a representation that includes eight more dimensions than reported in our analysis. Through experience we have found that applying an initial screen that selects a grid of SNPs separated by 10 Kb approximates a tag SNP selection fairly well. Next we apply a formal tag SNP selection process to remove any remaining SNPs with r2>0.04. Using the tag SNPs reported in our analysis we found d = 8, a result that is quite robust to slight variations in the SNP selection. For instance, using various choices of tag SNPs ranging in number from 15,000 to 80,000 yielded similar results. But using 10,000 SNPs we find only d = 5 dimensions. This suggests that there is an inflection point in the information content of the SNP panel.
