The distribution of fitness effects among beneficial mutations

We know little about the distribution of fitness effects among new beneficial mutations, a problem that partly reflects the rarity of these changes. Surprisingly, though, population genetic theory allows us to predict what this distribution should look like under fairly general assumptions. Using extreme value theory, I derive this distribution and show that it has two unexpected properties. First, the distribution of beneficial fitness effects at a gene is exponential. Second, the distribution of beneficial effects at a gene has the same mean regardless of the fitness of the present wild-type allele. Adaptation from new mutations is thus characterized by a kind of invariance: natural selection chooses from the same spectrum of beneficial effects at a locus independent of the fitness rank of the present wild type. I show that these findings are reasonably robust to deviations from several assumptions. I further show that one can back calculate the mean size of new beneficial mutations from the observed mean size of fixed beneficial mutations.     

The distribution of fitness effects of new mutations

The distribution of fitness effects (DFE) of new mutations is a fundamental entity in genetics that has implications ranging from the genetic basis of complex disease to the stability of the molecular clock. It has been studied by two different approaches: mutation accumulation and mutagenesis experiments, and the analysis of DNA sequence data. The proportion of mutations that are advantageous, effectively neutral and deleterious varies between species, and the DFE differs between coding and non-coding DNA. Despite these differences between species and genomic regions, some general principles have emerged: advantageous mutations are rare, and those that are strongly selected are exponentially distributed; and the DFE of deleterious mutations is complex and multi-modal.     

The distribution of fitness effects among beneficial mutations in Fisher's geometric model of adaptation

Recent models of adaptation at the DNA sequence level assume that the fitness effects of new mutations show certain statistical properties. In particular, these models assume that the distribution of fitness effects among new mutations is in the domain of attraction of the so-called Gumbel-type extreme value distribution. This assumption has not, however, been justified on any biological or theoretical grounds. In this note, I study random mutation in one of the simplest models of mutation and adaptation-Fisher's geometric model. I show that random mutation in this model yields a distribution of mutational effects that belongs to the Gumbel type. I also show that the distribution of fitness effects among rare beneficial mutations in Fisher's model is asymptotically exponential. I confirm these analytic findings with exact computer simulations. These results provide some support for the use of Gumbel-type extreme value theory in studies of adaptation and point to a surprising connection between recent phenotypic- and sequence-based models of adaptation: in both, the distribution of fitness effects among rare beneficial mutations is approximately exponential.     

The distribution of fitness effects of new deleterious amino acid mutations in humans

The distribution of fitness effects of new mutations is a fundamental parameter in genetics. Here we present a new method by which the distribution can be estimated. The method is fairly robust to changes in population size and admixture, and it can be corrected for any residual effects if a model of the demography is available. We apply the method to extensively sampled single-nucleotide polymorphism data from humans and estimate the distribution of fitness effects for amino acid changing mutations. We show that a gamma distribution with a shape parameter of 0.23 provides a good fit to the data and we estimate that >50% of mutations are likely to have mild effects, such that they reduce fitness by between one one-thousandth and one-tenth. We also infer that <15% of new mutations are likely to have strongly deleterious effects. We estimate that on average a nonsynonymous mutation reduces fitness by a few percent and that the average strength of selection acting against a nonsynonymous polymorphism is approximately 9 x 10(-5). We argue that the relaxation of natural selection due to modern medicine and reduced variance in family size is not likely to lead to a rapid decline in genetic quality, but that it will be very difficult to locate most of the genes involved in complex genetic diseases.     

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

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

Rate of deleterious mutation and the distribution of its effects on fitness in vesicular stomatitis virus

Despite their importance, the parameters describing the spontaneous deleterious mutation process have not been well described in many organisms. If mutations are important for the evolution of every living organism, their importance becomes critical in the case of RNA-based viruses, in which the frequency of mutation is orders of magnitude larger than in DNA-based organisms. The present work reports minimum estimates of the deleterious mutation rate, as well as the characterization of the distribution of deleterious mutational effects on the total fitness of the vesicular stomatitis virus (VSV). The estimates are based on mutation-accumulation experiments in which selection against deleterious mutations was minimized by recurrently imposing genetic bottlenecks of size one. The estimated deleterious mutation rate was 1.2 mutations per genome and generation, with a mean fitness effect of –0.39% per generation. At the end of the mutation-accumulation experiment, the average reduction in fitness was 38% and the distribution of accumulated deleterious effects was, on average, left-skewed. The magnitude of the skewness depends on the initial fitness of the clone analysed. The implications of our findings for the evolutionary biology of RNA viruses are discussed.     

