Detecting epistasis from an ensemble of adapting populations

The role that epistasis plays during adaptation remains an outstanding problem, which has received considerable attention in recent years. Most of the recent empirical studies are based on ensembles of replicate populations that adapt in a fixed, laboratory controlled condition. Researchers often seek to infer the presence and form of epistasis in the fitness landscape from the time evolution of various statistics averaged across the ensemble of populations. Here, we provide a rigorous analysis of what quantities, drawn from time series of such ensembles, can be used to infer epistasis for populations evolving under weak mutation on finite‐site fitness landscapes. First, we analyze the mean fitness trajectory—that is, the time course of the ensemble average fitness. We show that for any epistatic fitness landscape and starting genotype, there always exists a non‐epistatic fitness landscape that produces the exact same mean fitness trajectory. Thus, the presence of epistasis is not identifiable from the mean fitness trajectory. By contrast, we show that two other ensemble statistics—the time evolution of the fitness variance across populations, and the time evolution of the mean number of substitutions—can detect certain forms of epistasis in the underlying fitness landscape.     

The contrasting genetic architecture of wing size, viability, and development time in a rainforest species and its more widely distributed relative

Divergence among populations can occur via additive genetic effects and/or because of epistatic interactions among genes. Here we use line-cross analysis to compare the importance of epistasis in divergence among two sympatric Drosophila species from eastern Australia, one (D. serrata) distributed continuously and the other (D. birchii) confined to rainforest habitats that are often disjunct. For D. serrata, crosses indicated that development time and wing size differences were due to additive genetic effects, while for viability there were digenic epistatic effects. Crosses comparing geographically close populations as well as those involving the most geographically distant populations (including the southern species border) revealed epistatic interactions, whereas crosses at an intermediate distance showed no epistasis. In D. birchii, there was no evidence of epistasis for viability, although for development time and wing size there was epistasis in the cross between the most geographically diverged populations. Strong epistasis has not developed among the D. birchii populations, and this habitat specialist does not show stronger epistasis than D. serrata. Given that epistasis has been detected in crosses with other species from eastern Australia, including the recently introduced D. melanogaster, the results point to epistasis not being directly linked to divergence times among populations.     

Epistasis causes outbreeding depression in eucalypt hybrids

The genetic architecture underlying species differentiation is essential for understanding the mechanisms of speciation and post-zygotic reproductive barriers which exist between species. We undertook line-cross analysis of multiple hybrid (F₁, F₂ and backcrosses) and pure-species populations of two diploid eucalypt species from different subseries, Eucalyptus globulus and Eucalyptus nitens, to unravel the genetic architecture of their differentiation. The populations were replicated on two sites and monitored for growth and survival over a 14-year period. The hybrids exhibited severe outbreeding depression which increased with age. Of the composite additive, dominance and epistatic effects estimated, the additive × additive epistatic component was the most important in determining population divergence in both growth and survival. Significant dominance × dominance epistasis was also detected for survival at several ages. While favourable dominance and, in the case of survival, dominance × dominance epistasis could produce novel gene combinations which enhance hybrid fitness, at the population level, these effects were clearly overridden by adverse additive × additive epistasis which appears to be a major driver of overall outbreeding depression in the hybrid populations. The lack of model fit at older ages suggested that even high-order epistatic interactions may potentially have a significant contribution to outbreeding depression in survival. The estimated composite genetic parameters were generally stable across sites. Our results argue that the development of favourable epistasis is a key mechanism underlying the genetic divergence of eucalypt species, and epistasis is an important mechanism underlying the evolution of post-zygotic reproductive barriers.     

