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.     

Evolutionary dynamics, epistatic interactions, and biological information

We investigate a definition of biological information that connects population genetics with the tools of information theory by focusing on the distribution of genotypes found in a population. Previous research has treated loci as non-interacting by making specific approximations in the calculation of information-theoretic quantities. We expand earlier mathematical forms to include epistasis, or interactions between mutations at all pairs of loci. Application of our improved measure of biological information to evolution on two-locus, two-allele fitness landscapes demonstrates that mutual information between loci reflects epistatic interaction of mutations. Finally, we consider four-locus, two-allele fitness landscapes with modular structure. As modular interactions are inherently epistatic, we demonstrate that our refined approximation provides insight into the underlying structure of these non-trivial fitness landscapes.     

On the evolution of epistasis II: a generalized Wright-Kimura framework

The evolution of fitness interactions between genes at two major loci is studied where the alleles at a third locus modify the epistatic interaction between the two major loci. The epistasis is defined by a parameter epsilon and a matrix structure that specifies the nature of the interactions. When epsilon=0 the two major loci have additive fitnesses, and when these are symmetric the interaction matrices studied here produce symmetric viabilities of the Wright [1952. The genetics of quantitative variability. In: Reeve, E.C.R., Waddington, C.H. (Eds.), Quantitative Inheritance. Her Majesty's Stationary Office, London]-Kimura [1956. A model of a genetic system which leads to closer linkage by natural selection. Evolution 10, 278-281] form. Two such interaction matrices are studied, for one of which epistasis as measured by |epsilon| always increases, and for the other it increases when the linkage between the major loci is tight enough and there is initial linkage disequilibrium. Increase of epistasis does not necessarily coincide with increase in equilibrium mean fitness.     

Two-locus epistasis with sexually antagonistic selection: a genetic Parrondo's paradox

An example is provided where, with antagonistic selection and epistatic interaction of alleles at two loci, an autosomal allele can rise in frequency, persist in the population, and even continue to fixation, despite having an apparently lower average fitness than the alternative allele, in a process similar to Parrondo's paradox.     

Genomewide analysis of epistatic effects for quantitative traits in barley

The doubled-haploid (DH) barley population (Harrington x TR306) developed by the North American Barley Genome Mapping Project (NABGMP) for QTL mapping consisted of 145 lines and 127 markers covering a total genome length of 1270 cM. These DH lines were evaluated in approximately 25 environments for seven quantitative traits: heading, height, kernel weight, lodging, maturity, test weight, and yield. We applied an empirical Bayes method that simultaneously estimates 127 main effects for all markers and 127(127-1)/2=8001 interaction effects for all marker pairs in a single model. We found that the largest main-effect QTL (single marker) and the largest epistatic effect (single pair of markers) explained approximately 18 and 2.6% of the phenotypic variance, respectively. On average, the sum of all significant main effects and the sum of all significant epistatic effects contributed 35 and 6% of the total phenotypic variance, respectively. Epistasis seems to be negligible for all the seven traits. We also found that whether two loci interact does not depend on whether or not the loci have individual main effects. This invalidates the common practice of epistatic analysis in which epistatic effects are estimated only for pairs of loci of which both have main effects.     

GENETIC ARCHITECTURE AND POSTZYGOTIC REPRODUCTIVE ISOLATION: EVOLUTION OF BATESON–DOBZHANSKY–MULLER INCOMPATIBILITIES IN A POLYGENIC MODEL