Species range expansion by beneficial mutations

A species' range can be limited when there is no genetic variation for a trait that allows for adaptation to more extreme environments. We study how range expansion occurs by the establishment of a new mutation that affects a quantitative trait in a spatially continuous population. The optimal phenotype for the trait varies linearly in space. The survival probabilities of new mutations affecting the trait are found by simulation. Shallow environmental gradients favour mutations that arise nearer to the range margin and that have smaller phenotypic effects than do steep gradients. Mutations that become established in shallow environmental gradients typically result in proportionally larger range expansions than those that establish in steep gradients. Mutations that become established in populations with high maximum growth rates tend to originate nearer to the range edge and to cause relatively smaller range expansion than mutations that establish in populations with low maximum growth rates. Under plausible parameter values, mutations that allow for range expansion tend to have large phenotypic effects (more than one phenotypic standard deviation) and cause substantial range expansions (15% or more). Sexual reproduction allows for larger range expansions and adaptation to more extreme environments than asexual reproduction.     

Distributions of beneficial fitness effects in RNA

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

Evaluating the within-host fitness effects of mutations fixed during virus adaptation to different ecotypes of a new host

The existence of genetic variation for resistance in host populations is assumed to be essential to the spread of an emerging virus. Models predict that the rate of spread slows down with the increasing frequency and higher diversity of resistance alleles in the host population. We have been using the experimental pathosystem Arabidopsis thaliana—tobacco etch potyvirus (TEV) to explore the interplay between genetic variation in host''s susceptibility and virus diversity. We have recently shown that TEV populations evolving in A. thaliana ecotypes that differ in susceptibility to infection gained within-host fitness, virulence and infectivity in a manner compatible with a gene-for-gene model of host–parasite interactions: hard-to-infect ecotypes were infected by generalist viruses, whereas easy-to-infect ecotypes were infected by every virus. We characterized the genomes of the evolved viruses and found cases of host-driven convergent mutations. To gain further insights in the mechanistic basis of this gene-for-gene model, we have generated all viral mutations individually as well as in specific combinations and tested their within-host fitness effects across ecotypes. Most of these mutations were deleterious or neutral in their local ecotype and only a very reduced number had a host-specific beneficial effect. We conclude that most of the mutations fixed during the evolution experiment were so by drift or by selective sweeps along with the selected driver mutation. In addition, we evaluated the ruggedness of the underlying adaptive fitness landscape and found that mutational effects were mostly multiplicative, with few cases of significant epistasis.     

Epistasis and frequency dependence influence the fitness of an adaptive mutation in a diversifying lineage

The opportunity for a mutation to invade a population can dramatically vary depending on the context in which this mutation occurs. Such context dependence is difficult to document as it requires the ability to measure how a mutation affects phenotypes and fitness and to manipulate the context in which the mutation occurs. We identified a mutation in a gene encoding a global regulator in one of two ecotypes that diverged from a common ancestor during 1200 generations of experimental evolution. We replaced the ancestral allele by the mutant allele, and vice versa, in several clones isolated during the time course of the evolution experiment, and compared the phenotype and fitness of clones isogenic except for the focal mutation. We show that the fitness and phenotype of the mutation are strongly affected by epistatic interactions between genes in the same genome, as well as by frequency dependent selection resulting from biotic interactions between individuals in the same population. We conclude that amongst the replicate population in which it spread, the mutation we identified is only adaptive when occurring in specific genomes and competing with specific individuals. This study thus demonstrates that the opportunity for an adaptive mutation to spread in an evolutionary lineage can only be understood in the light of its genomic and competitive environments.     

