Epistasis and Quantitative Traits: Using Model Organisms to Study Gene–Gene Interactions

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Epistasis and quantitative traits: using model organisms to study gene–gene interactions

Trudy F. C. Mackay Abstract | The role of epistasis in the genetic architecture of quantitative traits is controversial, despite the biological plausibility that nonlinear molecular interactions underpin the genotype–phenotype map. This controversy arises because most genetic variation for quantitative traits is additive. However, additive variance is consistent with pervasive epistasis. In this Review, I discuss experimental designs to detect the contribution of epistasis to quantitative trait phenotypes in model organisms. These studies indicate that epistasis is common, and that additivity can be an emergent property of underlying genetic interaction networks. Epistasis causes hidden quantitative genetic variation in natural populations and could be responsible for the small additive effects, missing heritability and the lack of replication that are typically observed for human complex traits.

Main effect A major challenge of contemporary biology is to both to detect significant interactions and to sample the The effect of a variable understand how naturally occurring variation in DNA landscape of possible genetic interactions. The statistical averaged over all other sequences causes phenotypic variation in quantitative challenge is the severe penalty that is incurred for testing variables; also known as traits. Efforts to chart the genotype–phenotype map for multiple hypotheses. The computational challenge is the marginal effect. quantitative traits using both linkage and association large number of tests that must be evaluated. Genetically Heterosis study designs have mainly focused on estimating addi tractable model organisms afford the opportunity to use The phenomenon whereby the tive effects of single loci (that is, the main effect of the experimental designs that incorporate both new muta mean value of a quantitative polymorphic locus averaged over all other genotypes). tions and segregating variants to detect epistasis, and trait in the F progeny of two 1 However, quantitative variation in phenotypes must many recent studies in model organisms have highlighted inbred lines exceeds, in the direction of increased fitness, result, in part, from multifactorial genetic perturbation the importance of epistasis in the genetic architecture of either the mean value of of highly dynamic, interconnected and nonlinear devel quantitative traits. In this Review, I describe the quanti the parental lines (that is, opmental, neural, transcriptional, metabolic and bio tative genetics of epistasis and the reasons that the role mid-parent heterosis) or the chemical networks1. Thus, epistasis (that is, nonlinear of epistasis has been controversial. I then review experi mean value of the best parent interactions between segregating loci) is a biologically mental methods to detect epistasis in yeast, Drosophila (that is, high parent heterosis); also known as hybrid vigour. plausible feature of the genetic architecture of quantita melanogaster, mice, Arabidopsis thaliana and maize, and tive traits. Deriving genetic interaction networks from summarize empirical results showing that epistasis is epistatic interactions between loci will improve our pervasive. I discuss the implications of pervasive epista understanding of biological systems that give rise to sis in model organisms for evolutionary models of the variation in quantitative traits2, as well as of mechanisms maintenance of quantitative genetic variation and specia that underlie genetic homeostasis3,4 and speciation5,6. tion, and for both animal and plant breeding. Given that Department of Biological Sciences, Campus Box 7614, Knowledge of interacting loci will improve predictions epistasis is pervasive in model organisms, it is also likely North Carolina State of individual disease risk in humans, response to natural to be a hallmark of the genetic architecture of human University, Raleigh, North selection in the wild, and artificial selection and inbreed complex traits. I discuss how underlying epistasis can Carolina 27695–7614, USA. ing depression (and its converse, heterosis) in agricultural give rise to the small additive effects, missing heritability e‑mail: animal and crop species. and the lack of replication that are typically observed in [email protected] doi:10.1038/nrg3627 Mapping epistatic interactions is challenging exp human genome-wide association studies. I do not dis Published online erimentally, statistically and computationally. The experi cuss statistical and computational methods for assessing 3 December 2013 mental challenge is the large sample sizes that are required epistasis, as these have been reviewed previously7,8.

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a b X2X2 X1X2 X1X1 X1X1 X1X2 X2X2

Y1Y1 aX + aY + aaXY dX + aY + daXY –aX + aY – aaXY –aX 0 dX aX Y1Y2 aX + dY + adXY dX + dY + ddXY –aX + dY – adXY

Y2Y2 Y1Y2 Y1Y1 Y2Y2 aX – aY – aaXY dX – aY – daXY –aX – aY + aaXY

–aY dY 0 aY

c Y1Y1 Y1Y2 Y2Y2 Phenotype Phenotype Phenotype

X2X2 X1X2 X1X1 X2X2 X1X2 X1X1 X2X2 X1X2 X1X1

Nature Reviews | Genetics Figure 1 | Two-locus genotypic effects. Genotypic values for loci X and Y, each with two alleles (X1, X2, Y1 and Y2), are shown (part a). The additive effect (a) of each locus is one half the difference in mean phenotype between the two homozygous genotypes. The dominance effect (d) is the difference between the mean phenotype of the heterozygous genotype and the average phenotype of the two homozygous genotypes10. d = 0 indicates additive gene action; d ≠ 0 denotes departures from additivity due to dominance. Genotypic values for two-locus genotypes are shown (part b). The first two terms for each genotype denote the additive combination of single-locus additive and dominance effects.

With epistasis, additional terms that reflect additive-by-additive (aaXY), additive-by-dominance (adXY and daXY) and

dominance-by-dominance (ddXY) epistasis contribute to the genotypic value. Graphical representations of genotypic effects at two biallelic loci are shown (part c). The left panel shows additive gene action at locus X, partial dominance at locus Y and no epistasis between X and Y. The middle panel shows epistasis in which the additive effect of locus Y is

much greater in the X1X1 genetic background than that in the X2X2 genetic background. The right panel shows epistasis

in which the additive effects of locus X are opposite in the Y1Y1 and Y2Y2 genetic backgrounds.

Missing heritability The phenomenon whereby the fraction of total phenotypic Quantitative genetics of epistasis on whether one focuses on epistatic interactions at the variance that is explained by In classical Mendelian genetics, epistasis refers to the level of individual genotypes or at the level of epistatic all individually significant loci masking of genotypic effects at one locus by genotypes genetic variance in populations2,9. Epistatic interactions in human genome-wide of another, as reflected by a departure from expected at the level of individual genotypic values (known as association analyses for di‑hybrid cross2 15 common diseases and Mendelian segregation ratios in a . In genetical, biological or physiological epistasis ) are inde quantitative traits is typically quantitative genetics, epistasis refers to any statistical pendent of allele frequencies at the interacting loci. In much less than the heritability interaction between genotypes at two or more loci9–11. populations, the total genetic variance is partitioned into that is estimated from Epistasis can refer to a modification of the additive orthogonal components that are attributable to additive, relationships among relatives. effects and/or dominance effects of the interacting loci dominance and epistatic variance, which depend on 10,11 Di‑hybrid cross (FIG. 1a,b); for two diploid loci, it can be easily visualized allele frequencies . A cross between parental lines by plotting the phenotypes of the nine different geno Epistasis (FIG. 2a) can have peculiar effects in popula that are fixed for alternative types (FIG. 1c). Epistatic interactions for quantitative traits tions because the effects of one locus (that is, the tar alleles at two unlinked loci (for fall into two categories: a change of the magnitude of get locus) vary depending on the allele frequency of an example, A A B B x A A B B , 1 1 2 2 2 2 1 1 (FIG. 2b) where A and B denote the loci effects, in which the phenotype of one locus is either interacting locus . If the allele frequency of the and the subscripts represent enhanced or suppressed by genotypes at the other locus; interacting locus varies among populations, the effect the alleles) in which nine or a change of the direction of effects. In the absence of of the target locus can be significant in one popula genotypes segregate in the epistasis the estimates of additive and dominance effects tion but not in another, or can even be of the opposite F generation. 2 at each locus are the same, regardless of the genotype of sign. Epistatically interacting loci generate substantial Dominance effects the other locus. With epistasis, the effect of one locus additive genetic variance over much of the allele fre Differences between depends on the genotype at its interacting locus. quency spectrum because of non-zero main (that is, the genotypic values of the The role of epistasis in the genetic architecture of additive) effects (FIG. 2c). Epistatic variance is maximal heterozygous genotypes and quantitative traits has been controversial since early when both interacting loci are at intermediate fre the average genotypic values 12,13 of the homozygous genotypes formulations of quantitative genetic theory , and this quencies and is of much smaller magnitude than the 7,14 at loci that affect quantitative controversy continues today . Different perspectives additive genetic variance unless the genotypic values traits. regarding the importance of epistasis arise, depending at one locus are in opposite directions in the different

