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

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

Gene conversion may aid adaptive peak shifts

Gene conversion is often viewed as a homogenizing force that opposes adaptive evolution. The objective of this study is to suggest a potential role for gene conversion in adaptive evolution of proteins through aiding the transfer of a population from one adaptive peak to another. Our hypothesis starts with the observation that a tandem gene duplication may result in an extra gene copy that is released from selective constraints. In such cases, individually deleterious mutations may accumulate on the extra copy of the gene, and through gene conversion these mutations may subsequently be presented to the functioning gene for selection en masse. Thus, groups of mutations that jointly confer a selective advantage may regularly be made available for selection. We present a mathematical model of this process and identify the range of rates of gene conversion, gene duplication and mutation under which it may operate. The results indicate that the process may be biologically feasible if the rate of appearance of the potentially beneficial mutations is not too small in relation to the rates of null mutation and of gene conversion. This process appears to be a possible mechanism for effecting adaptive peak shifts in large populations. We show that all the evolutionary steps in the proposed model may have occurred in the evolution of primate gamma -globin genes. We suggest that hide-and-release mechanisms for genetic variation may constitute a more general principal of evolvability.     

Rate of adaptive peak shifts with partial genetic robustness

How adaptive evolution occurs with individually deleterious but jointly beneficial mutations has been one of the major problems in population genetics theory. Adaptation in this case is commonly described as a population's escape from a local peak to a higher peak on Sewall Wright's fitness landscape. Recent molecular genetic and computational studies have suggested that genetic robustness can facilitate such peak shifts. If phenotypic expressions of new mutations are suppressed under genetic robustness, mutations that are otherwise deleterious can accumulate in the population as neutral variants. When the robustness is perturbed by an environmental change or a major mutation, these variants become exposed to natural selection. It is argued that this process promotes adaptation because allelic combinations enriched under genetic robustness can then be positively selected. Here, I propose simple two- and three-locus models of adaptation with partial genetic robustness as suggested by recent studies. The waiting time until the fixation of an adaptive haplotype was observed in stochastic simulations and compared to the expectation without robustness. It is shown that peak shifts can be delayed or accelerated depending on the conditions of genetic robustness. The evolutionary significance of these processes is discussed.     

Environmental change exposes beneficial epistatic interactions in a catalytic RNA

Natural selection drives populations of individuals towards local peaks in a fitness landscape. These peaks are created by the interactions between individual mutations. Fitness landscapes may change as an environment changes. In a previous contribution, we discovered a variant of the Azoarcus group I ribozyme that represents a local peak in the RNA fitness landscape. The genotype at this peak is distinguished from the wild-type by four point mutations. We here report ribozyme fitness data derived from constructing all possible combinations of these point mutations. We find that these mutations interact epistatically. Importantly, we show that these epistatic interactions change qualitatively in the three different environments that we studied. We find examples where the relative fitness of a ribozyme can change from neutral or negative in one environment, to positive in another. We also show that the fitness effect of a specific GC-AU base pair switch is dependent on both the environment and the genetic context. Moreover, the mutations that we study improve activity at the cost of decreased structural stability. Environmental change is ubiquitous in nature. Our results suggest that such change can facilitate adaptive evolution by exposing new peaks of a fitness landscape. They highlight a prominent role for genotype-environment interactions in doing so.     

ADAPTIVE WALKS AND DISTRIBUTION OF BENEFICIAL FITNESS EFFECTS

We study the adaptation dynamics of a maladapted asexual population on rugged fitness landscapes with many local fitness peaks. The distribution of beneficial fitness effects is assumed to belong to one of the three extreme value domains, viz. Weibull, Gumbel, and Fréchet. We work in the strong selection‐weak mutation regime in which beneficial mutations fix sequentially, and the population performs an uphill walk on the fitness landscape until a local fitness peak is reached. A striking prediction of our analysis is that the fitness difference between successive steps follows a pattern of diminishing returns in the Weibull domain and accelerating returns in the Fréchet domain, as the initial fitness of the population is increased. These trends are found to be robust with respect to fitness correlations. We believe that this result can be exploited in experiments to determine the extreme value domain of the distribution of beneficial fitness effects. Our work here differs significantly from the previous ones that assume the selection coefficient to be small. On taking large effect mutations into account, we find that the length of the walk shows different qualitative trends from those derived using small selection coefficient approximation.     

