Beneficial mutations, hitchhiking and the evolution of mutation rates in sexual populations

Non-hypermutator cancers access driver mutations through reversals in germline mutational bias

Cancer is an evolutionary disease driven by mutations in asexually-reproducing somatic cells. In asexual microbes, bias reversals in the mutation spectrum can speed adaptation by increasing access to previously undersampled beneficial mutations. By analyzing tumors from 20 tissues, along with normal tissue and the germline, we demonstrate this effect in cancer. Non-hypermutated tumors reverse the germline mutation bias and have consistent spectra across tissues. These spectra changes carry the signature of hypoxia, and they facilitate positive selection in cancer genes. Hypermutated and non-hypermutated tumors thus acquire driver mutations differently: hypermutated tumors by higher mutation rates and non-hypermutated tumors by changing the mutation spectrum to reverse the germline mutation bias.

(Epi)mutation Rates and the Evolution of Composite Trait Architectures

AbstractMutation rates vary widely along genomes and across inheritance systems. This suggests that complex traits-resulting from the contributions of multiple determinants-might be composite in terms of the underlying mutation rates. Here we investigate through mathematical modeling whether such a heterogeneity may drive changes in a trait's architecture, especially in fluctuating environments, where phenotypic instability can be beneficial. We first identify a convexity principle related to the shape of the trait's fitness function, setting conditions under which composite architectures should be adaptive or, conversely and more commonly, should be selected against. Simulations reveal, however, that applying this principle to realistic evolving populations requires taking into account pervasive epistatic interactions that take place in the system. Indeed, the fate of a mutation affecting the architecture depends on the (epi)genetic background, which itself depends on the current architecture in the population. We tackle this problem by borrowing the adaptive dynamics framework from evolutionary ecology-where it is routinely used to deal with such resident/mutant dependencies-and find that the principle excluding composite architectures generally prevails. Yet the predicted evolutionary trajectories will typically depend on the initial architecture, possibly resulting in historical contingencies. Finally, by relaxing the large population size assumption, we unexpectedly find that not only the strength of selection on a trait's architecture but also its direction depend on population size, revealing a new occurrence of the recently identified phenomenon coined "sign inversion."

Simulating the Effect of Environmental Change on Evolving Populations

This study uses evolutionary simulations to explore the strategies that emerge to enable populations to cope with random environmental changes in situations where lifetime learning approaches are not available to accommodate them. In particular, it investigates how the average magnitude of change per unit time and the persistence of the changes (and hence the resulting autocorrelation of the environmental time series) affect the change tolerances, population diversities, and extinction timescales that emerge. Although it is the change persistence (often discussed in terms of environmental noise color) that has received most attention in the recent literature, other factors, particularly the average change magnitude, interact with this and can be more important drivers of the adaptive strategies that emerge. Moreover, when running simulations, the choice of change representation and normalization can also affect the outcomes. Detailed simulations are presented that are designed to explore all these issues. They also reveal significant dependences on the associated mutation rates and the extent to which they can evolve, and they clarify how evolution often leads populations into strategies with higher risks of extinction. Overall, this study shows how modeling the effect of environmental change requires more care than may have previously been realized.

Stem cell mutations, associated cancer risk, and consequences for regenerative medicine

Mutation accumulation in stem cells has been associated with cancer risk. However, the presence of numerous mutant clones in healthy tissues has raised the question of what limits cancer initiation. Here, we review recent developments in characterizing mutation accumulation in healthy tissues and compare mutation rates in stem cells during development and adult life with corresponding cancer risk. A certain level of mutagenesis within the stem cell pool might be beneficial to limit the size of malignant clones through competition. This knowledge impacts our understanding of carcinogenesis with potential consequences for the use of stem cells in regenerative medicine.

Shifts in Mutation Bias Promote Mutators by Altering the Distribution of Fitness Effects

AbstractRecent experimental evidence demonstrates that shifts in mutational biases-for example, increases in transversion frequency-can change the distribution of fitness effects of mutations (DFE). In particular, reducing or reversing a prevailing bias can increase the probability that a de novo mutation is beneficial. It has also been shown that mutator bacteria are more likely to emerge if the beneficial mutations they generate have a larger effect size than observed in the wild type. Here, we connect these two results, demonstrating that mutator strains that reduce or reverse a prevailing bias have a positively shifted DFE, which in turn can dramatically increase their emergence probability. Since changes in mutation rate and bias are often coupled through the gain and loss of DNA repair enzymes, our results predict that the invasion of mutator strains will be facilitated by shifts in mutation bias that offer improved access to previously undersampled beneficial mutations.

Life history and deleterious mutation rate coevolution

The cost of germline maintenance gives rise to a trade-off between lowering the deleterious mutation rate and investing in life history functions. Therefore, life history and the mutation rate coevolve, but this coevolution is not well understood. We develop a mathematical model to analyse the evolution of resource allocation traits, which simultaneously affect life history and the deleterious mutation rate. First, we show that the invasion fitness of such resource allocation traits can be approximated by the basic reproductive number of the least-loaded class; the expected lifetime production of offspring without deleterious mutations born to individuals without deleterious mutations. Second, we apply the model to investigate (i) the coevolution of reproductive effort and germline maintenance and (ii) the coevolution of age-at-maturity and germline maintenance. This analysis provides two resource allocation predictions when exposure to environmental mutagens is higher. First, selection favours higher allocation to germline maintenance, even if it comes at the expense of life history functions, and leads to a shift in allocation towards reproduction rather than survival. Second, life histories tend to be faster, characterised by individuals with shorter lifespans and smaller body sizes at maturity. Our results suggest that mutation accumulation via the cost of germline maintenance can be a major force shaping life-history traits.

