of SNPs of lower MAF to generate an approximately uniform distribution of genotyped SNPs (Figure 2b–c). As the number of causal SNPs increased we found that the frequency of the most associated common variant changed, based on the most likely coupling pattern. When k = 1, as discussed above, out of all common SNPs segregating in the population, the genotyped SNP which tags the most variance from the causal SNP (i.e., has the highest r 2) is the SNP with the lowest MAF in which the minor allele is coupled with the rare causal variant. When k>1, the genotyped SNP which explains the highest proportion of variance (R 2) of the quantitative trait is a SNP where one of its alleles is coupled with more rare variants than the other allele. The highest R 2 across all SNPs segregating in the population will occur for the SNP with the lowest allele frequency that fulfils this criterion. From the simulations, the mean frequency of the most associated genotyped SNP allele was 0.13 for one rare variant and <0.3 for up to 18 rare variants with a trend that the frequency of the most associated allele increased with more rare variants in