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genetic backgrounds (FIG. 2d). Additive genetic vari Figure 2 | Quantitative genetics of additive-by- ▶ ance therefore accounts, in theory, for most of the total additive interactions. The four double homozygote genetic variance for a wide range of allele frequencies genotypes at two hypothetical bi‑allelic loci (X and Y) are depicted. Model 1 is an epistatic model in which the in the presence of epistasis10,11,14 (FIG. 2e). effect of locus X is greater in the Y Y genetic background Most observed genetic variance for quantitative 1 1 than that in the Y2Y2 genetic background; Model 2 is an traits is additive. Such genetic variance could be either epistatic model in which the effect of locus X is of ‘real’, if most loci that affect the trait have additive gene similar magnitude but in the opposite direction in the action, or ‘apparent’ from non-zero main effects that Y1Y1 genetic background, compared with that in the Y2Y2 arise from epistatic gene action at many loci. This dis genetic background (part a). The additive effect of locus X tinction is not important if the goal is to estimate herit depends on the frequency at locus Y (part b). Additive

ability, to predict phenotype from genetic relationships genetic variance (VA; part c), additive-by-additive genetic 16,17 variance (V ; part ) and the ratio of additive among individuals or to predict short-term response AA d to artificial and natural selection because all of these genetic variance to the total genetic variance (V /(V + V ); part e) for Models 1 and 2 are shown. depend on additive variance that is specific to the A A AA population of interest10,11. However, knowing whether additive variance is an emergent property of underlying epistasis becomes crucial if the goals are to function Epistasis between small numbers of mutations. Studies ally dissect the genotype–phenotype map, to determine using limited numbers of random mutations, or muta genetic interaction networks, to understand the effects tions that affect the same trait, show that epistasis is of mutational perturbations on standing variation, to pre common. In Escherichia coli, 14 of 27 (52%) pairs of dict long-term responses to artificial and natural selec random mutations that were tested showed epistasis tion, and to understand the consequences of genetic for fitness18. In D. melanogaster, 35 of 128 (27%) tests drift and inbreeding on quantitative traits. for epistasis among pairs of random mutations had sig To distinguish between real and apparent additive nificant effects on quantitative traits that are involved in genetic variance, we need to obtain evidence for the intermediary metabolism. These epistatic effects were existence of epistasis, as well as to estimate genotypic large and occurred between mutations without signifi values at causal, potentially epistatic, pairs of loci (or cant main effects19. Diallel cross designs among small indeed at loci that are involved in higher order inter numbers of P‑element mutations that affected olfac actions). Genetically tractable model organisms allow tory, locomotor, aggressive behaviour and lifespan in analyses of epistatic interactions using: mutations that D. melanogaster revealed extensive epistasis and defined are generated in a common homozygous genetic back new genetic interaction networks20–23. These interaction ground; quantitative genetic analyses of both inbred networks were influenced by environmental condi lines and outbred populations; chromosome substitu tions, sex and the presence or absence of an additional Standing variation tion, introgression and near-isogenic lines; and induced interacting mutation21,22. Allelic variation that is mutations as foci for exploring such interactions with currently segregating within a population, as opposed to segregating variants. The ability to construct mapping Genome-wide interaction screens. A few model systems alleles that appear as the result populations from crosses of inbred lines in which all are amenable to experimental analyses of genome-wide of new mutation events. allele frequencies are 0.5 is particularly powerful, as this genetic interaction networks. An analysis of deletions maximizes both epistatic variance and frequency of the for all 6,000 genes in Saccharomyces cerevisiae revealed Introgression rarer two-locus genotypes. that only 20% of the genome is essential for survival, at The substitution of a genomic 24 region from one strain with least under optimal growth conditions . This observa that of another, typically by Epistasis between mutations tion attests to the robustness of biological networks to repeated backcrosses. Mutations that have been induced in the same homozy mutational perturbation and sets the stage for synthetic gous genetic background are excellent resources for enhancement genetics in this species25. The collection Diallel cross A class of experimental designs estimating the magnitude and the nature of digenic of deletion mutants, together with high-throughput that are used to estimate both epistatic interactions. Epistasis occurs if the difference methods for generating and selecting double mutants, additive and non-additive in phenotype of the double mutant cannot be predicted measuring growth rate and quantifying fitness25, has variance components for a from the combined effects of the single mutants. The facilitated large-scale genetic interaction screens quantitative trait from all double-mutant phenotype can be either more mutant in yeast26–30. Carrying out tests for all ~18 million possible crosses among a population of inbred lines. than expected (which is known as synergistic, enhanc possible pairwise interactions remains a practical Full diallel designs include ing, aggravating or negative epistasis) or less mutant impossibility even in this genetically tractable model reciprocal crosses, whereas than expected (which is known as antagonistic, sup system. Therefore, the yeast global genetic network half-diallel designs do not; pressing, alleviating or positive epistasis). The advan architecture was investigated using a set of query muta parental lines can be included or excluded in either case. tage of this method is that the interacting partners are tions that were chosen to represent biological pathways known, which facilitates the construction of genetic of interest. Interactions were examined either between Synthetic enhancement interaction networks. A disadvantage is that it does not each of the query mutations and a larger number of A type of epistatic interaction easily scale beyond pairwise interactions and to large target mutations26,29,30 or for all possible pairwise com whereby the phenotype of a numbers of mutations, as a comprehensive evaluation binations of the query mutations27,28. Similar strategies double mutant is more severe 2 than that predicted from the of n pairwise interactions requires the generation of ~n have been adopted for systematic mapping of genetic 31,32 additive effects of the single genotypes which, in practice, prevents exploration of the interactions in Caenorhabditis elegans and in D. mel‑ mutants. entire interaction space. anogaster cell lines33 using RNA interference (RNAi).

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Model 1 Model 2 Larger-scale studies26,27,29–31,33 that use qualitative assays a 20 20 typically find that ~1–3% of interactions have signifi cant effects, whereas smaller-scale studies28,32 that use 18 18 quantitative assays identify a larger number of interac 16 16 tions (~13–35%). These studies have been instrumental Y1Y1 in determining the general properties of genetic inter 14 14 Y2Y2 (BOX 1) Phenotype Phenotype action networks . The scale-free and small-world 12 12 properties of these networks imply that the major fea

10 10 tures of network topology can be inferred by focusing X1X1 X2X2 X1X1 X2X2 on major hub genes and on interactions among the Locus X genotype Locus X genotype genes with which they interact.

Gene expression-based screens. Mutations typically b 5 5 have pleiotropic effects on many phenotypes; there 4 3 fore, focusing on only one phenotype will not uncover the full spectrum of possible interactions. Genome- 3 1 wide analyses of differences in gene expression in the 2 –1 presence of single and double mutations relative to the control can be used to place genes in an interaction

Eﬀect of locus X 1 Eﬀect of locus X –3 network in the absence of organismal-level pheno 0 –5 types23,34–36. This approach is particularly powerful for 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 higher eukaryotes that have long generation intervals Frequency of Y Frequency of Y 1 1 and that lack high-throughput methods for generating double mutants and for accurately measuring com c 1.0 1.0 plex organismal quantitative traits, but for which large 0.9 0.9 37–41 25 collections of mutations are available . In D. mela‑ 0.8 0.8 1 1 nogaster, single mutations have pleiotropic effects on 0.7 0.7 20 22,23,42 0.6 0.6 hundreds of gene expression traits . The genes 15 0.5 0.5 for which expression is altered in the mutant genetic VA 0.4 0.4 10 background are thus candidate genes for inclusion in a 0.3 0.3 genetic interaction network that affects the organismal Frequency of X Frequency Frequency of X Frequency 5 0.2 0.2 phenotype associated with the focal mutation. A large 0.1 0.1 0 proportion of such candidate genes indeed show epista 0.0 0.0 sis with the focal mutation42. Thus, combining muta 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Frequency of Y Frequency of Y tional perturbations with gene expression is a powerful 1 1 approach to iteratively reverse-engineer networks. The large numbers of candidate genes that are implicated by d 1.0 1.0 gene expression profiling indicates that the interaction 0.9 0.9 15 0.8 0.8 space is large. 1 1 0.7 0.7 0.6 0.6 10 Epistasis between QTLs 0.5 0.5 To what extent does the extensive epistasis that is VAA 0.4 0.4 5 implicated by analyses of induced mutations translate 0.3 0.3 Frequency of X Frequency Frequency of X Frequency to epistatic interactions in natural populations? The 0.2 0.2 ability to construct inbred lines, artificial selection 0.1 0.1 0 0.0 0.0 lines and chromosome substitution lines, as well as to

