streptococcus pneumoniae

The appearance of new mutations within a population provides the raw material for evolution. The consistent decline in fitness observed in classical mutation accumulation studies has provided support for the long-held view that deleterious mutations are more common than beneficial mutations. Here we present results of a study using a mutation accumulation design with the bacterium Streptococcus pneumoniae in which the fitness of the derived populations increased. This rise in fitness was associated specifically with adaptation to survival during brief stationary phase periods between single-colony population bottlenecks. To understand better the population dynamics behind this unanticipated adaptation, we developed a maximum likelihood model describing the processes of mutation and stationary-phase selection in the context of frequent population bottlenecks. Using this model, we estimate that the rate of beneficial mutations may be as high as 4.8×10(-4) events per genome for each time interval corresponding to the pneumococcal generation time. This rate is several orders of magnitude higher than earlier estimates of beneficial mutation rates in bacteria but supports recent results obtained through the propagation of small populations of Escherichia coli. Our findings indicate that beneficial mutations may be relatively frequent in bacteria and suggest that in S. pneumoniae, which develops natural competence for transformation, a steady supply of such mutations may be available for sampling by recombination.     

Testing the extreme value domain of attraction for distributions of beneficial fitness effects

In modeling evolutionary genetics, it is often assumed that mutational effects are assigned according to a continuous probability distribution, and multiple distributions have been used with varying degrees of justification. For mutations with beneficial effects, the distribution currently favored is the exponential distribution, in part because it can be justified in terms of extreme value theory, since beneficial mutations should have fitnesses in the extreme right tail of the fitness distribution. While the appeal to extreme value theory seems justified, the exponential distribution is but one of three possible limiting forms for tail distributions, with the other two loosely corresponding to distributions with right-truncated tails and those with heavy tails. We describe a likelihood-ratio framework for analyzing the fitness effects of beneficial mutations, focusing on testing the null hypothesis that the distribution is exponential. We also describe how to account for missing the smallest-effect mutations, which are often difficult to identify experimentally. This technique makes it possible to apply the test to gain-of-function mutations, where the ancestral genotype is unable to grow under the selective conditions. We also describe how to pool data across experiments, since we expect few possible beneficial mutations in any particular experiment.     

Fitness effects of mutations in bacteria

Mutation is the primary source of variation in any organism. Without it, natural selection cannot operate and organisms cannot adapt to novel environments. Mutation is also generally a source of defect: many mutations are not neutral but cause fitness decreases in the organisms where they arise. In bacteria, another important source of variation is horizontal gene transfer. This source of variation can also cause beneficial or deleterious effects. Determining the distribution of fitness effects of mutations in different environments and genetic backgrounds is an active research field. In bacteria, knowledge of these distributions is key for understanding important traits. For example, for determining the dynamics of microorganisms with a high genomic mutation rate (mutators), and for understanding the evolution of antibiotic resistance, and the emergence of pathogenic traits. All of these characteristics are extremely relevant for human health both at the individual and population levels. Experimental evolution has been a valuable tool to address these questions. Here, we review some of the important findings of mutation effects in bacteria revealed through laboratory experiments.     

Multiple adaptive substitutions during evolution in novel environments

We consider an asexual population under strong selection-weak mutation conditions evolving on rugged fitness landscapes with many local fitness peaks. Unlike the previous studies in which the initial fitness of the population is assumed to be high, here we start the adaptation process with a low fitness corresponding to a population in a stressful novel environment. For generic fitness distributions, using an analytic argument we find that the average number of steps to a local optimum varies logarithmically with the genotype sequence length and increases as the correlations among genotypic fitnesses increase. When the fitnesses are exponentially or uniformly distributed, using an evolution equation for the distribution of population fitness, we analytically calculate the fitness distribution of fixed beneficial mutations and the walk length distribution.     

The distribution of beneficial and fixed mutation fitness effects close to an optimum

The distribution of the selection coefficients of beneficial mutations is pivotal to the study of the adaptive process, both at the organismal level (theories of adaptation) and at the gene level (molecular evolution). A now famous result of extreme value theory states that this distribution is an exponential, at least when considering a well-adapted wild type. However, this prediction could be inaccurate under selection for an optimum (because fitness effect distributions have a finite right tail in this case). In this article, we derive the distribution of beneficial mutation effects under a general model of stabilizing selection, with arbitrary selective and mutational covariance between a finite set of traits. We assume a well-adapted wild type, thus taking advantage of the robustness of tail behaviors, as in extreme value theory. We show that, under these general conditions, both beneficial mutation effects and fixed effects (mutations escaping drift loss) are beta distributed. In both cases, the parameters have explicit biological meaning and are empirically measurable; their variation through time can also be predicted. We retrieve the classic exponential distribution as a subcase of the beta when there are a moderate to large number of weakly correlated traits under selection. In this case too, we provide an explicit biological interpretation of the parameters of the distribution. We show by simulations that these conclusions are fairly robust to a lower adaptation of the wild type and discuss the relevance of our findings in the context of adaptation theories and experimental evolution.     

