Fixation of clonal lineages under Muller's ratchet

For clonal lineages of finite size that differ in their deleterious mutational effects, the probability of fixation is investigated by mathematical theory and Monte Carlo simulations. If these fitness effects are sufficiently small in one or both lineages, then the lineage with the less deleterious effects will become fixed with high probability. If, however, in both lineages the deleterious effects are larger than a threshold s(c), then the probability of fixation is independent of the fitness effects and depends only on the initial frequencies of the lineages. This threshold decreases with decreasing genomic mutation rate U and increases with population size N. (For N = 10(5), we have s(c) approximately = 0.1 if U = 1, and s(c) approximately = 0.015 if U = 0.1). Above the threshold, the competition is not driven by the ratio of mean fitnesses of the lineages, but by the relative sizes of the zero-mutation classes, which are independent of the fitness effects of the mutations. After the loss of the zero-mutation class of a lineage, the other lineage will spread to fixation with high probability and within a short time span. If the mutation rates of the lineages differ substantially, the lineage with the lower mutation rate is fixed with very high probability unless the lineage with the larger mutation rate has very slightly deleterious mutational effects. If the mutation rates differ by not more than a few percent, then the lineage with the higher mutation rate and the more deleterious effects can become fixed with appreciable probability for a certain range of parameters. The independence of the fixation probability on the fitness effects in a single population leads to dramatic effects in metapopulations: lineages with more deleterious effects have a much higher fixation probability. The critical value s(c), above which this phenomenon occurs, decreases as the migration rate between the subpopulations decreases.     

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.     

Sexual selection and its effect on the fixation of an asexual clone

Sexual selection is a powerful and ubiquitous force in sexual populations. It has recently been argued that sexual selection can eliminate the twofold cost of sex even with low genomic mutation rates. By means of differential male mating success, deleterious mutations in males become more deleterious than in females, and it has been shown that sexual selection can drastically reduce the mutational load in a sexual population, with or without any form of epistasis. However, any mechanism that claims to maintain sexual reproduction must be able to prevent the fixation of an asexual mutant clone with a twofold fitness advantage. Here, I show that despite very strong sexual selection, the fixation of an asexual mutant cannot be prevented under reasonable genomic mutation rates. Sexual selection can have a strong effect on the average mutational load in a sexual population, but as it cannot prevent the fixation of an asexual mutant, it is unlikely to play a key role on the maintenance of sexual reproduction.     

Properties of spontaneous mutations affecting quantitative traits

Recent mutation accumulation results from invertebrate species suggest that mild deleterious mutation is far less frequent than previously thought, implying smaller expressed mutational loads. Although the rate (lambda) and effect (s) of very slight deleterious mutation remain unknown, most mutational fitness decline would come from moderately deleterious mutation (s approximately 0.2, lambda approximately 0.03), and this situation would not qualitatively change in harsh environments. Estimates of the average coefficient of dominance (h) of non-severe deleterious mutations are controversial. The typical value of h = 0.4 can be questioned, and a lower estimate (about 0.1) is suggested. Estimated mutational parameters are remarkably alike for morphological and fitness component traits (excluding lethals), indicating low mutation rates and moderate mutational effects, with a distribution generally showing strong negative asymmetry and little leptokurtosis. New mutations showed considerable genotype-environment interaction. However, the mutational variance of fitness-component traits due to non-severe detrimental mutations did not increase with environmental harshness. For morphological traits, a class of predominantly additive mutations with no detectable effect on fitness and relatively small effect on the trait was identified. This should be close to that responsible for standing variation in natural populations.     

Mutational bias for body size in rhabditid nematodes

Mutational bias is a potentially important agent of evolution, but it is difficult to disentangle the effects of mutation from those of natural selection. Mutation-accumulation experiments, in which mutations are allowed to accumulate at very small population size, thus minimizing the efficiency of natural selection, are the best way to separate the effects of mutation from those of selection. Body size varies greatly among species of nematode in the family rhabditidae; mutational biases are both a potential cause and a consequence of that variation. We report data on the cumulative effects of mutations that affect body size in three species of rhabditid nematode that vary fivefold in adult size. Results are very consistent with previous studies of mutations underlying fitness in the same strains: two strains of Caenorhabditis briggsae decline in body size about twice as fast as two strains of C. elegans, with a concomitant higher point estimate of the genomic mutation rate; the confamilial Oscheius myriophila is intermediate. There is an overall mutational bias, such that mutations reduce size on average, but the bias appears consistent between species. The genetic correlation between mutations that affect size and those underlying fitness is large and positive, on average.     

