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 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.     

Impact of epistasis and pleiotropy on evolutionary adaptation

Evolutionary adaptation is often likened to climbing a hill or peak. While this process is simple for fitness landscapes where mutations are independent, the interaction between mutations (epistasis) as well as mutations at loci that affect more than one trait (pleiotropy) are crucial in complex and realistic fitness landscapes. We investigate the impact of epistasis and pleiotropy on adaptive evolution by studying the evolution of a population of asexual haploid organisms (haplotypes) in a model of N interacting loci, where each locus interacts with K other loci. We use a quantitative measure of the magnitude of epistatic interactions between substitutions, and find that it is an increasing function of K. When haplotypes adapt at high mutation rates, more epistatic pairs of substitutions are observed on the line of descent than expected. The highest fitness is attained in landscapes with an intermediate amount of ruggedness that balance the higher fitness potential of interacting genes with their concomitant decreased evolvability. Our findings imply that the synergism between loci that interact epistatically is crucial for evolving genetic modules with high fitness, while too much ruggedness stalls the adaptive process.     

Initial mutations direct alternative pathways of protein evolution

Whether evolution is erratic due to random historical details, or is repeatedly directed along similar paths by certain constraints, remains unclear. Epistasis (i.e. non-additive interaction between mutations that affect fitness) is a mechanism that can contribute to both scenarios. Epistasis can constrain the type and order of selected mutations, but it can also make adaptive trajectories contingent upon the first random substitution. This effect is particularly strong under sign epistasis, when the sign of the fitness effects of a mutation depends on its genetic background. In the current study, we examine how epistatic interactions between mutations determine alternative evolutionary pathways, using in vitro evolution of the antibiotic resistance enzyme TEM-1 β-lactamase. First, we describe the diversity of adaptive pathways among replicate lines during evolution for resistance to a novel antibiotic (cefotaxime). Consistent with the prediction of epistatic constraints, most lines increased resistance by acquiring three mutations in a fixed order. However, a few lines deviated from this pattern. Next, to test whether negative interactions between alternative initial substitutions drive this divergence, alleles containing initial substitutions from the deviating lines were evolved under identical conditions. Indeed, these alternative initial substitutions consistently led to lower adaptive peaks, involving more and other substitutions than those observed in the common pathway. We found that a combination of decreased enzymatic activity and lower folding cooperativity underlies negative sign epistasis in the clash between key mutations in the common and deviating lines (Gly238Ser and Arg164Ser, respectively). Our results demonstrate that epistasis contributes to contingency in protein evolution by amplifying the selective consequences of random mutations.     

On the evolution of epistasis III: the haploid case with mutation

Whether interaction between genes is better represented by synergistic or antagonistic epistasis has been a focus of experimental research in bacterial population genetics. Our previous research on evolution of modifiers of epistasis in diploid systems has indicated that the strength of positive or negative epistasis should increase provided linkage disequilibrium is maintained. Here we study a modifier of epistasis in fitness between two loci in a haploid system. Epistasis is modified in the neighborhood of a mutation-selection balance. We show that when linkage in the three-locus system is tight, an increase in the frequency of a modifier allele that induces either more negative or more positive epistasis is possible. Epistasis here can be measured on either an additive or multiplicative scale.     

Epistasis in monkeyflowers

Epistasis contributes significantly to intrapopulation variation in floral morphology, development time, and male fitness components of Mimulus guttatus. This is demonstrated with a replicated line-cross experiment involving slightly over 7000 plants. The line-cross methodology is based on estimates for means. It thus has greater power than the variance partitioning approaches historically used to estimate epistasis within populations. The replication of the breeding design across many pairs of randomly extracted, inbred lines is necessary given the diversity of multilocus genotypes residing within an outbred deme. Male fitness is shown to exhibit synergistic epistasis, an accelerating decline in fitness with inbreeding. Synergism is a necessary, but not sufficient, condition for a mutational deterministic hypothesis for the evolutionary maintenance of sexual reproduction. Unlike male fitness measures, flower morphology and development time yield positive evidence of epistasis but not of synergism. The results for these traits suggest that epistatic effects are variable across genetic backgrounds or sets of interacting loci.     