Factors affecting the genetic load in Drosophila: synergistic epistasis and correlations among fitness components

Two factors that can affect genetic load, synergistic epistasis and sexual selection, were investigated in Drosophila melanogaster. A set of five chromosomal regions containing visible recessive mutations were put together in all combinations to create a full set of 32 homozygous lines fixed for different numbers of known mutations. Two measures of fitness were made for each line: productivity (a combined measure of fecundity and egg-to-adult survivorship) and competitive male mating success. Productivity, but not male mating success, showed a pattern of strong average synergistic epistasis, such that the log fitness declined nonlinearly with increasing numbers of mutations. Synergistic epistasis is known to reduce the mutation load. Both fitness components show some positive and some negative interactions between specific sets of mutations. Furthermore, alleles with deleterious effects on productivity tend to also diminish male mating success. Given that male mating success can affect relative fitness without changing the mean productivity of a population, these additional effects would lead to lower frequencies and lower fixation rates of deleterious alleles without higher costs to the mean fitness of the population.     

The effects of parasitism and inbreeding on the competitive ability in Daphnia magna: evidence for synergistic epistasis

Synergistic epistasis for fitness is often assumed in models of how selection acts on the frequency and distribution of deleterious mutations. Evidence for synergistic epistasis would exist if the logarithm of fitness declines more quickly with number of deleterious mutations, than predicted by a linear decline. This can be studied indirectly by quantifying the effect of different levels of inbreeding on fitness. Here, six sets (different genetic backgrounds) of three increasingly inbred Daphnia magna clones were used to assess their relative fitness according to changes in frequency in a competition experiment against a tester clone. A novelty of the mating procedure was that the inbreeding coefficients (F) of the three clones belonging to each set increased in steps of 0.25 independent of the (unknown) inbreeding coefficient of the common ancestor. The equal increase of the inbreeding coefficients is important, because deviations influence the quantification of inbreeding depression, its variance and the detection of epistasis. In a simple mathematical model we show that when working with a partially inbred population inbreeding depression is underestimated, the variance of fitness is increased, and the detection of epistasis more difficult. Further, to examine whether an interaction between inbreeding and parasitism exists, each inbred clone was tested with and without a microsporidium infection (Octosporea bayeri). We found a nonlinear decrease of the logarithm of fitness across the three levels of inbreeding, indicating synergistic epistasis. The interaction term between parasitism and inbreeding was not significant. Our results suggest that deleterious mutations may be purged effectively once the level of inbreeding is high, but that parasitism seems not to influence this effect.     

A test for epistasis among induced mutations in Caenorhabditis elegans

Synergistic epistasis, in which deleterious mutations tend to magnify each other's effects, is a necessary component of the mutational deterministic hypothesis for the maintenance of sexual production. We tested for epistasis for life-history traits in the soil nematode Caenorhabditis elegans by inducing mutations in two genetic backgrounds: a wild-type strain and a set of genetically loaded lines that contain large numbers of independent mildly detrimental mutations. There was no significant difference between the effect of new mutations on the wild-type background and the genetically loaded background for four out of five fitness correlates. In these four cases, the maximum level of epistasis compatible with the data was very low. The fifth trait, late productivity, is not likely to be an important component of fitness. This suggests either that specific environmental conditions are required to cause epistasis or that synergistic epistasis is not a general phenomenon. We also suggest a new mechanism by which deleterious mutations may provide an advantage to sexual reproduction under low selection coefficients.     

EPISTATIC INTERACTIONS DETERMINE THE MUTATIONAL PATHWAYS AND COEXISTENCE OF LINEAGES IN CLONAL ESCHERICHIA COLI POPULATIONS

Understanding how diversity emerges in a single niche is not fully understood. Rugged fitness landscapes and epistasis between beneficial mutations could explain coexistence among emerging lineages. To provide an experimental test of this notion, we investigated epistasis among four pleiotropic mutations in rpoS, mglD, malT, and hfq present in two coexisting lineages that repeatedly fixed in experimental populations of Escherichia coli. The mutations were transferred into the ancestral background individually or in combination of double or triple alleles. The combined competitive fitness of two or three beneficial mutations from the same lineage was consistently lower than the sum of the competitive fitness of single mutants—a clear indication of negative epistasis within lineages. We also found sign epistasis (i.e., the combined fitness of two beneficial mutations lower than the ancestor), not only from two different lineages (i.e., hfq and rpoS) but also from the same lineage (i.e., mglD and malT). The sign epistasis between loci of different lineages indeed indicated a rugged fitness landscape, providing an epistatic explanation for the coexistence of distinct rpoS and hfq lineages in evolving populations. The negative and sign epistasis between beneficial mutations within the same lineage can further explain the order of mutation acquisition.     

