The Threshold Model As a General Purpose Normalizing Transformation

The estimation of heritabilities and genetic correlations is based on the assumption that the trait distributions are normal. When the distributions are not normal it is advisable to transform the data to produce normality. However, it is possible that no suitable transformation can be found. The purpose of the present paper is to point out that the threshold model of quantitative genetics can be used as a generalized transformation. To utilize this method it is only necessary to divide the data at the median (approximately) and code the two halves as 0 and 1. Estimates can then be made using algorithms outlined herein. A simulation study shows that the threshold transformation gave unbiased estimates of the heritability and genetic correlation in all cases. The 95% confidence limits correctly included the true heritability value in the required 95% of cases, while the estimated confidence region for the genetic correlation was also correct provided that the geometric mean heritability was greater than approximately 0.15, a restriction that applied also to the normally distributed data. Confidence intervals estimated from the non-normal data were consistently too small. The method is illustrated using data on the proportion of diapausing eggs produced by the cricket, Allonemobius socius.