Pleiotropy, epistasis and the genetic architecture of quantitative traits

Abstract

Pleiotropy (whereby one genetic polymorphism affects multiple traits) and epistasis (whereby non-linear interactions between genetic polymorphisms affect the same trait) are fundamental aspects of the genetic architecture of quantitative traits. Recent advances in the ability to characterise the effects of polymorphic variants on molecular and organismal phenotypes in human and model organism populations has revealed the prevalence of pleiotropy and unexpected shared molecular genetic bases among quantitative traits, including diseases. By contrast, epistasis is common between polymorphic loci associated with quantitative traits in model organisms, such that alleles at one locus have different effects in different genetic backgrounds, but is rarely observed for human quantitative traits and common diseases. Here, we review the concepts and recent inferences about pleiotropy and epistasis and discuss factors that contribute to similarities and differences between the genetic architecture of quantitative traits in model organisms and humans.

Toc blurb

In this Review, Mackay and Anholt discuss how epistasis and pleiotropy contribute to the genetic architecture of quantitative traits and outline factors that might explain observed differences in their prevalence between model organisms and humans.

Introduction

Quantitative traits display continuous phenotypic variation in populations, which is attributable to the simultaneous segregation of the many polymorphic loci that affect each trait and their sensitivity to environmental effects^1–3. As quantitative traits (such as morphology, behaviour, physiology, disease susceptibility, survival, and fertility) account for most of the phenotypic variation observed in populations, understanding the genetic basis of quantitative variation is important for human health, agriculture, and the study of evolution. Understanding the genotype-phenotype relationship for quantitative traits can help identify genes associated with human diseases that can be targeted for treatment with approved drugs⁴, and understanding the genetic basis of differential drug responses can identify patients for which the therapy will be effective, while minimizing deleterious side effects⁵. Polygenic risk scores can predict the genetic predisposition to disease, enabling appropriate lifestyle changes before the age of disease onset⁶. Genomic prediction of breeding values in agricultural species can markedly increase selection responses⁷. The genetic basis of phenotypic variation for ecologically relevant quantitative traits determines how rapidly populations can respond to natural selection⁸; conservation efforts to maintain this variation can reduce inbreeding depression and limit loss of biodiversity.

Our understanding of the genetic architecture [G] of quantitative traits is shaped by the results of studies that map quantitative trait loci (QTLs) by linkage to or association with polymorphic molecular markers in model organisms and agriculturally important animal and crop species³ and, more recently, by large genome wide association studies (GWAS) for human quantitative traits and complex diseases⁹. It is now clear that the ‘many’ loci that affect quantitative traits equates to hundreds to thousands of associated molecular polymorphisms. Most highly powered genome-wide association analyses have been performed in human populations, but there are limits to mapping genes and variants associated with quantitative traits, including molecular phenotypes, in humans. The limit to the precision of association mapping in any species is linkage disequilibrium ($LD$), that is, the extent to which molecular markers in close physical proximity are not independent. The human genome is organized in blocks within which $LD$ is high; therefore, determining which of the multiple polymorphisms in $LD$ are truly causal for the trait is difficult. Furthermore, only human tissues that can be obtained through blood draws, biopsies, or from post-mortem samples can be studied and these are not always relevant to the trait of interest. In humans, not all pleiotropic traits are measured on the same individuals, nor is it possible to control the environment to which each person is exposed. These limitations can be overcome to some extent in studies using model organisms, in which the genetic background and environment can be controlled, mutations can be created to systematically evaluate the gene-quantitative trait phenotype relationship and gene editing can be used to functionally validate candidate genes and polymorphisms statistically associated with quantitative traits in vivo. Model organism studies also enable genetic variation to be quantified and multiple quantitative trait phenotypes measured on the same genotypes in trait-relevant tissues to assess the contribution of molecular phenotypes to organismal level quantitative genetic variation. General features of the genetic architecture of quantitative traits inferred from model organisms are likely to be applicable to humans, and vice versa. Since fundamental biological pathways are evolutionarily conserved across taxa, orthologous genes may affect variation in the same quantitative traits between humans and genetic model organisms. However, the extent to which specific QTLs are conserved between model organisms and humans is limited by differences in genome size and organization, demographic history and biology.

Most QTL mapping studies utilise simple statistical models that evaluate the effects of variation at each polymorphic molecular marker for one or a few traits individually. Greater complexity arises when considering that genes affect multiple quantitative traits (pleiotropy) and act in non-linear genetic interaction networks (epistasis). Pleiotropy implicates unexpected mechanistic associations between traits¹⁰; can improve the precision of mapping genes and variants associated with quantitative traits¹¹; and affects responses to artificial or natural selection¹². Molecular networks associated with quantitative traits can be deduced from pleiotropic effects of high-dimensional molecular phenotypes such as gene expression traits and metabolites¹³. With epistasis, alleles have different effects in different genetic backgrounds, which causes variable allelic effects among individuals and populations¹⁴ and affects the magnitude of expressed quantitative genetic variation¹⁵. Genetic networks inferred from epistatic interactions can be used to improve the accuracy of predicting quantitative trait phenotypes from genomic data¹⁶.

Here, we discuss the concepts of pleiotropy and epistasis for quantitative traits, methods for detecting and quantifying pleiotropy and epistasis, and the evolutionary consequences of pleiotropy and epistasis. We compare inferences about pleiotropy and epistasis between genetic model organisms and human populations and discuss reasons for some apparent discrepancies in these features of genetic architecture between the model systems and humans.

Pleiotropy

Pleiotropy was initially defined as the phenomenon whereby a single gene independently affects two or more phenotypes (that is, traits)^17,18. A more rigorous definition of pleiotropy is when the additive effects [G] and/or dominance effects [G] of a polymorphic variant are non-zero for two or more traits (Figure 1a). True pleiotropy indicates shared genetic architecture affecting the traits and can occur when a polymorphism independently affects more than one trait (‘horizontal’ pleiotropy, Figure 1b), or when a polymorphism affects one trait which in turn affects another (‘mediating’ pleiotropy, Figure 1c)¹⁹. Mutations affecting hair and coat colour in mammals often have pleiotropic effects on vision and hearing – examples of horizontal pleiotropy²⁰. An example of mediating pleiotropy would be a variant that is associated with both an increase in low-density lipoprotein (LDL) cholesterol and an increased risk of coronary artery disease, since the increase in LDL cholesterol is a causal risk factor for developing this disease²¹. Different polymorphisms in a single gene can have different effects on different traits, some of which may be pleiotropic, others of which may affect only one trait. For example, different molecular polymorphisms at the Catsup locus in Drosophila melanogaster are independently associated with variation in longevity, locomotor behaviour, and sensory bristle number²². Therefore, Catsup is a pleiotropic gene, but the individual polymorphisms do not have pleiotropic effects on all the measured traits.

Figure 1|. Pleiotropy for quantitative traits.

a, Shown are the genotypes and genotypic effects for a single locus (A) with two alleles (A₁, A₂). For a given trait, the additive effect ($a$) of locus A is $({\mu }_{A1A1}-{\mu }_{A2A2})/2$, where ${\mu }_{A1A1}$ and ${\mu }_{A2A2}$ are, respectively, the mean of the trait for all individuals with genotype A₁A₁ or A₂A₂ in the population. The dominance effect ($d$) of locus A is ${\mu }_{A1A2}-({\mu }_{A1A1}+{\mu }_{A2A2})/2$, where ${\mu }_{A1A2}$ is the mean of the trait for all individuals with genotype A₁A₂ in the population². The locus contributes to a quantitative trait if $a$ and/or $d$ have non-zero values. If multiple traits are measured, pleiotropy exists between any traits for which $a$ and/or $d\ne 0$, here, traits 2 and 3. The genetic correlation between traits 2 and 3 depends on the frequencies of the A₁ and A₂ alleles in the population (Box 1). Panels b-d illustrate different types of pleiotropy, true pleiotropy (b, c) and apparent pleiotropy (d). The black horizontal lines denote a genomic region and the circles represent single nucleotide polymorphisms (SNPs). Blue circles denote SNPs affecting one or more quantitative traits (that is, $a$ and/or $d\ne 0$). b, Horizontal pleiotropy is a form of true pleiotropy whereby the same SNP independently affects two (or more) quantitative traits; for example, mammalian coat colour and hearing. c, Mediating (or vertical) pleiotropy is a form of true pleiotropy whereby a SNP affects one trait, which in turn affects a second trait; for example, low-density lipoprotein (LDL) levels and risk of coronary artery disease (CAD). d, Apparent pleiotropy occurs when the traits are not caused by a common SNP but rather by two (or more) SNPs that are in linkage disequilibrium ($LD$) and each affects one of the traits. Here, SNP2 affects one trait and SNP3 affects a second trait, and there is strong $LD$ between SNP2 and SNP3, indicated by the blue horizontal arrow. $LD$ can be at any scale, from within a single gene to between genes.

