Estimating genetic variance contributed by a quantitative trait locus: removing nuisance parameters.

The main objective of mapping quantitative trait loci (QTL) and genome-wide association studies (GWAS) is to identify and locate QTLs on the genome. Estimating the sizes of QTL is equally important as identifying the QTLs. The size of a QTL is often measured by the QTL variance, or the proportion of phenotypic variance explained by the QTL, known as the QTL heritability. The reported QTL heritability is biased upward for small-sized QTLs estimated from small samples, especially in GWAS with a very small P-value threshold accommodating to Bonferroni correction for multiple tests. The phenomenon is called the Beavis effect. Methods of correcting the Beavis effect have been developed for additive effect models. Corresponding methods are not available for QTLs with more than one effect, such as QTLs including dominance and other genetic effects. In this study, we developed explicit formulas for estimating the variances and heritability for QTL with multiple effects. We also developed a method to remove nuisance parameters via an annihilator matrix. Finally, biases in estimated QTL variances caused by the Beavis effect are investigated and corrected. The new method is demonstrated by analyzing the 1000 grain weight (KGW) trait in a hybrid rice population.