The Bateson–Dobzhansky–Muller model predicts that postzygotic isolation evolves due to the accumulation of incompatible epistatic interactions, but few studies have quantified the relationship between genetic architecture and patterns of reproductive divergence. We examined how the direction and magnitude of epistatic interactions in a polygenic trait under stabilizing selection influenced the evolution of hybrid incompatibilities. We found that populations evolving independently under stabilizing selection experienced suites of compensatory allelic changes that resulted in genetic divergence between populations despite the maintenance of a stable, high‐fitness phenotype. A small number of loci were then incompatible with multiple alleles in the genetic background of the hybrid and the identity of these incompatibility loci changed over the evolution of the populations. For F₁ hybrids, reduced fitness evolved in a window of intermediate strengths of epistatic interactions, but F₂ and backcross hybrids evolved reduced fitness across weak and moderate strengths of epistasis due to segregation variance. Strong epistatic interactions constrained the allelic divergence of parental populations and prevented the development of reproductive isolation. Because many traits with varying genetic architectures must be under stabilizing selection, our results indicate that polygenetic drift is a plausible hypothesis for the evolution of postzygotic reproductive isolation.     

Epistasis and the mutation load: a measurement-theoretical approach

An approximate solution for the mean fitness in mutation-selection balance with arbitrary order of epistatic interaction is derived. The solution is based on the assumptions of coupling equilibrium and that the interaction effects are multilinear. We find that the effect of m-order epistatic interactions (i.e., interactions among groups of m loci) on the load is dependent on the total genomic mutation rate, U, to the mth power. Thus, higher-order gene interactions are potentially important if U is large and the interaction density among loci is not too low. The solution suggests that synergistic epistasis will decrease the mutation load and that variation in epistatic effects will elevate the load. Both of these results, however, are strictly true only if they refer to epistatic interaction strengths measured in the optimal genotype. If gene interactions are measured at mutation-selection equilibrium, only synergistic interactions among even numbers of genes will reduce the load. Odd-ordered synergistic interactions will then elevate the load. There is no systematic relationship between variation in epistasis and load at equilibrium. We argue that empirical estimates of gene interaction must pay attention to the genetic background in which the effects are measured and that it may be advantageous to refer to average interaction intensities as measured in mutation-selection equilibrium. We derive a simple criterion for the strength of epistasis that is necessary to overcome the twofold disadvantage of sex.     

Purging deleterious mutations under self fertilization: paradoxical recovery in fitness with increasing mutation rate in Caenorhabditis elegans

Background

The accumulation of deleterious mutations can drastically reduce population mean fitness. Self-fertilization is thought to be an effective means of purging deleterious mutations. However, widespread linkage disequilibrium generated and maintained by self-fertilization is predicted to reduce the efficacy of purging when mutations are present at multiple loci.

Methodology/Principal Findings

We tested the ability of self-fertilizing populations to purge deleterious mutations at multiple loci by exposing obligately self-fertilizing populations of Caenorhabditis elegans to a range of elevated mutation rates and found that mutations accumulated, as evidenced by a reduction in mean fitness, in each population. Therefore, purging in obligate selfing populations is overwhelmed by an increase in mutation rate. Surprisingly, we also found that obligate and predominantly self-fertilizing populations exposed to very high mutation rates exhibited consistently greater fitness than those subject to lesser increases in mutation rate, which contradicts the assumption that increases in mutation rate are negatively correlated with fitness. The high levels of genetic linkage inherent in self-fertilization could drive this fitness increase.

Conclusions

Compensatory mutations can be more frequent under high mutation rates and may alleviate a portion of the fitness lost due to the accumulation of deleterious mutations through epistatic interactions with deleterious mutations. The prolonged maintenance of tightly linked compensatory and deleterious mutations facilitated by self-fertilization may be responsible for the fitness increase as linkage disequilibrium between the compensatory and deleterious mutations preserves their epistatic interaction.     