Apparent pleiotropy refers to the situation whereby different molecular polymorphisms in $LD$ independently affect different traits (Figure 1d). Apparent pleiotropy can occur not only within genes but also in multi-gene haplotypes [G] in regions of high $LD$, where a single variant can serve as a proxy for all variants in the haplotype. Apparent pleiotropy can disappear over time in a random mating population because $LD$ decreases as the number of generations of recombination increases. In the case of tightly linked variants in the same or different genes with independent effects on traits, the distinction between true and apparent pleiotropy may be moot in a particular population, but the pleiotropic effects of the polymorphism(s) will differ between populations with different patterns of $LD$.

In addition to the classic definition of pleiotropy referring to two different quantitative traits, the concept can be extended to the same trait measured in males versus females or in different macro-environments (any environmental variable that can be reproduced across individuals)²³. Imperfect genetic correlations between males and females cause genotype-by-sex interactions, showing that the genetic basis of the trait is not identical in the two sexes. Similarly, imperfect genetic correlations between a trait measured across environments causes genotype-by-environment interactions, indicating that the genetic basis of the trait varies across environments. Genotype-by-sex and genotype-by-environment interactions are often observed in model organisms^24–26 but their contributions to genetic architecture are typically not examined in human studies.

Quantifying pleiotropy

Quantifying pleiotropy from induced mutations.

The clearest demonstration of pleiotropy is when a single mutation has been induced in a homozygous strain. In this case, the only difference between the mutant and wild type strains is homozygosity for alternative alleles at the mutated locus. If the phenotypes of multiple quantitative traits are measured on the mutant and wild type strains and their additive effects computed², non-zero additive effects for more than one trait indicate pleiotropy that is not confounded by $LD$ (Figure 1a).

Collections of mutations or RNA interference (RNAi) constructs designed to target most genes in the genome are available for Saccharomyces cerevisiae²⁷, Caenorhabditis elegans²⁸, Arabidopsis thaliana²⁹, D. melanogaster^30–32 and Mus musculus³³. These collections have largely been used for forward genetic screens to identify genes affecting phenotypes of interest to specific laboratories but are also suitable for quantifying pleiotropy across studies. For example, the most straightforward organismal phenotypes to quantify in yeast are fitness [G] and growth rate, and these have been assessed for strains from the yeast deletion collection under many environmental conditions to quantify pleiotropy from gene-by-environment interactions^27,34. Similarly, the effects of D. melanogaster P-element [G] insertional mutations have been measured for multiple organismal quantitative traits^35–40 (Figure 2). There have also been large-scale efforts in laboratory mice to couple genome-wide mutagenesis with high throughput phenotyping to understand the pleiotropic functions of, ultimately, all genes in the mammalian genome^33,41–45. All of these studies have shown that pleiotropic effects on organismal level phenotypes are ubiquitous. However, not all genes have equal levels of pleiotropy. Some mutations are highly pleiotropic and affect many traits, while others affect a few traits, only one trait, or no traits⁴⁶. This pattern is reflected in Gene Ontology (GO) terms associated with genes curated from functional analyses of mutations by individual laboratories in each model organism community⁴⁷.

Figure 2 |. Pleiotropy of P-element insertions in D. melanogaster.

Additive effects of P-element insertions in 53 genes on ten quantitative traits are indicated. All P-element insertions are in the same genetic background. Cell colours indicate whether the P-element increases or decreases the trait value relative to the control: blue cells denote decreases and red cells denote increases. The intensity of the colour (dark, medium and light) denotes deviations from the mean of co-isogenic controls exceeding the 95%, 99% and 99.9% confidence intervals, respectively. The light green cells indicate decreased trait values in males and increased trait values in females for the P-element insertion compared to the control. Black cells are not significantly different from the control, and grey cells indicate traits for which the effect of the P-element insertion was not measured. All traits were measured for males and females. Effects on all sleep traits³⁸ are given for males and females separately. Effects on abdominal and sternopleural bristle numbers³⁵, startle response³⁷, olfactory behavior³⁶, starvation resistance³⁹ and ethanol sensitivity⁴⁰ are pooled across sexes, unless sex-specific effects for females (♀) or males (♂) are specified. This figure illustrates the ubiquity of pleiotropy, that pleiotropic effects exhibit antagonistic pleiotropy across traits, and that pleiotropy can be sex-specific and even sex-antagonistic.

The magnitude of pleiotropy and the distribution of pleiotropic effects depends on the numbers of traits and mutations that are assessed. The ability to quantify gene expression, protein abundance and metabolites genome-wide enables large numbers of intermediate molecular phenotypes to be quantified at once and the pleiotropic effects of genetic variation on these phenotypes to be examined. Analysis of gene expression in a subset of genes from the yeast deletion collection showed that most mutations affected the expression of the deleted genes themselves (cis-regulatory mutations) as well as many other co-regulated genes (trans-regulatory mutations)^48–50. The number of trans-co-regulated genes was not uniform across the mutations and could be described with a ‘scale-free’ transcriptional network topology, whereby a few genes, when individually deleted, affected the transcription of large numbers of downstream target genes while deletion of other genes affected the transcription of fewer target genes^49,50. Yeast trans-regulatory mutations have more pleiotropic effects than cis-regulatory mutations^51,52. Similar magnitudes of pleiotropy of gene expression were found for single P-element mutations in D. melanogaster^53,54. These observations show how a mutation in a single gene can potentially affect multiple organismal phenotypes by altering expression levels of other genes and provide insight into the molecular and mechanistic basis of pleiotropy. Similar mechanistic insight can be obtained by profiling multiple mutations that affect a focal phenotype^53,54 and determining common gene expression traits. For example, transcriptional profiling of seven D. melanogaster mutations associated with increased lifespan revealed 553 transcripts that were co-regulated in four or more of the seven genotypes⁵⁴. These transcripts were encoded by genes affecting reproduction, chemosensation, metabolism, immunity and/or defense response, and function and development of the nervous system.

Many rare diseases in humans are caused by de novo mutations that typically have pleiotropic effects⁵⁵. In recent years it has become possible to perform genome-scale forward genetic screens in human cell lines using CRISPR-Cas9 gene editing. Methods such as Perturb-Seq, which combine these large-scale mutagenesis approaches with rich single cell transcriptional phenotyping of each CRISPR-induced perturbation reveal widespread functional transcriptional pleiotropy at the cellular level in humans⁵⁶.

Quantifying pleiotropy from natural variation.

Many induced mutations demonstrate pleiotropy at the gene level. However, because genes often contain multiple domains with different functions, it is possible that induced mutations have larger effects (for example, on all or multiple functions) and are more pleiotropic than naturally occurring polymorphisms, which have survived the sieve of natural selection and may have more subtle and specific effects. Quantitative genetics theory^2,3 shows that correlations between different quantitative trait phenotypes in a natural population are caused by shared genetic variation affecting both traits (genetic correlation) or because the environmental circumstances experienced by an individual affect the traits in the same direction (environmental correlation) (Box 1). The genetic correlation is attributable to directional pleiotropy for all loci affecting both traits and is a genome wide population average (Box1). In the absence of population molecular markers, cross-trait genetic and environmental correlations are estimated from any experimental design that enables heritability [G] to be estimated from relatives, when both traits are measured on all relatives^2,3. However, genetic correlations can be measured across all loci in linkage or association mapping populations without the need for related individuals, to estimate pleiotropy globally across the genome. Pleiotropy can also be assessed locally in linkage and association mapping populations to infer pleiotropy contributed by individual loci.

Box 1 |. Phenotypic, genetic and environmental correlations.