Epistasis in polygenic traits and the evolution of genetic architecture under stabilizing selection

We consider the effects of epistasis in a polygenic trait in the balance of mutation and stabilizing selection. The main issues are the genetic variation maintained in equilibrium and the evolution of the mutational effect distribution. The model assumes symmetric mutation and a continuum of alleles at all loci. Epistasis is modeled proportional to pairwise products of the single-locus effects. A general analytical formalism is developed. Assuming linkage equilibrium, we derive results for the equilibrium mutation load and the genetic and mutational variance in the house of cards and the Gaussian approximation. The additive genetic variation maintained in mutation-selection balance is reduced by any pattern of the epistatic interactions. The mutational variance, in contrast, is often increased. Large differences in mutational effects among loci emerge, and a negative correlation among (standard mean) locus mutation effects and mutation rates is predicted. Contrary to the common view since Waddington, we find that stabilizing selection in general does not lead to canalization of the trait. We propose that canalization as a target of selection instead occurs at the genic level. Here, primarily genes with a high mutation rate are buffered, often at the cost of decanalization of other genes. An intuitive interpretation of this view is given in the discussion.     

Epistasis Can Facilitate the Evolution of Reproductive Isolation by Peak Shifts: A Two-Locus Two-Allele Model

The influence of epistasis on the evolution of reproductive isolation by peak shifts is studied in a two-locus two-allele model of a quantitative genetic character under stabilizing selection. Epistasis is introduced by a simple multiplicative term in the function that maps gene effects onto genotypic values. In the model with only additive effects on the trait, the probability of a peak shift and the amount of reproductive isolation are always inversely related, i.e., the higher the peak shift rate, the lower the amount of reproductive isolation caused by the peak shift. With epistatic characters there is no consistent relationship between these two values. Interestingly, there are causes where both transition rates as well as the amount of reproductive isolation are increased relative to the additive model. This effect has two main causes: a shift in the location of the transition point, and the hybrids between the two alternative optimal genotypes have lower average fitness in the epistatic case. A review of the empirical literature shows that the fitness relations resulting in higher peak shift rates and more reproductive isolation are qualitatively the same as those observed for genes causing hybrid inferiority.     

Influence of Gene Interaction on Complex Trait Variation with Multilocus Models

Although research effort is being expended into determining the importance of epistasis and epistatic variance for complex traits, there is considerable controversy about their importance. Here we undertake an analysis for quantitative traits utilizing a range of multilocus quantitative genetic models and gene frequency distributions, focusing on the potential magnitude of the epistatic variance. All the epistatic terms involving a particular locus appear in its average effect, with the number of two-locus interaction terms increasing in proportion to the square of the number of loci and that of third order as the cube and so on. Hence multilocus epistasis makes substantial contributions to the additive variance and does not, per se, lead to large increases in the nonadditive part of the genotypic variance. Even though this proportion can be high where epistasis is antagonistic to direct effects, it reduces with multiple loci. As the magnitude of the epistatic variance depends critically on the heterozygosity, for models where frequencies are widely dispersed, such as for selectively neutral mutations, contributions of epistatic variance are always small. Epistasis may be important in understanding the genetic architecture, for example, of function or human disease, but that does not imply that loci exhibiting it will contribute much genetic variance. Overall we conclude that theoretical predictions and experimental observations of low amounts of epistatic variance in outbred populations are concordant. It is not a likely source of missing heritability, for example, or major influence on predictions of rates of evolution.     

Coalescent under the evolution of coadaptation

Adaptation to novel environments arises either from new beneficial mutations or by utilizing pre‐existing genetic variation. When standing variation is used as the source of new adaptation, fitness effects of alleles may be altered through an environmental change. Alternatively, changes in epistatic genetic backgrounds may convert formerly neutral mutations into beneficial alleles in the new genetic background. By extending the coalescent theory to describe the genealogical histories of two interacting loci, I here investigated the hitchhiking effect of epistatic selection on the amount and pattern of sequence diversity at the linked neutral regions. Assuming a specific form of epistasis between two new mutations that are independently neutral, but together form a coadapted haplotype, I demonstrate that the footprints of epistatic selection differ markedly between the interacting loci depending on the order and relative timing of the two mutational events, even though both mutations are equally essential for the formation of an adaptive gene combination. Our results imply that even when neutrality tests could detect just a single instance of adaptive substitution, there may, in fact, be numerous other hidden mutations that are left undetected, but still play indispensable roles in the evolution of a new adaptation. We expect that the integration of the coalescent framework into the general theory of polygenic inheritance would clarify the connection between factors driving phenotypic evolution and their consequences on underlying DNA sequence changes, which should further illuminate the evolutionary foundation of coadapted systems.     

