Mixture models in quantitative genetics and applications to animal breeding

Finite mixture models are helpful for uncovering heterogeneity due to hidden structure; for example, unknown major genes. The first part of this article gives examples and reviews quantitative genetics issues of continuous characters having a finite mixture of Gaussian components. 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. Formulae for assessing the effect of mass selection operating on a mixture are given. Expressions for the genetic correlation between a mixture and a Gaussian trait are presented. If there is heterogeneity in a population at the genetic or environmental levels, then genetic parameters based on theory treating distributions as homogeneous can lead to misleading interpretations. Subsequently, methods for parameter estimation (e.g., maximum likelihood) are reviewed, and the Bayesian approach is illustrated via an application to somatic cell scores in dairy cattle.