Mixture models in quantitative genetics and applications to animal breeding

Abstract

-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.

Mixture Mixed Models: Biennial Growth as a Latent Variable in Coffee Bean Progenies

“…This circumstance explains not only the high temporal dependence (covariance) between residuals throughout the years, but also the sudden fluctuations in residual variance for the mixed models observed in the present study. Gianola et al (2007) observed a similar behavior for the error component in mixture models and considered this difference to be attributable to variability between the means for the two mixture components, which is not considered in the conventional mixed model. When a population presents heterogeneity at the genetic or environmental level, genetic parameters based on a theory that derives the estimators assuming that homogeneous distributions can lead to erroneous interpretations (Gianola et al, 2007).…”

“…Gianola et al (2007) observed a similar behavior for the error component in mixture models and considered this difference to be attributable to variability between the means for the two mixture components, which is not considered in the conventional mixed model. When a population presents heterogeneity at the genetic or environmental level, genetic parameters based on a theory that derives the estimators assuming that homogeneous distributions can lead to erroneous interpretations (Gianola et al, 2007). Therefore, the estimated variance components in mixed models tend to be biased when latent variables that affect stochastic processes exist.…”

“…Conventional models for the phenotypic evaluation of coffee may lead to inference errors when fitted to data originating from stochastic processes other than Gaussian ones (Gianola et al, 2007). The production data for the different coffee progenies used in the present study were apparently formed by a mixture of two Gaussian distributions.…”