Epistasis from functional dependence of fitness on underlying traits

Epistasis between mutations in two genes is thought to reflect an interdependence of their functions. While sometimes epistasis is predictable using mechanistic models, its roots seem, in general, hidden in the complex architecture of biological networks. Here, we ask how epistasis can be quantified based on the mathematical dependence of a system-level trait (e.g. fitness) on lower-level traits (e.g. molecular or cellular properties). We first focus on a model in which fitness is the difference between a benefit and a cost trait, both pleiotropically affected by mutations. We show that despite its simplicity, this model can be used to analytically predict certain properties of the ensuing distribution of epistasis, such as a global negative bias, resulting in antagonism between beneficial mutations, and synergism between deleterious ones. We next extend these ideas to derive a general expression for epistasis given an arbitrary functional dependence of fitness on other traits. This expression demonstrates how epistasis relative to fitness can emerge despite the absence of epistasis relative to lower level traits, leading to a formalization of the concept of independence between biological processes. Our results suggest that epistasis may be largely shaped by the pervasiveness of pleiotropic effects and modular organization in biological networks.     

The contribution of the mitochondrial genome to sex‐specific fitness variance

Maternal inheritance of mitochondrial DNA (mtDNA) facilitates the evolutionary accumulation of mutations with sex‐biased fitness effects. Whereas maternal inheritance closely aligns mtDNA evolution with natural selection in females, it makes it indifferent to evolutionary changes that exclusively benefit males. The constrained response of mtDNA to selection in males can lead to asymmetries in the relative contributions of mitochondrial genes to female versus male fitness variation. Here, we examine the impact of genetic drift and the distribution of fitness effects (DFE) among mutations—including the correlation of mutant fitness effects between the sexes—on mitochondrial genetic variation for fitness. We show how drift, genetic correlations, and skewness of the DFE determine the relative contributions of mitochondrial genes to male versus female fitness variance. When mutant fitness effects are weakly correlated between the sexes, and the effective population size is large, mitochondrial genes should contribute much more to male than to female fitness variance. In contrast, high fitness correlations and small population sizes tend to equalize the contributions of mitochondrial genes to female versus male variance. We discuss implications of these results for the evolution of mitochondrial genome diversity and the genetic architecture of female and male fitness.     

Perspective: Sign epistasis and genetic constraint on evolutionary trajectories

Epistasis for fitness means that the selective effect of a mutation is conditional on the genetic background in which it appears. Although epistasis is widely observed in nature, our understanding of its consequences for evolution by natural selection remains incomplete. In particular, much attention focuses only on its influence on the instantaneous rate of changes in frequency of selected alleles via epistatic contribution to the additive genetic variance for fitness. Thus, in this framework epistasis only has evolutionary importance if the interacting loci are simultaneously segregating in the population. However, the selective accessibility of mutational trajectories to high fitness genotypes may depend on the genetic background in which novel mutations appear, and this effect is independent of population polymorphism at other loci. Here we explore this second influence of epistasis on evolution by natural selection. We show that it is the consequence of a particular form of epistasis, which we designate sign epistasis. Sign epistasis means that the sign of the fitness effect of a mutation is under epistatic control; thus, such a mutation is beneficial on some genetic backgrounds and deleterious on others. Recent experimental innovations in microbial systems now permit assessment of the fitness effects of individual mutations on multiple genetic backgrounds. We review this literature and identify many examples of sign epistasis, and we suggest that the implications of these results may generalize to other organisms. These theoretical and empirical considerations imply that strong genetic constraint on the selective accessibility of trajectories to high fitness genotypes may exist and suggest specific areas of investigation for future research.     