PERSPECTIVE: SPONTANEOUS DELETERIOUS MUTATION

Mildly deleterious mutation has been invoked as a leading explanation for a diverse array of observations in evolutionary genetics and molecular evolution and is thought to be a significant risk of extinction for small populations. However, much of the empirical evidence for the deleterious-mutation process derives from studies of Drosophila melanogaster, some of which have been called into question. We review a broad array of data that collectively support the hypothesis that deleterious mutations arise in flies at rate of about one per individual per generation, with the average mutation decreasing fitness by about only 2% in the heterozygous state. Empirical evidence from microbes, plants, and several other animal species provide further support for the idea that most mutations have only mildly deleterious effects on fitness, and several other species appear to have genomic mutation rates that are of the order of magnitude observed in Drosophila. However, there is mounting evidence that some organisms have genomic deleterious mutation rates that are substantially lower than one per individual per generation. These lower rates may be at least partially reconciled with the Drosophila data by taking into consideration the number of germline cell divisions per generation. To fully resolve the existing controversy over the properties of spontaneous mutations, a number of issues need to be clarified. These include the form of the distribution of mutational effects and the extent to which this is modified by the environmental and genetic background and the contribution of basic biological features such as generation length and genome size to interspecific differences in the genomic mutation rate. Once such information is available, it should be possible to make a refined statement about the long-term impact of mutation on the genetic integrity of human populations subject to relaxed selection resulting from modern medical procedures.     

Mutational History of a Human Cell Lineage from Somatic to Induced Pluripotent Stem Cells

The accuracy of replicating the genetic code is fundamental. DNA repair mechanisms protect the fidelity of the genome ensuring a low error rate between generations. This sustains the similarity of individuals whilst providing a repertoire of variants for evolution. The mutation rate in the human genome has recently been measured to be 50–70 de novo single nucleotide variants (SNVs) between generations. During development mutations accumulate in somatic cells so that an organism is a mosaic. However, variation within a tissue and between tissues has not been analysed. By reprogramming somatic cells into induced pluripotent stem cells (iPSCs), their genomes and the associated mutational history are captured. By sequencing the genomes of polyclonal and monoclonal somatic cells and derived iPSCs we have determined the mutation rates and show how the patterns change from a somatic lineage in vivo through to iPSCs. Somatic cells have a mutation rate of 14 SNVs per cell per generation while iPSCs exhibited a ten-fold lower rate. Analyses of mutational signatures suggested that deamination of methylated cytosine may be the major mutagenic source in vivo, whilst oxidative DNA damage becomes dominant in vitro. Our results provide insights for better understanding of mutational processes and lineage relationships between human somatic cells. Furthermore it provides a foundation for interpretation of elevated mutation rates and patterns in cancer.     

A comprehensive model of mutations affecting fitness and inferences for Arabidopsis thaliana

As the ultimate source of genetic variation, spontaneous mutation is essential to evolutionary change. Theoretical studies over several decades have revealed the dependence of evolutionary consequences of mutation on specific mutational properties, including genomic mutation rates, U, and the effects of newly arising mutations on individual fitness, s. The recent resurgence of empirical effort to infer these properties for diverse organisms has not achieved consensus. Estimates, which have been obtained by methods that assume mutations are unidirectional in their effects on fitness, are imprecise. Both because a general approach must allow for occurrence of fitness-enhancing mutations, even if these are rare, and because recent evidence demands it, we present a new method for inferring mutational parameters. For the distribution of mutational effects, we retain Keightley's assumption of the gamma distribution, to take advantage of the flexibility of its shape. Because the conventional gamma is one sided, restricting it to unidirectional effects, we include an additional parameter, rho, as an amount it is displaced from zero. Estimation is accomplished by Markov chain Monte Carlo maximum likelihood. Through a limited set of simulations, we verify the accuracy of this approach. We apply it to analyze data on two reproductive fitness components from a 17-generation mutation-accumulation study of a Columbia accession of Arabidopsis thaliana in which 40 lines sampled in three generations were assayed simultaneously. For these traits, U approximately/= 0.1-0.2, with distributions of mutational effects broadly spanning zero, such that roughly half the mutations reduce reproductive fitness. One evolutionary consequence of these results is lower extinction risks of small populations of A. thaliana than expected from the process of mutational meltdown. A comprehensive view of the evolutionary consequences of mutation will depend on quantitatively accounting for fitness-enhancing, as well as fitness-reducing, mutations.     