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 map quantitative trait loci (QTLs) that affect complex

Frequency of Y1 Frequency of Y1 traits by linkage and association, facilitates analyses of epistasis between naturally occurring variants in model e 1.0 1.0 organisms. 0.9 0.9 1.0 0.8 0.8 Comparing broad- and narrow-sense heritability. Nar 1 1 0.7 0.7 0.8 row-sense heritability (h2) refers to the fraction of the 0.6 0.6 0.6 phenotypic variance of a quantitative trait that is due to VA 0.5 0.5 additive genetic variance, whereas broad-sense herit 0.4 0.4 0.4 VA+VAA ability (H2) refers to the fraction of the phenotypic vari 0.3 0.3

Frequency of X Frequency of X Frequency 0.2 0.2 0.2 ance that is due to all components of genetic variance. 0.1 0.1 0 In model organisms that can be crossed and inbred, one 0.0 0.0 can obtain unbiased estimates of h2 either from half- 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 sib family designs or from the response to directional 2 Frequency of Y1 Frequency of Y1 artificial selection. The genetic component of H that

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Box 1 | Properties of genetic interaction networks captures more genetic diversity and has increased mapping precision; however, it is prone to artefactual Genetic interaction networks in Saccharomyces cerevisiae25–30, Caenorhabditis LD that is induced by population structure and has 31,32 33 elegans and Drosophila melanogaster share common properties that are likely to be reduced power to detect QTLs that have minor allele generalizable to genetic interaction networks in other species. frequencies <0.5 (REF. 21). • The fitness of the double mutant tends to be lower than expected if the genes act in Epistasis between QTLs is estimated by fitting a separate but compensatory pathways, and higher than expected if the genes act in the same pathway. statistical model that includes both the main effects of each QTL and the effects of the QTL–QTL interaction • The distribution of the number of interactions per gene (that is, connectivity) follows a term (FIG. 4). The use of multifactorial perturbations power law distribution, such that many genes have no or few interactions, and a few genes have many interactions. Genes that have many interacting partners are hubs in in epistasis screens has the advantage that many inter the interaction network. actions can be tested using genotypes and phenotypes • Genetic interaction networks are small-world networks, such that the shortest path that are determined for a reasonably small number of between a pair of genes is small, which results in dense local neighbourhoods of individuals. As a result, it is more efficient for explor genes that interact with each other. ing interaction space than laboriously constructing all • Genetic interactions occur among functionally related genes that belong to the same possible pairwise combinations of mutant alleles. The pathway or biological process. The ‘guilt-by-association’ principle can thus be used to power to detect epistasis between QTLs in mapping infer the function of a computationally predicted gene from the function of the genes populations that are derived from inbred lines is maxi with which it genetically interacts. mal because all polymorphic alleles have frequencies of • Network hub genes have the following characteristics compared with genes that have 0.5. However, in small mapping populations the num fewer interactions: they are more important for fitness; they are more pleiotropic; ber of lines that carry the rarer double-homozygous their mRNAs are expressed at higher levels; they are more sensitive to environmental genotype classes is small, which increases the variance perturbations; and they are more evolutionarily conserved. in the mean value of the trait within each class. In addi • Genetic interaction networks are mostly decoupled from protein–protein interaction tion, other segregating QTLs can confound the estimate networks. of epistasis for the tested pair of loci. These factors, • Although properties of genetic network architecture are conserved across species, together with the severe multiple testing penalty for pair the network connectivities are not conserved. wise epistasis screens, make it difficult to detect all but extremely strong interactions, particularly in associa tion mapping populations in which allele frequencies is estimated from fully inbred lines is due to additive are not balanced. Given these inherent biases against variance and additive-by‑additive epistatic variance10 detecting epistasis, most studies only evaluate additive (BOX 2). Thus, epistatic variance can be inferred to con QTL effects. However, epistasis is often found when it tribute to the genetic architecture of traits for which H2 is evaluated in linkage-mapping populations. Epistatic is much greater than is expected from strictly additive effects can be as large as main effects and can occur variance (BOX 2). However, further gene mapping studies between QTLs that are not individually significant. are necessary to identify the individual loci that affect Traits for which epistatic interactions have been the traits. detected in QTL-mapping experiments include sporu lation efficiency43,44 and gene expression traits45 in yeast; QTL–QTL interactions. QTLs are mapped either by thermal preference in C. elegans46; bristle number, linkage to, or by association with, molecular markers. wing shape, longevity, enzyme activity, metabolic rate In model organisms, linkage mapping is typically car and flight velocity in D. melanogaster20,21; body weight and ried out using line cross analyses. Linkage-mapping adiposity traits47–50, litter size51 and serum insulin-like populations are established by crossing two lines that growth factor 1 (REF. 52) in mice; growth rate53,54 in chick differ genetically for the trait of interest and by generat ens; growth rate55 and metabolites56,57 in A. thaliana; and

ing backcrosses, F2 or advanced intercross individuals, differences in whole-plant and inflorescence architecture or recombinant inbred lines (RILs)10,11 (FIG. 3a). Asso between maize and teosinte58. Although these studies ciation mapping uses samples of individuals or inbred show that epistasis cannot be ignored when describing lines from a natural population. In both cases molecu the genetic architecture of complex traits, QTL map lar marker genotypes and quantitative trait phenotypes ping alone does not identify the causal interacting genes are obtained for members of the mapping population. because the QTL intervals contain many loci. Standard statistical methods are used to determine Model organisms allow further dissection of QTLs. whether there is a significant difference in phenotype First, one can construct near-isogenic lines, in which a between marker genotypes, in which case the QTL that region that contains the QTL is introgressed into the affects the trait is either linked to, or in linkage dis isogenic background of one of the parental lines, and Multiple testing penalty 21 The downward adjustment of equilibrium (LD) with, the marker locus . These tests successive generations of recombination are used to nar the significance threshold for are carried out for each marker in turn, and genomic row the QTL down to a small genomic interval (FIG. 3d). individual statistical tests that regions for which the p‑value of the test passes an This approach was used to confirm the epistatic effects of is required when multiple appropriate threshold that accounts for multiple tests two QTLs that do not have individual main effects for hypothesis tests are carried correspond to the position of the QTL. Association C. elegans thermal preference, but for which the inter out on a single data set; for n independent tests, the Bonfer- mapping can be carried out either for candidate genes action accounted for 50% of the total variance in this 46 roni-adjusted 5% significance or genome wide. Compared with linkage mapping that behaviour . Similarly, genetic dissection of A. thaliana threshold is 0.05/n. uses a population of the same size, association mapping near-isogenic lines for a region that has no overall effect