The distribution of fitness effects of spontaneous mutations in Chlamydomonas reinhardtii inferred using frequency changes under experimental evolution

The distribution of fitness effects (DFE) for new mutations is fundamental for many aspects of population and quantitative genetics. In this study, we have inferred the DFE in the single-celled alga Chlamydomonas reinhardtii by estimating changes in the frequencies of 254 spontaneous mutations under experimental evolution and equating the frequency changes of linked mutations with their selection coefficients. We generated seven populations of recombinant haplotypes by crossing seven independently derived mutation accumulation lines carrying an average of 36 mutations in the haploid state to a mutation-free strain of the same genotype. We then allowed the populations to evolve under natural selection in the laboratory by serial transfer in liquid culture. We observed substantial and repeatable changes in the frequencies of many groups of linked mutations, and, surprisingly, as many mutations were observed to increase as decrease in frequency. Mutation frequencies were highly repeatable among replicates, suggesting that selection was the cause of the observed allele frequency changes. We developed a Bayesian Monte Carlo Markov Chain method to infer the DFE. This computes the likelihood of the observed distribution of changes of frequency, and obtains the posterior distribution of the selective effects of individual mutations, while assuming a two-sided gamma distribution of effects. We infer that the DFE is a highly leptokurtic distribution, and that approximately equal proportions of mutations have positive and negative effects on fitness. This result is consistent with what we have observed in previous work on a different C. reinhardtii strain, and suggests that a high fraction of new spontaneously arisen mutations are advantageous in a simple laboratory environment.     

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.     

The distribution of fitness effects in an uncertain world

The distribution of fitness effects (DFE) among new mutations plays a critical role in adaptive evolution and the maintenance of genetic variation. Although fitness landscape models predict several key features of the DFE, most theory to date focuses on predictable environmental conditions, while ignoring stochastic environmental fluctuations that feature prominently in the ecology of many organisms. Here, we derive an extension of Fisher's geometric model that incorporates two common effects of environmental variation: (1) nonadaptive genotype‐by‐environment interactions (G × E), in which the phenotype of a given genotype varies across environmental contexts; and (2) random fluctuation of the fitness optimum, which generates fluctuating selection. We show that both factors cause a mismatch between the DFE within single generations and the distribution of geometric mean fitness effects (averaged over multiple generations) that governs long‐term evolutionary change. Such mismatches permit strong evolutionary constraints—despite an abundance of beneficial fitness variation within single environmental contexts—and to conflicting DFE estimates from direct versus indirect inference methods. Finally, our results suggest an intriguing parallel between the genetics and ecology of evolutionary constraints, with environmental fluctuations and pleiotropy placing qualitatively similar limits on the availability of adaptive genetic variation.     

The Impact of Macroscopic Epistasis on Long-Term Evolutionary Dynamics

Genetic interactions can strongly influence the fitness effects of individual mutations, yet the impact of these epistatic interactions on evolutionary dynamics remains poorly understood. Here we investigate the evolutionary role of epistasis over 50,000 generations in a well-studied laboratory evolution experiment in Escherichia coli. The extensive duration of this experiment provides a unique window into the effects of epistasis during long-term adaptation to a constant environment. Guided by analytical results in the weak-mutation limit, we develop a computational framework to assess the compatibility of a given epistatic model with the observed patterns of fitness gain and mutation accumulation through time. We find that a decelerating fitness trajectory alone provides little power to distinguish between competing models, including those that lack any direct epistatic interactions between mutations. However, when combined with the mutation trajectory, these observables place strong constraints on the set of possible models of epistasis, ruling out many existing explanations of the data. Instead, we find that the data are consistent with a “two-epoch” model of adaptation, in which an initial burst of diminishing-returns epistasis is followed by a steady accumulation of mutations under a constant distribution of fitness effects. Our results highlight the need for additional DNA sequencing of these populations, as well as for more sophisticated models of epistasis that are compatible with all of the experimental data.     

The Environment Affects Epistatic Interactions to Alter the Topology of an Empirical Fitness Landscape

The fitness effect of mutations can be influenced by their interactions with the environment, other mutations, or both. Previously, we constructed 32 ( = 2⁵) genotypes that comprise all possible combinations of the first five beneficial mutations to fix in a laboratory-evolved population of Escherichia coli. We found that (i) all five mutations were beneficial for the background on which they occurred; (ii) interactions between mutations drove a diminishing returns type epistasis, whereby epistasis became increasingly antagonistic as the expected fitness of a genotype increased; and (iii) the adaptive landscape revealed by the mutation combinations was smooth, having a single global fitness peak. Here we examine how the environment influences epistasis by determining the interactions between the same mutations in two alternative environments, selected from among 1,920 screened environments, that produced the largest increase or decrease in fitness of the most derived genotype. Some general features of the interactions were consistent: mutations tended to remain beneficial and the overall pattern of epistasis was of diminishing returns. Other features depended on the environment; in particular, several mutations were deleterious when added to specific genotypes, indicating the presence of antagonistic interactions that were absent in the original selection environment. Antagonism was not caused by consistent pleiotropic effects of individual mutations but rather by changing interactions between mutations. Our results demonstrate that understanding adaptation in changing environments will require consideration of the combined effect of epistasis and pleiotropy across environments.     