Epistasis between QTLs for bone density variation in Copenhagen × dark agouti F2 rats

The variation in several of the risk factors for osteoporotic fracture, including bone mineral density (BMD), has been shown to be strongly influenced by genetic differences. However, the genetic architecture of BMD is complex in both humans and in model organisms. We previously reported quantitative trait locus (QTL) results for BMD from a genome screen of 828 F2 progeny of Copenhagen and dark agouti rats. These progeny also provide an excellent opportunity to search for epistatic effects, or interaction between genetic loci, that contribute to fracture risk. Microsatellite marker data from a 20-cM genome screen was analyzed along with weight-adjusted bone density (DXA and pQCT) phenotypic data using the R/qtl software package. Genotype and phenotype data were permuted to determine genome-wide significance thresholds for the full model and epistasis (interaction) LOD scores corresponding to an alpha level of 0.01. A novel locus on chromosome 15 and a previously reported chromosome 14 QTL demonstrated a strong epistatic effect on BMD at the femur by DXA (LOD = 5.4). Two novel QTLs on chromosomes 2 and 12 were found to interact to affect total BMD at the femur midshaft by pQCT (LOD = 5.0). These results provide new information regarding the mode of action of previously identified QTL in the rat, as well as identifying novel loci that act in combination with known QTL or with other novel loci to contribute to BMD variation.     

Epistasis for fitness-related quantitative traits in Arabidopsis thaliana grown in the field and in the greenhouse

The extent to which epistasis contributes to adaptation, population differentiation, and speciation is a long-standing and important problem in evolutionary genetics. Using recombinant inbred (RI) lines of Arabidopsis thaliana grown under natural field conditions, we have examined the genetic architecture of fitness-correlated traits with respect to epistasis; we identified both single-locus additive and two-locus epistatic QTL for natural variation in fruit number, germination, and seed length and width. For fruit number, we found seven significant epistatic interactions, but only two additive QTL. For seed germination, length, and width, there were from two to four additive QTL and from five to eight epistatic interactions. The epistatic interactions were both positive and negative. In each case, the magnitude of the epistatic effects was roughly double that of the effects of the additive QTL, varying from -41% to +29% for fruit number and from -5% to +4% for seed germination, length, and width. A number of the QTL that we describe participate in more than one epistatic interaction, and some loci identified as additive also may participate in an epistatic interaction; the genetic architecture for fitness traits may be a network of additive and epistatic effects. We compared the map positions of the additive and epistatic QTL for germination, seed width, and seed length from plants grown in both the field and the greenhouse. While the total number of significant additive and epistatic QTL was similar under the two growth conditions, the map locations were largely different. We found a small number of significant epistatic QTL x environment effects when we tested directly for them. Our results support the idea that epistatic interactions are an important part of natural genetic variation and reinforce the need for caution in comparing results from greenhouse-grown and field-grown plants.     

Pleiotropic Effects of a Mitochondrial–Nuclear Incompatibility Depend upon the Accelerating Effect of Temperature in Drosophila

Interactions between mitochondrial and nuclear gene products that underlie eukaryotic energy metabolism can cause the fitness effects of mutations in one genome to be conditional on variation in the other genome. In ectotherms, the effects of these interactions are likely to depend upon the thermal environment, because increasing temperature accelerates molecular rates. We find that temperature strongly modifies the pleiotropic phenotypic effects of an incompatible interaction between a Drosophila melanogaster polymorphism in the nuclear-encoded, mitochondrial tyrosyl-transfer (t)RNA synthetase and a D. simulans polymorphism in the mitochondrially encoded tRNA^Tyr. The incompatible mitochondrial–nuclear genotype extends development time, decreases larval survivorship, and reduces pupation height, indicative of decreased energetic performance. These deleterious effects are ameliorated when larvae develop at 16° and exacerbated at warmer temperatures, leading to complete sterility in both sexes at 28°. The incompatible genotype has a normal metabolic rate at 16° but a significantly elevated rate at 25°, consistent with the hypothesis that inefficient energy metabolism extends development in this genotype at warmer temperatures. Furthermore, the incompatibility decreases metabolic plasticity of larvae developed at 16°, indicating that cooler development temperatures do not completely mitigate the deleterious effects of this genetic interaction. Our results suggest that the epistatic fitness effects of metabolic mutations may generally be conditional on the thermal environment. The expression of epistatic interactions in some environments, but not others, weakens the efficacy of selection in removing deleterious epistatic variants from populations and may promote the accumulation of incompatibilities whose fitness effects will depend upon the environment in which hybrids occur.     

