Transformation of a nonnormal distribution of quantitative traits for breeding purposes

Abstract

Some continuous quantitative traits such as yield are not always normally distributed. This article proposes an underlying normal distribution—called the equivalent normal distribution—to help analyze and interpret the distribution of such data. The mean and standard deviation of this distribution are estimated through the regression of the theoretical (assuming normality) selection intensity on the corresponding observed standardized selection differential at each selection rate that may be applied (as many selection rates as individuals in the distribution). This simple and pragmatic transformation does not require scale transformations, which sometimes obscure biological interpretation. A possible biological interpretation of the Equivalent Normal Distribution is presented; it considers the difference between the potential and the eventually observed performance. This method allows comparisons between distributions of apparently different shapes. Simulations furthermore indicated that Equivalent statistics, compared with observed statistics, allowed an improved prediction of genetic values and estimation of realised heritability.