Most cancers carry a substantial deleterious load due to Hill-Robertson interference

Cancer genomes exhibit surprisingly weak signatures of negative selection^1,2. This may be because selective pressures are relaxed or because genome-wide linkage prevents deleterious mutations from being removed (Hill-Robertson interference)³. By stratifying tumors by their genome-wide mutational burden, we observe negative selection (dN/dS ~ 0.56) in low mutational burden tumors, while remaining cancers exhibit dN/dS ratios ~1. This suggests that most tumors do not remove deleterious passengers. To buffer against deleterious passengers, tumors upregulate heat shock pathways as their mutational burden increases. Finally, evolutionary modeling finds that Hill-Robertson interference alone can reproduce patterns of attenuated selection and estimates the total fitness cost of passengers to be 46% per cell on average. Collectively, our findings suggest that the lack of observed negative selection in most tumors is not due to relaxed selective pressures, but rather the inability of selection to remove deleterious mutations in the presence of genome-wide linkage.

A modified fluctuation assay reveals a natural mutator phenotype that drives mutation spectrum variation within Saccharomyces cerevisiae

Although studies of Saccharomyces cerevisiae have provided many insights into mutagenesis and DNA repair, most of this work has focused on a few laboratory strains. Much less is known about the phenotypic effects of natural variation within S. cerevisiae’s DNA repair pathways. Here, we use natural polymorphisms to detect historical mutation spectrum differences among several wild and domesticated S. cerevisiae strains. To determine whether these differences are likely caused by genetic mutation rate modifiers, we use a modified fluctuation assay with a CAN1 reporter to measure de novo mutation rates and spectra in 16 of the analyzed strains. We measure a 10-fold range of mutation rates and identify two strains with distinctive mutation spectra. These strains, known as AEQ and AAR, come from the panel’s ‘Mosaic beer’ clade and share an enrichment for C > A mutations that is also observed in rare variation segregating throughout the genomes of several Mosaic beer and Mixed origin strains. Both AEQ and AAR are haploid derivatives of the diploid natural isolate CBS 1782, whose rare polymorphisms are enriched for C > A as well, suggesting that the underlying mutator allele is likely active in nature. We use a plasmid complementation test to show that AAR and AEQ share a mutator allele in the DNA repair gene OGG1, which excises 8-oxoguanine lesions that can cause C > A mutations if left unrepaired.

The rate and molecular spectrum of mutation are selectively maintained in yeast

What determines the rate (μ) and molecular spectrum of mutation is a fundamental question. The prevailing hypothesis asserts that natural selection against deleterious mutations has pushed μ to the minimum achievable in the presence of genetic drift, or the drift barrier. Here we show that, contrasting this hypothesis, μ substantially exceeds the drift barrier in diverse organisms. Random mutation accumulation (MA) in yeast frequently reduces μ, and deleting the newly discovered mutator gene PSP2 nearly halves μ. These results, along with a comparison between the MA and natural yeast strains, demonstrate that μ is maintained above the drift barrier by stabilizing selection. Similar comparisons show that the mutation spectrum such as the universal AT mutational bias is not intrinsic but has been selectively preserved. These findings blur the separation of mutation from selection as distinct evolutionary forces but open the door to alleviating mutagenesis in various organisms by genome editing.

How natural selection shapes the rate and molecular spectrum of mutations is debated. Yeast mutation accumulation experiments identify a gene promoting mutagenesis and show stabilizing selection maintaining the mutation rate above the drift barrier. Selection also preserves the mutation spectrum.

Self-selection of evolutionary strategies: adaptive versus non-adaptive forces

The evolution of complex genetic networks is shaped over the course of many generations through multiple mechanisms. These mechanisms can be broken into two predominant categories: adaptive forces, such as natural selection, and non-adaptive forces, such as recombination, genetic drift, and random mutation. Adaptive forces are influenced by the environment, where individuals better suited for their ecological niche are more likely to reproduce. This adaptive force results in a selective pressure which creates a bias in the reproduction of individuals with beneficial traits. Non-adaptive forces, in contrast, are not influenced by the environment: Random mutations occur in offspring regardless of whether they improve the fitness of the offspring. Both adaptive and non-adaptive forces play critical roles in the development of a species over time, and both forces are intrinsically linked to one another. We hypothesize that even under a simple sexual reproduction model, selective pressure will result in changes in the mutation rate and genome size. We tested this hypothesis by evolving Boolean networks using a modified genetic algorithm. Our results demonstrate that changes in environmental signals can result in selective pressure which affects mutation rate.

Somatic Mutation and Evolution in Plants

Somatic mutations are common in plants, and they may accumulate and be passed on to gametes. The determinants of somatic mutation accumulation include the intraorganismal selective effect of mutations, the number of cell divisions that separate the zygote from the formation of gametes, and shoot apical meristem structure and branching. Somatic mutations can promote the evolution of diploidy, polyploidy, sexual recombination, outcrossing, clonality, and separate sexes, and they may contribute genetic variability in many other traits. The amplification of beneficial mutations via intraorganismal selection may relax selection to reduce the genomic mutation rate or to protect the germline in plants. The total rate of somatic mutation, the distribution of selective effects and fates in the plant body, and the degree to which the germline is sheltered from somatic mutations are still poorly understood. Our knowledge can be improved through empirical estimates of mutation rates and effects on cell lineages and whole organisms, such as estimates of the reduction in fitness of progeny produced by within- versus between-flower crosses on the same plant, mutation coalescent studies within the canopy, and incorporation of somatic mutation into theoretical models of plant evolutionary genetics.

