The overall effect of population structure on our association results seems to be small, once recent migrants from outside Europe are excluded. Estimates of over-dispersion of the association trend test statistics (usually denoted λ; ref. 15) ranged from 1.03 and 1.05 for RA and T1D, respectively, to 1.08-1.11 for the remaining diseases. Some of this over-dispersion could be due to factors other than structure, and this possibility is supported by the fact that inclusion of the two ancestry informative principal components as covariates in the association tests reduced the over-dispersion estimates only slightly (Supplementary Table 6), as did stratification by geographical region. This impression is confirmed on noting that P values with and without correction for structure are similar (Supplementary Fig. 9). We conclude that, for most of the genome, population structure has at most a small confounding effect in our study, and as a consequence the analyses reported below do not correct for structure. In principle, apparent associations in the few genomic regions identified in Table 1 as showing strong geographical differentiation should be interpreted with caution, but none arose in our analyses.