Genome structure and the benefit of sex

We examine the behavior of sexual and asexual populations in modular multipeaked fitness landscapes and show that sexuals can systematically reach different, higher fitness adaptive peaks than asexuals. Whereas asexuals must move against selection to escape local optima, sexuals reach higher fitness peaks reliably because they create specific genetic variants that "skip over" fitness valleys, moving from peak to peak in the fitness landscape. This occurs because recombination can supply combinations of mutations in functional composites or "modules," that may include individually deleterious mutations. Thus when a beneficial module is substituted for another less-fit module by sexual recombination it provides a genetic variant that would require either several specific simultaneous mutations in an asexual population or a sequence of individual mutations some of which would be selected against. This effect requires modular genomes, such that subsets of strongly epistatic mutations are tightly physically linked. We argue that such a structure is provided simply by virtue of the fact that genomes contain many genes each containing many strongly epistatic nucleotides. We briefly discuss the connections with "building blocks" in the evolutionary computation literature. We conclude that there are conditions in which sexuals can systematically evolve high-fitness genotypes that are essentially unevolvable for asexuals.     

The effects of weak selection on neutral diversity at linked sites

The effects of selection on variability at linked sites have an important influence on levels and patterns of within-population variation across the genome. Most theoretical models of these effects have assumed that selection is sufficiently strong that allele frequency changes at the loci concerned are largely deterministic. These models have led to the conclusion that directional selection for selectively favorable mutations, or against recurrent deleterious mutations, reduces nucleotide site diversity at linked neutral sites. Recent work has shown, however, that fixations of weakly selected mutations, accompanied by significant stochastic changes in allele frequencies, can sometimes cause higher diversity at linked sites when compared with the effects of fixations of neutral mutations. This study extends this work by deriving approximate expressions for the mean conditional times to fixation and loss of mutations subject to selection, and analyzing the conditions under which selection increases rather than reduces these times. Simulations are used to examine the relations between diversity at a neutral site and the fixation and loss times of mutations at a linked site that is subject to selection. It is shown that the long-term level of neutral diversity can be increased over the purely neutral value by recurrent fixations and losses of linked, weakly selected dominant or partially dominant favorable mutations, or linked recessive or partially recessive deleterious mutations. The results are used to examine the conditions under which associative overdominance, as opposed to background selection, is likely to operate.     

Deleterious Mutations, Apparent Stabilizing Selection and the Maintenance of Quantitative Variation

Apparent stabilizing selection on a quantitative trait that is not causally connected to fitness can result from the pleiotropic effects of unconditionally deleterious mutations, because as N. Barton noted, "...individuals with extreme values of the trait will tend to carry more deleterious alleles...." We use a simple model to investigate the dependence of this apparent selection on the genomic deleterious mutation rate, U; the equilibrium distribution of K, the number of deleterious mutations per genome; and the parameters describing directional selection against deleterious mutations. Unlike previous analyses, we allow for epistatic selection against deleterious alleles. For various selection functions and realistic parameter values, the distribution of K, the distribution of breeding values for a pleiotropically affected trait, and the apparent stabilizing selection function are all nearly Gaussian. The additive genetic variance for the quantitative trait is kQa2, where k is the average number of deleterious mutations per genome, Q is the proportion of deleterious mutations that affect the trait, and a2 is the variance of pleiotropic effects for individual mutations that do affect the trait. In contrast, when the trait is measured in units of its additive standard deviation, the apparent fitness function is essentially independent of Q and a2; and beta, the intensity of selection, measured as the ratio of additive genetic variance to the "variance" of the fitness curve, is very close to s = U/k, the selection coefficient against individual deleterious mutations at equilibrium. Therefore, this model predicts appreciable apparent stabilizing selection if s exceeds about 0.03, which is consistent with various data. However, the model also predicts that beta must equal Vm/VG, the ratio of new additive variance for the trait introduced each generation by mutation to the standing additive variance. Most, although not all, estimates of this ratio imply apparent stabilizing selection weaker than generally observed. A qualitative argument suggests that even when direct selection is responsible for most of the selection observed on a character, it may be essentially irrelevant to the maintenance of variation for the character by mutation-selection balance. Simple experiments can indicate the fraction of observed stabilizing selection attributable to the pleiotropic effects of deleterious mutations.     

