It is worth noting that although we attempted to simulate phenotypes so that results may be tabulated across allele frequencies, by keeping heritability constant per Equation (1), this does not guarantee that power will be independent of allele frequency. Heritability represents, in some sense, the amount of information about the phenotype and genotype relationship. How that relates to power is not completely predictable and will depend on additional factors, such as analysis methods, genetic model (e.g. dominance here), and particularly imputation accuracy. However, even for the true genotypes, it is difficult to calibrate power at low allele frequencies in samples of finite size. For example, in Figures 2D and 3D, power is reduced at low frequencies of the dominant allele. This is due to the requirement of having a homozygote—a rare genotype at low allele frequency and thus less likely to be observed near its expected proportion—for a shift in phenotypic mean; e.g., this phenomenon is more pronounced in Figure 3D where the sample size is 50. In fact, it is for this reason that we included results for true genotypes (where the “correction” for allele frequency, etc., was not perfect).