The phenotypic correlation (${\rho }_{PXY}$) between two quantitative traits $X$ and $Y$ can be estimated in a population where measurements of both traits on a sample of individuals are available: ${\rho }_{PXY}={cov}_{PXY}/{\sigma }_{PX}{\sigma }_{PY}$ (${cov}_{PXY}$ is the covariance of $X$ and $Y$ and ${\sigma }_{PX}$ and ${\sigma }_{PY}$ are their phenotypic standard deviations). ${\rho }_{PXY}$ can be decomposed into genetic (${\rho }_{GXY}$) and environmental (${\rho }_{EXY}$) correlations between traits $X$ and $Y$. The cross-trait genetic correlation is defined as the correlation of breeding values between the two traits. The breeding value of an individual is determined by the mean value of its progeny when mated to random individuals in the population, expressed as a deviation from the population mean^1–3. Breeding values for each genotype at a locus affecting a quantitative trait are a function of allele frequencies ($p$ and $q$ for A₁ and A₂ alleles at locus A, respectively) and the average effects of the alleles it carries. The average effects of alleles A₁ (${\alpha }_1$) and A₂ (${\alpha }_2$) are ${\alpha }_1=q[a+d\left(q-p\right)]$ and ${\alpha }_2=-p\left[a+d\left(q-p\right)\right],$ and the breeding values of the A₁A₁, A₁A₂ and A₂A₂ genotypes are $2{\alpha }_1,{\alpha }_1+{\alpha }_2$ and $2{\alpha }_2$, repectively^1–3. $a$ is the additive effect and $d$ is the dominance effect (Figure 1a).

Non-zero values for cross-trait genetic correlations indicates pleiotropy between the traits^1–3. However, a genetic correlation of zero does not always mean that pleiotropy is absent. In the figure, the average effects of biallelic loci on trait $X$ (${\alpha }_{1X}, {\alpha }_{2X}$) are plotted against their average effects on trait $Y$ (${\alpha }_{1Y}, {\alpha }_{2Y}$). Both alleles of a given locus are coloured the same and each locus has a different colour. In panels a and b, the average effects of all loci are non-zero for both traits indicating that the loci are pleiotropic and the traits have shared genetic variation. When taken across all loci, the cross-trait genetic correlations are positive in a and negative in b. In c, the average effects of both loci are non-zero and the loci are therefore pleiotropic. However, one locus has a positive genetic correlation and the other a negative genetic correlation, which cancel out to give an overall genetic correlation of zero. Genetic correlations cannot detect this type of pleiotropy. In d, the average effect of each locus is zero for at least one of the two traits: there is no pleiotropy, and the genetic correlation is zero. The non-zero effects are owing to non-genetic (environmental) effects on both traits and non-additive genetic variation (dominance and epistasis).

In model organisms, pleiotropy can be assessed at the level of individual haplotypes or single nucleotide polymorphisms (SNPs) by using publicly available inbred linkage and association mapping populations that are genotyped for dense polymorphic molecular markers or have their genomes fully sequenced. The linkage mapping populations are derived by crossing two or more inbred strains, followed by inbreeding (or self-fertilization) of the F₂ or later segregating generations to near homozygosity. The association mapping populations are obtained by inbreeding (or self-fertilization) of individuals collected from a natural population to near homozygosity. Recombinant inbred lines derived from bi-or multi-parental crosses of inbred strains, diverse inbred strains and heterogeneous outbred stocks are available for linkage mapping in mice⁵⁷ and rats⁵⁸; experimental results from studies using these resources to map quantitative traits, including intermediate molecular phenotypes, are curated in searchable databases that can be mined to assess pleiotropy^59–61. In D. melanogaster, the inbred, fully sequenced Drosophila Genetic Reference Panel (DGRP) lines^62,63 are available for association mapping and the D. melanogaster Synthetic Population Resource (DSPR)⁶⁴ for linkage mapping. Panels of recombinant inbred lines for linkage mapping and wild-derived inbred lines for association mapping are also available for C. elegans⁶⁵ and A. thaliana^66,67. Most model organism studies designed to detect pleiotropic QTLs for organismal traits have typically found them^{24–26,68,69}. Examples include a study in C. elegans mapping QTLs for 24 traits upon exposure to 16 toxins which found 33 QTLs that mapped to one of three regions associated with many toxins⁶⁸. A study in S. cerevisiae mapping QTLs affecting fitness in 18 different growth conditions identified 449 pleiotropic QTLs⁶⁹.

In humans, many large, highly powered GWAS have been performed for quantitative traits and diseases. Although individual level data are reported for studies using large publicly available BioBanks^70,71, results of disease GWAS are only available as summary statistics (effect size, P-value, standard error of associated polymorphisms)⁷², rather than at the level of individual SNPs. Moreover, most GWAS only evaluate a single phenotype. Thus assessing pleiotropy from GWAS required new methods to be developed to estimate cross-trait genetic correlations across different studies using summary statistics^{10,11,19,73,74}. If large numbers of individuals are assessed for the same constellation of genetically correlated traits, considering all traits in a single GWAS can boost the power to detect SNP associations and to predict disease risk^11,19. Large-scale BioBanks^70,71 for which dense genotypes or exome or whole genome sequencing data have been linked to deep phenotyping information via electronic health records have enabled phenome-wide association studies (PheWAS)^75,76. PheWAS evaluates associations of each molecular polymorphism with a plethora of phenotypes to uncover pleiotropy between traits at an unprecedented scale. Collectively, GWAS-based studies have shown substantial pleiotropy between human quantitative traits that is sometimes unexpected, and that there is variation in the sign and/or magnitude of pleiotropy between the same traits across the genome^{10,11,74,77,78}. Moreover, a large meta-analysis of 4,155 GWAS confirmed extensive pleiotropy for human quantitative traits, with 90% of GWAS loci overlapping multiple traits⁷⁹. Most of these studies mapped individual molecular polymorphisms associated with two or more traits^{73–76,78,79} and a few also estimated global genetic correlations^77,79. This prevalence of pleiotropy is particularly evident for psychiatric disorders. There is a shared genetic basis between risk of schizophrenia and bipolar disorder⁷⁷; between multiple psychiatric disorders and variation in calcium channel genes⁷⁸; between anorexia nervosa and schizophrenia, anorexia and obesity, and educational attainment and several diseases⁷⁴; and risk between schizophrenia and Parkinson’s disease¹⁰. The shared genetic architecture between these disorders provides new biological insight into potential common disease processes.

Once pleiotropy at a locus has been established between two or more traits, it is important to discriminate between true pleiotropy and apparent pleiotropy due to $LD$ (Figure 1), as only the former reflects shared genetic underpinnings. Apparent pleiotropy from $LD$ is likely to be common in most model organism linkage mapping populations due to the large $LD$ blocks tagged by each molecular marker. Although the extent of $LD$ is greatly reduced in model organism outbred populations and multi-parental mapping populations as well as human association mapping studies, $LD$ as a potential cause of pleiotropy always needs to be ruled out. Statistical co-localization methods can help address this question^10,74, but the gold standard is experimental validation. First, all variants in $LD$ with the putative pleiotropic variant that could potentially cause the multiple trait associations need to be identified, followed by fine-mapping by further generations of recombination in model organisms⁸⁰ or by performing GWAS for the same traits in a population with high-density genotypes in humans⁸¹. Advances in genome editing using CRISPR-based approaches⁸² have revolutionized our ability to functionally validate pleiotropic SNP associations in model organisms using scarless allelic replacement⁸³ or base-editing⁸⁴. Functional validation in humans can be done by gene editing in cell lines⁸⁵ from the relevant tissue(s) but is restricted to traits that can be measured in cells. In the future, massively parallel CRISPR-based screens^56,86 have the potential to functionally validate pleiotropic SNP effects.

Once true pleiotropy has been confirmed, mediation analyses are used to discriminate between horizontal and mediating pleiotropy (Figure 1b,c). One type of mediation analysis uses conditional regression models of the effect of the polymorphism on the traits, conditioning on either trait $X$ or trait $Y$^87,88. If conditioning on trait $X$ removes the effect on trait $Y$, but conditioning on trait $Y$ does not remove the effect on trait $X$, then trait $X$ mediates trait $Y$. With horizontal pleiotropy, conditioning the polymorphism effect on either trait will not remove the effect on the other. Classical statistical mediation analyses define the relationship between an exposure variable ($X$), a mediator variable ($M$), and an outcome variable ($Y$)^89,90. The effects to be estimated are the total effect of $X$ on $Y$, the effect of $X$ on $M$, the effect of $M$ on $Y$, and the effect of $X$ on $Y$ after accounting for the effect of $M$. The models are then used to partition the total effect of $X$ on $Y$ into a direct effect and a mediation effect. Mendelian Randomization methods are a class of mediation analyses where $X$ is a genetic polymorphism that affects trait $Y$ solely via its effects on the mediator trait $X$ (mediated pleiotropy) and assumes there is no horizontal pleiotropy^19,91,92. More recent Mendelian Randomization methods that detect and correct for horizontal pleiotropy are capable of distinguishing horizontal and mediated pleiotropy. These methods show that horizontal pleiotropy is common among human quantitative traits⁹³ and was observed in ~50% of significant causal relationships⁹⁴.