(In)exhaustible Suppliers for Evolution? Epistatic Selection Tunes the Adaptive Potential of Nongenetic Inheritance

Nongenetic inheritance media-from methyl-accepting cytosines to culture-tend to mutate more frequently than DNA sequences. Whether this makes them inexhaustible suppliers for adaptive evolution will depend on the effect of nongenetic mutations (hereafter, epimutations) on fitness-related traits. Here we investigate how these effects might themselves evolve, specifically whether natural selection may set boundaries to the adaptive potential of nongenetic inheritance media because of their higher mutability. In our model, the genetic and epigenetic contributions to a nonneutral phenotype are controlled by an epistatic modifier locus, which evolves under the combined effects of drift and selection. We show that a pure genetic control evolves when the environment is stable-provided that the population is large-such that the phenotype becomes robust to frequent epimutations. When the environment fluctuates, however, selection on the modifier locus also fluctuates and can overall produce a large nongenetic contribution to the phenotype, especially when the epimutation rate matches the rate of environmental variation. We further show that selection on the modifier locus is generally insensitive to recombination, meaning it is mostly direct, that is, not relying on subsequent effects in future generations. These results suggest that unstable inheritance media might significantly contribute to fitness variation of traits subject to highly variable selective pressures but little to traits responding to scarcely variable aspects of the environment. More generally, our study demonstrates that the rate of mutation and the adaptive potential of any inheritance media should not be seen as independent properties.

Elevated mutation rates are unlikely to evolve in sexual species, not even under rapid environmental change

BACKGROUND

Organisms are expected to respond to changing environmental conditions through local adaptation, range shift or local extinction. The process of local adaptation can occur by genetic changes or phenotypic plasticity, and becomes especially relevant when dispersal abilities or possibilities are somehow constrained. For genetic changes to occur, mutations are the ultimate source of variation and the mutation rate in terms of a mutator locus can be subject to evolutionary change. Recent findings suggest that the evolution of the mutation rate in a sexual species can advance invasion speed and promote adaptation to novel environmental conditions. Following this idea, this work uses an individual-based model approach to investigate if the mutation rate can also evolve in a sexual species experiencing different conditions of directional climate change, under different scenarios of colored stochastic environmental noise, probability of recombination and of beneficial mutations. The color of the noise mimicked investigating the evolutionary dynamics of the mutation rate in different habitats.

RESULTS

The results suggest that the mutation rate in a sexual species experiencing directional climate change scenarios can evolve and reach relatively high values mainly under conditions of complete linkage of the mutator locus and the adaptation locus. In contrast, when they are unlinked, the mutation rate can slightly increase only under scenarios where at least 50% of arising mutations are beneficial and the rate of environmental change is relatively fast. This result is robust under different scenarios of stochastic environmental noise, which supports the observation of no systematic variation in the mutation rate among organisms experiencing different habitats.

CONCLUSIONS

Given that 50% beneficial mutations may be an unrealistic assumption, and that recombination is ubiquitous in sexual species, the evolution of an elevated mutation rate in a sexual species experiencing directional climate change might be rather unlikely. Furthermore, when the percentage of beneficial mutations and the population size are small, sexual species (especially multicellular ones) producing few offspring may be expected to react to changing environments not by adaptive genetic change, but mainly through plasticity. Without the ability for a plastic response, such species may become - at least locally - extinct.

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.

Pourquoi le taux de mutation n’est-il jamais égal à zéro ?

Alfred H. Sturtevant fut le premier à s’en étonner : le taux de mutation est faible mais n’atteint jamais zéro. Pourtant, la plupart des mutations qui modifient le phénotype ont un effet délétère, les individus qui produisent le moins de mutants génèrent donc plus de descendants viables et fertiles. La sélection naturelle devrait ainsi progressivement faire tendre le taux de mutation vers zéro au cours des générations. Des analyses récentes suggèrent que ce taux dépend principalement de la taille efficace des génomes et de l’effectif efficace des populations. Le maintien de taux de mutation plus élevés que nécessaire illustrerait les limites de la sélection naturelle dans un monde vivant constitué de populations de taille finie.

Mutation Rate Evolution in Partially Selfing and Partially Asexual Organisms

Different factors can influence the evolution of the mutation rate of a species: costs associated with DNA replication fidelity, indirect selection caused by the mutations produced (that should generally favor lower mutation rates, given that most mutations affecting fitness are deleterious), and genetic drift, which may render selection acting on weak mutators inefficient. In this paper, we use a two-locus model to compute the strength of indirect selection acting on a modifier locus that affects the mutation rate toward a deleterious allele at a second, linked, locus, in a population undergoing partial selfing or partial clonality. The results show that uniparental reproduction increases the effect of indirect selection for lower mutation rates. Extrapolating to the case of a whole genome with many deleterious alleles, and introducing a direct cost to DNA replication fidelity, the results can be used to compute the evolutionarily stable mutation rate, U In the absence of mutational bias toward higher U, the analytical prediction fits well with individual-based, multilocus simulation results. When such a bias is added into the simulations, however, genetic drift may lead to the maintenance of higher mutation rates, and this effect may be amplified in highly selfing or highly clonal populations due to their reduced effective population size.