Neofunctionalization of duplicated genes under the pressure of gene conversion

Neofunctionalization occurs when a neofunctionalized allele is fixed in one of duplicated genes. This is a simple fixation process if duplicated genes accumulate mutations independently. However, the process is very complicated when duplicated genes undergo concerted evolution by gene conversion. Our simulations demonstrate that the process could be described with three distinct stages. First, a newly arisen neofunctionalized allele increases in frequency by selection, but gene conversion prevents its complete fixation. These two factors (selection and gene conversion) that work in opposite directions create an equilibrium, and the time during which the frequency of the neofunctionalized allele drifts around the equilibrium value is called the temporal equilibrium stage. During this temporal equilibrium stage, it is possible that gene conversion is inactivated by mutations, which allow the complete fixation of the neofunctionalized allele. And then, permanent neofunctionalization is achieved. This article develops basic population genetics theories on the process to permanent neofunctionalization under the pressure of gene conversion. We obtain the probability and time that the frequency of a newly arisen neofunctionalized allele reaches the equilibrium value. It is also found that during the temporal equilibrium stage, selection exhibits strong signature in the divergence in the DNA sequences between the duplicated genes. The spatial distribution of the divergence likely has a peak around the site targeted by selection. We provide an analytical expression of the pattern of divergence and apply it to the human red- and green-opsin genes. The theoretical prediction well fits the data when we assume that selection is operating for the two amino acid differences in exon 5, which are believed to account for the major part of the functional difference between the red and green opsins.     

Apparent directional selection by biased pleiotropic mutation

Pleiotropic effects of deleterious mutations are considered to be among the factors responsible for genetic constraints on evolution by long-term directional selection acting on a quantitative trait. If pleiotropic phenotypic effects are biased in a particular direction, mutations generate apparent directional selection, which refers to the covariance between fitness and the trait owing to a linear association between the number of mutations possessed by individuals and the genotypic values of the trait. The present analysis has shown how the equilibrium mean value of the trait is determined by a balance between directional selection and biased pleiotropic mutations. Assuming that genes act additively both on the trait and on fitness, the total variance-standardized directional selection gradient was decomposed into apparent and true components. Experimental data on mutation bias from the bristle traits of Drosophila and life history traits of Daphnia suggest that apparent selection explains a small but significant fraction of directional selection pressure that is observed in nature; the data suggest that changes induced in a trait by biased pleiotropic mutation (i.e., by apparent directional selection) are easily compensated for by (true) directional selection.     

The Rate of Compensatory Evolution

A two-locus model is presented to analyze the evolution of compensatory mutations occurring in stems of RNA secondary structures. Single mutations are assumed to be deleterious but harmless (neutral) in appropriate combinations. In proceeding under mutation pressure, natural selection and genetic drift from one fitness peak to another one, a population must therefore pass through a valley of intermediate deleterious states of individual fitness. The expected time for this transition is calculated using diffusion theory. The rate of compensatory evolution, k(c), is then defined as the inverse of the expected transition time. When selection against deleterious single mutations is strong, k(c) depends on the recombination fraction r between the two loci. Recombination generally reduces the rate of compensatory evolution because it breaks up favorable combinations of double mutants. For complete linkage, k(c) is given by the rate at which favorable combinations of double mutants are produced by compensatory mutation. For r>0, k(c) decreases exponentially with r. In contrast, k(c) becomes independent of r for weak selection. We discuss the dynamics of evolutionary substitutions of compensatory mutants in relation to WRIGHT's shifting balance theory of evolution and use our results to analyze the substitution process in helices of mRNA secondary structures.     