Diverse phenotypic and genetic responses to short‐term selection in evolving Escherichia coli populations

Beneficial mutations fuel adaptation by altering phenotypes that enhance the fit of organisms to their environment. However, the phenotypic effects of mutations often depend on ecological context, making the distribution of effects across multiple environments essential to understanding the true nature of beneficial mutations. Studies that address both the genetic basis and ecological consequences of adaptive mutations remain rare. Here, we characterize the direct and pleiotropic fitness effects of a collection of 21 first‐step beneficial mutants derived from naïve and adapted genotypes used in a long‐term experimental evolution of Escherichia coli. Whole‐genome sequencing was able to identify the majority of beneficial mutations. In contrast to previous studies, we find diverse fitness effects of mutations selected in a simple environment and few cases of genetic parallelism. The pleiotropic effects of these mutations were predominantly positive but some mutants were highly antagonistic in alternative environments. Further, the fitness effects of mutations derived from the adapted genotypes were dramatically reduced in nearly all environments. These findings suggest that many beneficial variants are accessible from a single point on the fitness landscape, and the fixation of alternative beneficial mutations may have dramatic consequences for niche breadth reduction via metabolic erosion.     

The Consistency of Beneficial Fitness Effects of Mutations across Diverse Genetic Backgrounds

Parallel and convergent evolution have been remarkably common observations in molecular adaptation but primarily in the context of the same genotype adapting to the same conditions. These phenomena therefore tell us about the stochasticity and limitations of adaptation. The limited data on convergence and parallelism in the adaptation of different genotypes conflict as to the importance of such events. If the effects of beneficial mutations are highly context dependent (i.e., if they are epistatic), different genotypes should adapt through different mutations. Epistasis for beneficial mutations has been investigated but mainly through measurement of interactions between individually beneficial mutations for the same genotype. We examine epistasis for beneficial mutations at a broader genetic scale by measuring the fitness effects of two mutations beneficial for the ssDNA bacteriophage ID11 in eight different, related genotypes showing 0.3-3.7% nucleotide divergence from ID11. We found no evidence for sign epistasis, but the mutations tended to have much smaller or no effects on fitness in the new genotypes. We found evidence for diminishing-returns epistasis; the effects were more beneficial for lower-fitness genotypes. The patterns of epistasis were not determined by phylogenetic relationships to the original genotype. To improve our understanding of the patterns of epistasis, we fit the data to a model in which each mutation had a constant, nonepistatic phenotypic effect across genotypes and the phenotype-fitness map had a single optimum. This model fit the data well, suggesting that epistasis for these mutations was due to nonlinearity in the phenotype-fitness mapping and that the likelihood of parallel evolution depends more on phenotype than on genotype.     

Positive Epistasis Drives the Acquisition of Multidrug Resistance

The evolution of multiple antibiotic resistance is an increasing global problem. Resistance mutations are known to impair fitness, and the evolution of resistance to multiple drugs depends both on their costs individually and on how they interact—epistasis. Information on the level of epistasis between antibiotic resistance mutations is of key importance to understanding epistasis amongst deleterious alleles, a key theoretical question, and to improving public health measures. Here we show that in an antibiotic-free environment the cost of multiple resistance is smaller than expected, a signature of pervasive positive epistasis among alleles that confer resistance to antibiotics. Competition assays reveal that the cost of resistance to a given antibiotic is dependent on the presence of resistance alleles for other antibiotics. Surprisingly we find that a significant fraction of resistant mutations can be beneficial in certain resistant genetic backgrounds, that some double resistances entail no measurable cost, and that some allelic combinations are hotspots for rapid compensation. These results provide additional insight as to why multi-resistant bacteria are so prevalent and reveal an extra layer of complexity on epistatic patterns previously unrecognized, since it is hidden in genome-wide studies of genetic interactions using gene knockouts.     