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on growth rate revealed two epistatically interacting that have larger effects than classical mapping popula QTLs that affect growth rate, for one of which the effect tions for a wide variety of blood chemistry, bone and on growth rate was in opposite directions in the differ behavioural traits. In addition, the sum of the effects of ent genetic backgrounds55. Second, one can carry out individual QTLs is several orders of magnitude greater transformation and allelic replacement to prove that than the difference in phenotype between the paren variants are causal, as well as to engineer all possible tal strains60–62. Similar results are found for aggressive combinations of causal variants to investigate epistasis behaviour in D. melanogaster63. These results indicate at nucleotide resolution. These approaches were used that the combined effects of individual introgressed in D. melanogaster to show that each of three domains in regions in the genome of the donor line are less than the Alcohol dehydrogenase (Adh) gene, as well as an additive. Less-than-additive effects of introgressed intragenic epistatic interaction, contributed to the QTLs have also been demonstrated for several fruit difference in Adh protein levels between the Fast and quality traits in tomato64,65. Slow electrophoretic alleles59. Similarly, in S. cerevisiae, For different allele frequencies of interacting loci, epi strong epistasis for causal variants that affect sporulation static interactions lead to different main effects of each efficiency43,44 was revealed. of the interacting loci (FIG. 2b). Thus, they also lead to a A powerful QTL mapping design is to introgress lack of replication of estimated QTL effects in popula genomic regions from one strain into the genetic back tions in which allele frequencies of causal interacting loci ground of another. This can be done either at the level differ66. In model organisms one can construct mapping of entire chromosomes to create a panel of chromo populations that have different QTL allele frequencies to some substitution strains60 (FIG. 3b) or for introgressions determine how often allelic effects vary; in this case, the that tile across the genome of the donor line (FIG. 3c), lack of replication of QTL effects can identify potentially as for genome-tagged mice61. A fairly small number of interacting loci. The D. melanogaster Genetic Reference introgression lines can be used to map QTLs with high Panel (DGRP) is a collection of ~200 sequenced inbred precision. Epistasis occurs if the sum of the effects of lines that are derived from a single population, which the introgressed fragments is significantly greater than, allows genome-wide association mapping for quantita or significantly less than, the mean difference in phe tive traits using all polymorphic molecular variants67. notype between the two parental strains. In rodents, Flyland is a large outbred advanced intercross popula introgression designs detect more QTLs, as well as QTLs tion that is derived from 40 DGRP lines68. In this popu lation, QTLs can be rapidly mapped by phenotyping large numbers of individual flies and by sequencing pools of individual flies from the phenotypic extremes Box 2 | Evidence for epistasis from narrow- and broad-sense heritability of the distribution; QTLs have significant differences in The response to a single generation of artificial selection for a quantitative trait is allele frequencies between the two pools of sequenced given by the breeder’s equation: R = h2S. R is the difference between the mean of the flies68,69. None of the QTLs that were detected in the parental generation and the mean of the offspring generation. h2 is the narrow-sense DGRP for each of three quantitative traits were repli 2 heritability: h = (VA + ½VAA)/VP, where VA is the additive genetic variance, and VAA is the cated in extreme QTL mapping in the Flyland popula additive-by-additive genetic variance, ignoring higher order epistatic interactions for tion. However, 50–60% of the QTLs that were detected simplicity. V is the phenotypic variance: V = V + V + V , where V is the P P A AA E E for the three traits in either population were involved environmental variance. The selection differential (S) is the difference between the in at least one epistatic interaction, and these interac mean of the parental population and the mean of the selected group10. The narrow-sense heritability is thus h2 = R/S. If selection is carried out over several tions perturbed common, biologically plausible and 68 generations, the narrow-sense heritability can be estimated from the regression of the highly connected genetic networks . Although these cumulated response (ΣR) on the cumulated selection differential (ΣS); that is, h2 = ΣR/ΣS. analyses indicate pervasive epistasis, the challenge By contrast, broad-sense heritabilities that are determined from variation among remains to determine which of the statistically predicted completely homozygous inbred lines, ignoring higher order additive-by-additive interactions are biologically important. 2 epistatic interactions, are H = (2VA + 4VAA)/VP, where VP = 2VA + 4VAA + VE (REF. 100). Note that in this scenario there is no dominance variance and no epistatic interaction Epistasis between mutations and QTLs variance terms that involve dominance, as there are no heterozygotes. If all variation Analyses of epistasis between induced mutations do not is additive (that is, V = 0), then H2 among inbred lines is related to h2 from artificial AA scale well to large numbers of mutations but have the selection from the outbred populations from which the inbred lines were derived: advantage that the interacting partners are specified. H2 = 2h2/(1 + h2)101. h2and H2 values for Drosophila melanogaster behavioural traits are given in the table102–106. In all cases H2 values are greater than those expected from Analyses of epistasis between QTLs have the advantage strictly additive variance, which implies that epistatic variance contributes to the that interactions among large numbers of polymor genetic architecture of these traits. phisms and genes can be evaluated; however, owing to the severe multiple testing penalty, there will be large Trait Observed Expected numbers of false-positive associations among the top interactions for which there is the highest level of statis h2 H2 H2 = 2h2/(1+h2) tical support. An alternative strategy is to carry out one- Copulation latency 0.07 0.25 0.13 dimensional screens that evaluate the phenotypic effects Startle response 0.16 0.58 0.28 of a known mutation in different genetic backgrounds. Aggressive behaviour 0.09 0.78 0.17 Although these designs have not yet been implemented on a large scale, many studies indicate that this will be Ethanol knock-down time 0.08 0.24 0.15 a powerful approach.

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3 a P1 P2 Waddington noted the contrast between the large effects of mutations and their phenotypic variability, as well as the apparent stability of wild-type strains, despite exposure to naturally occurring genetic and environ mental perturbations. He coined the term ‘canalization’ to refer to the buffering of natural variation against such perturbations. In modern parlance, genetic canalization refers to suppressing (that is, less-than-additive) epistatic F1: P1 × P2 interactions between naturally segregating variants. To the extent that these interactions occur between differ ent genetic loci, one can probe both the nature and the magnitude of the naturally occurring epistatic modifier loci by asking to what extent they modify the effects of a mutant allele. One of the first experiments to show the occurrence BC : F × P F : F × F BC : F × P 1 1 1 2 1 1 2 1 2 of naturally segregating epistatic modifiers of a muta tion was Rendel’s introgression of a scute (sc) mutation into a wild-derived background70. D. melanogaster has four large scutellar bristles on the dorsal thorax, and this number is invariant in nature. Mutations at sc reduce this number to an average of one or less. In a wild-type genetic background that is segregating for sc and sc+ RILs alleles, the number of scutellar bristles changed to ~3 in sc mutants and to 5–6 in sc+ individuals following artificial selection for increased bristle number. These results are consistent with the selection of epistatic modifiers of sc that were segregating in the initial pop ulation and that suppressed the mutant sc phenotype. However, the genetic backgrounds for this experiment were not well defined. More recently, introgressions of b C1 C2 C3 mutant Ultrabithorax, Antennapedia, sevenless and scal‑ loped alleles into different wild-derived D. melanogaster backgrounds have demonstrated variation outside the invariant wild-type phenotype for, respectively, haltere size, shape and bristle number71,72; the antenna-to-leg c C1 C2 C3 transformation homeotic phenotype72; eye roughness and size73; and wing morphology74. The epistatic effects ranged from complete suppression to enhancement of the mutant phenotype. A variant of the mutant introgression design is to cross the mutant allele to a sample of wild-derived lines

and to evaluate phenotypes of F1 genotypes. The advan tage of this method is that it is easier to implement than constructing introgression lines; the disadvantage is that any phenotypic variation cannot be attributed to allelic complementation (that is, dominance effects) or to non- allelic complementation (that is, epistasis) unless the d C1 C2 C3 experiment is carried out in a QTL-mapping popula tion. In D. melanogaster, crosses of a dominant Epidermal growth factor receptor mutation to wild-derived lines give a range of eye roughness phenotypes73,75. Approximately

1–2% of F1 progeny from crosses of D. melanogaster strains that carry mutant alleles of the heat shock protein gene Hsp90 (also known as Hsp83) to outbred strains had Figure 3 | Genotypes for mapping QTLs between two genetically divergent Nature Reviews | Genetics a wide variety of morphological abnormalities, which lines. Parental lines (P1 and P2) are crossed to produce an F1 generation (part a). Common segregating generations that are used for quantitative trait locus (QTL) mapping are suggests that Hsp90 normally suppresses alleles that affect 76 backcrosses of the F to either parental line (BC and BC ); the F generation, which multiple phenotypes . These results indicate that popula 1 1 2 2 tions harbour a hidden reservoir of genetic variation for is derived from mating F1 individuals; and recombinant inbred lines (RILs), which are invariant traits that is only revealed in the ‘decanalizing’ derived by inbreeding F2 families. Experimental designs that are based on introgression use chromosome substitution lines (part b), introgression lines (part c) or near-isogenic background of the mutation. Such variation has been lines (part d); three chromosomes (C1–C3) are depicted for each type of lines. called potential variance or cryptic genetic variation77.

