Detection of SNP epistasis effects of quantitative traits using an extended Kempthorne model

Abstract

The existence of a large number of single nucleotide polymorphisms (SNPs) provides opportunities and challenges to screen DNA variations affecting complex traits using a candidate gene analysis. In this article, four types of epistasis effects of two candidate gene SNPs with Hardy-Weinberg disequilibrium (HWD) and linkage disequilibrium (LD) are considered: additive ϫ additive, additive ϫ dominance, dominance ϫ additive, and dominance ϫ dominance. The Kempthorne genetic model was chosen for its appealing genetic interpretations of the epistasis effects. The method in this study consists of extension of Kempthorne's definitions of 35 individual genetic effects to allow HWD and LD, genetic contrasts of the 35 extended individual genetic effects to define the 4 epistasis effects, and a linear model method for testing epistasis effects. Formulas to predict statistical power (as a function of contrast heritability, sample size, and type I error) and sample size (as a function of contrast heritability, type I error, and type II error) for detecting each epistasis effect were derived, and the theoretical predictions agreed well with simulation studies. The accuracy in estimating each epistasis effect and rates of false positives in the absence of all or three epistasis effects were evaluated using simulations. The method for epistasis testing can be a useful tool to understand the exact mode of epistasis, to assemble genome-wide SNPs into an epistasis network, and to assemble all SNP effects affecting a phenotype using pairwise epistasis tests.single nucleotide polymorphism; quantitative trait; linkage disequilibrium; Hardy-Weinberg disequilibrium THE SIGNIFICANCE OF EPISTASIS in complex traits has been well recognized (3,12,16,17). It has been hypothesized that epistasis is ubiquitous in determining susceptibility to common human diseases. Observations supporting this hypothesis include deviations from Mendelian ratios, molecular interactions in gene regulation and biochemical and metabolic systems, nonrepeatable positive effects of single polymorphisms, and gene interaction effects commonly found when properly investigated (16). Large epistasis networks found in yeast (19, 21) also point to the ubiquitous nature of epistasis. The presence of a large number of single nucleotide polymorphisms (SNPs) provides opportunities and challenges to identify DNA variations associated with complex traits using SNPs as candidate genes. A number of studies on SNP-disease association have been reported (2,7,8,20,24), but most current candidate gene studies focus on single gene effects. Ongoing studies of geneotyping up to 500,000 SNPs on 2,000 individuals have been reported (1). Such large-scale SNP studies would be capable of detecting certain epistasis effects. 1For two bi-allelic genes unaffected by the environment, a total of 512 disease models are possible, but the number of nonredundant models is in the range of 50 -102 (12). For two bi-allelic genes such as two SNP loci with quantitative measures, epistasis effects are typica...

Epistasis Between Calpain 1 and Its Inhibitor Calpastatin Within Breeds of Cattle

“…This may generate samples that exhibit HWD and LD between unlinked loci, so the methods that are used should either account for this or should be unaffected by population structure, or the data should be shown to be in HWE and LE. Nevertheless, methods that assume the data are in HWE and LE are only under a large disadvantage for samples of N , 200 in detecting epistasis, and spurious detection of epistasis with incorrect models will be primarily of the additive by additive component (Mao et al 2006).…”

“…Several alternative approaches have been proposed either to estimate or to describe epistasis for quantitative variation (Cockerham 1954;Kempthorne 1954;Cheverud and Routman 1995;Hansen and Wagner 2001;Barton and Turelli 2004;Zeng et al 2005;Mao et al 2006) using different mathematical symbols and fundamental assumptions. The methods of Cockerham and Kempthorne were independent attempts to partition the epistasis defined by Fisher in 1918 while that of Cheverud and Routman was an attempt at defining epistasis without explicit use of allele frequencies.…”

Estimation of epistasis in doubled haploid barley populations considering interactions between all possible marker pairs

“…With increasing evidence supporting the claim that epistatic interactions are usually involved in the genetic variation of complex traits (Mao et al 2006;Tabanao and Bernardo 2007), several complicated mapping models were developed to analyze epistatic effects: expanded composite interval mapping (CIM) to multiple interval mapping (Kao et al 1999), mixed linear model based CIM (Wang et al 1999), Bayesian approach (Yang et al 2007;Yi et al 2007), and weighted multiple linear regression (Bocianowski 2012c). Jannink and Jansen (2001) suggested mapping QTLs with epistasis between QTLs and backgrounds using one-dimensional genome search.…”

Quantitative genetics theory for genomic selection and efficiency of genotypic value prediction in open-pollinated populations

“…We should also highlight the fact that extension of the Kempthorne's model for SNP effects (Mao et al, 2006) is a third alternative model for genomic prediction. However, compared to previous models, Kempthorne's model is much less parsimonious.…”