Systems genetics and regulatory variation

Technological developments in genome-wide profiling of gene expression, metabolites and proteins combined with the ability to map organismal level QTLs in linkage mapping populations catalyzed the field of systems genetics^95,96. We focus here on the genetics of gene expression since these analyses are the most common, but the same principles and results hold for other molecular phenotypes. Early studies in experimentally tractable organisms showed that the levels of expressed transcripts are quantitative traits that vary between sexes, ages and genotypes^97,98 and between natural populations⁹⁹. The first experiments mapping QTLs associated with variation in gene expression (expression QTLs, eQTLs) were in yeast^100–102, followed by studies in mice¹⁰³, maize¹⁰⁴, A. thaliana¹⁰⁵, D. melanogaster¹⁰⁶, C. elegans¹⁰⁷ and human cell lines^103,108,109.

These pioneering studies showed that large numbers of transcripts were genetically variable, often with high heritabilities, and mapped to one or more genomic loci proximal (cis-eQTLs) or distal (trans-eQTLs) to the gene encoding each transcript. Some trans-eQTLs were associated with variation in expression of large numbers of genes. Cis-eQTLs initially encompassed many Mb to either side of the genes encoding the transcripts due to the poor resolution of small linkage mapping populations; thus, many cis-eQTLs identified in the early studies could have been trans-eQTLs. The genetically variable transcripts clustered into distinct genetically correlated transcriptional modules (Figure 3a,b). Enrichment analysis for Gene Ontology categories, Kyoto Encyclopedia of Genes and Genomes pathways, protein-protein interactions, tissue-specific expression, and transcription factor binding sites¹³ provide functional insight into gene modules, and functions of non-annotated genes in these modules can be inferred by their genetic correlation with genes of known function (Figure 3c). Furthermore, the genetically variable transcripts (or transcriptional modules) can also be genetically correlated with organismal quantitative traits (Figure 3c), provided the transcripts are assessed in tissues that are relevant to the organismal trait of interest^13,95,96,103. These observations led to the hypothesis that cis-eQTLs could affect organismal quantitative traits by perturbing transcriptional (and other) molecular phenotypes that in turn affect disease liability, thus giving mechanistic insights into the biological basis of disease which was not possible from mapping QTLs associated with the organismal phenotypes. Systems genetic analyses model the pleiotropic relationships between the genetic polymorphisms associated with the organismal quantitative trait, the genetic polymorphisms associated with cis-eQTLs, and the gene expression traits associated with the organismal quantitative trait to infer causal relationships between genetic variation, networks of molecular phenotypes, and organismal quantitative traits^13,87,88,110.

Figure 3 |. Systems genetic analysis of pleiotropy.

a, Modular organization of gene expression correlations for 16 pleiotropic genes, showing two distinct networks of genes 1–11 and 12–16. Red cells depict positive correlations, blue cells negative correlations and grey cells no significant correlations of pairwise gene expression. Gene 11 is negatively correlated with all genes in the smaller network. b, Network view of the same data. The genes are indicated as nodes and the pairwise correlations are edges between nodes, with red edges for positive correlations and blue edges for negative correlations. The arrows indicate that genes 11 and 15 are associated with cis-expression Quantitative Trait Loci (eQTLs). The cis-eQTL for gene 11 is a trans-eQTL for the other genes in both the large and small networks and the cis-eQTL for gene 15 is a trans-eQTL for the other genes in the small network. Mendelian randomization or mediation analyses will give the extent to which the pleiotropic effects of the cis-eQTLs are horizontal or mediating. c, Pleiotropic effects of gene expression networks on quantitative traits. The large module is positively correlated (red arrow) with Trait 1 and negatively correlated (blue arrow) with Trait 2 and the small module is positively correlated with Trait 2 and negatively correlated with Trait 1. Traits 1 and 2 are negatively correlated. The module enrichment for GO terms and pathways provides mechanistic insight about the traits.

The hypothesis that molecular genetic polymorphisms affect variation in organismal quantitative traits via effects on gene regulation is supported by human studies showing that SNPs associated with organismal quantitative traits are enriched for eQTLs^111–113 and deoxyribonuclease I (DNase I) hypersensitive sites¹¹⁴ [G], and that SNPs in DNase I hypersensitivity sites¹¹⁵ and other functional annotations^114,116 explain more heritability than SNPs in coding regions across many common diseases. The Genotype-Tissue Expression project has collected genotype and whole genome gene expression data from post-mortem human samples of 54 non-diseased tissues from nearly 1,000 individuals, and mapped eQTLs for each tissue¹¹⁷. This reference transcriptome database has been used to predict gene expression in human populations for which genetic polymorphisms and organismal phenotypes have been assessed to enable transcriptome-wide association studies to detect pleiotropy between gene expression and the organismal phenotypes^118,119. The eQTLGen Consortium, a large-scale effort to map eQTLs in blood from over 30,000 individuals, showed that nearly 90% of genes had eQTLs, the expression of which was associated with over 1,200 quantitative traits¹²⁰.

The ubiquity of eQTLs, large numbers of QTLs in non-coding and presumably regulatory genomic regions, and association of variation in gene expression with variation in quantitative trait phenotypes led to the proposal that the genetic basis of human quantitative traits is ‘omnigenic’, such that many loci indirectly affect many traits via highly interconnected gene regulatory networks driven by trans-eQTLs with small effects in disease-relevant cells and tissues^121,122. This model and the systems genetics analyses rely strongly on the assumption that most organismal trait QTLs correspond to eQTLs and that variation in gene expression in relevant tissues is pleiotropically correlated with variation in organismal quantitative traits. These associations have not been observed in D. melanogaster, where organismal trait QTLs are not enriched for eQTLs and neither eQTLs nor gene expression levels are associated with quantitative traits more than expected by chance^123,124. This could be because sample sizes were small, because gene expression was profiled in whole animals and not relevant tissues, or because $LD$ decays rapidly with physical distance in D. melanogaster, giving greater mapping precision than for humans and thus separating QTLs from eQTLs. More recently, human studies that fine-mapped QTLs and eQTLs showed that the overlap between QTLs and eQTLs is much smaller than previously thought^125–127. Furthermore, formal tests show that only 11% of disease heritability is mediated by levels of gene expression¹²⁸. It is likely that assays of baseline gene expression from bulk tissues described above are not as relevant to disease status as are eQTLs inferred from single cell expression data¹²⁹.

Pleiotropy and evolution

A major focus of evolutionary quantitative genetics is to understand the mechanisms by which genetic variation for quantitative traits is maintained, which depends on the relationship between the trait and fitness. Most quantitative traits are thought to be under stabilizing natural selection, whereby intermediate phenotypes have the highest fitness and extreme phenotypes are deleterious². Quantitative traits that are fitness components are subject to directional natural selection for trait phenotypes associated with increased fitness, and purifying natural selection for trait phenotypes that decrease fitness. Neutral quantitative traits are those for which there is no association between trait values and fitness. It is exceedingly difficult to quantify fitness. However, both purifying and stabilizing selection cause a negative correlation between the effect size of variants associated with the trait and their minor allele frequency. This phenomenon is a hallmark of association studies in humans^130,131 and model organisms⁶², suggesting that most quantitative traits are under natural selection and not neutral. Thus, there is pleiotropy between effects on quantitative traits and fitness.

Stabilizing, directional and purifying selection reduce genetic variation; therefore, models in which loss of genetic variation from selection are balanced by a gain of genetic variation from the input of new spontaneous mutations (mutation-selection balance, MSB) have been explored. Early MSB models considered that stabilizing selection is directly on the trait of interest (‘real’ stabilizing selection)¹³². However, these models cannot be applied to many independent traits without incurring significant genetic load¹³³, and they assume many new mutations are beneficial. Models of ‘apparent’ stabilizing selection^133,134 explicitly invoke pleiotropic effects of new mutations on quantitative traits and fitness. These models assume all pleiotropic effects on other traits are subsumed into the fitness effect, that mutations have a bivariate distribution of effects on both the trait and fitness, and that trait effects can be positive or negative, but fitness effects are always deleterious. The appearance of stabilizing selection is generated because extreme phenotypes have more mutations. However, alleles maintained under an apparent stabilizing selection model have large effects on the quantitative trait and are only mildly deleterious. These early models made assumptions about numbers and allele frequencies of loci affecting quantitative traits and their relationship to fitness, which were unknown. A more recent model of MSB under stabilizing selection¹³⁵ explicitly accounts for the effective number of pleiotropic traits and shows that MSB can maintain genetic variation for quantitative traits for a range of minor allele frequencies.

