We began by simulating a population of 40,000 haplotypes, and selected causal variants according to our chosen model of association. We selected 10,000 haplotypes, paired together at random to form 5,000 individuals in our “analysis cohort”, and generated their phenotypes according to their genotypes at the causal variants. We then selected a further 2,000 haplotypes in our “discovery panel”, used here to represent the deep re-sequencing data we expect from the 1,000 Genomes project. Over all simulations, the mean number of rare variants with at least two copies of the minor allele in the discovery panel was 52.2. We assumed that each of these rare variants was taken forward for genotyping in the analysis cohort, and tested for association using both RVT1 and RVT2.