Identifying quantitative trait locus by genetic background interactions in association studies

Abstract

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

Figure 1.—

Power to detect epistatic variance plotted against the simulated QTL minor allele frequency. Power was estimated in bins of 400 simulation runs with consecutive QTL minor allele frequencies.

Figure 2.—

Squared error of the estimated epistatic variance plotted against the simulated QTL minor allele frequency. Each point represents one simulation run. The black line is the overall mean squared error.

Figure 3.—

Estimated epistatic variance plotted against simulated epistatic variance for setting 8. Simulated epistatic variance depended on stochastic simulation. The black line shows equal estimated and simulated variances. The gray line is the linear regression of estimated on simulated variance.

Figure 4.—

True τ₁ deviation from model (10) plotted against the deviation predicted by the mixed model analysis from a single setting 2 simulation. (A) Plot for individuals homozygous at the marked QTL. To increase graph legibility, τ₁ has been increased and decreased slightly for Q₁Q₁ and Q₂Q₂ individuals, respectively. Note that τ₁ can be predicted even for individuals who do not carry the Q₁ allele. (B) Plot for individuals heterozygous at the marked QTL.