The distribution of the eigengap statistic used to determine the number of significant axes of ancestry is well approximated by a function of the sample size, provided the number of tag SNPs is relatively large (L>10,000). For a genome-wide association study we expect to have at least this number available. For smaller numbers of SNPs the distribution also depends on L. Consequently the cutoff value provided herein for the test does not apply. For smaller numbers of SNPs it is necessary to simulate the distribution of the eigengap statistic. Further study will be required to obtain an asymptotic theory such as applied to eigenvalues of ϒϒ′ [Patterson et al., 2006].