Estimation of the rate and effect of new beneficial mutations in asexual populations

The rate and effect of available beneficial mutations are key parameters in determining how a population adapts to a new environment. However, these parameters are poorly known, in large part because of the difficulty of designing and interpreting experiments to examine the rare and intrinsically stochastic process of mutation occurrence. We present a new approach to estimate the rate and selective advantage of beneficial mutations that underlie the adaptation of asexual populations. We base our approach on the analysis of experiments that track the effect of newly arising beneficial mutations on the dynamics of a neutral marker in evolving bacterial populations and develop efficient estimators of mutation rate and selective advantage. Using extensive simulations, we evaluate the accuracy of our estimators and conclude that they are quite robust to the use of relatively low experimental replication. To validate the predictions of our model, we compare theoretical and experimentally determined estimates of the selective advantage of the first beneficial mutation to fix in a series of ten replicate populations. We find that our theoretical predictions are not significantly different from experimentally determined selection coefficients. Application of our method to suitably designed experiments will allow estimation of how population evolvability depends on demographic and initial fitness parameters.     

Increased fitness of Pseudomonas fluorescens Pf0-1 leucine auxotrophs in soil

The annotation process of a newly sequenced bacterial genome is largely based on algorithms derived from databases of previously defined RNA and protein-encoding gene structures. This process generally excludes the possibility that the two strands of a given stretch of DNA can each harbor a gene in an overlapping manner. While the presence of such structures in eukaryotic genomes is considered to be relatively common, their counterparts in prokaryotic genomes are just beginning to be recognized. Application of an in vivo expression technology has previously identified 22 discrete genetic loci in Pseudomonas fluorescens Pf0-1 that were specifically activated in the soil environment, of which 10 were present in an antisense orientation relative to previously annotated genes. This observation led to the hypothesis that the physiological role of overlapping genetic structures may be relevant to growth conditions outside artificial laboratory media. Here, we examined the role of one of the overlapping gene pairs, iiv19 and leuA2, in soil. Although iiv19 was previously demonstrated to be preferentially activated in the soil environment, its absence did not alter the ability of P. fluorescens to colonize or survive in soil. Surprisingly, the absence of the leuA2 gene conferred a fitness advantage in the soil environment when leucine was supplied exogenously. This effect was determined to be independent of the iiv19 gene, and further analyses revealed that amino acid antagonism was the underlying mechanism behind the observed fitness advantage of the bacterium in soil. Our findings provide a potential mechanism for the frequent occurrence of auxotrophic mutants of Pseudomonas spp. in the lungs of cystic fibrosis patients.     

Mobile genetic elements in the genome of the beneficial rhizobacterium Pseudomonas fluorescens Pf-5

Background

Three percent of the world's population is chronically infected with hepatitis C virus (HCV) and thus at risk of developing liver cancer. Although precise mechanisms regulating HCV entry into hepatic cells are still unknown, several cell surface proteins have been identified as entry factors for this virus. Among these molecules, the tetraspanin CD81 is essential for HCV entry. Interestingly, CD81 is also required for Plasmodium infection. A major characteristic of tetraspanins is their ability to interact with each other and other transmembrane proteins to build tetraspanin-enriched microdomains (TEM).

Results

In our study, we describe a human hepatoma Huh-7 cell clone (Huh-7w7) which has lost CD81 expression and can be infected by HCV when human CD81 (hCD81) or mouse CD81 (mCD81) is ectopically expressed. We took advantage of these permissive cells expressing mCD81 and the previously described MT81/MT81w mAbs to analyze the role of TEM-associated CD81 in HCV infection. Importantly, MT81w antibody, which only recognizes TEM-associated mCD81, did not strongly affect HCV infection. Furthermore, cholesterol depletion, which inhibits HCV infection and reduces total cell surface expression of CD81, did not affect TEM-associated CD81 levels. In addition, sphingomyelinase treatment, which also reduces HCV infection and cell surface expression of total CD81, raised TEM-associated CD81 levels.

Conclusion

In contrast to Plasmodium infection, our data show that association of CD81 with TEM is not essential for the early steps of HCV life cycle, indicating that these two pathogens, while using the same molecules, invade their host by different mechanisms.     

Duration and fitness dependence of quasispecies memory.

