Power of the mixed linear model to detect phenotypic effects including gene by environment interactions. An SNP with differential effects across environments was simulated based on pearl millet and maize association mapping populations (see text for details). The main effect of the SNP (S) and the interaction between this SNP and the environment (S × E) were fitted with mixed linear model. The power of the model was calculated as the ratio of the number of runs in which a given effect was significantly detected out of the total number of runs. Power is plotted for h2 = 0.75 and according to allele frequency (q), genetic effect ratio (r) and λ. The parameter λ measured the variation in the magnitude of the SNP effect and the environment. The largest panel (maize, n = 277 individuals) performed globally better. However, the relative variation in power as a function of the parameters showed similar features in both panels. Power increased with an increase in r and was higher with common allele frequencies (q = 0.5, q = 0.25). The ability to detect the interaction was particularly sensitive to λ. The highest range of power (for example power > 80%) corresponded overall to relatively large parameter values. This indicates that these current mapping frameworks might be limiting for traits that are fundamentally shaped by loci with very small effects.