Is heterosis an artefact governed by the choice of scale?

Abstract

When estimating heterosis it is often necessary to transform either the data or, within the context of generalized linear models, the linear predictor, to satisfy certain assumptions. In this note it will be argued that the amount of heterosis is scale-dependent varying with the kind of transformation. The same applies for the examination of dominance in quantitative genetics. We exemplify the varying heterotic effect with phenotypic data of maize roots. Either a data transformation or a generalized linear mixed model with appropriately chosen link function is applied to the data. It is concluded that care should be exercised when transforming data in phenotypic as well as quantitative-genetic studies because partial dominance or heterosis may be removed by a suitably chosen transformation. With data transformations, even overdominance or better parent heterosis may disappear. When a data transformation is needed to meet the usual statistical assumptions such as normality and homogeneity of variance, a back-transformation to the original scale may be necessary, depending on what is deemed the appropriate scale for assessing genetic effects.