We simulated a phenotype by first selecting a proportion r of causal variants at random from the common and uncommon SNPs, leaving Nc common causal and Nn uncommon causal SNPs. We then selected a fraction of phenotypic variance α explained by the uncommon SNPs. At α=0.0 uncommon variants had no effect and the genetic basis of the phenotype was entirely determined by common variants. We then chose effect sizes for each common and uncommon SNP by drawing from normal distributions N(0,(1-α)h2/(Nc)) and N(0,(α)h2/(Nn)) respectively. The genetic element of the phenotype was generated by taking the inner product of the causal variants, normalized to have mean 0 and variance 1 in the admixed population, and the effect sizes for the variants. Normally distributed random noise was added such that the total heritability in the population was h2. The FSTC of the common and uncommon SNPs was 0.15 and 0.25 respectively. The study FSTC used to estimate heritability was the weighted mean 0.15(1-α) + 0.25α as described in the derivation above. Setting individuals with the lowest P% of phenotypes as cases and all other as controls generated dichotomous phenotypes with prevalence P.