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© 2014 Macmillan Publishers Limited. All rights reserved REVIEWS 3E 5D 7D 9A 11C 12E 15A 17C 21E 27B 30AB 33E 35B 38E 43E 46C 49D 50D 57C 60E 63A 65D 68B 69D 71E 73D 76B 77E 82D 85F 87E 88E 91A 92A 93B 96A 97D 98A 99B 100A 16D 19A 22F 29F 30D 34EF 38A 43A 46A 48D 50B 50F 57F 61A 65A 67D 68C 70C 72A 76A 77A 78D 85A 87B 87F 89B 91D 93A 94D 96F 97E 99A 99E 1B 4F 6E 7E 10D 11D 14C 1B 3E 4F 5D 6E 7D 7E 9A 10D 11C 11D 12E 14C 15A 16D 17C 19A 21E 22F 27B 29F 30AB 30D 33E 34EF 35B 38A 38E 43A 43E 46A 46C 48D 49D 50B 50D 50F 57C 57F 60E 61A 63A 65A 65D 67D 68B 68C 69D 70C 71E 72A 73D 76A 76B 77A 77E 78D 82D 85A 85F 87B 87E 87F 88E 89B 91A 91D 92A 93A 93B 94D 96A 96F 97D 97E 98A 99A 99B 99E 100A

p < 0.0001 0.0001 ≤ p < 0.001 0.001 ≤ p < 0.01 0.01 ≤ p < 0.05 p ≥ 0.05

Figure 4 | Two-dimensional search for epistatic interactions. Data from an experiment mappingNature QTLsReviews that | Geneticsaffect Drosophila melanogaster lifespan in a recombinant inbred line population are depicted107. The x and y axes show the marker loci. Two main-effect QTLs are indicated at cytological positions 46C–49D and at 50D (shown in red boxes). The body of the graph depicts the p‑values of the QTL–QTL interaction terms. Main-effect QTLs do not interact with each other, but they do interact with QTLs that do not have significant main effects. QTLs without significant main effects show significant interaction effects.

Experimental designs for assessing epistasis between demonstrate epistasis for the extended-lifespan pheno mutations and QTLs can be adapted to determine the type that is caused by the overexpression of a human effects of naturally segregating epistatic modifiers of superoxide dismutase transgene in motorneurons78. mutations that affect traits which show quantitative phe Similarly, epistasis was found between several mutations notypic variation in natural populations. In this case, the that affect startle response79 (FIG. 5), olfactory behaviour effects of both the mutant and the wild-type alleles of the and sleep traits80 in different DGRP line backgrounds. locus in question need to be assessed for the quantita Moreover, there is epistasis between a null myostatin tive trait phenotype in different genetic backgrounds in allele and genetic background for growth traits in mice81;

either an introgression or an F1 design. Epistasis occurs between the disease resistance mutation Rp1‑D21 and if the additive effect of the mutation varies with genetic genetic background for the hypersensitive response in background, which is detected as a significant interac maize82; and for an RNAi knockdown HSP90 allele and tion between the mutant and background genotypes. genetic background for both morphological and life These designs have been used in D. melanogaster to history traits in A. thaliana83.

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Only a few studies so far have analysed QTL-mapping interconnected genetic networks that are enriched for bio populations to map, either by linkage or by association, logically plausible gene ontology categories, and metabolic loci that interact with focal mutations72,74,75,81–83. Some stud and cellular pathways. Analyses of epistasis reveal that ies have used candidate gene association analyses to test much quantitative genetic variation is hidden and is not whether the mutant allele interacts with naturally occur apparent from analyses of main effects of causal variants, ring alleles at the mutant locus75 or with naturally occurring and that additivity is an emergent property of underlying variants at a known interacting locus74. Others carried epistatic networks. Furthermore, several types of obser out unbiased genome scans in a QTL-mapping popula vations suggest that natural populations have evolved tion72,81–83, which typically uncovered unlinked interacting suppressing epistatic interactions as homeostatic (that is, loci that do not have significant main effects. canalizing) mechanisms. These observations include less- than-additive interactions between QTLs; cryptic genetic Implications of pervasive epistasis variation for invariant phenotypes in natural populations The studies reviewed here indicate that epistasis is a com that can only be observed in the presence of a decana mon feature of the genetic architecture of quantitative lizing mutation; and naturally segregating variation that traits in model organisms. By extension, the same is likely generally suppresses the effects of induced mutations for to be true for quantitative traits in other organisms in quantitative traits. which gene–gene interactions are more difficult to detect, This realization is paradigm shifting. Rather than including humans. The epistatic interactions that have perceiving phenotypic variation for quantitative traits in been detected define previously uncharacterized, highly natural populations as highly variable, it may be more

a C1 C2 C3 C1 C2 C3 Expected Observed DGRP_1 wt DGRP_1 M DGRP_1 wt + 2a DGRP_1 M DGRP_2 wt DGRP_2 M DGRP_2 wt + 2a DGRP_2 M DGRP_3 wt DGRP_3 M DGRP_3 wt + 2a DGRP_3 M DGRP_4 wt DGRP_4 M DGRP_4 wt + 2a DGRP_4 M DGRP_5 wt DGRP_5 M DGRP_5 wt + 2a DGRP_5 M • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • DGRP_i wt DGRP_i M DGRP_i wt + 2a DGRP_i M

Expected – observed = estimate of interaction eﬀect (I)

b neur Figure 5 | Epistasis between naturally occurring variation and mutations in D. melanogaster. A graphical Crc representation shows genotypes of i homozygous Drosophila melanogaster Genetic Reference Panel (DGRP) lines (DGRP_i), in which C1, C2 and C3 represent the three Csp major chromosomes (part a). Co‑isogenic C2 chromosomes that contain either a wild-type allele (wt) or a mutant allele HLH-m7 25 (M; red star) of a focal gene that affects a quantitative trait 20 have been introgressed into each DGRP line. The lola 15 quantitative trait is measured for all pairs of wild-type and

10 I mutant DGRP introgression lines. The difference in Mutation emc 5 phenotype between the wild-type and mutant alleles in the background on which the mutant was generated is 2a. 0 If there are only additive effects on the phenotype, then Sema-1a –5 the expectation is that the effect of the mutation will be the same on each DGRP line background, and the Sema-5c expected phenotype of the ith DGRP line with the mutant C2 allele is DGRP_i wt + 2a. If this is not the case, then the mir-317 difference between the expected and the observed phenotypes is due to epistasis. Estimates of epistatic interactions (I) for ten mutations that affect startle robo response in 20 DGRP backgrounds79 are shown (part b). The interaction effects vary among mutations and DGRP lines. These effects are large and predominantly positive; DGRP_391DGRP_517DGRP_437DGRP_357DGRP_365DGRP_208DGRP_714DGRP_301DGRP_358DGRP_852DGRP_399DGRP_380DGRP_375DGRP_362DGRP_730DGRP_360DGRP_307DGRP_303DGRP_786DGRP_335 that is, naturally occurring variation suppresses the effects DGRP line of the mutations.

