Originally published as Genetics Published Articles Ahead of Print on April 19, 2006.

Genetics, Vol. 173, 2247-2255, August 2006, Copyright © 2006
doi:10.1534/genetics.105.054197

On the Quantitative Genetics of Mixture Characters

Daniel Gianola^*,,1, Bjorg Heringstad and Jorgen Odegaard

^* Department of Animal Sciences, University of Wisconsin, Madison, Wisconsin 53706 and Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, N-1432 Ås, Norway

¹ Corresponding author: Department of Animal Sciences, 1675 Observatory Dr., Madison, WI 53706.
E-mail: gianola{at}calshp.cals.wisc.edu

Finite mixture models are helpful for uncovering heterogeneity due to hidden structure. Quantitative genetics issues of continuous characters having a finite mixture of Gaussian components as statistical distribution are explored in this article. The partition of variance in a mixture, the covariance between relatives under the supposition of an additive genetic model, and the offspring–parent regression are derived. Formulas for assessing the effect of mass selection operating on a mixture are given. Expressions for the genetic and phenotypic correlations between mixture and Gaussian traits and between two mixture traits are presented. It is found that, if there is heterogeneity in a population at the genetic or environmental level, then genetic parameters based on theory treating distributions as homogeneous can lead to misleading interpretations. Some peculiarities of mixture characters are: heritability depends on the mean values of the component distributions, the offspring–parent regression is nonlinear, and genetic or phenotypic correlations cannot be interpreted devoid of the mixture proportions and of the parameters of the distributions mixed.

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