Antagonistic pleiotropy (AP)¹² is a form of balancing selection that can maintain variation for life history traits. AP between variants with beneficial effects on fitness early in life but detrimental effects on fitness late in life will cause senescence because the force of natural selection declines with age^12,136. These arguments can be extended to variants that have AP effects in males and females, or between different macro-environments. AP will thus constrain response to natural selection while maintaining alleles at intermediate frequencies. AP is frequently observed in model organisms. In Escherichia coli, mutations in the hfq gene have AP effects on fitness under different growth rate conditions¹³⁷. In S. cerevisiae, 32 of 49 long-lived mutations tested had reduced fitness compared to wild type¹³⁸, and competitive fitness assays between the yeast deletion collection mutations and the wild type under six growth conditions uncovered substantial AP¹³⁹. The age-1 allele in C. elegans confers increased lifespan and resistance to pathogens and temperature stress relative to the wild type allele, but has AP effects on fertility, with reduced fertility early in life and increased fertility late in life relative to the wild type allele¹⁴⁰. In D. melanogaster, P-element mutations show AP across many traits (Figure 2). P-element mutations associated with increased lifespan have deleterious effects on resistance to starvation stress⁵⁴, and mutations and genetic constructs with large effects on lifespan are often sterile¹². Further, P-element mutations often exhibit AP between males and females^41–45. AP has been described for D. melanogaster natural polymorphisms associated with different quantitative traits^24,141 and for the same variants evaluated in different macro-environments¹⁴¹. In humans, there is emerging evidence for AP between alleles associated with protective effects on disease early in life and increased risk of disease late in life¹⁴², between alleles associated with early reproduction and late age disease and that are protective for one disease but risk factors for another disease^143,144.

Pleiotropy is critical in models of adaptation. If pleiotropy is universal such that most polymorphisms will have some pleiotropic effects¹⁴⁵ or that all polymorphisms affect all traits (the infinitesimal model carried to the extreme), then pleiotropy will constrain evolution because it becomes likely that a polymorphism will have a deleterious effect on at least one trait. Pleiotropy introduces a ‘cost of complexity’, such that new mutations are less likely to be beneficial in complex organisms than simple organisms, thus impeding evolutionary advances^146,147.

Epistasis

Epistasis was first described in the context of crosses between individuals that are heterozygous for large-effect alleles at two loci affecting the same trait^148,149. In such crosses, a departure of the observed phenotypic ratios from those expected from segregation of unlinked genotypes infers the presence of epistasis (Figure 4a,b), which can mask the expected phenotype or result in a new phenotype. Epistasis between polymorphisms with large effects has been utilized to infer the order of genes in biochemical pathways and gene-gene interaction networks in developmental pathways. For quantitative traits, epistasis is generalized to refer to any non-additive interaction between two loci affecting the same trait¹ (that is, the effects of the two-locus genotypes cannot be predicted from the average effects of each locus separately) (Box 2; Figure 4). Epistasis causes context-specific effects, such that the additive effect of one locus depends on the genotype of the other locus. The effect of the interacting locus can change the magnitude and/or the direction of the additive effect of the focal locus on the trait¹⁵⁰ (Figure 4c,d). Epistatic interactions can be ‘suppressing’, where the effect of the double homozygote genotype is less than expected given the effects of the two single homozygote genotypes (sometimes called ‘less than additive’); or ‘enhancing’, where the effect of the double homozygote genotype is greater than expected given the effects of the two single homozygote genotypes (sometimes called ‘more than additive’). Knowledge of epistatic interactions is critical for predicting quantitative trait phenotypes from individual genotypes with implications for precision medicine and agriculture^16,151–154.

Figure 4|. Epistasis for Mendelian and quantitative trait loci.

a, Phenotypes and phenotypic ratios for two Mendelian loci (A, B), each with two alleles (A₁, A₂, B₁, B₂), when the A₁ and B₁ alleles are dominant and there is no epistasis. The nine genotypes and their expected Mendelian segregation ratios from crossing two A₁A₂B₁B₂ individuals (9:3:3:1) are given for each of the one- and two-locus genotypes in parentheses. b, The same nine two-locus genotypes when there is recessive epistasis. Rather than the expected ratio, the phenotypes are present in a 9:3:4 ratio for blue, red and black, respectively. The B₂B₂ genotype is epistatic to all genotypes at the A locus. c-d, Examples of epistasis for a quantitative trait. In each panel, the phenotype of the quantitative trait (y-axis) is plotted against the three genotypes at the A locus genotype (x-axis), separately for the B₁B₁ (blue), B₁B₂ (red) and B₂B₂ (black) genotypes. c, Variance epistasis: the difference between the slope gradients shows that the additive effect at the A locus is greater in the B₁B₁ genetic background than in the B₂B₂ genetic background. There is no dominance since the mean phenotype of the A₁A₂ genotype is the same as the average of the A₁A₁ and A₂A₂ genotypes for each of the B locus genotypes. d, Sign epistasis: the difference in the direction of the slopes shows that the additive effect of the A locus changes sign between the B₁B₁ and B₂B₂ genetic backgrounds.

Box 2 |. Effects and Variance Components.

For two loci (A and B) affecting the same quantitative trait, the effect of any two-locus genotype can be written as the sum of the additive ($a_A$ and $a_B$) and dominance ($d_A$ and $d_B$) effects of the constituent genotypes, and the epistatic effects ($i$) from any interaction between genotypes (see table). These effects can be estimated from knowledge of the mean phenotype of a quantitative trait for individuals in the population of each of the nine causal two-locus genotypes.

Genotype (frequency)	B1B1 (${\mathit{p}}_{\mathit{B}}^2$)	B1B2 ($2{\mathit{p}}_{\mathit{B}}{\mathit{q}}_{\mathit{B}}$)	B2B2 (${\mathit{q}}_{\mathit{B}}^2$)
A1A1 ($p_A^2$)	$a_A+a_B+i_{A1A1B1B1}$ ($p_A^2{p}_B^2$)	$a_A+d_B+i_{A1A1B1B2}$ ($p_A^{2}2p_B{q}_B$)	$a_A-a_B+i_{A1A1B2B2}$ ($p_A^2{q}_B^2$)
A1A2 ($2p_A{q}_A$)	$d_A+a_B+i_{A1A2B1B1}$ ($2p_A{q}_A{p}_B^2$)	$d_A+d_B+i_{A1A2B1B2}$ ($2p_A{q}_{A}2p_B{q}_B$)	$d_A-a_B+i_{A1A2B2B2}$ ($2p_A{q}_A{q}_B^2$)
A2A2 ($q_A^2$)	${-a}_A+a_B+i_{A2A2B1B1}$ ($q_A^2{p}_B^2$)	${-a}_A+d_B+i_{A2A2B1B2}$ ($q_A^{2}2p_B{q}_B$)	${-a}_A-a_B+i_{A2A2B2B2}$ ($q_A^2{q}_B^2$)