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.

Evolving mutation rate advances the invasion speed of a sexual species

Background

Many species are shifting their ranges in response to global climate change. Range expansions are known to have profound effects on the genetic composition of populations. The evolution of dispersal during range expansion increases invasion speed, provided that a species can adapt sufficiently fast to novel local conditions. Genetic diversity at the expanding range border is however depleted due to iterated founder effects. The surprising ability of colonizing species to adapt to novel conditions while being subjected to genetic bottlenecks is termed ‘the genetic paradox of invasive species’. Mutational processes have been argued to provide an explanation for this paradox. Mutation rates can evolve, under conditions that favor an increased rate of adaptation, by hitchhiking on beneficial mutations through induced linkage disequilibrium. Here we argue that spatial sorting, iterated founder events, and population structure benefit the build-up and maintenance of such linkage disequilibrium. We investigate if the evolution of mutation rates could play a role in explaining the ‘genetic paradox of invasive species’ for a sexually reproducing species colonizing a landscape of gradually changing conditions.

Results

We use an individual-based model to show the evolutionary increase of mutation rates in sexual populations during range expansion, in coevolution with the dispersal probability. The observed evolution of mutation rate is adaptive and clearly advances invasion speed both through its effect on the evolution of dispersal probability, and the evolution of local adaptation. This also occurs under a variable temperature gradient, and under the assumption of 90% lethal mutations.

Conclusions

In this study we show novel consequences of the particular genetic properties of populations under spatial disequilibrium, i.e. the coevolution of dispersal probability and mutation rate, even in a sexual species and under realistic spatial gradients, resulting in faster invasions. The evolution of mutation rates can therefore be added to the list of possible explanations for the ‘genetic paradox of invasive species’. We conclude that range expansions and the evolution of mutation rates are in a positive feedback loop, with possibly far-reaching ecological consequences concerning invasiveness and the adaptability of species to novel environmental conditions.

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-017-0998-8) contains supplementary material, which is available to authorized users.

Genetic drift, selection and the evolution of the mutation rate

As one of the few cellular traits that can be quantified across the tree of life, DNA-replication fidelity provides an excellent platform for understanding fundamental evolutionary processes. Furthermore, because mutation is the ultimate source of all genetic variation, clarifying why mutation rates vary is crucial for understanding all areas of biology. A potentially revealing hypothesis for mutation-rate evolution is that natural selection primarily operates to improve replication fidelity, with the ultimate limits to what can be achieved set by the power of random genetic drift. This drift-barrier hypothesis is consistent with comparative measures of mutation rates, provides a simple explanation for the existence of error-prone polymerases and yields a formal counter-argument to the view that selection fine-tunes gene-specific mutation rates.

Known mutator alleles do not markedly increase mutation rate in clinical Saccharomyces cerevisiae strains

Natural selection has the potential to act on all phenotypes, including genomic mutation rate. Classic evolutionary theory predicts that in asexual populations, mutator alleles, which cause high mutation rates, can fix due to linkage with beneficial mutations. This phenomenon has been demonstrated experimentally and may explain the frequency of mutators found in bacterial pathogens. By contrast, in sexual populations, recombination decouples mutator alleles from beneficial mutations, preventing mutator fixation. In the facultatively sexual yeast Saccharomyces cerevisiae, segregating alleles of MLH1 and PMS1 have been shown to be incompatible, causing a high mutation rate when combined. These alleles had never been found together naturally, but were recently discovered in a cluster of clinical isolates. Here we report that the incompatible mutator allele combination only marginally elevates mutation rate in these clinical strains. Genomic and phylogenetic analyses provide no evidence of a historically elevated mutation rate. We conclude that the effect of the mutator alleles is dampened by background genetic modifiers. Thus, the relationship between mutation rate and microbial pathogenicity may be more complex than once thought. Our findings provide rare observational evidence that supports evolutionary theory suggesting that sexual organisms are unlikely to harbour alleles that increase their genomic mutation rate.

Dynamics and Fate of Beneficial Mutations Under Lineage Contamination by Linked Deleterious Mutations

Beneficial mutations drive adaptive evolution, yet their selective advantage does not ensure their fixation. Haldane's application of single-type branching process theory showed that genetic drift alone could cause the extinction of newly arising beneficial mutations with high probability. With linkage, deleterious mutations will affect the dynamics of beneficial mutations and might further increase their extinction probability. Here, we model the lineage dynamics of a newly arising beneficial mutation as a multitype branching process. Our approach accounts for the combined effects of drift and the stochastic accumulation of linked deleterious mutations, which we call lineage contamination We first study the lineage-contamination phenomenon in isolation, deriving dynamics and survival probabilities (the complement of extinction probabilities) of beneficial lineages. We find that survival probability is zero when [Formula: see text] where U is deleterious mutation rate and [Formula: see text] is the selective advantage of the beneficial mutation in question, and is otherwise depressed below classical predictions by a factor bounded from below by [Formula: see text] We then put the lineage contamination phenomenon into the context of an evolving population by incorporating the effects of background selection. We find that, under the combined effects of lineage contamination and background selection, ensemble survival probability is never zero but is depressed below classical predictions by a factor bounded from below by [Formula: see text] where [Formula: see text] is mean selective advantage of beneficial mutations, and [Formula: see text] This factor, and other bounds derived from it, are independent of the fitness effects of deleterious mutations. At high enough mutation rates, lineage contamination can depress fixation probabilities to values that approach zero. This fact suggests that high mutation rates can, perhaps paradoxically, (1) alleviate competition among beneficial mutations, or (2) potentially even shut down the adaptive process. We derive critical mutation rates above which these two events become likely.