Amino Acid Covariation in a Functionally Important Human Immunodeficiency Virus Type 1 Protein Region Is Associated With Population Subdivision

The frequently reported amino acid covariation of the highly polymorphic human immunodeficiency virus type 1 (HIV-1) exterior envelope glycoprotein V3 region has been assumed to reflect fitness epistasis between residues. However, nonrandom association of amino acids, or linkage disequilibrium, has many possible causes, including population subdivision. If the amino acids at a set of sequence sites differ in frequencies between subpopulations, then analysis of the whole population may reveal linkage disequilibrium even if it does not exist in any subpopulation. HIV-1 has a complex population structure, and the effects of this structure on linkage disequilibrium were investigated by estimating within- and among-subpopulation components of variance in linkage disequilibrium. The amino acid covariation previously reported is explained by differences in amino acid frequencies among virus subpopulations in different patients and by nonsystematic disequilibrium among patients. Disequilibrium within patients appears to be entirely due to differences in amino acid frequencies among sampling time points and among chemokine coreceptor usage phenotypes of virus particles, but not source tissues. Positive selection explains differences in allele frequencies among time points and phenotypes, indicating that these differences are adaptive rather than due to genetic drift. However, the absence of a correlation between linkage disequilibrium and phenotype suggests that fitness epistasis is an unlikely cause of disequilibrium. Indeed, when population structure is removed by analyzing sequences from a single time point and phenotype, no disequilibrium is detectable within patients. These results caution against interpreting amino acid covariation and coevolution as evidence for fitness epistasis.     

Multigenerational effects of inbreeding in Cucurbita pepo ssp. texana (Cucurbitaceae)

The shape of the fitness function relating the decline in fitness with coefficient of inbreeding (f) can provide evidence concerning the genetic basis of inbreeding depression, but few studies have examined inbreeding depression across a range of f using noncultivated species. Futhermore, studies have rarely examined the effects of inbreeding depression in the maternal parent on offspring fitness. To estimate the shape of the fitness function, we examined the relationship between f and fitness across a range off from 0.000 to 0.875 for components of both male and female fitness in Cucurbita pepo ssp. texana. Each measure of female fitness declined with f, including pistillate flower number, fruit number, seed number per fruit, seed mass per fruit, and percentage seed germination. Several aspects of male fitness also declined with f, including staminate flower number, pollen number per flower, and the number of days of flowering, although cumulative inbreeding depression was less severe for male (0.34) than for female function (0.39). Fitness tended to decline linearly with f between f = 0.00 and f = 0.75 for most traits and across cumulative lifetime fitness (mean = 0.66), suggesting that individual genes causing inbreeding depression are additive and the result of many alleles of small effect. However, most traits also showed a small reduction in inbreeding depression between f = 0.75 and f = 0.875, and evidence of purging or diminishing epistasis was found for in vitro pollen-tube growth rate. To examine inbreeding depression as a maternal effect, we performed outcross pollinations on f = 0.0 and f = 0.5 mothers and found that depression due to maternal inbreeding was 0.07, compared to 0.10 for offspring produced through one generation of selfing. In at least some families, maternal inbreeding reduced fruit number, seed number and mass, staminate flower number, pollen diameter, and pollen-tube growth rate. Collectively these results suggest that, while the fitness function appears to be largely linear for most traits, maternal effects may compound the effects of inbreeding depression in multigenerational studies, though this may be partially offset by purging or diminishing epistasis.     