Weak Epistasis Generally Stabilizes Phenotypes in a Mouse Intercross

The extent and strength of epistasis is commonly unresolved in genetic studies, and observed epistasis is often difficult to interpret in terms of biological consequences or overall genetic architecture. We investigated the prevalence and consequences of epistasis by analyzing four body composition phenotypes—body weight, body fat percentage, femoral density, and femoral circumference—in a large F2 intercross of B6-lit/lit and C3.B6-lit/lit mice. We used Combined Analysis of Pleiotropy and Epistasis (CAPE) to examine interactions for the four phenotypes simultaneously, which revealed an extensive directed network of genetic loci interacting with each other, circulating IGF1, and sex to influence these phenotypes. The majority of epistatic interactions had small effects relative to additive effects of individual loci, and tended to stabilize phenotypes towards the mean of the population rather than extremes. Interactive effects of two alleles inherited from one parental strain commonly resulted in phenotypes closer to the population mean than the additive effects from the two loci, and often much closer to the mean than either single-locus model. Alternatively, combinations of alleles inherited from different parent strains contribute to more extreme phenotypes not observed in either parental strain. This class of phenotype-stabilizing interactions has effects that are close to additive and are thus difficult to detect except in very large intercrosses. Nevertheless, we found these interactions to be useful in generating hypotheses for functional relationships between genetic loci. Our findings suggest that while epistasis is often weak and unlikely to account for a large proportion of heritable variance, even small-effect genetic interactions can facilitate hypotheses of underlying biology in well-powered studies.     

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.     

Epistasis and Its Contribution to Genetic Variance Components

We present a new parameterization of physiological epistasis that allows the measurement of epistasis separate from its effects on the interaction (epistatic) genetic variance component. Epistasis is the deviation of two-locus genotypic values from the sum of the contributing single-locus genotypic values. This parameterization leads to statistical tests for epistasis given estimates of two-locus genotypic values such as can be obtained from quantitative trait locus studies. The contributions of epistasis to the additive, dominance and interaction genetic variances are specified. Epistasis can make substantial contributions to each of these variance components. This parameterization of epistasis allows general consideration of the role of epistasis in evolution by defining its contribution to the additive genetic variance.     

Systematic detection of epistatic interactions based on allele pair frequencies

Epistatic genetic interactions are key for understanding the genetic contribution to complex traits. Epistasis is always defined with respect to some trait such as growth rate or fitness. Whereas most existing epistasis screens explicitly test for a trait, it is also possible to implicitly test for fitness traits by searching for the over- or under-representation of allele pairs in a given population. Such analysis of imbalanced allele pair frequencies of distant loci has not been exploited yet on a genome-wide scale, mostly due to statistical difficulties such as the multiple testing problem. We propose a new approach called Imbalanced Allele Pair frequencies (ImAP) for inferring epistatic interactions that is exclusively based on DNA sequence information. Our approach is based on genome-wide SNP data sampled from a population with known family structure. We make use of genotype information of parent-child trios and inspect 3×3 contingency tables for detecting pairs of alleles from different genomic positions that are over- or under-represented in the population. We also developed a simulation setup which mimics the pedigree structure by simultaneously assuming independence of the markers. When applied to mouse SNP data, our method detected 168 imbalanced allele pairs, which is substantially more than in simulations assuming no interactions. We could validate a significant number of the interactions with external data, and we found that interacting loci are enriched for genes involved in developmental processes.     

Epistasis interaction of QTL effects as a genetic parameter influencing estimation of the genetic additive effect

Epistasis, an additive-by-additive interaction between quantitative trait loci, has been defined as a deviation from the sum of independent effects of individual genes. Epistasis between QTLs assayed in populations segregating for an entire genome has been found at a frequency close to that expected by chance alone. Recently, epistatic effects have been considered by many researchers as important for complex traits. In order to understand the genetic control of complex traits, it is necessary to clarify additive-by-additive interactions among genes. Herein we compare estimates of a parameter connected with the additive gene action calculated on the basis of two models: a model excluding epistasis and a model with additive-by-additive interaction effects. In this paper two data sets were analysed: 1) 150 barley doubled haploid lines derived from the Steptoe × Morex cross, and 2) 145 DH lines of barley obtained from the Harrington × TR306 cross. The results showed that in cases when the effect of epistasis was different from zero, the coefficient of determination was larger for the model with epistasis than for the one excluding epistasis. These results indicate that epistatic interaction plays an important role in controlling the expression of complex traits.     

Population structure, levels of selection, and the evolution of intracellular symbionts

Many obligately intracellular symbionts exhibit a characteristic set of genetic changes that include an increase in substitution rates, loss of many genes, and apparent destabilization of many proteins and structural RNAs. Authors have suggested that these changes are due to increased mutation rates, or, more commonly, decreased effective population size due to population bottlenecks at the symbiont or, perhaps, host level. I propose that the increase in substitution rates and accumulation of deleterious mutations is a consequence of the population structure imposed on the endosymbionts by strict host association, loss of horizontal transmission and potentially conflicting levels of selection. I analyze a population genetic model of endosymbiont evolution, and demonstrate that substitution rates will increase, and the effect of those substitutions on endosymbiont fitness will become more deleterious as horizontal transmission among hosts decreases. Additionally, I find that there is a critical level of horizontal transmission below which natural selection cannot effectively purge deleterious mutations, leading to an expected loss of fitness over time. This critical level varies across loci with the degree of correlation between host and endosymbiont fitness, and may help explain differential retention and loss of certain genes.     

