Power of the mixed linear model to detect phenotypic effects including three way interactions. The data were simulated using pearl millet and maize panels (see text for details). The set of simulated effects consists of SNP main effect (S), SNP by environment interaction (S × E), ancestry by SNP interaction (Q × S) and three way interaction between ancestry, SNP and environment (Q × S × E). The power to detect each effect is plotted for heritability h2 = 0.75 and the allele frequency q = 0.5, according to the effect ratio r, and the parameter λ which influences variations in the effect with the environment. Power increased with an increase in r for all effects, and a strong effect of λ was observed for the interactions. The highest range of power (say power > 80%) was reached only with relatively large effect size. Otherwise, there was a relative improvement in power for the maize panel (3 times larger than pearl millet panel).