variance of the estimate of the regression coefficient is(3)If the samples are unrelated and the phenotypes have been standardized with mean of 0 and variance of 1, then and . Since is small, there is hardly any variance in that can be explained by so that . We therefore have(4)Under circumstances when is large, for example when the GRM is calculated from pedigree data, a substantial proportion of variance in could be explained by , so that will be smaller than and the sampling variance of estimate of genetic variance will be reduced accordingly. In general, and the residual variance in equation (2) depend on the number of SNP that are used to calculate the GRM and their correlation structure. Although can be calculated empirically from the data, theoretical work suggest it is approximately 2×10−5 for genome-wide coverage of common SNPs in human populations [21]. Since the phenotypic variance is usually estimated with very high precision,(5)This suggests that the standard error (SE) of depends only on sample size, and is approximately . We show by simulations based on real genotype data (Text S1) that this approximation is very accurate (Figure 1 and Table S1). The SEs calculated from the approximation