Modelling epistatic effects of embryo and endosperm QTL on seed quality traits

Coordinated expression of embryo and endosperm tissues is required for proper seed development. The coordination among these two tissues is controlled by the interaction between multiple genes expressed in the embryo and endosperm genomes. In this article, we present a statistical model for testing whether quantitative trait loci (QTL) active in different genomes, diploid embryo and triploid endosperm, epistatically affect a trait expressed on the endosperm tissue. The maximum likelihood approach, implemented with the EM algorithm, was derived to provide the maximum likelihood estimates of the locations of embryo- and endosperm-specific QTL and their main effects and epistatic effects. This model was used in a real example for rice in which two QTL, one from the embryo genome and the other from the endosperm genome, exert a significant interaction effect on gel consistency on the endosperm. Our model has successfully detected Waxy, a candidate gene in the embryo genome known to regulate one of the major steps of amylose biosynthesis in the endosperm. This model will have great implications for agricultural and evolutionary genetic research.     

MHC polymorphism and disease resistance to vibrio anguillarum in 8 families of half-smooth tongue sole (Cynoglossus semilaevis)

Background

Most quantitative traits are controlled by multiple quantitative trait loci (QTL). The contribution of each locus may be negligible but the collective contribution of all loci is usually significant. Genome selection that uses markers of the entire genome to predict the genomic values of individual plants or animals can be more efficient than selection on phenotypic values and pedigree information alone for genetic improvement. When a quantitative trait is contributed by epistatic effects, using all markers (main effects) and marker pairs (epistatic effects) to predict the genomic values of plants can achieve the maximum efficiency for genetic improvement.

Results

In this study, we created 126 recombinant inbred lines of soybean and genotyped 80 makers across the genome. We applied the genome selection technique to predict the genomic value of somatic embryo number (a quantitative trait) for each line. Cross validation analysis showed that the squared correlation coefficient between the observed and predicted embryo numbers was 0.33 when only main (additive) effects were used for prediction. When the interaction (epistatic) effects were also included in the model, the squared correlation coefficient reached 0.78.

Conclusions

This study provided an excellent example for the application of genome selection to plant breeding.     

Epistatic interaction is an important genetic basis of grain yield and its components in maize

A population of 294 recombinant inbred lines (RIL) derived from Yuyu22, an elite maize hybrid extending broadly in China, has been constructed to investigate the genetic basis of grain yield, and associated yield components in maize. The main-effect quantitative trait loci (QTL), digenic epistatic interactions, and their interactions with the environment for grain yield and its three components were identified by using the mixed linear model approach. Thirty-two main-effect QTL and forty-four pairs of digenic epistatic interactions were detected for the four measured traits in four environments. Our results suggest that both additive effects and epistasis (additive × additive) effects are important genetic bases of grain yield and its components in the RIL population. Only 30.4% of main-effect QTL for ear length were involved in epistatic interactions. This implies that many loci in epistatic interactions may not have significant effects for traits alone but may affect trait expression by epistatic interaction with the other loci.     

Little epistasis for anxiety-related measures in the DeFries strains of laboratory mice

Recent advances in methodologies for testing epistatic interactions, combined with several successes in demonstrating genetic interaction effects in animal and human genetics, have rekindled interest in the role of epistatic influences on complex traits. It has even been suggested that the unacknowledged presence of epistasis vitiates the genetic dissection of human and animal behavior. Here we report a genome-wide interaction analysis of 1636 F₂ mice to show that epistasis is of minimal importance in an animal model of anxiety. By using a sufficiently large sample of F₂ animals, we provide evidence that interaction effects between any two loci contribute less than 5% to the total phenotypic variance in multiple tests of anxiety. We conclude that interactions between loci do not necessarily vitiate the genetic analysis of behavior in at least one animal model of anxiety.     

