If our procedure for correcting for incomplete LD between SNPs and causal variants is correct, the variance explained by the causal variants should not depend on the number of SNPs used. To show that this is so, we randomly sampled 10%, 20%, …, and 100% of all the ~295K SNPs and estimated the variance explained by causal variants for each group of SNPs using both raw and adjusted estimates of relationships (assuming c = 0; Fig. 2). For the raw estimates of relationships, the proportion of variance explained increases with the number of SNPs because prediction error is reduced through inclusion of more SNPs. When the relationship estimates are adjusted for prediction error, the proportions of variance explained are independent from the number of SNPs and agree with an estimate of ~0.54 but have larger s.e. when fewer SNPs are used.