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.

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.

Evolutionary Stability of Minimal Mutation Rates in an Evo-epidemiological Model

We consider the evolution of mutation rate in a seasonally forced, deterministic, compartmental epidemiological model with a transmission-virulence trade-off. We model virulence as a quantitative genetic trait in a haploid population and mutation as continuous diffusion in the trait space. There is a mutation rate threshold above which the pathogen cannot invade a wholly susceptible population. The evolutionarily stable (ESS) mutation rate is the one which drives the lowest average density, over the course of one forcing period, of susceptible individuals at steady state. In contrast with earlier eco-evolutionary models in which higher mutation rates allow for better evolutionary tracking of a dynamic environment, numerical calculations suggest that in our model the minimum average susceptible population, and hence the ESS, is achieved by a pathogen strain with zero mutation. We discuss how this result arises within our model and how the model might be modified to obtain a nonzero optimum.

Extensive de novo mutation rate variation between individuals and across the genome of Chlamydomonas reinhardtii

Describing the process of spontaneous mutation is fundamental for understanding the genetic basis of disease, the threat posed by declining population size in conservation biology, and much of evolutionary biology. Directly studying spontaneous mutation has been difficult, however, because new mutations are rare. Mutation accumulation (MA) experiments overcome this by allowing mutations to build up over many generations in the near absence of natural selection. Here, we sequenced the genomes of 85 MA lines derived from six genetically diverse strains of the green alga Chlamydomonas reinhardtii. We identified 6843 new mutations, more than any other study of spontaneous mutation. We observed sevenfold variation in the mutation rate among strains and that mutator genotypes arose, increasing the mutation rate approximately eightfold in some replicates. We also found evidence for fine-scale heterogeneity in the mutation rate, with certain sequence motifs mutating at much higher rates, and clusters of multiple mutations occurring at closely linked sites. There was little evidence, however, for mutation rate heterogeneity between chromosomes or over large genomic regions of 200 kbp. We generated a predictive model of the mutability of sites based on their genomic properties, including local GC content, gene expression level, and local sequence context. Our model accurately predicted the average mutation rate and natural levels of genetic diversity of sites across the genome. Notably, trinucleotides vary 17-fold in rate between the most and least mutable sites. Our results uncover a rich heterogeneity in the process of spontaneous mutation both among individuals and across the genome.

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.

Mutation rates: how low can you go?

Two recent reports combine mutation accumulation and whole-genome sequencing to measure mutation rates in microbes with unusual genome sizes and life cycles. The results are broadly consistent with the hypothesis that genetic drift plays a role in shaping genomic mutation rates across a wide range of taxa.

Stabilizing selection, purifying selection, and mutational bias in finite populations

Genomic traits such as codon usage and the lengths of noncoding sequences may be subject to stabilizing selection rather than purifying selection. Mutations affecting these traits are often biased in one direction. To investigate the potential role of stabilizing selection on genomic traits, the effects of mutational bias on the equilibrium value of a trait under stabilizing selection in a finite population were investigated, using two different mutational models. Numerical results were generated using a matrix method for calculating the probability distribution of variant frequencies at sites affecting the trait, as well as by Monte Carlo simulations. Analytical approximations were also derived, which provided useful insights into the numerical results. A novel conclusion is that the scaled intensity of selection acting on individual variants is nearly independent of the effective population size over a wide range of parameter space and is strongly determined by the logarithm of the mutational bias parameter. This is true even when there is a very small departure of the mean from the optimum, as is usually the case. This implies that studies of the frequency spectra of DNA sequence variants may be unable to distinguish between stabilizing and purifying selection. A similar investigation of purifying selection against deleterious mutations was also carried out. Contrary to previous suggestions, the scaled intensity of purifying selection with synergistic fitness effects is sensitive to population size, which is inconsistent with the general lack of sensitivity of codon usage to effective population size.

The evolution of mutation rate in an antagonistic coevolutionary model with maternal transmission of parasites

By constantly selecting for novel genotypes, coevolution between hosts and parasites can favour elevated mutation rates. Models of this process typically assume random encounters. However, offspring are often more likely to encounter their mother's parasites. Because parents and offspring are genetically similar, they may be susceptible to the same parasite strains and thus, in hosts, maternal transmission should select for mechanisms that decrease intergenerational genetic similarity. In parasites, however, maternal transmission should select for genetic similarity. We develop and analyse a model of host and parasite mutation rate evolution when parasites are maternally inherited. In hosts, we find that maternal transmission has two opposing effects. First, it eliminates coevolutionary cycles that previous work shows select for higher mutation. Second, it independently selects for higher mutation rates, because offspring that differ from their mothers are more likely to avoid infection. In parasites, however, the two effects of maternal transmission act in the same direction. As for hosts, maternal transmission eliminates coevolutionary cycles, thereby reducing selection for increased mutation. Unlike for hosts, however, maternal transmission additionally selects against higher mutation by favouring parasite offspring that are the same as their mothers.

