Epistasis: Obstacle or Advantage for Mapping Complex Traits? Koen J. F. Verhoeven1, George Casella2, Lauren M. McIntyre3* 1 Netherlands Institute of Ecology (NIOO-KNAW), Department of Terrestrial Ecology, Heteren, The Netherlands, 2 Department of Statistics and Genetics Institute, University of Florida, Gainesville, Florida, United States of America, 3 Genetics Institute, Department of Molecular Genetics and Microbiology and Department of Statistics, University of Florida, Gainesville, Florida, United States of America Abstract Identification of genetic loci in complex traits has focused largely on one-dimensional genome scans to search for associations between single markers and the phenotype. There is mounting evidence that locus interactions, or epistasis, are a crucial component of the genetic architecture of biologically relevant traits. However, epistasis is often viewed as a nuisance factor that reduces power for locus detection. Counter to expectations, recent work shows that fitting full models, instead of testing marker main effect and interaction components separately, in exhaustive multi-locus genome scans can have higher power to detect loci when epistasis is present than single-locus scans, and improvement that comes despite a much larger multiple testing alpha-adjustment in such searches. We demonstrate, both theoretically and via simulation, that the expected power to detect loci when fitting full models is often larger when these loci act epistatically than when they act additively. Additionally, we show that the power for single locus detection may be improved in cases of epistasis compared to the additive model. Our exploration of a two step model selection procedure shows that identifying the true model is difficult. However, this difficulty is certainly not exacerbated by the presence of epistasis, on the contrary, in some cases the presence of epistasis can aid in model selection. The impact of allele frequencies on both power and model selection is dramatic. Citation: Verhoeven KJF, Casella G, McIntyre LM (2010) Epistasis: Obstacle or Advantage for Mapping Complex Traits? PLoS ONE 5(8): e12264. doi:10.1371/ journal.pone.0012264 Editor: Joel S. Bader, Johns Hopkins University, United States of America Received April 15, 2009; Accepted April 19, 2010; Published August 26, 2010 Copyright: ß 2010 Verhoeven et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: The authors gratefully acknowledge support from National Science Foundation Division of Biological Sciences 0821954, National Institutes of Health (NIH) 1R01GM077618 and NIH 1R01GM081704. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: [email protected] Introduction linkage methods [e.g. 16,17,18,19] and some population-based methods [e.g. 20,21] use the knowledge of relationships and As technology becomes more cost effective, the amount and transmission of alleles among family members combined with scale of data available for answering fundamental questions about marker-phenotype tests to infer linkage and/or association. As the underlying genetic contribution to phenotypic outcomes of with QTL, the choice of test statistics and approaches is the subject interest has dramatically increased. Genetic markers, particularly of much research and discussion. biallelic single nucleotide polymorphisms (SNPs), have been Association mapping is the testing of the null hypothesis that a developed for a wide variety of organisms [1], and current SNP genetic marker is not associated with a phenotype of interest in an discovery techniques and reduced genotyping costs make it feasible ‘unstructured’ population or rather a population without explicit to score tens of thousands of markers in many individuals [2,3,4,5]. information on pedigree relations [22], although accounting for The plethora of data has sparked interest in developing relatedness among members of the population due to population methodology for hypothesis testing for association mapping. substructuring has been shown to be critical [e.g. 23,24]. The Testing for marker-phenotype associations is done within the development of large numbers of SNP markers has made context of a specific experimental design [e.g. 6,7,8]. The population based genome-wide association testing increasingly experimental design controls the structure of the population under feasible [25,26,27,28]. consideration and is therefore a critical component to account for Empirical studies suggest a prominent role for gene interactions in subsequent modeling and testing. If the population is (epistasis) in the genetic control of many traits [e.g. 29,30,31, constructed experimentally, allele frequencies are held constant 32,33,34,35,36]. The most well understood genetic models for across loci, and are often equal. When the genetic structure of the gene interactions are described in terms of qualitative (Mendelian) population is under experimental control testing marker-pheno- rather than quantitative traits [37]. In these qualitative trait type association is often referred to as QTL mapping [7]. In QTL models gene interactions typically result in masking or covering mapping, the issue of which test statistics to use to detect main the effect of some alleles. For example, in an additive model with effects has been discussed quite broadly [e.g. 9,10,11,12,13,14,15]. two biallelic loci there are nine distinct genotypes. In a recessive Such one-dimensional genome scans have been enormously epistasis model for a qualitative trait, all effects having the popular resulting in more than 5,000 publications. Pedigree-based combination aa for one locus (regardless of the alleles at another PLoS ONE | www.plosone.org 1 August 2010 | Volume 5 | Issue 8 | e12264 Epistasis Increases Power locus) have a common outcome. In a quantitative trait model, this [47] and Evans et al. [39] showed that fitting full models in two-locus corresponds to an equality of means. In this study a series of genome scans often yields higher detection power than single-locus epistatic cases that are quantitative in nature but based upon such scans when epistasis is in fact present. This was despite a dramatically biological or molecular definitions of epistasis are considered. lower significance threshold for individual tests after multiple testing Some of these molecular patterns of epistasis have been observed alpha adjustment in the pairwise search. In a QTL mapping context for quantitative traits [e.g. 34]. They are depicted in Figure 1 (b–f). for binary traits, Coffman et al. [46] evaluated testing full models and We also consider the additive model (Figure 1a). How these forms showed via simulation that in this context QTL detection power is of molecular epistasis translate into statistical epistasis, i.e. the larger in the presence of epistasis compared to purely additive QTL. deviation from additivity in a statistical linear model, depends on In this paper, the impacts of molecular forms of epistasis on allele frequencies at the locus of interest [38,39]. For instance, in statistical power are explored in an association mapping context. case f (Figure 1f) interactions occur in the absence of main effects Cases where two loci are jointly responsible for a fixed range of when allele frequencies are equal (0.5), but marginal effects arise phenotypic variation are studied. The impact of the genetic model and can be picked up in one-dimensional genome scans when (additive or epistatic) on locus detection power is studied. Using a allele frequencies are different. Thus, the term epistasis has linear models framework, the F test of the full model and the F biological interpretations that can be quite distinct from the test of the marginal effects are evaluated. The power of the F test statistical interaction alone [40,41]. In addition, typical gene is shown to be larger under cases of molecular epistasis compared interaction effects that have been described will result in a subset of to the additive model. Molecular epistasis also changes the possible statistical interactions [40]. marginal effects and the power for single locus test of association. There is debate about how to model and test for both main These expectations are derived under simple assumptions and for effects and interactions when epistasis is present [e.g. 32,39, equal allele frequencies and fully balanced data. As association 42,43,44,45,46,47,48]. In the context of QTL mapping, consid- mapping data are not likely to be balanced, empirical estimates for eration of molecular interactions among loci has led to the power of association tests under various conditions are derived constructing models with multiple markers and, using the factor via simulation. As predicted, the presence of molecular epistasis effects construction, testing the main effects and the interaction does, in many cases, have a positive effect on power. When allele effects separately [e.g. 43,49,50,51,52]. The power for the frequencies are disparate (that is, when one of the alleles occurs at detection of the interaction effect alone in the factor effects model low frequency) as in many association mapping contexts, epistasis can be quite small especially after accounting