Once we established the causal SNPs, we used a linear model to simulate continuous phenotypes such that the causal SNPs aggregated to explain a fixed proportion of the phenotypic variance (). This phenotypic variance was partitioned equally amongst all the causal SNPs (qualitatively similar results were obtained when phenotypic variance was unevenly partitioned among causal variants (see Figure S6)). In particular, the individual's phenotype was drawn according to , where is the total number of causal variants, is the effect size of the causal SNP, is number of copies of the risk allele (randomly assigned as reference or alternate) for individual m, and . Finally, we calculated association Z-scores () at each SNP by taking the Wald statistic from the regression of the on , where Y is a vector of phenotypes for M individuals and is the vector of corresponding genotypes for the SNP at the locus. For simulations that required loci greater than 10 KB, we instead drew Z-scores from a Multivariate Normal distribution with covariance equal to LD based on the European 1 KG and non-centrality parameters