Neural networks enable efficient and accurate simulation-based inference of evolutionary parameters from adaptation dynamics

The rate of adaptive evolution depends on the rate at which beneficial mutations are introduced into a population and the fitness effects of those mutations. The rate of beneficial mutations and their expected fitness effects is often difficult to empirically quantify. As these 2 parameters determine the pace of evolutionary change in a population, the dynamics of adaptive evolution may enable inference of their values. Copy number variants (CNVs) are a pervasive source of heritable variation that can facilitate rapid adaptive evolution. Previously, we developed a locus-specific fluorescent CNV reporter to quantify CNV dynamics in evolving populations maintained in nutrient-limiting conditions using chemostats. Here, we use CNV adaptation dynamics to estimate the rate at which beneficial CNVs are introduced through de novo mutation and their fitness effects using simulation-based likelihood–free inference approaches. We tested the suitability of 2 evolutionary models: a standard Wright–Fisher model and a chemostat model. We evaluated 2 likelihood-free inference algorithms: the well-established Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) algorithm, and the recently developed Neural Posterior Estimation (NPE) algorithm, which applies an artificial neural network to directly estimate the posterior distribution. By systematically evaluating the suitability of different inference methods and models, we show that NPE has several advantages over ABC-SMC and that a Wright–Fisher evolutionary model suffices in most cases. Using our validated inference framework, we estimate the CNV formation rate at the GAP1 locus in the yeast Saccharomyces cerevisiae to be 10^−4.7 to 10⁻⁴ CNVs per cell division and a fitness coefficient of 0.04 to 0.1 per generation for GAP1 CNVs in glutamine-limited chemostats. We experimentally validated our inference-based estimates using 2 distinct experimental methods—barcode lineage tracking and pairwise fitness assays—which provide independent confirmation of the accuracy of our approach. Our results are consistent with a beneficial CNV supply rate that is 10-fold greater than the estimated rates of beneficial single-nucleotide mutations, explaining the outsized importance of CNVs in rapid adaptive evolution. More generally, our study demonstrates the utility of novel neural network–based likelihood–free inference methods for inferring the rates and effects of evolutionary processes from empirical data with possible applications ranging from tumor to viral evolution.

This study shows that simulation-based inference of evolutionary dynamics using neural networks can yield parameter values for fitness and mutation rate that are difficult to determine experimentally, including those of copy number variants (CNVs) during experimental adaptive evolution of yeast.     

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.     

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.     

HIV-1 protease catalytic efficiency effects caused by random single amino acid substitutions

Protein evolution has occurred by successive fixation of individual mutations. The probability of fixation depends on the fitness of the mutation, and the arising variant can be deleterious, neutral, or beneficial. Despite its relevance, only few studies have estimated the distribution of fitness effects caused by random single mutations on protein function. The human immunodeficiency virus type 1 (HIV-1) protease was chosen as a model protein to quantify protein's tolerability to random single mutations. After determining the enzymatic activity of 107 single random mutants, we found that 86% of single mutations were deleterious for the enzyme catalytic efficiency and 54% lethal. Only 2% of the mutations significantly increased the catalytic efficiency of the enzyme. These data demonstrate the vulnerability of HIV-1 protease to single random mutations. When a second random mutagenesis library was constructed from an HIV-1 protease carrying a highly deleterious single mutation (D30N), a higher proportion of mutations with neutral or beneficial effect were found, 26% and 9%, respectively. Importantly, antagonist epistasis was observed between deleterious mutations. In particular, the mutation N88D, lethal for the wild-type protease, restored the wild-type catalytic efficiency when combined with the highly deleterious mutation D30N. The low tolerability to single random substitutions shown here for the wild-type HIV-1 protease contrasts with its in vivo ability to generate an adaptive variation. Thus, the antagonist epistasis between deleterious or lethal mutations may be responsible for increasing the protein mutational robustness and evolvability.     

The effect of spontaneous mutations on competitive ability

Understanding the impact of spontaneous mutations on fitness has many theoretical and practical applications in biology. Although mutational effects on individual morphological or life‐history characters have been measured in several classic genetic model systems, there are few estimates of the rate of decline due to mutation for complex fitness traits. Here, we estimate the effects of mutation on competitive ability, an important complex fitness trait, in a model system for ecological and evolutionary genomics, Daphnia. Competition assays were performed to compare fitness between mutation‐accumulation (MA) lines and control lines from eight different genotypes from two populations of Daphnia pulicaria after 30 and 65 generations of mutation accumulation. Our results show a fitness decline among MA lines relative to controls as expected, but highlight the influence of genomic background on this effect. In addition, in some assays, MA lines outperform controls providing insight into the frequency of beneficial mutations.     

Experimental estimate of the abundance and effects of nearly neutral mutations in the RNA virus phi 6

Although the frequency and effects of neutral and nearly neutral mutations are critical to evolutionary patterns and processes governed by genetic drift, the small effects of such mutations make them difficult to study empirically. Here we present the results of a mutation-accumulation experiment designed to assess the frequencies of deleterious mutations with undetectable effects. We promoted the accumulation of spontaneous mutations by subjecting independent lineages of the RNA virus 6 to repeated population bottlenecks of a single individual. We measured fitness following every bottleneck to obtain a complete picture of the timing and effects of the accumulated mutations with detectable effects and sequenced complete genomes to determine the number of mutations that were undetected by the fitness assays. To estimate the effects of the undetected mutations, we implemented a likelihood model developed for quantitative trait locus (QTL) data (Otto and Jones 2000) to estimate the number and effects of the undetected mutations from the measured number and effects of the detected mutations. Using this method we estimated a deleterious mutation rate of U = 0.03 and a gamma effects distribution with mean s=0.093 and coefficient of variation = 0.204. Although our estimates of U and s fall within the range of recent mutation rate and effect estimates in eukaryotes, the fraction of mutations with detectable effects on laboratory fitness (39%) appears to be far higher in 6 than in eukaryotes.