Extraordinary genome stability in the ciliate Paramecium tetraurelia

Mutation plays a central role in all evolutionary processes and is also the basis of genetic disorders. Established base-substitution mutation rates in eukaryotes range between ∼5 × 10(-10) and 5 × 10(-8) per site per generation, but here we report a genome-wide estimate for Paramecium tetraurelia that is more than an order of magnitude lower than any previous eukaryotic estimate. Nevertheless, when the mutation rate per cell division is extrapolated to the length of the sexual cycle for this protist, the measure obtained is comparable to that for multicellular species with similar genome sizes. Because Paramecium has a transcriptionally silent germ-line nucleus, these results are consistent with the hypothesis that natural selection operates on the cumulative germ-line replication fidelity per episode of somatic gene expression, with the germ-line mutation rate per cell division evolving downward to the lower barrier imposed by random genetic drift. We observe ciliate-specific modifications of widely conserved amino acid sites in DNA polymerases as one potential explanation for unusually high levels of replication fidelity.

Interrelationship between HIV-1 fitness and mutation rate

Differences in replication fidelity, as well as mutator and antimutator strains, suggest that virus mutation rates are heritable and prone to natural selection. Human immunodeficiency virus type 1 (HIV-1) has many distinct advantages for the study of mutation rate optimization given the wealth of structural and biochemical data on HIV-1 reverse transcriptase (RT) and mutants. In this study, we conducted parallel analyses of mutation rate and viral fitness. In particular, a panel of 10 RT mutants-most having drug resistance phenotypes-was analyzed for their effects on viral fidelity and fitness. Fidelity differences were measured using single-cycle vector assays, while fitness differences were identified using ex vivo head-to-head competition assays. As anticipated, virus mutants possessing either higher or lower fidelity had a corresponding loss in fitness. While the virus panel was not chosen randomly, it is interesting that it included more viruses possessing a mutator phenotype rather than viruses possessing an antimutator phenotype. These observations provide the first description of an interrelationship between HIV-1 fitness and mutation rate and support the conclusion that mutator and antimutator phenotypes correlate with reduced viral fitness. In addition, the findings here help support a model in which fidelity comes at a cost of replication kinetics and may help explain why retroviruses like HIV-1 and RNA viruses maintain replication fidelity near the extinction threshold.

High mutation rates in the mitochondrial genomes of Daphnia pulex

Despite the great utility of mitochondrial DNA (mtDNA) sequence data in population genetics and phylogenetics, key parameters describing the process of mitochondrial mutation (e.g., the rate and spectrum of mutational change) are based on few direct estimates. Furthermore, the variation in the mtDNA mutation process within species or between lineages with contrasting reproductive strategies remains poorly understood. In this study, we directly estimate the mtDNA mutation rate and spectrum using Daphnia pulex mutation-accumulation (MA) lines derived from sexual (cyclically parthenogenetic) and asexual (obligately parthenogenetic) lineages. The nearly complete mitochondrial genome sequences of 82 sexual and 47 asexual MA lines reveal high mtDNA mutation rate of 1.37 × 10(-7) and 1.73 × 10(-7) per nucleotide per generation, respectively. The Daphnia mtDNA mutation rate is among the highest in eukaryotes, and its spectrum is dominated by insertions and deletions (70%), largely due to the presence of mutational hotspots at homopolymeric nucleotide stretches. Maximum likelihood estimates of the Daphnia mitochondrial effective population size reveal that between five and ten copies of mitochondrial genomes are transmitted per female per generation. Comparison between sexual and asexual lineages reveals no statistically different mutation rates and highly similar mutation spectra.

The lower bound to the evolution of mutation rates

Despite substantial attention from theoreticians, the evolutionary mechanisms that drive intra- and interspecific variation in the mutation rate remain unclear. It has often been argued that mutation rates associated with the major replicative polymerases have been driven down to their physiological limits, defined as the point at which further enhancement in replication fidelity incurs a cost in terms of reproductive output, but no evidence in support of this argument has emerged for cellular organisms. Here, it is suggested that the lower barrier to mutation rate evolution may ultimately be defined not by molecular limitations but by the power of random genetic drift. As the mutation rate is reduced to a very low level, a point will eventually be reached at which the small advantage of any further reduction is overwhelmed by the power of drift. This hypothesis is consistent with a number of observations, including the inverse relationship between the per-site mutation rate and genome size in microbes, the negative scaling between the per-site mutation rate and effective population size in eukaryotes, and the elevated error rates associated with less frequently deployed polymerases and repair pathways.

Mutator dynamics in sexual and asexual experimental populations of yeast

Background

In asexual populations, mutators may be expected to hitchhike with associated beneficial mutations. In sexual populations, recombination is predicted to erode such associations, inhibiting mutator hitchhiking. To investigate the effect of recombination on mutators experimentally, we compared the frequency dynamics of a mutator allele (msh2Δ) in sexual and asexual populations of Saccharomyces cerevisiae.

Results

Mutator strains increased in frequency at the expense of wild-type strains in all asexual diploid populations, with some approaching fixation in 150 generations of propagation. Over the same period of time, mutators declined toward loss in all corresponding sexual diploid populations as well as in haploid populations propagated asexually.

Conclusions

We report the first experimental investigation of mutator dynamics in sexual populations. We show that a strong mutator quickly declines in sexual populations while hitchhiking to high frequency in asexual diploid populations, as predicted by theory. We also show that the msh2Δ mutator has a high and immediate realized cost that is alone sufficient to explain its decline in sexual populations. We postulate that this cost is indirect; namely, that it is due to a very high rate of recessive lethal or strongly deleterious mutation. However, we cannot rule out the possibility that msh2Δ also has unknown directly deleterious effects on fitness, and that these effects may differ between haploid asexual and sexual populations. Despite these reservations, our results prompt us to speculate that the short-term cost of highly deleterious recessive mutations can be as important as recombination in preventing mutator hitchhiking in sexual populations.