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accurate to wonder why there is not more variation in Two major unresolved questions in evolutionary organismal phenotypes, given the large amount of seg biology concern the mechanisms that maintain quan regating molecular genetic polymorphism. Genome- titative variation in natural populations, and the causes wide association studies in both model organisms67 and of adaptation and speciation. The puzzle of maintaining humans84 typically find an inverse relationship between quantitative variation10,87,88 arises because heritabilities minor allele frequency and additive effect, such that the of quantitative traits are appreciable in natural popu rarer alleles are associated with larger effects than lations such that the magnitudes of genetic and envi the more common alleles. Statistically, rare alleles must ronmental variation are approximately equal. However, have larger effects than common alleles to be detected in most quantitative traits seem to be under strong stabiliz a mapping population of the same size; the puzzle is why ing selection89, which reduces genetic variation. Direct so few common alleles of large effect are found to segre estimates of mutational variance for quantitative traits in gate within natural populations. One possible explana many model organisms are ~0.001 of the environmental tion is that rare alleles have large effects because they are variance90. Most theoretical models that assess the pos relatively new mutations compared with common alleles, sibility that quantitative genetic variation is maintained and epistatic modifiers that ameliorate their effects have by a balance between elimination of variation by stabi not yet occurred in the population. Common alleles are lizing selection and re‑introduction by mutation cannot presumably older and could achieve an intermediate simultaneously account for the empirical estimates89,91. frequency owing to a modifier mutation at another locus Estimates of mutational variance are too low to gener that suppresses the effect of the polymorphism. ate the observed levels of genetic variance under strong However, QTLs that are detected by linkage map selection. Suppressing epistasis between QTLs could ping in populations derived from crosses of inbred lines cause overestimates of the strength of stabilizing selec typically have moderately large effects20,21. Possibly, these tion, and suppressing epistasis between mutations could loci were not common in the populations from which lead to underestimates of the magnitude of mutational the parental inbred lines were derived. Alternatively, the variation. This necessitates a revision of the inference lines that survived inbreeding could be enriched for that mutation–selection balance does not account for compatible epistatic interactions that were decanalized much segregating variation for traits under stabilizing 79 Minor allele frequency by crossing to a different genetic background. In this selection . Furthermore, both inbreeding and genetic The frequency of the less case, one would predict that adding further parental drift cause variation in allele frequencies from the paren common allele at a bi‑allelic lines to linkage-mapping populations might incorpo tal population. With epistasis, this can result in the ‘con locus. rate additional canalizing alleles, such that more QTLs version’ of epistatic variance to additive variance, which with smaller effects will be found in these populations potentially enables rapid adaptation to new environ Founder-effect speciation 92–94 13 models than in populations that are derived from crosses of two ments . Epistasis is central to Wright’s models of the A class of models for the inbred lines. This prediction seems to be borne out in an genetic basis of evolution and to founder-effect speciation evolution of reproductive outbred advanced intercross population that is derived models92. With epistasis, the genetic architecture of isolation that is based on from eight inbred mouse strains85, as well as in the maize response to natural selection will be different in different changes in selection pressures and on allele frequencies nested association-mapping population that consists of populations and will potentially increase the likelihood 5,6 of epistatically interacting 200 RILs from each of 25 crosses between diverse inbred of the evolution of Dobzhansky–Muller incompatibilities loci, which result from lines and a single common parental line86. and consequent speciation events. the establishment of a Pervasive epistasis has consequences for plant and Epistasis is one of several non-mutually exclusive new population in a new animal breeding, evolutionary biology and human explanations for the small effects, missing heritability environment from a small number of individuals. genetics. Applied breeding programmes rely on artifi and the lack of replication of top trait-associated variants cial selection within populations, as well as on trans in different populations in human genome-wide associa Dobzhansky–Muller fer of exotic genetic material to elite lines, to improve tion studies84. First, with suppressing epistasis, additive incompatibilities quantitative traits of agronomic importance. In the pres effects of common interacting loci will be small. Second, Substitutions that occur during 2 divergence of two lineages; ence of epistasis, the genetic architecture of response estimates of h in humans are obtained from twice the these substitutions are neutral to artificial selection from the same base population difference in the correlation of monozygotic and dizy in the respective genetic could differ among replicate lines, as well as within the gotic twins10, and these estimates are biased upward in backgrounds of the two same line over time, owing to allele frequency drift and the presence of dominance and epistasis. Thus, suppress lineages but cause a reduction to changes in frequency of causal alleles as a result of ing epistasis could potentially account for the high levels in fertility and/or viability in hybrids between the two selection. Loci that have beneficial effects in one genetic of heritability and the small amounts of additive genetic lineages. background will not have the same effects when they are variation that have been estimated from mapped loci in introgressed into another background, unless interact human populations. Third, estimates of additive effects Genomic prediction methods ing loci are identified and co‑introgressed. Many mod of causal alleles will differ between populations that have Models that are derived from a discovery sample which ern breeding programmes use additive models that are different allele frequencies but the same underlying epi 66,68 consists of individuals with based on both dense molecular markers and estimates of static genetic architecture . Additive genomic prediction measured phenotypes and trait phenotypes from a reference population to predict methods that use all variants explain a much higher pro genome-wide marker data; breeding values of selection candidates on the basis of portion of phenotypic variance in human genome-wide these models are used to only genotypic information16,17; in the presence of epista association studies than that obtained by summing the predict individual phenotypes in an independent sample from sis, genomic prediction may be poor if the frequency of variance explained from individual markers that exceed 95 the same population using only causal alleles varies between the reference and the test the genome-wide significance threshold , but the pre genome-wide marker data. populations. diction accuracy of these methods is low in independent

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populations96,97. Genomic prediction methods that allow much larger scale and by taking advantage of decreasing non-additive effects98.99 are likely to increase the accuracy costs of sequencing individual genomes, as well as pros of individual risk prediction, but understanding the biol pects for high-throughput and accurate measurements ogy of human quantitative traits and complex diseases of quantitative trait phenotypes21. Molecular variants, will require knowledge of the underlying loci. both singly and in combination, perturb transcriptional, metabolic and protein–protein interaction networks Conclusions and future prospects which, in turn, causally affect organismal phenotypes21. Mapping epistatic interactions is statistically and experi However, systems genetic models so far only consider mentally challenging. Much progress in understanding additive effects of variants on transcripts and traits21. In and predicting genetic interaction networks that affect the future, we must assess the effects of pairwise and quantitative traits has been made by taking advantage of higher order epistatic interactions between polymor the unique resources and experimental designs that are phic DNA variants on molecular interaction networks available for model organisms. Epistasis is common and and, in turn, evaluate their effects on organismal phe can cause cryptic genetic variation for quantitative traits notypes to understand the mechanistic basis of epistasis. in natural populations; however, the mapping of causal Only then will we be able to go beyond describing the interacting variants is in its infancy. Future advances phenomenon of epistasis to predicting and testing its will be made by using these experimental designs on a consequences for genetic systems.