These effects cannot be directly estimated in a random mating population for which we do not have polymorphic molecular marker information to distinguish effects at each of the many loci affecting the trait. However, the total genetic variance (${\sigma }_G^2$) can be partitioned into additive (${\sigma }_A^2$), dominance (${\sigma }_D^2$) and epistatic (${\sigma }_I^2$) variance components. Any population variance is defined as the mean of the squared deviations from the mean. The population mean for two loci in a randomly mating population is obtained by multiplying the effects for each two locus genotypes by their allele frequency and summing over all genotypes. The population mean for two unlinked loci $={\mu }_{GAB}=a_A\left(p_A-q_A\right)+2d_A{p}_A{q}_A+a_B\left(p_B-q_B\right)+2d_B{p}_B{q}_B+i_{\dots .},$ where $i_{\dots .}$ Is the population average epistatic interaction obtained by multiplying the frequency of each genotype by its corresponding epistatic effect and summing over all genotypes¹⁷⁸. The average effects of each locus (${\alpha }_{A1},{\alpha }_{A2},{\alpha }_{B1}{\alpha }_{B2}$) are computed in the same manner as the single locus average effects (Box 1). For example, ${\alpha }_{A1}=q_A[a_A+d_A\left(q_A-p_A\right)]+(p_A{i}_{A1A1..}+q_A{i}_{A1A2..}-i_{\dots .})$ and ${\alpha }_{A2}={-p}_A[a_A+d_A\left(q_A-p_A\right)]+\left(p_A{i}_{A1A2..}+q_A{i}_{A2A2..}-i_{\dots .}\right)$ (Ref. 178). The expressions for ${\alpha }_{B1}$ and ${\alpha }_{B2}$ take the same form. Additive variance (${\sigma }_A^2$) is the variance of breeding values, where the breeding value for each genotype is the sum of the average effects of the alleles it carries. The breeding value for each of the nine two-locus genotypes includes the allele frequencies of each locus, values of $a$ and $d$ for each locus, and the population average epistatic interaction. Therefore, ${\sigma }_A^2$ also includes these terms. The dominance variance (${\sigma }_D^2$) includes allele frequencies and terms for $d$ for each locus and average values of $i$, and the epistatic variance (${\sigma }_I^2$) includes allele frequencies and genotype-specific values of $i$ (see Ref. 176 for a full explanation).

One consequence of defining genetic variance components in terms of deviations from the population mean is that additive, dominance and epistatic variance components are not the same as additive, dominance and epistatic effects. A second consequence is that variance components will vary in populations with different allele frequencies. Although we want to know the actual effects, which are independent of allele frequencies, the absence of molecular marker information requires that inferences about genetic variation are drawn from the variance caused by the alleles, thereby confounding effects and frequencies.

Quantifying Epistasis

Quantifying epistasis from induced mutations.

Epistatic interactions for quantitative traits can be assessed directly using large collections of mutations or RNAi constructs and wild type alleles at two (or more) loci that have been generated in a common homozygous genetic background; the only genetic variation is therefore at the loci of interest. Each test for digenic epistasis requires all nine two-locus genotypes (Figure 5a) and estimates of quantitative trait phenotypes for each. A two- way analysis of variance is then performed to estimate the main effects of Genotype 1, Genotype 2, and the Genotype 1 $\times$ Genotype 2 interaction. A significant interaction term indicates the presence of epistasis. These data can then be used to estimate additive ($a$) and dominance ($d$) effects for each locus and the epistatic interaction ($i$) for each genotype (Figure 5a). If only homozygous effects are considered, these analyses are performed for the four double homozygous genotypes. Such studies were pioneered at a genome-wide scale in S. cerevisiae, where the generation of haploid double mutations can be automated and high-throughput assays for growth rate, a proxy for fitness, are possible^155–157. Since generating and evaluating all possible 11.5 million two-locus epistatic interactions ($~n^2$ pairs for $n$ mutations) from the 4,800 viable haploid yeast deletions is experimentally intractable, these studies chose a set of query mutations belonging to a functional category of interest to screen the entire set of deletion mutations. Digenic epistatic interactions observed in yeast have scale-free interaction network topologies that tend to connect genes with similar biological functions. Screens for trigenic epistatic interactions in yeast found that these higher order interactions occurred between functionally related as well as more distantly related functional categories, and that the trigenic interaction network was 100 times larger than the global digenic network¹⁵⁸. Global interaction networks with similar properties were found using cell-based RNAi screens in C. elegans^159,160, D. melanogaster¹⁶¹ and mammalian¹⁶² and human¹⁶³ cell lines.

Figure 5|. Epistatic effects and epistatic variance.

An example of epistasis between Quantitative Trait Loci (QTLs) is shown for hatch weight of chickens in an F₂ population derived from a cross between the White Leghorn domestic chicken and the wild red jungle fowl¹⁹². a, The plot shows the mean hatch weights for each of the nine two-locus genotypes. Epistasis is evident from the changes in direction and magnitude of the effects of the A locus depending on the genotype of the B locus. The table shows estimates of the additive, dominance and epistatic effects ($a,d,i$) and the total genotypic value for each genotype, using these means. Note that some dominance and epistatic effects are much greater than the additive effects. (b-d) Although some dominance and epistatic effects are larger than additive effects, the magnitude of the additive genetic variance (b) is greater than that of the dominance variance (c) or epistatic variance (d) for most allele frequencies. The effects ($a,d,i$) remain constant regardless of allele frequencies. However, the population variance components change as allele frequencies change, which is why low levels of epistatic variance does not mean epistasis can be ignored, and why no inferences about genetic architecture in terms of effects can be made from estimates of variance components.

Epistatic interactions are also observed in more focused screens to identify epistatic modifiers of known genes or processes. Examples include epistatic interactions among tubulin mutations affecting growth of neurites in C. elegans¹⁶⁴; epistatic modifiers of the Apc^Min colorectal cancer model¹⁶⁵ and retinal dysplasia model¹⁶⁶ in mice; epistatic interactions among D. melanogaster P-element mutations affecting intermediary metabolism¹⁶⁷, aggressive¹⁶⁸ and locomotor⁴² behaviour, and lifespan⁵⁴; and epistasis between A. thaliana transcription factors affecting growth and defense¹⁶⁹. Applications of advanced gene editing methods reveal epistasis between mutations within single genes^170–172.

Quantifying epistasis from natural variation.

Classical quantitative genetics theory^1,2 enables us to make inferences about the fraction of the phenotypic variance for a quantitative trait in a population that is attributable to genetic variance and to environmental variance. In the absence of detailed knowledge of the additive ($a$), dominance ($d$) and epistatic ($i$) effects for each of $n$ genotyped loci causing genetic variation for the trait in the population, the theory splits the genetic variance into additive genetic variance [G] (${\sigma }_A^2$), dominance genetic variance (${\sigma }_D^2$) and epistatic (${\sigma }_I^2$) genetic variance components, the magnitude of each of which depends on $a,d$ and/or $i$ and allele frequencies (Box 2). Notably, $a,d$ and $i$ effects do not translate directly to ${\sigma }_A^2,{\sigma }_D^2$ and ${\sigma }_I^2$ variance components^{2,3,173–175}: classical quantitative genetics theory confounds effects and allele frequencies such that inferences about the former cannot be made from estimates of the latter (Box 2). Thus, the magnitude of epistatic effects (sometimes called physiological or biological epistasis)^176,177 cannot be inferred from epistatic variance component estimates (sometimes called statistical epistasis)^176,177 – it is possible to have large epistatic effects but undetectable epistatic variance when minor allele frequencies are low^173–175 (Figure 5).

All variance components depend on allele frequencies at the loci affecting the trait and are usually greatest when alleles are at intermediate frequencies. Two populations with the same estimates of $a,d$ and $i$ for all loci affecting a quantitative trait will have different variance components (and mean trait values) when the frequency of the minor allele at all loci is low than when both alleles at all loci are at intermediate frequencies^{2,3,173–175} (Figure 5). Furthermore, genetic variance components are estimated in random mating populations by regressions or correlations of trait phenotypes between common relatives: offspring and their parents, full- and half-siblings, and, in humans, fraternal and identical twins^2,3. ${\sigma }_A^2$ has the largest contribution to genetic variance and components of ${\sigma }_I^2$ the smallest for all types of common relatives except monozygotic twins, for which all variance components contribute equally. There are more variance components contributing to the resemblance between relatives than can be estimated for any one type of common relatives; therefore, epistatic variance is generally assumed to be absent. Thus, in the presence of epistatic variance estimates of ${\sigma }_A^2$ are biased upwards by ${\sigma }_I^2$ for all types of common relatives, and markedly so for monozygotic twins.

Epistatic effects can be directly estimated between QTLs in linkage mapping populations and have been found in model organisms and agricultural crops. One of the first examples of pervasive epistasis was from crosses among genotypes in which short genomic regions from one species of tomato were introgressed into the homozygous genetic background of another tomato species¹⁷⁸. Approximately 30% of the tested QTL interactions showed less-than-additive epistasis, a phenomenon that was replicated in a larger study with introgressions of different tomato species¹⁷⁹. The first experiments to map QTLs in D. melanogaster using molecular markers also showed epistasis for numbers of sensory bristles on different body parts^180,181, which was surprising because these were considered to be quintessentially additive traits in flies based on variance component estimates. There are many other examples of epistasis between QTLs for organismal traits in yeast^182–187, nematode worms¹⁸⁸, D. melanogaster^189,190, mice¹⁹¹ and chickens^192,193. Epistasis is also common between QTLs affecting molecular quantitative traits in yeast¹⁹⁴ and A. thaliana^195,196. Incorporating QTL × QTL interactions improves phenotypic prediction in association mapping populations¹⁶. Epistasis between QTLs can be as large as the QTL main effects and can involve QTLs with no significant main effects. However, the studies described above used recombinant inbred lines derived from crosses of two parental strains, which maximizes the potential to detect epistatic interactions because allele frequencies at all polymorphic loci are 0.5. In humans, epistasis has been reported between candidate genes affecting susceptibility to diabetes^197,198 and inflammatory bowel disease¹⁹⁹.