The duration and fitness dependence of memory in viral quasispecies evolving in cell culture have been investigated using two genetic markers of foot-and-mouth disease virus (FMDV). In lineages of antigenic variant FMDV RED, which reverted to FMDV RGD, memory FMDV RED genomes were detected after 50 infectious cycles, and memory level was fitness dependent. In growth-competition experiments between a reference FMDV RGD and two different FMDV RED populations, a 7.6-fold higher fitness of the initial FMDV RED population resulted in 30 to 100-fold higher memory level. In lineages of low-fitness clones containing an elongated internal polyadenylate tract, revertants lacking excess adenylate residues became dominant by passage 20. However, genomes including a larger number of adenylate residues were detected as memory genomes after at least 150 infectious cycles. Thus, quasispecies memory can be durable and is fitness dependent, as predicted from the growth competition of two mutant forms of a genome. An understanding of factors influencing quasispecies memory levels and duration may have implications for the extended diagnosis of viruses based on the quantification of minority genomes.     

Evolutionary rescue by beneficial mutations in environments that change in space and time

A factor that may limit the ability of many populations to adapt to changing conditions is the rate at which beneficial mutations can become established. We study the probability that mutations become established in changing environments by extending the classic theory for branching processes. When environments change in time, under quite general conditions, the establishment probability is approximately twice the ‘effective selection coefficient’, whose value is an average that gives most weight to a mutant''s fitness in the generations immediately after it appears. When fitness varies along a gradient in a continuous habitat, increased dispersal generally decreases the chance a mutation establishes because mutations move out of areas where they are most adapted. When there is a patch of favourable habitat that moves in time, there is a maximum speed of movement above which mutations cannot become established, regardless of when and where they first appear. This critical speed limit, which is proportional to the mutation''s maximum selective advantage, represents an absolute constraint on the potential of locally adapted mutations to contribute to evolutionary rescue.     

Fitness effects of fixed beneficial mutations in microbial populations

Beneficial mutations are intuitively relevant to understanding adaptation, yet not all beneficial mutations are of consequence to the long-term evolutionary outcome of adaptation. Many beneficial mutations-mostly those of small effect-are lost due either to (1) genetic drift or to (2) competition among clones carrying different beneficial mutations, a phenomenon called the "Hill-Robertson effect" for sexual populations and "clonal interference" for asexual populations. Competition among clones becomes more prevalent with increasing genetic linkage and increasing population size, and it is thus generally characteristic of microbial populations. Together, these two phenomena suggest that only those beneficial mutations of large fitness effect should achieve fixation, despite the fact that most beneficial mutations produced are predicted to have very small fitness effects. Here, we confirm this prediction-both empirically and theoretically-by showing that fitness effects of fixed beneficial mutations follow a distribution whose mode is positive.     

The fitness effects of synonymous mutations in DNA and RNA viruses

Despite being silent with respect to protein sequence, synonymous nucleotide substitutions can be targeted by natural selection directly at the DNA or RNA level. However, there has been no systematic assessment of how frequent this type of selection is. Here, we have constructed 53 single random synonymous substitution mutants of the bacteriophages Qβ and ΦX174 by site-directed mutagenesis and assayed their fitness. Analysis of this mutant collection and of previous studies undertaken with a variety of single-stranded (ss) viruses demonstrates that selection at synonymous sites is stronger in RNA viruses than in DNA viruses. We estimate that this type of selection contributes approximately 18% of the overall mutational fitness effects in ssRNA viruses under our assay conditions and that random synonymous substitutions have a 5% chance of being lethal to the virus, whereas in ssDNA viruses, these figures drop to 1.4% and 0%, respectively. In contrast, the effects of nonsynonymous substitutions appear to be similar in ssRNA and ssDNA viruses.     

Mutational fitness effects in RNA and single-stranded DNA viruses: common patterns revealed by site-directed mutagenesis studies

The fitness effects of mutations are central to evolution, yet have begun to be characterized in detail only recently. Site-directed mutagenesis is a powerful tool for achieving this goal, which is particularly suited for viruses because of their small genomes. Here, I discuss the evolutionary relevance of mutational fitness effects and critically review previous site-directed mutagenesis studies. The effects of single-nucleotide substitutions are standardized and compared for five RNA or single-stranded DNA viruses infecting bacteria, plants or animals. All viruses examined show very low tolerance to mutation when compared with cellular organisms. Moreover, for non-lethal mutations, the mean fitness reduction caused by single mutations is remarkably constant (0.10–0.13), whereas the fraction of lethals varies only modestly (0.20–0.41). Other summary statistics are provided. These generalizations about the distribution of mutational fitness effects can help us to better understand the evolution of RNA and single-stranded DNA viruses.