1. Kauffman, S. A. The Origins of Order (Oxford Univ. 19. Clark, A. G. & Wang, L. Epistasis in measured 36. Carter, G. W. et al. Prediction of phenotype and gene Press,1993). genotypes: Drosophila P‑element insertions. Genetics expression for combinations of mutations. Mol. Syst. 2. Phillips, P. C. Epistasis — the essential role of gene 147, 157–163 (1997). Biol. 3, 96 (2007). interactions in the structure and evolution of genetic 20. Flint, J. & Mackay, T. F. C. Genetic architecture of 37. Bellen, H. J. et al. The Drosophila gene disruption systems. Nature Rev. Genet. 9, 855–867 (2008). quantitative traits in mice, flies, and humans. Genome project: progress using transposons with distinctive This is a comprehensive review that describes the Res. 19, 723–733 (2009). site specificities. Genetics 188, 731–743 (2011). importance of studying genetic interactions with 21. Mackay, T. F. C., Stone, E. A. & Ayroles, J. F. 38. Dietzl, G. et al. A genome-wide transgenic RNAi library respect to dissecting regulatory pathways, mapping The genetics of quantitative traits: challenges and for conditional gene inactivation in Drosophila. Nature the genetic basis of complex traits and prospects. Nature Rev. Genet. 10, 565–577 (2009). 448, 151–156 (2007). understanding both the structure and the evolution 22. Magwire, M. M. et al. Quantitative and molecular 39. Sabrautzki, S. et al. New mouse models for metabolic of complex systems. genetic analyses of mutations increasing Drosophila bone diseases generated by genome-wide ENU 3. Waddington, C. H. Canalization of development and life span. PLoS Genet. 6, e1001037 (2010). mutagenesis. Mamm. Genome 23, 416–430 the inheritance of acquired characters. Nature 150, 23. Zwarts, L. et al. Complex genetic architecture of (2012). 563–565 (1942). Drosophila aggressive behavior. Proc. Natl Acad. Sci. 40. O’Rourke, E. J., Conery, A. L. & Moy, T. I. Whole-animal 4. Waddington, C. H. The Strategy of Genes (George USA 108, 17070–17075 (2011). high-throughput screens: the C. elegans model. Allen and Unwin,1957). 24. Giaever, G. et al. Functional profiling of the Methods Mol. Biol. 486, 57–75 (2009). 5. Dobzhansky, T. Genetics and the Origin of Species Saccharomyces cerevisiae genome. Nature 418, 41. O’Malley, R. C., Alonso, J. M., Kim, C. J., Leisse, T. J. & (Columbia Univ. Press,1937). 387–391 (2002). Ecker, J. R. An adapter ligation-mediated PCR method 6. Muller, H. J. in The New Systematics (ed. Huxley, J. S.) 25. Boone, C., Bussey, H. & Andrews, B. J. for high-throughput mapping of T‑DNA inserts in the 185–268 (Clarendon, 1940). Exploring genetic interactions and networks with Arabidopsis genome. Nature Protoc. 2, 2910–2917 7. Carlborg, O. & Haley, C. S. Epistasis: too often yeast. Nature Rev. Genet. 8, 437–449 (2007). (2007). neglected in complex trait studies? Nature Rev. Genet. 26. Tong, A. H. et al. Global mapping of the yeast genetic 42. Anholt, R. R. H. et al. The genetic architecture of 5, 618–625 (2004). interaction network. Science 303, 808–813 (2004). odor-guided behavior in Drosophila: epistasis and the 8. Cordell, H. J. Detecting gene–gene interactions that This paper describes the first high-throughput transcriptome. Nature Genet. 35, 180–184 (2003). underlie human diseases. Nature Rev. Genet. 10, analysis of synthetic lethal genetic interaction This is the first study to show that genes that 392–404 (2009). mapping in yeast, from which the first large-scale are transcriptionally co‑regulated in a mutant 9. Cheverud, J. M. & Routman, E. J. Epistasis and its genetic interaction network was derived. background themselves affect the same trait as contribution to genetic variance components. Genetics 27. Collins, S. R., Schuldiner, M., Krogan, N. & the focal mutations, and that mutations in these 139, 1455–1461 (1995). Weissman, J. S. A strategy for extracting and analyzing genes epistatically interact with the focal This is the first paper to clearly articulate the large-scale quantitative epistatic interaction data. mutation. difference between the effect of epistasis on Genome Biol. 7, R63 (2006). 43. Deutschbauer, A. M. & Davis, R. W. Quantitative trait individual genotypes — which is independent of 28. St Onge, R. P. et al. Systematic pathway analysis loci mapped to single-nucleotide resolution in yeast. allele frequency — and the contribution of epistasis using high-resolution fitness profiling of Nature Genet. 37, 1333–1340 (2005). to epistatic variance for a quantitative trait, which combinatorial gene deletions. Nature Genet. 39, 44. Gerke, J., Lorenz, K. & Cohen, B. Genetic interactions does depend on allele frequency. 199–206 (2007). between transcription factors cause natural variation 10. Falconer, D. S. & Mackay, T. F. C. Introduction to 29. Costanzo, M. et al. The genetic landscape of a cell. in yeast. Science 323, 498–501 (2009). Quantitative Genetics (Longman, 1996). Science 327, 425–431 (2010). 45. Brem, R. B., Storey, J. D., Whittle, J. & Kruglyak, L. 11. Lynch, M. & Walsh, J. B. Genetics and Analysis of 30. Szappanos, B. et al. An integrated approach to Genetic interactions between polymorphisms that Quantitative Traits (Sinauer Associates, 1998). characterize genetic interaction networks in yeast affect gene expression in yeast. Nature 436, 701–703 12. Fisher, R. A. The Genetical Theory of Natural Selection metabolism. Nature Genet. 43, 656–662 (2011). (2005). (Clarendon, 1930). 31. Lehner, B., Crombie, C., Tischler, J., Fortunato, A. & 46. Gaertner, B. E., Parmenter, M. D., Rockman, M. V., 13. Wright, S. Evolution in Mendelian populations. Fraser, A. G. Systematic mapping of genetic Kruglyak, L. & Phillips, P. C. More than the sum of its Genetics 16, 97–159 (1931). interactions in Caenorhabditis elegans identifies parts: a complex epistatic network underlies natural 14. Hill, W. G., Goddard, M. E. & Visscher, P. M. Data and common modifiers of diverse signaling pathways. variation in thermal preference behavior in theory point to mainly additive genetic variance for Nature Genet. 38, 896–903 (2006). Caenorhabditis elegans. Genetics 192, 1533–1542 complex traits. PLoS Genet. 4, e1000008 (2008). This study describes the first large-scale mapping (2012). 15. Alvarez-Castro, J. M. & Carlborg, O. A unified model of genetic interaction networks in a metazoan, 47. Cheverud, J. M. et al. Genetic architecture of adiposity for functional and statistical epistasis and its which was done by feeding hypomorphic C. elegans in the cross of LG/J and SM/J inbred mice. Mamm. application in quantitative trait loci analysis. Genetics mutants with arrays of bacteria that expressed Genome 12, 3–12 (2001). 176, 1151–1167 (2007). double-stranded RNAi molecules which target 48. Stylianou, I. M. et al. Quantitative trait locus analysis 16. Meuwissen, T. H., Hayes, B. J. & Goddard, M. E. specific signalling pathways. for obesity reveals multiple networks of interacting Prediction of total genetic value using genome-wide 32. Byrne, A. B. et al. A global analysis of genetic loci. Mamm. Genome 17, 22–36 (2006). dense marker maps. Genetics 157, 1819–1829 (2001). interactions in Caenorhabditis elegans. J. Biol. 6, 8 49. Jarvis, J. P. & Cheverud, J. M. Mapping the epistatic 17. Hayes, B. J., Lewin, H. A. & Goddard, M. E. (2007). network underlying murine reproductive fatpad The future of livestock breeding: genomic selection for 33. Horn, T. et al. Mapping of signaling networks through variation. Genetics 187, 597–610 (2011). efficiency, reduced emissions intensity, and adaptation. synthetic genetic interaction analysis by RNAi. Nature 50. Leamy, L. J., Gordon, R. R. & Pomp, D. Sex-, diet-, and Trends Genet. 29, 206–214 (2013). Methods 8, 341–346 (2011). cancer-dependent epistatic effects on complex traits in 18. Elena, S. F. & Lenski, R. E. Test of synergistic 34. Van Driessche, N. et al. Epistasis analysis with global mice. Front. Genet. 2, 71 (2011). interactions among deleterious mutations in bacteria. transcriptional phenotypes. Nature Genet. 37, 51. Peripato, A. C. et al. Epistasis affecting litter size in Nature 390, 395–398 (1997). 471–477 (2005). mice. J. Evol. Biol. 17, 593–602 (2004). This is one of the first studies to show epistasis for 35. Aylor, D. L. & Zeng, Z.‑B. From classical genetics to 52. Hanlon, P. et al. Three-locus and four-locus QTL new mutations that affect fitness, using the E. coli quantitative genetics to systems biology: modeling interactions influence mouse insulin-like growth model system. epistasis. PLoS Genet. 4, e1000029 (2008). factor‑I. Physiol. Genom. 26, 46–54 (2006).