Estimating epistatic effects in genome-wide association mapping studies is challenging. First, there are many more molecular polymorphisms to test for associations and pairwise interactions (in the order of 10⁶ and 10¹², respectively, in humans). Therefore, accounting for multiple tests using a Bonferroni correction means an interaction would need to have a P-value < 5 × 10⁻¹⁴ to be declared significant, so only very large epistatic effects can be detected. Second, epistasis cannot be evaluated if the minor allele frequency at both loci is low, because sufficient individuals that are homozygous for both rare alleles need to be present to completely specify the model. Third, the focal SNPs that tag an $LD$ block are not necessarily causal. The magnitude of the additive effect estimated by an associated SNP is smaller than that of the true SNP by an amount that depends on the $LD$ between the focal and true SNPs²⁰⁰; and any epistatic effects are even more seriously underestimated. Screening for epistatic interactions is not usually performed in human GWAS because of the low statistical power to detect them and the strong emphasis on variance explained by associated SNPs, rather than estimating additive, dominance and epistatic effects as is done in model organisms. Using the population definition of effects means that the ‘additive’ effect of SNPs is confounded with dominance and epistatic effects, and that epistatic variance is minimized by definition and is negligible when minor allele frequencies are low^{174,175,201,202}. However, the goals of precision medicine and precision agriculture are to predict individual phenotypes from their own genotypes, which require estimates of effects, not variance contributed, of SNPs and pairs of SNPs.

Methods to prioritize pairs of SNPs to evaluate for epistatic interactions should reduce the multiple testing penalty. In the presence of epistasis, the additive effect of a focal polymorphism will change when the frequency of the interacting polymorphism changes^14,203,204. This suggests a way to test for epistasis either by deliberately perturbing allele frequencies between two association mapping populations or by taking advantage of random allele frequency differentiation among closely related populations. Large, trait-specific epistatic interaction networks were identified in D. melanogaster^203,204 using the former approach. Most epistatic interactions in these studies^203,204 were such that the homozygotes for the two minor alleles were associated with the most extreme phenotype, with no phenotypic differences between the other two-locus genotypes. This suggests that screening for variance-QTLs (that is, SNPs for which there is a difference in variance of the trait between the genotypes) (Figure 6) may be a useful approach to identify SNPs that possibly interact with other SNPs in the genome, thus reducing the numbers of pairwise SNPs to test for association²⁰⁵. Screens for variance eQTLs affecting genome-wide gene expression have been successful in D. melanogaster¹²⁵ and humans^206,207, and variance eQTLs interacted epistatically with other eQTLs^125,207. Identifying pairs of SNPs with long-range $LD$ possibly due to epistatic selection²⁰⁸ is another strategy for reducing the number of tests for epistasis.

Figure 6 |. Variance Quantitative Trait Loci and epistasis.

a, Homozygous variants at a locus affecting the variance of a quantitative trait phenotype. The black dashed line connects the mean phenotype of the two genotypes, which are not significantly different. However, the variance among individuals with the GG genotype is greater than the variance among individuals with the CC genotype; this can be detected by an analysis of variance heterogeneity. b, Homozygous variants at a second locus are indicated by blue and red circles. The blue dashed line connects the means of the CCAA and GGAA genotypes, which are not significantly different. The red dashed line connects the means of the CCTT and GGTT genotypes, which are significantly different. The different slopes of these lines indicate epistasis. The TT and AA genotypes have the same mean phenotype in the CC genetic background, but different mean phenotypes in the GG genetic background. Performing association mapping analyses for heterogeneity of variance among genotypes at a focal locus can help prioritize variants to include in analyses of two-locus epistasis, thus reducing the multiple testing penalty incurred by genome-wide epistasis screens.

In contrast to the underestimation of epistatic effects in association mapping populations, epistasis is usually found when gene editing is used to engineer naturally occurring SNPs into a common genetic background. In yeast, the fitness effects of over 1,800 naturally polymorphic variants were assessed in four different genetic backgrounds²⁰⁹. A total of 24% of these SNPs only affected fitness in one genetic background, indicating epistasis. In human cells, individual and combinatorial editing of three genes showed strong epistatic interactions affecting cellular and transcriptomic phenotypes²¹⁰.

Quantifying epistasis from natural variation and induced mutations.

Another approach to reduce the multiple testing penalty for detecting epistasis is to screen genome-wide for interactions between a focal SNP or mutant allele and all other polymorphisms. Most rare human diseases have variable phenotypic manifestations of disease severity, age of onset and progression^211,212. In addition, population sequencing shows that unaffected individuals can have genotypes that are known to cause rare diseases^213,214. Moreover, polygenic background affects disease risk for heterozygous carriers of rare monogenic disease alleles in natural populations^215,216. This variation in penetrance and expressivity is likely attributable to epistasis. Identifying genetic modifiers of rare human diseases is challenging due to low statistical power to formally test for interactions with small numbers of patients but is important as modifier alleles that suppress the disease phenotype may lead to new therapeutic targets.

Epistatic interactions between mutations and genetic background are also observed in model organisms. Seven yeast deletion mutations had variable fitness effects when crossed to genotypes from a QTL mapping population²¹⁷, and evaluation of the effects of deletion mutations in four yeast genetic backgrounds showed that ~19% had background-dependent fitness effects²¹⁸. Similarly, there is considerable evidence for variable phenotypic effects of the same mutation in different D. melanogaster genetic backgrounds^15,219–221.

The DGRP and other D. melanogaster inbred lines with full genome sequences can be used to map naturally occurring epistatic modifiers of mutations. This can be done by crossing genotypes with a wild type or mutant allele for the focal polymorphism in otherwise identical genetic backgrounds to the DGRP lines, phenotyping the F₁ offspring for a relevant quantitative trait, and performing a GWAS on the difference in the trait mean between the wild type and mutant alleles^222,223. If the mutation or RNAi knockdown of the focal gene has an effect that lies well outside the range of natural variation, it is only necessary to cross the mutant allele to the DGRP lines and perform the GWAS analysis on the trait phenotype in the F₁ progeny^224–227. Genetic background effects are significant for all such studies published to date, reflecting the ubiquity of epistasis. If the focal mutation is in a D. melanogaster ortholog of a human gene associated with a rare disease, human orthologs of the D. melanogaster modifier genes can be tested for epistatic effects in humans.

Epistasis and evolution

There are many ways in which epistasis can contribute to evolution, including by maintaining genetic variation in natural populations, affecting long-term response to natural selection, reducing the burden of deleterious mutations, and promoting speciation^228,229. Suppressing epistasis, whereby naturally occurring variants ameliorate mutational effects, is often observed in natural populations^{15,63,211–227}. Suppressing epistasis buffers the effects of new mutations and causes genetic canalization, whereby cryptic genetic variation¹⁵ persists in natural populations that can be revealed in the presence of a de-canalizing mutation^15,230. This gives the population the ability to evolve under circumstances in which the previously neutral genetic variation becomes adaptive or deleterious^{219,231–233}. Epistatic variance depends on allele frequencies, and natural selection changes allele frequencies. It is therefore possible that epistatic variance caused by alleles at intermediate frequency in an equilibrium population can become additive genetic variance as allele frequencies change in a population under selection, thereby accelerating the selection response in later generations^234–237. Epistatic variance for fitness is also the basis of Wright’s rugged adaptive landscapes that are a central tenet of his shifting balance theory of evolution²³⁸ [G]. Epistasis is the foundation for Dobzhansky-Muller incompatibilities required for speciation^239,240, whereby alleles that are neutral or beneficial in the genetic backgrounds of two genetically divergent populations are highly deleterious in the hybrids between the populations.

