Supplementary Table III presents the false-positive error rate of the trend test for association, T_Fmds, adjusting for up to three axes of genetic variation, according to the three selection criteria described above. Results are presented over 5,000 replicates for a range of FST, for a significance level of 5%. The selection criteria makes little difference to the false-positive error rate, presumably because the inclusion of axes of genetic variation in the logistic regression model that do not correlate with disease does not impact on the association analysis, because the additional degrees of freedom required are small compared to the sample size. A similar conclusion is reached in terms of the effect of selection criteria on power, as presented in supplementary Table IV, for a SNP with minor allele frequency of 20% in the source population and a heterozygous genotype relative risk of 1.5. However, if we were to include many more axes of genetic variation without selection, we would expect larger differences in the false-positive error rate and power between approaches, particularly in the absence of population structure. Therefore, one