The balance between mutators and nonmutators in asexual populations

Mutator alleles, which elevate an individual's mutation rate from 10 to 10,000-fold, have been found at high frequencies in many natural and experimental populations. Mutators are continually produced from nonmutators, often due to mutations in mismatch-repair genes. These mutators gradually accumulate deleterious mutations, limiting their spread. However, they can occasionally hitchhike to high frequencies with beneficial mutations. We study the interplay between these effects. We first analyze the dynamics of the balance between the production of mutator alleles and their elimination due to deleterious mutations. We find that when deleterious mutation rates are high in mutators, there will often be many "young," recently produced mutators in the population, and the fact that deleterious mutations only gradually eliminate individuals from a population is important. We then consider how this mutator-nonmutator balance can be disrupted by beneficial mutations and analyze the circumstances in which fixation of mutator alleles is likely. We find that dynamics is crucial: even in situations where selection on average acts against mutators, so they cannot stably invade, the mutators can still occasionally generate beneficial mutations and hence be important to the evolution of the population.

Fitness-dependent mutation rates in finite populations

Mutation rate may be condition dependent, whereby individuals in poor condition, perhaps from high mutation load, have higher mutation rates than individuals in good condition. Agrawal (J. Evol. Biol.15, 2002, 1004) explored the basic properties of fitness-dependent mutation rate (FDMR) in infinite populations and reported some heuristic results for finite populations. The key parameter governing how infinite populations evolve under FDMR is the curvature (k) of the relationship between fitness and mutation rate. We extend Agrawal's analysis to finite populations and consider dominance and epistasis. In finite populations, the probability of long-term existence depends on k. In sexual populations, positive curvature leads to low equilibrium mutation rate, whereas negative curvature results in high mutation rate. In asexual populations, negative curvature results in rapid extinction via 'mutational meltdown', whereas positive curvature sometimes allows persistence. We speculate that fitness-dependent mutation rate may provide the conditions for genetic architecture to diverge between sexual and asexual taxa.

Rapid decline in fitness of mutation accumulation lines of gonochoristic (outcrossing) Caenorhabditis nematodes

Evolutionary theory predicts that the strength of natural selection to reduce the mutation rate should be stronger in self-fertilizing than in outcrossing taxa. However, the relative efficacy of selection on mutation rate relative to the many other factors influencing the evolution of any species is poorly understood. To address this question, we allowed mutations to accumulate for ∼100 generations in several sets of "mutation accumulation" (MA) lines in three species of gonochoristic (dieocious) Caenorhabditis (C. remanei, C. brenneri, C. sp. 5) as well as in a dioecious strain of the historically self-fertile hermaprohodite C. elegans. In every case, the rate of mutational decay is substantially greater in the gonochoristic taxa than in C. elegans (∼4× greater on average). Residual heterozygosity in the ancestral controls of these MA lines introduces some complications in interpreting the results, but circumstantial evidence suggests the results are not primarily due to inbreeding depression resulting from residual segregating variation. The results suggest that natural selection operates to optimize the mutation rate in Caenorhabditis and that the strength (or efficiency) of selection differs consistently on the basis of mating system, as predicted by theory. However, context-dependent environmental and/or synergistic epistasis could also explain the results.

Kick-starting the ratchet: the fate of mutators in an asexual population

Muller's ratchet operates in asexual populations without intergenomic recombination. In this case, deleterious mutations will accumulate and population fitness will decline over time, possibly endangering the survival of the species. Mutator mutations, i.e., mutations that lead to an increased mutation rate, will play a special role for the behavior of the ratchet. First, they are part of the ratchet and can come to dominance through accumulation in the ratchet. Second, the fitness-loss rate of the ratchet is very sensitive to changes in the mutation rate and even a modest increase can easily set the ratchet in motion. In this article we simulate the interplay between fitness loss from Muller's ratchet and the evolution of the mutation rate from the fixation of mutator mutations. As long as the mutation rate is increased in sufficiently small steps, an accelerating ratchet and eventual extinction are inevitable. If this can be countered by antimutators, i.e., mutations that reduce the mutation rate, an equilibrium can be established for the mutation rate at some level that may allow survival. However, the presence of the ratchet amplifies fluctuations in the mutation rate and, even at equilibrium, these fluctuations can lead to dangerous bursts in the ratchet. We investigate the timescales of these processes and discuss the results with reference to the genome degradation of the aphid endosymbiont Buchnera aphidicola.

Male mutation bias and possible long-term effects of human activities

The ability of a population to adapt to changing environments depends critically on the amount and kind of genetic variability it possesses. Mutations are an important source of new genetic variability and may lead to new adaptations, especially if the population size is large. Mutation rates are extremely variable between and within species, and males usually have higher mutation rates as a result of elevated rates of male germ cell division. This male bias affects the overall mutation rate. We examined the factors that influence male mutation bias, and focused on the effects of classical life-history parameters, such as the average age at reproduction and elevated rates of sperm production in response to sexual selection and sperm competition. We argue that human-induced changes in age at reproduction or in sexual selection will affect male mutation biases and hence overall mutation rates. Depending on the effective population size, these changes are likely to influence the long-term persistence of a population.