Warmer temperatures enhance beneficial mutation effects

Temperature determines the rates of all biochemical and biophysical processes, and is also believed to be a key driver of macroevolutionary patterns. It is suggested that physiological constraints at low temperatures may diminish the fitness advantages of otherwise beneficial mutations; by contrast, relatively high, benign, temperatures allow beneficial mutations to efficiently show their phenotypic effects. To experimentally test this “mutational effects” mechanism, we examined the fitness effects of mutations across a temperature gradient using bacterial genotypes from the early stage of a mutation accumulation experiment with Escherichia coli. While the incidence of beneficial mutations did not significantly change across environmental temperatures, the number of mutations that conferred strong beneficial fitness effects was greater at higher temperatures. The results therefore support the hypothesis that warmer temperatures increase the chance and magnitude of positive selection, with implications for explaining the geographic patterns in evolutionary rates and understanding contemporary evolution under global warming.     

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

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

Lethal mutagenesis and evolutionary epidemiology

The lethal mutagenesis hypothesis states that within-host populations of pathogens can be driven to extinction when the load of deleterious mutations is artificially increased with a mutagen, and becomes too high for the population to be maintained. Although chemical mutagens have been shown to lead to important reductions in viral titres for a wide variety of RNA viruses, the theoretical underpinnings of this process are still not clearly established. A few recent models sought to describe lethal mutagenesis but they often relied on restrictive assumptions. We extend this earlier work in two novel directions. First, we derive the dynamics of the genetic load in a multivariate Gaussian fitness landscape akin to classical quantitative genetics models. This fitness landscape yields a continuous distribution of mutation effects on fitness, ranging from deleterious to beneficial (i.e. compensatory) mutations. We also include an additional class of lethal mutations. Second, we couple this evolutionary model with an epidemiological model accounting for the within-host dynamics of the pathogen. We derive the epidemiological and evolutionary equilibrium of the system. At this equilibrium, the density of the pathogen is expected to decrease linearly with the genomic mutation rate U. We also provide a simple expression for the critical mutation rate leading to extinction. Stochastic simulations show that these predictions are accurate for a broad range of parameter values. As they depend on a small set of measurable epidemiological and evolutionary parameters, we used available information on several viruses to make quantitative and testable predictions on critical mutation rates. In the light of this model, we discuss the feasibility of lethal mutagenesis as an efficient therapeutic strategy.     

Recombination and the evolution of mutational robustness

Mutational robustness is the degree to which a phenotype, such as fitness, is resistant to mutational perturbations. Since most of these perturbations will tend to reduce fitness, robustness provides an immediate benefit for the mutated individual. However, robust systems decay due to the accumulation of deleterious mutations that would otherwise have been cleared by selection. This decay has received very little theoretical attention. At equilibrium, a population or asexual lineage is expected to have a mutation load that is invariant with respect to the selection coefficient of deleterious alleles, so the benefit of robustness (at the level of the population or asexual lineage) is temporary. However, previous work has shown that robustness can be favoured when robustness loci segregate independently of the mutating loci they act upon. We examine a simple two-locus model that allows for intermediate rates of recombination and inbreeding to show that increasing the effective recombination rate allows for the evolution of greater mutational robustness.     

Stress-induced mutagenesis and complex adaptation

Because mutations are mostly deleterious, mutation rates should be reduced by natural selection. However, mutations also provide the raw material for adaptation. Therefore, evolutionary theory suggests that the mutation rate must balance between adaptability—the ability to adapt—and adaptedness—the ability to remain adapted. We model an asexual population crossing a fitness valley and analyse the rate of complex adaptation with and without stress-induced mutagenesis (SIM)—the increase of mutation rates in response to stress or maladaptation. We show that SIM increases the rate of complex adaptation without reducing the population mean fitness, thus breaking the evolutionary trade-off between adaptability and adaptedness. Our theoretical results support the hypothesis that SIM promotes adaptation and provide quantitative predictions of the rate of complex adaptation with different mutational strategies.     

RATES OF FITNESS DECLINE AND REBOUND SUGGEST PERVASIVE EPISTASIS

Unraveling the factors that determine the rate of adaptation is a major question in evolutionary biology. One key parameter is the effect of a new mutation on fitness, which invariably depends on the environment and genetic background. The fate of a mutation also depends on population size, which determines the amount of drift it will experience. Here, we manipulate both population size and genotype composition and follow adaptation of 23 distinct Escherichia coli genotypes. These have previously accumulated mutations under intense genetic drift and encompass a substantial fitness variation. A simple rule is uncovered: the net fitness change is negatively correlated with the fitness of the genotype in which new mutations appear—a signature of epistasis. We find that Fisher's geometrical model can account for the observed patterns of fitness change and infer the parameters of this model that best fit the data, using Approximate Bayesian Computation. We estimate a genomic mutation rate of 0.01 per generation for fitness altering mutations, albeit with a large confidence interval, a mean fitness effect of mutations of ?0.01, and an effective number of traits nine in mutS^? E. coli. This framework can be extended to confront a broader range of models with data and test different classes of fitness landscape models.     

Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity,Determinism, and Genetic Assimilation

Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother’s old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother’s old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington’s genetic assimilation. Our model is able to quantify the evolution of the assimilation because it characterizes the fitness consequences of variation.     

Mutation accumulation may be a minor force in shaping life history traits

Is senescence the adaptive result of tradeoffs between younger and older ages or the nonadaptive burden of deleterious mutations that act at older ages? To shed new light on this unresolved question we combine adaptive and nonadaptive processes in a single model. Our model uses Penna''s bit-strings to capture different age-specific mutational patterns. Each pattern represents a genotype and for each genotype we find the life history strategy that maximizes fitness. Genotypes compete with each other and are subject to selection and to new mutations over generations until equilibrium in gene-frequencies is reached. The mutation-selection equilibrium provides information about mutational load and the differential effects of mutations on a life history trait - the optimal age at maturity. We find that mutations accumulate only at ages with negligible impact on fitness and that mutation accumulation has very little effect on the optimal age at maturity. These results suggest that life histories are largely determined by adaptive processes. The non-adaptive process of mutation accumulation seems to be unimportant at evolutionarily relevant ages.     

Construction of a supF-based system for detection of mutations in the chromosomal DNA of Arabidopsis

The factors maintaining genomic integrity, which have been studied in detail in other species, have yet to be investigated in plants. Recent progress in gene-silencing technology has made it possible to produce transgenic plants with loss-of-function phenotypes for the effective analysis of these factors, even with the high redundancy of genes in plants. Therefore, a mutation-detection system for plants is necessary to estimate the biological function of a target gene for mutation frequencies and spectra. Here, we reported the development of a novel system to analyze mutations in the chromosomal DNA of plants. The supF gene of E. coli was used as a target for the mutation because it was possible to detect all mutational base changes. Based on the plasmid pTN30, which carries supF, we constructed a binary Ti vector for its introduction to Arabidopsis genomes. The system was validated by measuring mutations in both non-treated and mutagen-treated transgenic plants. DNA fragments including pTN30 were rescued from the plants, and introduced into E. coli KS40/pOF105 to isolate the supF mutant clones conferring both nalidixic acid and streptomycin resistance on transformants. We found that the mutation frequency was approximately three times higher with the ethyl methanesulfonate (EMS) treatment than without it and G:C to A:T transitions dominated, which was the most reasonable mutation induced by EMS. These results show that this system allowed for the rapid analysis of mutations in plants, and may be useful for analyzing plant genes related to the functions of genomic stability and monitoring environmental genotoxic substances.     

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.     

On the mutation rate of herpes simplex virus type 1

All seven DNA-based microbes for which carefully established mutation rates and mutational spectra were previously available displayed a genomic mutation rate in the neighborhood of 0.003 per chromosome replication. The pathogenic mammalian DNA virus herpes simplex type 1 has an estimated genomic mutation rate compatible with that value.     

Mutation-selection balance: ancestry,load, and maximum principle

We analyze the equilibrium behavior of deterministic haploid mutation-selection models. To this end, both the forward and the time-reversed evolution processes are considered. The stationary state of the latter is called the ancestral distribution, which turns out as a key for the study of mutation-selection balance. We find that the ancestral genotype frequencies determine the sensitivity of the equilibrium mean fitness to changes in the corresponding fitness values and discuss implications for the evolution of mutational robustness. We further show that the difference between the ancestral and the population mean fitness, termed mutational loss, provides a measure for the sensitivity of the equilibrium mean fitness to changes in the mutation rate. The interrelation of the loss and the mutation load is discussed. For a class of models in which the number of mutations in an individual is taken as the trait value, and fitness is a function of the trait, we use the ancestor formulation to derive a simple maximum principle, from which the mean and variance of fitness and the trait may be derived; the results are exact for a number of limiting cases, and otherwise yield approximations which are accurate for a wide range of parameters. These results are applied to threshold phenomena caused by the interplay of selection and mutation (known as error thresholds). They lead to a clarification of concepts, as well as criteria for the existence of error thresholds.