We used simulation studies to validate the method of estimating the variance explained by causal variants using genome-wide SNPs. We simulated a quantitative trait on the basis of the observed genotype data of 3,925 individuals and 294,831 SNPs in two ways: (i) randomly sampling causal variants from all the SNPs, and (ii) randomly sampling causal variants from the SNPs with MAF ≤ 0.1 (Supplementary Note). Table 2 shows that in case (i), if we included the causal variants in estimating the genetic relationships, we obtained an unbiased estimate of the proportion of phenotypic variance explained by the causal variants (in this case this is the heritability of the trait, because in a simulation we know that these causal variants explain all the genetic variance). When we excluded the causal variants, we underestimated heritability, as the relationship derived from SNPs overestimated the variation of the relationship at causal loci owing to imperfect LD. However, the heritability estimate recovered when we adjusted relationship estimates using equation [9] (Online Methods; c = 0). In case (ii), even if we included the causal variants