EVOLUTION OF THE GENETIC ARCHITECTURE UNDERLYING FITNESS IN THE PITCHER-PLANT MOSQUITO,WYEOMYIA SMITHII

We examined the genetic basis for evolutionary divergence among geographic populations of the pitcher-plant mosquito, Wyeomyia smithii, using protein electrophoresis and line-cross analysis. Line-cross experiments were performed under both low density, near-optimal conditions, and at high, limiting larval densities sufficient to reduce fitness (r_c) in parental populations by approximately 50%. We found high levels of electrophoretic divergence between ancestral and derived populations, but low levels of divergence between two ancestral populations and between two derived populations. Assessed under near-optimal conditions, the genetic divergence of fitness (r_c) between ancestral and derived populations, but not between two derived populations or between two ancestral populations, has involved both allelic (dominance) and genic (epistatic) interactions. The role of dominance and epistasis in the divergence of r_c among populations affects its component traits in a pattern that is unique to each cross. Patterns of genetic differentiation among populations of W. smithii provide evidence for a topographically complex “adaptive landscape” as envisioned by Wright in his “shifting balance” theory of evolution. Although we cannot definitively rule out the role of deterministic evolution in the divergence of populations on this landscape, ecological inference and genetic data are more consistent with a stochastic than a deterministic process. At high, limiting larval density, hybrid vigor is enhanced and the influence of epistasis disappears. Thus, under stressful conditions, the advantages to fitness due to hybrid heterozygosity can outweigh the deleterious effects of fragmented gene complexes. These results have important implications for the management of inbred populations. Outbreeding depression assessed in experimental crosses under benign lab, zoo, or farm conditions may not accurately reveal the increased advantages of heterozygosity in suboptimal or marginal conditions likely to be found in nature.     

Environment changes epistasis to alter trade‐offs along alternative evolutionary paths

The fitness effect of a mutation can depend on both its genetic background, known as epistasis, and the prevailing external environment. Many examples of these dependencies are known, but few studies consider both aspects in combination, especially as they affect mutations that have been selected together. We examine interactions between five coevolved mutations in eight diverse environments. We find that mutations are, on average, beneficial across environments, but that there is high variation in their fitness effects, including many examples of mutations conferring a cost in some, but not other, genetic background‐environment combinations. Indeed, even when global interaction trends are accounted for, specific local mutation interactions are common and differed across environments. One consequence of this dependence is that the range of trade‐offs in genotype fitness across selected and alternative environments are contingent on the particular evolutionary path followed over the mutation landscape. Finally, although specific interactions were common, there was a consistent pattern of diminishing returns epistasis whereby mutation effects were less beneficial when added to genotypes of higher fitness. Our results underline that specific mutation effects are highly dependent on the combination of genetic and external environments, and support a general relationship between a genotype's current fitness and its potential to increase in fitness.     

Speciation by Reinforcement: A Model Derived from Studies of Drosophila

Reinforcement is an increase in premating reproductive isolation between taxa resulting from selection against hybrids. We present a model of reinforcement with a novel type of selection on female mating behavior. Previous models of reinforcement have focused on the divergence of female mating preferences between nascent species. We suggest that an increase in the level of female mating discrimination can yield reinforcement without further divergence of either male characters or female preferences. This model indicates that selection on mating discrimination is a viable mechanism for reinforcement and may allow speciation under less stringent conditions than selection on female preference. This model also incorporates empirical results from genetic studies of hybrid fitness determination in Drosophila species. We find that the details of inheritance, which include sex-linked transmission, sex-limited fertility reduction, and X-autosome epistasis, have important effects on the likelihood of reinforcement. In particular, X-autosome epistasis for hybrid fitness determination facilitates reinforcement when hybrid fertility reduction occurs in males, but hinders the process when it occurs in females. HALDANE's rule indicates that hybrid sterility will generally evolve in males prior to females within nascent species. Thus, HALDANE's rule and X-autosome epistasis provide conditions that are surprisingly favorable for reinforcement in Drosophila.     