The Distribution of Fitness Effects of Beneficial Mutations in Pseudomonas aeruginosa

Understanding how beneficial mutations affect fitness is crucial to our understanding of adaptation by natural selection. Here, using adaptation to the antibiotic rifampicin in the opportunistic pathogen Pseudomonas aeruginosa as a model system, we investigate the underlying distribution of fitness effects of beneficial mutations on which natural selection acts. Consistent with theory, the effects of beneficial mutations are exponentially distributed where the fitness of the wild type is moderate to high. However, when the fitness of the wild type is low, the data no longer follow an exponential distribution, because many beneficial mutations have large effects on fitness. There is no existing population genetic theory to explain this bias towards mutations of large effects, but it can be readily explained by the underlying biochemistry of rifampicin–RNA polymerase interactions. These results demonstrate the limitations of current population genetic theory for predicting adaptation to severe sources of stress, such as antibiotics, and they highlight the utility of integrating statistical and biophysical approaches to adaptation.     

Deleterious Passengers in Adapting Populations

Most new mutations are deleterious and are eventually eliminated by natural selection. But in an adapting population, the rapid amplification of beneficial mutations can hinder the removal of deleterious variants in nearby regions of the genome, altering the patterns of sequence evolution. Here, we analyze the interactions between beneficial “driver” mutations and linked deleterious “passengers” during the course of adaptation. We derive analytical expressions for the substitution rate of a deleterious mutation as a function of its fitness cost, as well as the reduction in the beneficial substitution rate due to the genetic load of the passengers. We find that the fate of each deleterious mutation varies dramatically with the rate and spectrum of beneficial mutations and the deleterious substitution rate depends nonmonotonically on the population size and the rate of adaptation. By quantifying this dependence, our results allow us to estimate which deleterious mutations will be likely to fix and how many of these mutations must arise before the progress of adaptation is significantly reduced.     

Fitness landscapes emerging from pharmacodynamic functions in the evolution of multidrug resistance

Adaptive evolution often involves beneficial mutations at more than one locus. In this case, the trajectory and rate of adaptation is determined by the underlying fitness landscape, that is, the fitness values and mutational connectivity of all genotypes under consideration. Drug resistance, especially resistance to multiple drugs simultaneously, is also often conferred by mutations at several loci so that the concept of fitness landscapes becomes important. However, fitness landscapes underlying drug resistance are not static but dependent on drug concentrations, which means they are influenced by the pharmacodynamics of the drugs administered. Here, I present a mathematical framework for fitness landscapes of multidrug resistance based on Hill functions describing how drug concentrations affect fitness. I demonstrate that these ‘pharmacodynamic fitness landscapes’ are characterized by pervasive epistasis that arises through (i) fitness costs of resistance (even when these costs are additive), (ii) nonspecificity of resistance mutations to drugs, in particular cross‐resistance, and (iii) drug interactions (both synergistic and antagonistic). In the latter case, reciprocal drug suppression may even lead to reciprocal sign epistasis, so that the doubly resistant genotype occupies a local fitness peak that may be difficult to access by evolution. Simulations exploring the evolutionary dynamics on some pharmacodynamic fitness landscapes with both constant and changing drug concentrations confirm the crucial role of epistasis in determining the rate of multidrug resistance evolution.     

Mutational neighbourhood and mutation supply rate constrain adaptation in Pseudomonas aeruginosa

Understanding adaptation by natural selection requires understanding the genetic factors that determine which beneficial mutations are available for selection. Here, using experimental evolution of rifampicin-resistant Pseudomonas aeruginosa, we show that different genotypes vary in their capacity for adaptation to the cost of antibiotic resistance. We then use sequence data to show that the beneficial mutations associated with fitness recovery were specific to particular genetic backgrounds, suggesting that genotypes had access to different sets of beneficial mutations. When we manipulated the supply rate of beneficial mutations, by altering effective population size during evolution, we found that it constrained adaptation in some selection lines by restricting access to rare beneficial mutations, but that the effect varied among the genotypes in our experiment. These results suggest that mutational neighbourhood varies even among genotypes that differ by a single amino acid change, and this determines their capacity for adaptation as well as the influence of population biology processes that alter mutation supply rate.     