The effect of parasites on sex differences in selection

The life history strategies of males and females are often divergent, creating the potential for sex differences in selection. Deleterious mutations may be subject to stronger selection in males, owing to sexual selection, which can improve the mean fitness of females and reduce mutation load in sexual populations. However, sex differences in selection might also maintain sexually antagonistic genetic variation, creating a sexual conflict load. The overall impact of separate sexes on fitness is unclear, but the net effect is likely to be positive when there is a large sex difference in selection against deleterious mutations. Parasites can also have sex-specific effects on fitness, and there is evidence that parasites can intensify the fitness consequences of deleterious mutations. Using lines that accumulated mutations for over 60 generations, we studied the effect of the pathogenic bacterium Pseudomonas aeruginosa on sex differences in selection in the fruit fly Drosophila melanogaster. Pseudomonas infection increased the sex difference in selection, but may also have weakened the intersexual correlation for fitness. Our results suggest that parasites may increase the benefits of sexual selection.     

Sexual selection on spontaneous mutations strengthens the between‐sex genetic correlation for fitness

A proposed benefit to sexual selection is that it promotes purging of deleterious mutations from populations. For this benefit to be realized, sexual selection, which is usually stronger on males, must purge mutations deleterious to both sexes. Here, we experimentally test the hypothesis that sexual selection on males purges deleterious mutations that affect both male and female fitness. We measured male and female fitness in two panels of spontaneous mutation‐accumulation lines of the fly, Drosophila serrata, each established from a common ancestor. One panel of mutation accumulation lines limited both natural and sexual selection (LS lines), whereas the other panel limited natural selection, but allowed sexual selection to operate (SS lines). Although mutation accumulation caused a significant reduction in male and female fitness in both the LS and SS lines, sexual selection had no detectable effect on the extent of the fitness reduction. Similarly, despite evidence of mutational variance for fitness in males and females of both treatments, sexual selection had no significant impact on the amount of mutational genetic variance for fitness. However, sexual selection did reshape the between‐sex correlation for fitness: significantly strengthening it in the SS lines. After 25 generations, the between‐sex correlation for fitness was positive but considerably less than one in the LS lines, suggesting that, although most mutations had sexually concordant fitness effects, sex‐limited, and/or sex‐biased mutations contributed substantially to the mutational variance. In the SS lines this correlation was strong and could not be distinguished from unity. Individual‐based simulations that mimick the experimental setup reveal two conditions that may drive our results: (1) a modest‐to‐large fraction of mutations have sex‐limited (or highly sex‐biased) fitness effects, and (2) the average fitness effect of sex‐limited mutations is larger than the average fitness effect of mutations that affect both sexes similarly.     

Constrained evolution of a quantitative character by pleiotropic mutation

The long-term response to directional selection and its selection limit are derived for a quantitative character that is controlled by pleiotropic mutations with direct deleterious effect on fitness. Directional selection is assumed to be weaker than the selection acting directly on mutations via deleterious effects (purging selection), which renders all mutations to eventual elimination. The analysis embedding this restrictive assumption indicates that the evolutionary response of the character starting from an equilibrium state, in which mutation and purging selection balance but no directional selection is operating, decreases monotonically with time at an exponential rate. And the fading rate of responses is mostly determined by the direct deleterious effect. Contrary to the expectation by the standard selection limit theory based on fixation of extant genetic variation, the present model predicts that the selection limit depends on the intensity of directional selection, the limit being proportional to the ratio of the directional selection intensity to the direct deleterious effect. A slightly larger genetic variance is maintained at the selection limit than would be without directional selection.     

Natural selection affects multiple aspects of genetic variation at putatively neutral sites across the human genome

A major question in evolutionary biology is how natural selection has shaped patterns of genetic variation across the human genome. Previous work has documented a reduction in genetic diversity in regions of the genome with low recombination rates. However, it is unclear whether other summaries of genetic variation, like allele frequencies, are also correlated with recombination rate and whether these correlations can be explained solely by negative selection against deleterious mutations or whether positive selection acting on favorable alleles is also required. Here we attempt to address these questions by analyzing three different genome-wide resequencing datasets from European individuals. We document several significant correlations between different genomic features. In particular, we find that average minor allele frequency and diversity are reduced in regions of low recombination and that human diversity, human-chimp divergence, and average minor allele frequency are reduced near genes. Population genetic simulations show that either positive natural selection acting on favorable mutations or negative natural selection acting against deleterious mutations can explain these correlations. However, models with strong positive selection on nonsynonymous mutations and little negative selection predict a stronger negative correlation between neutral diversity and nonsynonymous divergence than observed in the actual data, supporting the importance of negative, rather than positive, selection throughout the genome. Further, we show that the widespread presence of weakly deleterious alleles, rather than a small number of strongly positively selected mutations, is responsible for the correlation between neutral genetic diversity and recombination rate. This work suggests that natural selection has affected multiple aspects of linked neutral variation throughout the human genome and that positive selection is not required to explain these observations.     