Impacts of mutation effects and population size on mutation rate in asexual populations: a simulation study

Background

In any natural population, mutation is the primary source of genetic variation required for evolutionary novelty and adaptation. Nevertheless, most mutations, especially those with phenotypic effects, are harmful and are consequently removed by natural selection. For this reason, under natural selection, an organism will evolve to a lower mutation rate. Overall, the action of natural selection on mutation rate is related to population size and mutation effects. Although theoretical work has intensively investigated the relationship between natural selection and mutation rate, most of these studies have focused on individual competition within a population, rather than on competition among populations. The aim of the present study was to use computer simulations to investigate how natural selection adjusts mutation rate among asexually reproducing subpopulations with different mutation rates.

Results

The competition results for the different subpopulations showed that a population could evolve to an "optimum" mutation rate during long-term evolution, and that this rate was modulated by both population size and mutation effects. A larger population could evolve to a higher optimum mutation rate than could a smaller population. The optimum mutation rate depended on both the fraction and the effects of beneficial mutations, rather than on the effects of deleterious ones. The optimum mutation rate increased with either the fraction or the effects of beneficial mutations. When strongly favored mutations appeared, the optimum mutation rate was elevated to a much higher level. The competition time among the subpopulations also substantially shortened.

Conclusions

Competition at the population level revealed that the evolution of the mutation rate in asexual populations was determined by both population size and mutation effects. The most striking finding was that beneficial mutations, rather than deleterious mutations, were the leading force that modulated the optimum mutation rate. The initial configuration of the population appeared to have no effect on these conclusions, confirming the robustness of the simulation method developed in the present study. These findings might further explain the lower mutation rates observed in most asexual organisms, as well as the higher mutation rates in some viruses.

The rate of establishment of complex adaptations

A central problem in evolutionary theory concerns the mechanisms by which adaptations requiring multiple mutations emerge in natural populations. We develop a series of expressions that clarify the scaling of the time to establishment of complex adaptations with population size, mutation rate, magnitude of the selective disadvantage of intermediate-state alleles, and the complexity of the adaptation. In general, even in the face of deleterious intermediate steps, the time to establishment is minimized in populations with very large size. Under a broad range of conditions, the time to establishment also scales by no more than the square of the mutation rate, regardless of the number of sites contributing to the adaptive change, demonstrating that the emergence of complex adaptations is only weakly constrained by the independent acquisition of mutations at the underlying sites. Mutator alleles with deleterious side effects have only moderate effects on the rate of adaptation in large populations but can cause a quantum decrease in the time to establishment of some adaptive alleles in small populations, although probably not at a high enough rate to offset the increased deleterious mutation load. Transient hypermutability, whereby a subset of gamete-producing cells mutate at an elevated rate in a nonheritable manner, may also elevate the rate of adaptation, although the effect is modest and appears to result from a simple increase in the rate of transitions between intermediate states rather than from the saltational production of doublet mutations. Taken together, these results illustrate the plausibility of the relatively rapid emergence of specific complex adaptations by conventional population genetic mechanisms and provide insight into the relative incidences of various paths of allelic adaptation in organisms with different population genetic features.

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 Pfix 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 Pfix successfully captures effects ii and iii when selection is fast compared to mutation (micro/s<<1). 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.

Deletion rate evolution and its effect on genome size and coding density

Deletion rates are thought to be important factors in determining the genome size of organisms in nature. Although it is indisputable that deletions, and thus deletion rates, affect genome size, it is unclear how, or indeed if, genome size is regulated via the deletion rate. Here, we employ a mathematical model to determine the evolutionary fate of deletion rate mutants. Simulations are employed to explore the interactions between deletions, deletion rate mutants, and genome size. The results show that, in this model, the fate of deletion rate mutants will depend on the fraction of essential genomic material, on the frequency of sexual recombination, as well as on the population size of the organism. We find that there is no optimal deletion rate in any state. However, at one critical coding density, all changes in deletion rate are neutral and the rate may drift either up or down. As a consequence, the coding density of the genome is expected to fluctuate around this critical density. Characteristic differences in the impact of deletion rate mutations on prokaryote and eukaryote genomes are described.

Evolution of mutation rates: phylogenomic analysis of the photolyase/cryptochrome family

Photoreactivation, one of the first DNA repair pathways to evolve, is the direct reversal of premutagenic lesions caused by ultraviolet (UV) irradiation, catalyzed by photolyases in a light-dependent, single-enzyme reaction. It has been experimentally shown that photoreactivation prevents UV mutagenesis in a broad range of species. In the absence of photoreactivation, UV-induced photolesions are repaired by the more complex and much less efficient nucleotide excision repair pathway. Despite their obvious beneficial effects, several lineages, including placental mammals, lost photolyase genes during evolution. In this study, we ask why photolyase genes have been lost in those lineages and discuss the significance of these losses in the context of the evolution of the genomic mutation rates. We first perform an extensive phylogenomic analysis of the photolyase/cryptochrome family, to assess what species lack each kind of photolyase gene. Then, we estimate the ratio of nonsynonymous to synonymous substitution rates in several groups of photolyase genes, as a proxy of the strength of purifying natural selection, and we ask whether less evolutionarily constrained photolyase genes are more likely lost. We also review functional data and compare the efficiency of different kinds of photolyases. We find that eukaryotic photolyases are, on average, less evolutionarily constrained than eubacterial ones and that the strength of natural selection is correlated with the affinity of photolyases for their substrates. We propose that the loss of photolyase genes in eukaryotic species may be due to weak natural selection and may result in a deleterious increase of their genomic mutation rates. In contrast, the loss of photolyase genes in prokaryotes may not cause an increase in the mutation rate and be neutral in most cases.