Sperm morphology and the evolution of intracellular sperm–egg interactions

Sperm morphology is incredibly diverse, even among closely related species, yet the coevolution between males and females of fertilization recognition systems is necessary for successful karyogamy (male and female pronuclear fusion). In most species, the entire sperm enters the egg during fertilization so sperm morphological diversity may impact the intracellular sperm–egg interactions necessary for karyogamy. We quantified morphological variation of sperm inside eggs prior to and following karyogamy in several species of Drosophila to understand whether evolution of sperm morphology could influence intracellular sperm–egg interactions (ISEIs). We measured seven parameters that describe ISEIs among species to determine whether these parameters varied both within a species across development and across species at the same developmental stage. We used heterospecific crosses to test the relative role of male origin, female origin, and interaction between the male and female in determining ISEIs. We found that sperm shape changed within a species as development proceeded and, at particular development stages, species varied in some ISEIs. Parental origin had an effect on some ISEIs, with a general trend for a stronger female effect. Overall, our findings identify conserved and variable ISEIs among species and demonstrate the potential to contribute understanding to gamete evolution and development.     

Testing for epistasis between deleterious mutations in a parasitoid wasp

Abstract.— Determining the way in which deleterious mutations interact to effect fitness is crucial to numerous areas in evolutionary biology. For example, if each additional mutation leads to a greater decrease in log fitness than the last, termed synergistic epistasis, then sex and recombination provide an advantage because they enable deleterious mutations to be eliminated more efficiently. However, there is a severe shortage of relevant empirical data, especially of the form that can help test mutational explanations for the widespread occurrence of sex. Here, we test for epistasis in the parasitic wasp Nasonia vitripennis , examining the fitness consequences of chemically induced deleterious mutations. We examine two components of fitness, both of which are thought to be important in natural populations of parasitic wasps: longevity and egg production. Our results show synergistic epistasis for longevity, but not for egg production.     

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.     

FIXATION OF MUTATORS IN ASEXUAL POPULATIONS: THE ROLE OF GENETIC DRIFT AND EPISTASIS

We study the evolutionary dynamics of an asexual population of nonmutators and mutators on a class of epistatic fitness landscapes. We consider the situation in which all mutations are deleterious and mutators are produced from nonmutators continually at a constant rate. We find that in an infinitely large population, a minimum nonmutator‐to‐mutator conversion rate is required to fix the mutators but an arbitrarily small conversion rate results in the fixation of mutators in a finite population. We calculate analytical expressions for the mutator fraction at mutation‐selection balance and fixation time for mutators in a finite population when the difference between the mutation rate for mutator and nonmutator is smaller (regime I) and larger (regime II) than the selection coefficient. Our main result is that in regime I, the mutator fraction and the fixation time are independent of epistasis but in regime II, mutators are rarer and take longer to fix when the decrease in fitness with the number of deleterious mutations occurs at an accelerating rate (synergistic epistasis) than at a diminishing rate (antagonistic epistasis). Our analytical results are compared with numerics and their implications are discussed.     

A test for Y‐linked additive and epistatic effects on surviving bacterial infections in Drosophila melanogaster

Y‐ and W‐chromosomes offer a theoretically powerful way for sexual dimorphism to evolve. Consistent with this possibility, Drosophila melanogaster Y‐chromosomes can influence gene regulation throughout the genome; particularly immune‐related genes. In order for Y‐linked regulatory variation (YRV) to contribute to adaptive evolution it must be comprised of additive genetic variance, such that variable Ys induce consistent phenotypic effects within the local gene pool. We assessed the potential for Y‐chromosomes to adaptively shape gram‐negative and gram‐positive bacterial defence by introgressing Ys across multiple genetic haplotypes from the same population. We found no Y‐linked additive effects on immune phenotypes, suggesting a restricted role for the Y to facilitate dimorphic evolution. We did find, however, a large magnitude Y by background interaction that induced rank order reversals of Y‐effects across the backgrounds (i.e. sign epistasis). Thus, Y‐chromosome effects appeared consistent within backgrounds, but highly variable among backgrounds. This large sign epistatic effect could constrain monomorphic selection in both sexes, considering that autosomal alleles under selection must spend half of their time in a male background where relative fitness values are altered. If the pattern described here is consistent for other traits or within other XY (or ZW) systems, then YRV may represent a universal constraint to autosomal trait evolution.     

