To illustrate the properties of the above methods in correcting for stratification at normally differentiated or unusually differentiated markers, in the presence or absence of family structure, we carried out two simulations. We considered a case-control study with two subpopulations POP1 and POP2, with 300 cases and 200 controls from POP1 and 200 cases and 300 controls from POP2. We simulated 99,900 normally differentiated markers based on FST(POP1,POP2)=0.01,39 and 100 unusually differentiated markers based on allele frequency difference equal to 0.6 with both minor allele frequencies uniformly distributed on [0.0,0.4]21. In simulation 1, all individuals were unrelated. In simulation 2, all individuals from POP1 were unrelated and individuals from POP2 included 80 case-case sibling pairs, 40 case-control sibling pairs and 130 control-control sibling pairs. We computed λGC for each of the following methods: uncorrected Armitage trend test, EIGENSTRAT21, EMMAX without PC covariates33, EMMAX with PC covariates33, and ROADTRIPS37 (see Web Resources). All PC runs used only one PC, but the additional inclusion of random PCs has little effect on results21. Power to detect causal variants may vary between methods, but