The effect of epistasis on sexually antagonistic genetic variation

There is increasing evidence of segregating sexually antagonistic (SA) genetic variation for fitness in laboratory and wild populations, yet the conditions for the maintenance of such variation can be restrictive. Epistatic interactions between genes can contribute to the maintenance of genetic variance in fitness and we suggest that epistasis between SA genes should be pervasive. Here, we explore its effect on SA genetic variation in fitness using a two locus model with negative epistasis. Our results demonstrate that epistasis often increases the parameter space showing polymorphism for SA loci. This is because selection in one locus is affected by allele frequencies at the other, which can act to balance net selection in males and females. Increased linkage between SA loci had more marginal effects. We also show that under some conditions, large portions of the parameter space evolve to a state where male benefit alleles are fixed at one locus and female benefit alleles at the other. This novel effect of epistasis on SA loci, which we term the ‘equity effect’, may have important effects on population differentiation and may contribute to speciation. More generally, these results support the suggestion that epistasis contributes to population divergence.     

Effects of epistasis on tests for linkage in self-pollinated species

Summary Tests for linkage based on covariances among relatives in self-pollinated species are usually based upon an assumption that epistasis is not important. This study was conducted to determine the impact of epistasis on, and to investigate the sensitivity of, such tests. Thirty covariances were calculated for each of ten non-epistatic and ten epistatic genetic models with varying probabilities of recombination between two coupling or repulsion loci. Each set of covariances was tested for linkage by comparing covariances calculated for the model with those expected for an additive-dominance model with no linkage. Results showed that the test for linkage is quite insensitive to the effects of linkage due to the disproportionate influence of inbreeding. Repulsion linkages should be easier to detect than coupling linkages for all models. Epistasis was found to mimic or counteract the effects of linkage. Tests for linkage based on covariances within a hierarchical mating design appear to be insensitive to linkage and may confuse the effects of linkage and epistasis.     

Effect of varying epistasis on the evolution of recombination

Whether recombination decelerates or accelerates a population's response to selection depends, at least in part, on how fitness-determining loci interact. Realistically, all genomes likely contain fitness interactions both with positive and with negative epistasis. Therefore, it is crucial to determine the conditions under which the potential beneficial effects of recombination with negative epistasis prevail over the detrimental effects of recombination with positive epistasis. Here, we examine the simultaneous effects of diverse epistatic interactions with different strengths and signs in a simplified model system with independent pairs of interacting loci and selection acting only on the haploid phase. We find that the average form of epistasis does not predict the average amount of linkage disequilibrium generated or the impact on a recombination modifier when compared to results using the entire distribution of epistatic effects and associated single-mutant effects. Moreover, we show that epistatic interactions of a given strength can produce very different effects, having the greatest impact when selection is weak. In summary, we observe that the evolution of recombination at mutation-selection balance might be driven by a small number of interactions with weak selection rather than by the average epistasis of all interactions. We illustrate this effect with an analysis of published data of Saccharomyces cerevisiae. Thus to draw conclusions on the evolution of recombination from experimental data, it is necessary to consider the distribution of epistatic interactions together with the associated selection coefficients.     

SELECTION BIASES THE PREVALENCE AND TYPE OF EPISTASIS ALONG ADAPTIVE TRAJECTORIES

The contribution to an organism's phenotype from one genetic locus may depend upon the status of other loci. Such epistatic interactions among loci are now recognized as fundamental to shaping the process of adaptation in evolving populations. Although little is known about the structure of epistasis in most organisms, recent experiments with bacterial populations have concluded that antagonistic interactions abound and tend to deaccelerate the pace of adaptation over time. Here, we use the NK model of fitness landscapes to examine how natural selection biases the mutations that substitute during evolution based on their epistatic interactions. We find that, even when beneficial mutations are rare, these biases are strong and change substantially throughout the course of adaptation. In particular, epistasis is less prevalent than the neutral expectation early in adaptation and much more prevalent later, with a concomitant shift from predominantly antagonistic interactions early in adaptation to synergistic and sign epistasis later in adaptation. We observe the same patterns when reanalyzing data from a recent microbial evolution experiment. These results show that when the order of substitutions is not known, standard methods of analysis may suggest that epistasis retards adaptation when in fact it accelerates it.