Cantet R J, Schaeffer L R, Smith C
Centre for Genetic Improvement of Livestock, Department of Animal and Poultry Science, University of Guelph, Ontario, Canada.
J Anim Sci. 1992 Jun;70(6):1730-41. doi: 10.2527/1992.7061730x.
Mixed-model equations for the reduced animal model with maternal effects and different genetic grouping of unknown parents for additive direct and maternal effects are derived. The matrices that relate the expected value and the variance of the breeding values of non-parents to the parents, as well as the different contributions of parental and non-parental breeding values, to the resulting mixed-model equations are presented. Mis-specification of additive maternal variance and the additive covariance between direct and maternal effects, arising from missing information on the dams of known individuals with records, is discussed. To avoid an incorrect specification of the variance-covariance matrix of the records without having to invert a nondiagonal variance of the residual terms, the breeding values of the unknown dams of individuals with records are included in the equations. Breeding values of non-parents are back-solved after the solutions for genetic groups and breeding values of parents are computed as simply as in cases in which maternal effects are absent. A numerical example is included to illustrate the derivations.
推导了具有母体效应的简化动物模型的混合模型方程，以及针对加性直接效应和母体效应的未知亲本的不同遗传分组。给出了将非亲本育种值的期望值和方差与亲本相关联的矩阵，以及亲本和非亲本育种值对所得混合模型方程的不同贡献。讨论了由于有记录的已知个体的母本信息缺失而导致的加性母体方差以及直接效应和母体效应之间的加性协方差的错误设定。为了避免在无需求逆残差项的非对角方差的情况下对记录的方差协方差矩阵进行错误设定，将有记录个体的未知母本的育种值纳入方程。在计算遗传组和亲本的育种值时，如同不存在母体效应的情况一样简单，之后再反解非亲本的育种值。包含一个数值示例来说明推导过程。
