For computational ease using REML, we decreased our sample size to the 2,680 samples in the NBS and 1966BC control cohorts of the WTCCC1 dataset, and we correspondingly restricted ourselves to only SNPs on chromosome 1. For this set of simulations, a dense set of SNPs was particularly important, so we used genotypes imputed to integrated phase1 v3 1000 Genomes [47] (URLs), giving us 360,106 SNPs after quality control. We again simulated quantitative phenotypes using an additive model, with effect sizes of causal SNPs drawn from a normal distribution with mean zero and variance determined by functional categories. Heritability was set to 0.5, and all SNPs were causal unless in a category simulated to have zero variance.