32 | JANUARY 2014 | VOLUME 15 www.nature.com/reviews/genetics

53. Carlborg, O., Jacobsson, L., Ahgren, P., Siegel, P. & 70. Rendel, J. M. Canalization of the scute phenotype of 89. Johnson, T. & Barton, N. Theoretical models of Andersson, L. Epistasis and the release of genetic Drosophila. Evolution 13, 425–439 (1959). selection and mutation on quantitative traits. variation during long-term selection. Nature Genet. 71. Gibson, G. & van Helden, S. Is function of the Phil. Trans. R. Soc. B 360, 1411–1425 (2005). 38, 418–420 (2006). Drosophila homeotic gene Ultrabithorax canalized? 90. Houle, D., Morikawa, B. & Lynch, M. Comparing This study documents the importance of epistatic Genetics 147, 1155–1168 (1997). mutational variabilities. Genetics 143, 1467–1483 interactions that govern long-term response to 72. Gibson, G., Wemple, M. & van Helden, S. Potential (1996). artificial selection for growth rate in chickens. variance affecting homeotic Ultrabithorax and 91. Zhang, X.‑S. & Hill, W. G. Genetic variability under 54. Pettersson, M., Besnier, F., Siegel, P. B. & Carlborg, O. Antennapedia phenotypes in Drosophila melanogaster. mutation selection balance. Trends Ecol. Evol. 20, Replication and explorations of high-order epistasis Genetics 151, 1081–1091 (1999). 468–470 (2005). using a large advanced intercross line pedigree. PLoS 73. Polaczyk, P. J., Gasperini, R. & Gibson, G. 92. Carson, H. L. & Templeton, A. R. Genetic revolutions in Genet. 7, e1002180 (2011). Naturally occurring genetic variation affects relation to speciation phenomena: the founding of new 55. Kroymann, J. & Mitchell-Olds, T. Epistasis and Drosophila photoreceptor determination. Dev. Genes populations. Annu. Rev. Ecol. Syst. 15, 97–131 balanced polymorphism influencing complex trait Evol. 207, 462–470 (1998). (1984). variation. Nature 435, 95–98 (2005). 74. Dworkin, I. et al. Genomic consequences of 93. Goodnight, C. J. On the effect of founder events on This paper reports the surprising observation that background effects on scalloped mutant expressivity in epistatic genetic variance. Evolution 41, 80–91 a small chromosome interval that has no effect on the wing of Drosophila melanogaster. Genetics 181, (1987). growth rate of A. thaliana contains two epistatically 1065–1076 (2009). 94. Tachida, H. & Cockerham, C. C. A building block model interacting QTLs that affect growth. 75. Dworkin, I., Palsson, A., Birdsall, K. & Gibson, G. for quantitative genetics. Genetics 121, 839–844 56. Wentzel, A. M. et al. Linking metabolic QTLs with Evidence that Egfr contributes to cryptic genetic (1989). network and cis-eQTLs controlling biosynthetic variation for photoreceptor determination in natural 95. Yang, J. et al. Common SNPs explain a large pathways. PLoS Genet. 3, 1687–1701 (2007). populations of Drosophila melanogaster. Curr. Biol. proportion of the heritability for human height. Nature 57. Rowe, H. C., Hansen, B. G., Halkier, B. A. & 13, 1888–1893 (2003). Genet. 42, 565–569 (2010). Kliebenstein, D. J. Biochemical networks and epistasis 76. Rutherford, S. L. & Lindquist, S. Hsp90 as a capacitor 96. Makowsky, R. et al. Beyond missing heritability: shape the Arabidopsis thaliana metabolome. Plant for morphological evolution. Nature 396, 336–342 prediction of complex traits. PLoS Genet. 7, Cell 20, 1199–1216 (2008). (1998). e1002051 (2011). 58. Doebley, J., Stec, A. & Gustus, C. teosinte branched1 77. Gibson, G. & Dworkin, I. Uncovering cryptic genetic 97. Benyamin, B. et al. Childhood intelligence is heritable, and the origin of maize: evidence for epistasis and the variation. Nature Rev. Genet. 5, 681–690 (2004). highly polygenic and associated with FNBP1L. Mol. evolution of dominance. Genetics 141, 333–346 This review documents the presence of cryptic Psychiatry http://dx.doi.org/10.1038/mp.2012.184 (1995). genetic variation for complex traits and argues (2013). 59. Stam, L. F. & Laurie, C. C. Molecular dissection of a that such variation is important in understanding 98. Hu, Z. et al. Genomic value prediction for quantitative major gene effect on a quantitative trait: the level of the genetic bases of common diseases in humans, traits under the epistatic model. BMC Genet. 12, 15 alcohol dehydrogenase expression in Drosophila artificial selection response in livestock and (2011). melanogaster. Genetics 144, 1559–1564 (1996). crops, and evolutionary responses to new 99. Long, N., Gianola, D., Rosa, G. J. & Weigel, K. A. This classic paper uses P‑element transformation mutations. Marker-assisted prediction of non-additive genetic to create all possible combinations of three 78. Spencer, C. C., Howell, C. E., Wright, A. R. & values. Genetica 139, 843–854 (2011). segments of the Adh gene and showed that each of Promislow, D. E. Testing an ‘aging gene’ in long-lived 100. Bulmer, M. G. The Mathematical Theory of the three segments affects Adh activity, and that Drosophila strains: increased longevity depends on Quantitative Genetics (Clarendon,1985). there is, surprisingly, epistasis between two sex and genetic background. Aging Cell 2, 123–130 101. Anholt, R. R. H. & Mackay, T. F. C. Principles of different regions within the gene. (2003). Behavioral Genetics (Elsevier, 2010). 60. Shao, H. et al. Genetic architecture of complex traits: 79. Yamamoto, A., Anholt, R. R. H. & Mackay, T. F. C. 102. Mackay, T. F. C. et al. Genetics and genomics of large phenotypic effects and pervasive epistasis. Epistatic interactions attenuate mutations affecting Drosophila mating behavior. Proc. Natl Acad. Sci. USA Proc. Natl Acad. Sci. USA 105, 19910–19914 (2008). startle behaviour in Drosophila melanogaster. Genet. 102 (Suppl. 1), 6622–6629 (2005). 61. Gale, G. D. et al. A genome-wide panel of congenic mice Res. 91, 373–382 (2009). 103. Ayroles, J. F. et al. Systems genetics of complex reveals widespread epistasis of behavior quantitative 80. Swarup, S. et al. Extensive epistasis for olfactory traits in Drosophila melanogaster. Nature Genet. 41, trait loci. Mol. Psychiatry 14, 631–645 (2009). behavior, sleep and waking activity in Drosophila 299–307 (2009). 62. Spiezio, S. H., Takada, T., Shiroishi, T. & Nadeau, J. H. melanogaster. Genet. Res. 94, 9–20 (2012). 104. Jordan, K. W., Carbone, M. A., Yamamoto, A., Genetic divergence and the genetic architecture of 81. Cheng, Y. et al. Mapping genetic loci that interact Morgan, T. J. & Mackay, T. F. C. Quantitative genomics complex traits in chromosome substitution strains of with myostatin to affect growth traits. Heredity 107, of locomotor behavior in Drosophila melanogaster. mice. BMC Genet. 13, 38 (2012). 565–573 (2011). Genome Biol. 8, R172 (2007). 63. Edwards, A. C. & Mackay, T. F. C. Quantitative trait loci 82. Chaikam, V. et al. Use of Mutant-Assisted Gene 105. Edwards, A. C., Rollmann, S. M., Morgan, T. J. & for aggressive behavior in Drosophila melanogaster. Identification and Characterization (MAGIC) to Mackay, T. F. C. Quantitative genomics of aggressive Genetics 182, 889–897 (2009). identify novel genetic loci that modify the maize behavior in Drosophila melanogaster. PLoS Genet. 2, 64. Eshed, Y. & Zamir, D. Less-than-additive epistatic hypersensitive response. Theor. Appl. Genet. 123, e154 (2006). interactions of quantitative trait loci in tomato. 985–997 (2011). 106. Morozova, T. V., Anholt, R. R. & Mackay, T. F. C. Genetics 143, 1807–1817 (1996). 83. Sangster, T. A. et al. HSP90‑buffered genetic variation Phenotypic and transcriptional response to selection 65. Causse, M., Chaïb, J., Lecomte, L., Buret, M. & is common in Arabidopsis thaliana. Proc. Natl Acad. for alcohol sensitivity in Drosophila melanogaster. Hospital, F. Both additivity and epistasis control the Sci. USA 105, 2969–2974 (2008). Genome Biol. 8, R231 (2007). genetic variation for fruit quality traits in tomato. 84. Manolio, T. A. et al. Finding the missing heritability 107. Leips, J. & Mackay, T. F. C. Quantitative trait loci for Theor. Appl. Genet. 115, 429–442 (2007). of complex diseases. Nature 461, 747–753 lifespan in Drosophila melanogaster: interactions with 66. Greene, C. S., Penrod, N. M., Williams, S. M. & (2009). genetic background and larval density. Genetics 155, Moore, J. H. Failure to replicate a genetic association 85. Valdar, W. et al. Genome-wide genetic association of 1773–1788 (2000). may provide important clues about genetic complex traits in heterogeneous stock mice. Nature architecture. PLoS ONE 4, e5639 (2009). Genet. 38, 879–887 (2006). Acknowledgements 67. Mackay, T. F. C. et al. The Drosophila melanogaster 86. Buckler, E. S. et al. The genetic architecture of maize The author thanks S. Zhou for helping with figures 2 and 5b, Genetic Reference Panel. Nature 482, 173–178 (2012). flowering time. Science 325, 714–718 (2009). and R. Anholt for comments on the manuscript. Work in the 68. Huang, W. et al. Epistasis dominates the genetic 87. Barton, N. H. & Turelli, M. Evolutionary quantitative Mackay laboratory is supported by the US National Institutes architecture of Drosophila quantitative traits. genetics: how little do we know? Annu. Rev. Genet. 23, of Health grants R01 GM45146, R01 GM076083, R01 Proc. Natl Acad. Sci. USA 109, 15553–15559 (2012). 337–370 (1989). GM59469 and R01 AA016560. 69. Ehrenreich, I. M. et al. Dissection of genetically 88. Barton, N. H. & Keightley, P. D. Understanding complex traits with extremely large pools of yeast quantitative genetic variation. Nature Rev. Genet. 3, Competing interests statement segregants. Nature 464, 1039–1042 (2010). 11–21 (2002). The author declares no competing interests.

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