Finite mixturemodels are helpful for uncovering heterogeneity due to hidden structure; forexample, unknown major genes. The first part of this article gives examplesand reviews quantitative genetics issues of continuous characters having a finitemixture of Gaussian components. The partition of variance in a mixture, thecovariance between relatives under the supposition of an additive genetic modeland the offspring-parent regression are derived. Formulae for assessing theeffect of mass selection operating on a mixture are given. Expressions for thegenetic correlation between a mixture and a Gaussian trait are presented. Ifthere is heterogeneity in a population at the genetic or environmental levels,then genetic parameters based on theory treating distributions as homogeneouscan lead to misleading interpretations. Subsequently, methods for parameterestimation (e.g., maximum likelihood) are reviewed, and the Bayesianapproach is illustrated via an application to somatic cell scores in dairy cattle.
