Liu Y, Zeng Z B
Department of Statistics, North Carolina State University, Raleigh, NC, USA.
J Anim Breed Genet. 2005 Aug;122(4):229-39. doi: 10.1111/j.1439-0388.2005.00525.x.
Marker-assisted genetic evaluation needs to infer genotypes at quantitative trait loci (QTL) based on the information of linked markers. As the inference usually provides the probability distribution of QTL genotypes rather than a specific genotype, marker-assisted genetic evaluation is characterized by the mixture model because of the uncertainty of QTL genotypes. It is, therefore, necessary to develop a statistical procedure useful for mixture model analyses. In this study, a set of mixture model equations was derived based on the normal mixture model and the EM algorithm for evaluating linear models with uncertain independent variables. The derived equations can be seen as an extension of Henderson's mixed model equations to mixture models and provide a general framework to deal with the issues of uncertain incidence matrices in linear models. The mixture model equations were applied to marker-assisted genetic evaluation with different parameterizations of QTL effects. A sire-QTL-effect model and a founder-QTL-effect model were used to illustrate the application of the mixture model equations. The potential advantages of the mixture model equations for marker-assisted genetic evaluation were discussed. The mixed-effect mixture model equations are flexible in modelling QTL effects and show desirable properties in estimating QTL effects, compared with Henderson's mixed model equations.
标记辅助遗传评估需要基于连锁标记的信息推断数量性状位点（QTL）的基因型。由于这种推断通常提供的是QTL基因型的概率分布而非特定基因型，鉴于QTL基因型的不确定性，标记辅助遗传评估具有混合模型的特征。因此，有必要开发一种适用于混合模型分析的统计程序。在本研究中，基于正态混合模型和用于评估具有不确定自变量的线性模型的期望最大化（EM）算法，推导了一组混合模型方程。所推导的方程可视为亨德森混合模型方程向混合模型的扩展，并为处理线性模型中不确定关联矩阵的问题提供了一个通用框架。混合模型方程被应用于具有不同QTL效应参数化的标记辅助遗传评估。使用父本-QTL-效应模型和奠基者-QTL-效应模型来说明混合模型方程的应用。讨论了混合模型方程在标记辅助遗传评估中的潜在优势。与亨德森混合模型方程相比，混合效应混合模型方程在QTL效应建模方面具有灵活性，并且在估计QTL效应方面表现出理想的特性。