Pleiotropy and Epistasis

Pleiotropy and epistasis are orthogonal concepts. However, genetically correlated gene expression networks and epistatic genetic interaction networks both have similar scale free network architectures, raising the possibility that pleiotropy and epistasis could be functionally related. For example, if epistatic interactions between mutations affect one trait in a model organism, we can determine experimentally whether there is epistasis between the mutations for other traits that show pleiotropy with the focal trait (epistatic pleiotropy). Alternatively, if we know the pleiotropic effects of a single mutation on organismal phenotypes and genome-wide gene expression (or other genetically correlated molecular networks), we can query whether mutations in the genes encoding the gene expression traits exhibit epistasis for the organismal trait(s) (pleiotropic epistasis).

Studies in D. melanogaster show that there may be reciprocal relationships between pleiotropy and epistasis. Single P-element mutations affecting olfactory behavior and fitness-related traits have pervasive pleiotropic effects on genome-wide gene expression, and mutations in genes encoding the pleiotropic gene expression traits do interact epistatically with the focal P-element mutations to affect the organismal traits^53,241. Furthermore, P-element mutations that exhibit epistasis for locomotor⁴² or aggressive¹⁶⁸ behavior also exhibit epistasis for brain morphology^42,168 and genome-wide gene expression¹⁶⁸. The epistatic networks are distinct but partially overlapping for the different pleiotropic traits.

Combined Analysis of Pleiotropy and Epistasis (CAPE) is a formal method to infer and interpret epistatic interactions among mutations that utilizes the pleiotropic effects of mutations on multiple organismal traits and gene expression traits^242,243. Application of CAPE to epistatic mutations affecting yeast mating and pheromone response and genome wide gene expression identified co-regulated transcriptional modules in common between traits and specific to each trait²⁴². Application of CAPE to RNAi single and double knockdown constructs for 93 D. melanogaster genes with pleiotropic effects on cell number, nuclear area and nuclear intensity identified enhancing and suppressing epistatic interactions that were consistent across the three phenotypes and that were not found by analysis of single phenotypes²⁴³. CAPE has also been used to derive an interaction network of module QTLs derived from genetically correlated gene expression traits in mouse kidney affected by trans-eQTLs from an F₂ linkage mapping population²⁴⁴ and to infer epistatic interactions between QTLs in a multi-parental mapping population of mice affecting pleiotropic organismal metabolic traits and liver gene expression²⁴⁵.

Another way in which pleiotropy and epistasis can be functionally related is to identify QTLs for which the correlation between two traits varies between the genotypes of a marker locus^246,247. Such relationship QTLs (rQTLs) exhibit genetic variation in pleiotropy, possibly caused by epistasis between the rQTLs and other loci. Epistatic interactions with rQTLs have been observed for mouse morphological traits^246,247 and in humans for metabolic traits and coronary heart disease associated with variation at the APOE locus²⁴⁸. Identification of rQTLs in human GWAS may increase the power to detect epistatic interactions.

Practical implications of pleiotropy and epistasis

Observations of pervasive pleiotropy emphasize the complexity of the genotype-phenotype map and highlight the importance of quantifying genetic variation for high-dimensional organismal phenotypes (phenomes) to fully understand pleiotropy²⁴⁹. Phenomes include molecular traits such as RNA abundance, chromatin state, protein abundance and isoforms and metabolites; organismal-level traits quantifying aspects of physiology, morphology (including high-resolution imaging), behaviour, and fitness-related traits; and individual microbiomes. Phenomes are not static, so quantification must account for variation between cells and across development in a range of environments. Plant²⁵⁰ and animal²⁵¹ breeders view the future of crop and animal improvement by integrating increasingly complex phenotypes in breeding programs. Crop and animal improvement programs may also transfer favorable alleles from one genotype to another. This could have unintended effects if these alleles have deleterious pleiotropic effects on other phenotypes.

The full extent of pleiotropy is unknown in humans and will require systematic integration of multi-omics, lifestyle, biomedical imaging, clinical measurements and electronic health records on a large scale and over time²⁵². Pleiotropic relationships can implicate predictive biomarkers of disease, leading to better disease prevention and diagnosis and clinical tests. Shared genetic etiology between diseases can indicate that both diseases may respond similarly to drug treatments. However, the converse is also possible if the correlation between diseases is negative: then drugs may have beneficial effects for one disease but detrimental effects for the other¹⁹.

A major goal of precision agriculture and precision medicine is accurate prediction of phenotypes from genotypes. Additive models will provide good prediction accuracy in most cases. For example, prediction accuracy of an additive model for human height is very high²⁵³, and application of additive models in animal and plant breeding are responsible for improving production trait phenotypes in agricultural species. Therefore, the additive model dominates empirical breeding programs and human complex trait genetics. However, epistatic effects are found in model organisms with the experimental tractability to detect genetic interactions when they are present. Epistasis is also thought to be the mechanism accounting for heterogeneous clinical symptoms of patients with the same mutation for rare human diseases. Knowledge of epistatic interactions can be important in agricultural breeding programs designed to simultaneously introgress multiple loci with individually favorable effects into the same genetic background. These efforts will not have the desired outcome if the loci exhibit suppressing epistasis^178,179. Simulations show that using an additive prediction model when there is widespread epistasis will have low accuracy, while accounting for epistasis in the prediction model greatly increases accuracy²⁵⁴. To illustrate this point, consider two loci (A, B) each with two alleles (A₁, A₂, B₁, B₂) and that only the A₂A₂B₂B₂ genotype causes a disease. If A₂ and B₂ are rare, the population average effects of these loci will be small, the genetic variance will be predominantly additive, and the A and B loci will not predict disease liability. However, if the true effects ($a,d,i$) were used, the effect of the A₂A₂B₂B₂ genotype will be large and predictive ability will be excellent²⁵⁵.

Conclusions and perspectives

Pleiotropy and epistasis are fundamental features of the genetic architecture of quantitative traits. Pleiotropy is pervasive in model organisms and humans for organismal level quantitative traits and highly dimensional molecular traits, such as genome-wide levels of gene expression traits, metabolites, and proteins. The molecular traits cluster into distinct pleiotropic modules enriched for common functional annotations. The pleiotropic associations between mutations and naturally segregating molecular variants with these modules provide the molecular basis of pleiotropy. Deep phenotyping of the same molecular polymorphisms can reveal unexpected shared genetic bases of different common diseases and quantitative traits. Pleiotropic effects of new mutations on quantitative traits and fitness can explain the maintenance of quantitative genetic variation by mutation-selection balance, and antagonistic pleiotropy between fitness components can constrain selection response and maintain genetic variation for fitness.

Epistasis is an important feature of the genetic architecture of quantitative traits in model organisms but there is little evidence for epistasis for complex traits in human populations. This could be attributable to the ability to estimate epistatic effects directly in model organisms and the difficulty in doing so in humans; and/or to the different parameterizations of epistasis used in humans (variance components) and model organisms (effects). The nature of epistatic interactions inferred from model organism studies suggest several future avenues to explore to increase the power to detect epistasis affecting human quantitative traits. These include screening for epistatic effects between variants in genes with similar biological functions associated with the trait; assessing heterogeneity of variance between SNP genotypes to identify focal variants for subsequent tests of epistatic interactions; and leveraging the functional relationship between pleiotropy and epistasis.

Glossary Terms

Genetic architecture

The loci, genomic locations and additive, dominance, epistatic and pleiotropic effects and allele frequencies of causal variants affecting a quantitative trait

Additive effect

one half of the difference in mean phenotypes associated with homozygous genotypes at a bi-allelic locus affecting a quantitative trait

Dominance effect

the difference between the mean phenotype of the heterozygous genotype and the mean phenotype of the two homozygous genotypes at a bi-allelic locus affecting a quantitative trait

Haplotype

Alleles at different loci on a chromosome that tend to be inherited together

P-element

A Drosophila transposable element that can be mobilized to new genomic locations by simple genetic crosses

Heritability

The ratio of the variance of additive genetic variance (narrow sense heritability) or the total genetic variance (broad sense heritability) to the total phenotypic variance

Deoxyribonuclease I (DNase I) hypersensitivity sites

accessible nucleosome-free chromatin regions sensitive to cleavage by the DNase I enzyme; these regions are inferred to be involved in gene regulation

Additive genetic variance

The variance of breeding values

Fitness

The contribution of offspring to the next generation, or reproductive success (viability and fertility) of an individual

Shifting balance theory of evolution

A model of evolution proposed by Sewell Wright that assumes widespread epistasis for fitness, natural selection, genetic drift and differentiation among subpopulations, and migration