A stochastic model for the development of Bateson-Dobzhansky-Muller incompatibilities that incorporates protein interaction networks

Speciation is characterized by the development of reproductive isolating barriers between diverging groups. Intrinsic post-zygotic barriers of the type envisioned by Bateson, Dobzhansky, and Muller are deleterious epistatic interactions among loci that reduce hybrid fitness, leading to reproductive isolation. The first formal population genetic model of the development of these barriers was published by Orr in 1995, and here we develop a more general model of this process by incorporating finite protein-protein interaction networks, which reduce the probability of deleterious interactions in vivo. Our model shows that the development of deleterious interactions is limited by the density of the protein-protein interaction network. We have confirmed our analytical predictions of the number of possible interactions given the number of allele substitutions by using simulations on the Saccharomyces cerevisiae protein-protein interaction network. These results allow us to define the rate at which deleterious interactions are expected to form, and hence the speciation rate, for any protein-protein interaction network.     

Molecular basis of adaptive convergence in experimental populations of RNA viruses

Characterizing the molecular basis of adaptation is one of the most important goals in modern evolutionary genetics. Here, we report a full-genome sequence analysis of 21 independent populations of vesicular stomatitis ribovirus evolved on the same cell type but under different demographic regimes. Each demographic regime differed in the effective viral population size. Evolutionary convergences are widespread both at synonymous and nonsynonymous replacements as well as in an intergenic region. We also found evidence for epistasis among sites of the same and different loci. We explain convergences as the consequence of four factors: (1) environmental homogeneity that supposes an identical challenge for each population, (2) structural constraints within the genome, (3) epistatic interactions among sites that create the observed pattern of covariation, and (4) the phenomenon of clonal interference among competing genotypes carrying different beneficial mutations. Using these convergences, we have been able to estimate the fitness contribution of the identified mutations and epistatic groups. Keeping in mind statistical uncertainties, these estimates suggest that along with several beneficial mutations of major effect, many other mutations got fixed as part of a group of epistatic mutations.     

Identifying quantitative trait locus by genetic background interactions in association studies

Association studies are designed to identify main effects of alleles across a potentially wide range of genetic backgrounds. To control for spurious associations, effects of the genetic background itself are often incorporated into the linear model, either in the form of subpopulation effects in the case of structure or in the form of genetic relationship matrices in the case of complex pedigrees. In this context epistatic interactions between loci can be captured as an interaction effect between the associated locus and the genetic background. In this study I developed genetic and statistical models to tie the locus by genetic background interaction idea back to more standard concepts of epistasis when genetic background is modeled using an additive relationship matrix. I also simulated epistatic interactions in four-generation randomly mating pedigrees and evaluated the ability of the statistical models to identify when a biallelic associated locus was epistatic to other loci. Under additive-by-additive epistasis, when interaction effects of the associated locus were quite large (explaining 20% of the phenotypic variance), epistasis was detected in 79% of pedigrees containing 320 individuals. The epistatic model also predicted the genotypic value of progeny better than a standard additive model in 78% of simulations. When interaction effects were smaller (although still fairly large, explaining 5% of the phenotypic variance), epistasis was detected in only 9% of pedigrees containing 320 individuals and the epistatic and additive models were equally effective at predicting the genotypic values of progeny. Epistasis was detected with the same power whether the overall epistatic effect was the result of a single pairwise interaction or the sum of nine pairwise interactions, each generating one ninth of the epistatic variance. The power to detect epistasis was highest (94%) at low QTL minor allele frequency, fell to a minimum (60%) at minor allele frequency of about 0.2, and then plateaued at about 80% as alleles reached intermediate frequencies. The power to detect epistasis declined when the linkage disequilibrium between the DNA marker and the functional polymorphism was not complete.