Variance components analyses are sensitive to outliers, kurtosis, and skewness in the trait distribution. Quantile normalization provides a practical way to deal with these problems in the context of gene mapping and, specifically, variance component analyses [61–63]. For traits that are approximately normally distributed, normalization has minimal impact on results. For other traits, normalization will not induce correlations between relatives not present in the original data and thus should not lead to erroneous inference of a heritable component for variation. To carry out quantile normalization, we first ranked the observations and then matched the percentile of each observation to the corresponding percentile in a standard normal distribution. Using the resulting percentiles, we replaced each observation with the corresponding z-score from the standard normal distribution. When ties were present, percentiles were averaged across all ties.