Natural selection on synonymous sites is correlated with gene length and recombination in Drosophila.

Evolutionary analysis of codon bias in Drosophila indicates that synonymous mutations are not neutral, but rather are subject to weak selection at the translation level. Here we show that the effectiveness of natural selection on synonymous sites is strongly correlated with the rate of recombination, in accord with the nearly neutral hypothesis. This correlation, however, is apparent only in genes encoding short proteins. Long coding regions have both a lower codon bias and higher synonymous substitution rates, suggesting that they are affected less efficiently by selection. Therefore, both the length of the coding region and the recombination rate modulate codon bias. In addition, the data indicate that selection coefficients for synonymous mutations must vary by a minimum of one or two orders of magnitude. Two hypotheses are proposed to explain the relationship among the coding region length, the codon bias, and the synonymous divergence and polymorphism levels across the range of recombination rates in Drosophila. The first hypothesis is that selection coefficients on synonymous mutations are inversely related to the total length of the coding region. The second hypothesis proposes that interference among synonymous mutations reduces the efficacy of selection on these mutations. We investigated this second hypothesis by carrying out forward simulations of weakly selected mutations in model populations. These simulations show that even with realistic recombination rates, this interference, which we call the "small-scale" Hill-Robertson effect, can have a moderately strong influence on codon bias.     

Negative clonal selection in tumor evolution

Development of cancer requires the acquisition of multiple oncogenic mutations and selection of the malignant clone. Cancer evolves within a finite host lifetime and mechanisms of carcinogenesis that accelerate this process may be more likely to contribute to the development of clinical cancers. Mutator mutations are mutations that affect genome stability and accelerate the acquisition of oncogenic mutations. However, mutator mutations will also accelerate the accumulation of mutations that decrease cell proliferation, increase apoptosis, or affect other key fitness parameters. These "reduced-fitness" mutations may mediate "negative clonal selection," i.e., selective elimination of premalignant mutator clones. Target reduced-fitness loci may be "recessive" (both copies must be mutated to reduce fitness) or "dominant" (single-copy mutation reduces fitness). A direct mathematical analysis is applied to negative clonal selection, leading to the conclusion that negative clonal selection against mutator clones is unlikely to be a significant effect under realistic conditions. In addition, the relative importance of dominant and recessive reduced-fitness mutations is quantitatively defined. The relative predominance of mutator mutations in clinical cancers will depend on several variables, including the tolerance of the genome for reduced-fitness mutations, particularly the number and potency of dominant reduced-fitness loci.     

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

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

Dietary stress does not strengthen selection against single deleterious mutations in Drosophila melanogaster

Stress is generally thought to increase the strength of selection, although empirical results are mixed and general conclusions are difficult because data are limited. Here we compare the fitness effects of nine independent recessive mutations in Drosophila melanogaster in a high- and low-dietary-stress environment, estimating the strength of selection on these mutations arising from both a competitive measure of male reproductive success and productivity (female fecundity and the subsequent survival to adulthood of her offspring). The effect of stress on male reproductive success has not been addressed previously for individual loci and is of particular interest with respect to the alignment of natural and sexual selection. Our results do not support the hypothesis that stress increases the efficacy of selection arising from either fitness component. Results concerning the alignment of natural and sexual selection were mixed, although data are limited. In the low-stress environment, selection on mating success and productivity were concordant for five of nine mutations (four out of four when restricted to those with significant or near-significant productivity effects), whereas in the high-stress environment, selection aligned for seven of nine mutations (two out of two when restricted to those having significant productivity effects). General conclusions as to the effects of stress on the strength of selection and the alignment of natural and sexual selection await data from additional mutations, fitness components and stressors.