Pervasive,yet idiosyncratic,epistatic pleiotropy during adaptation in a behaviourally complex microbe

Understanding how multiple mutations interact to jointly impact multiple ecologically important traits is critical for creating a robust picture of organismal fitness and the process of adaptation. However, this is complicated by both environmental heterogeneity and the complexity of genotype‐to‐phenotype relationships generated by pleiotropy and epistasis. Moreover, little is known about how pleiotropic and epistatic relationships themselves change over evolutionary time. The soil bacterium Myxococcus xanthus employs several distinct social traits across a range of environments. Here, we use an experimental lineage of M. xanthus that evolved a novel form of social motility to address how interactions between epistasis and pleiotropy evolve. Specifically, we test how mutations accumulated during selection on soft agar pleiotropically affect several other social traits (hard agar motility, predation and spore production). Relationships between changes in swarming rate in the selective environment and the four other traits varied greatly over time in both direction and magnitude, both across timescales of the entire evolutionary lineage and individual evolutionary time steps. We also tested how a previously defined epistatic interaction is pleiotropically expressed across these traits. We found that phenotypic effects of this epistatic interaction were highly correlated between soft and hard agar motility, but were uncorrelated between soft agar motility and predation, and inversely correlated between soft agar motility and spore production. Our results show that ‘epistatic pleiotropy’ varied greatly in magnitude, and often even in sign, across traits and over time, highlighting the necessity of simultaneously considering the interacting complexities of pleiotropy and epistasis when studying the process of adaptation.     

Mutation-selection balance and the evolutionary advantage of sex and recombination

Mutation-selection balance in a multi-locus system is investigated theoretically, using a modification of Bulmer's infinitesimal model of selection on a normally-distributed quantitative character, taking the number of mutations per individual (n) to represent the character value. The logarithm of the fitness of an individual with n mutations is assumed to be a quadratic, decreasing function of n. The equilibrium properties of infinitely large asexual populations, random-mating populations lacking genetic recombination, and random-mating populations with arbitrary recombination frequencies are investigated. With 'synergistic' epistasis on the scale of log fitness, such that log fitness declines more steeply as n increases, it is shown that equilibrium mean fitness is least for asexual populations. In sexual populations, mean fitness increases with the number of chromosomes and with the map length per chromosome. With 'diminishing returns' epistasis, such that log fitness declines less steeply as n increases, mean fitness behaves in the opposite way. Selection on asexual variants and genes affecting the rate of genetic recombination in random-mating populations was also studied. With synergistic epistasis, zero recombination always appears to be disfavoured, but free recombination is disfavoured when the mutation rate per genome is sufficiently small, leading to evolutionary stability of maps of intermediate length. With synergistic epistasis, an asexual mutant is unlikely to invade a sexual population if the mutation rate per diploid genome greatly exceeds unity. Recombination is selectively disadvantageous when there is diminishing returns epistasis. These results are compared with the results of previous theoretical studies of this problem, and with experimental data.     

Reciprocal sign epistasis is a necessary condition for multi-peaked fitness landscapes

Having multiple peaks within fitness landscapes critically affects the course of evolution, but whether their presence imposes specific requirements at the level of genetic interactions remains unestablished. Here we show that to exhibit multiple fitness peaks, a biological system must contain reciprocal sign epistatic interactions, which are defined as genetic changes that are separately unfavorable but jointly advantageous. Using Morse theory, we argue that it is impossible to formulate a sufficient condition for multiple peaks in terms of local genetic interactions. These findings indicate that systems incapable of reciprocal sign epistasis will always possess a single fitness peak. However, reciprocal sign epistasis should be pervasive in nature as it is a logical consequence of specificity in molecular interactions. The results thus predict that specific molecular interactions may yield multiple fitness peaks, which can be tested experimentally.