Dependence of epistasis on environment and mutation severity as revealed by in silico mutagenesis of phage t7

Understanding how interactions among deleterious mutations affect fitness may shed light on a variety of fundamental biological phenomena, including the evolution of sex, the buffering of genetic variations, and the topography of fitness landscapes. It remains an open question under what conditions and to what extent such interactions may be synergistic or antagonistic. To address this question, we employed a computer model for the intracellular growth of bacteriophage T7. We created in silico 90,000 mutants of phage T7, each carrying from 1 to 30 mutations, and evaluated the fitness of each by simulating its growth cycle. The simulations sought to account for the severity of single deleterious mutations on T7 growth, as well as the effect of the resource environment on our fitness measures. We found that mildly deleterious mutations interacted synergistically in poor-resource environments but antagonistically in rich-resource environments. However, severely deleterious mutations always interacted antagonistically, irrespective of environment. These results suggest that synergistic epistasis may be difficult to experimentally distinguish from nonepistasis because its effects appear to be most pronounced when the effects of mutations on fitness are most challenging to measure. Our approach demonstrates how computer simulations of developmental processes can be used to quantitatively study genetic interactions at the population level.     

The rank ordering of genotypic fitness values predicts genetic constraint on natural selection on landscapes lacking sign epistasis

Sewall Wright's genotypic fitness landscape makes explicit one mechanism by which epistasis for fitness can constrain evolution by natural selection. Wright distinguished between landscapes possessing multiple fitness peaks and those with only a single peak and emphasized that the former class imposes substantially greater constraint on natural selection. Here I present novel formalism that more finely partitions the universe of possible fitness landscapes on the basis of the rank ordering of their genotypic fitness values. In this report I focus on fitness landscapes lacking sign epistasis (i.e., landscapes that lack mutations the sign of whose fitness effect varies epistatically), which constitute a subset of Wright's single peaked landscapes. More than one fitness rank ordering lacking sign epistasis exists for L > 2 (where L is the number of interacting loci), and I find that a highly statistically significant effect exists between landscape membership in fitness rank-ordering partition and two different proxies for genetic constraint, even within this subset of landscapes. This statistical association is robust to population size, permitting general inferences about some of the characteristics of fitness rank orderings responsible for genetic constraint on natural selection.     

The distribution of fitness effects of new beneficial mutations in Pseudomonas fluorescens

Theoretical studies of adaptation emphasize the importance of understanding the distribution of fitness effects (DFE) of new mutations. We report the isolation of 100 adaptive mutants—without the biasing influence of natural selection—from an ancestral genotype whose fitness in the niche occupied by the derived type is extremely low. The fitness of each derived genotype was determined relative to a single reference type and the fitness effects found to conform to a normal distribution. When fitness was measured in a different environment, the rank order changed, but not the shape of the distribution. We argue that, even with detailed knowledge of the genetic architecture underpinning the adaptive types (as is the case here), the DFEs remain unpredictable, and we discuss the possibility that general explanations for the shape of the DFE might not be possible in the absence of organism-specific biological details.     

Inferring Genome-Wide Correlations of Mutation Fitness Effects between Populations

The effect of a mutation on fitness may differ between populations depending on environmental and genetic context, but little is known about the factors that underlie such differences. To quantify genome-wide correlations in mutation fitness effects, we developed a novel concept called a joint distribution of fitness effects (DFE) between populations. We then proposed a new statistic w to measure the DFE correlation between populations. Using simulation, we showed that inferring the DFE correlation from the joint allele frequency spectrum is statistically precise and robust. Using population genomic data, we inferred DFE correlations of populations in humans, Drosophila melanogaster, and wild tomatoes. In these species, we found that the overall correlation of the joint DFE was inversely related to genetic differentiation. In humans and D. melanogaster, deleterious mutations had a lower DFE correlation than tolerated mutations, indicating a complex joint DFE. Altogether, the DFE correlation can be reliably inferred, and it offers extensive insight into the genetics of population divergence.