Nilforooshan Mohammad Ali, Garrick Dorian
Livestock Improvement Corporation, Hamilton, New Zealand.
AL Rae Centre for Genetics and Breeding, School of Agriculture, Massey University, Palmerston North, New Zealand.
Front Genet. 2021 Mar 22;12:637626. doi: 10.3389/fgene.2021.637626. eCollection 2021.
Reduced models are equivalent models to the full model that enable reduction in the computational demand for solving the problem, here, mixed model equations for estimating breeding values of selection candidates. Since phenotyped animals provide data to the model, the aim of this study was to reduce animal models to those equations corresponding to phenotyped animals. Non-phenotyped ancestral animals have normally been included in analyses as they facilitate formation of the inverse numerator relationship matrix. However, a reduced model can exclude those animals and obtain identical solutions for the breeding values of the animals of interest. Solutions corresponding to non-phenotyped animals can be back-solved from the solutions of phenotyped animals and specific blocks of the inverted relationship matrix. This idea was extended to other forms of animal model and the results from each reduced model (and back-solving) were identical to the results from the corresponding full model. Previous studies have been mainly focused on reduced animal models that absorb equations corresponding to non-parents and solve equations only for parents of phenotyped animals. These two types of reduced animal model can be combined to formulate only equations corresponding to phenotyped parents of phenotyped progeny.
简化模型是与完整模型等效的模型，能够降低解决问题的计算需求，在此处是指用于估计选择候选个体育种值的混合模型方程。由于表型测定的动物为模型提供数据，本研究的目的是将动物模型简化为与表型测定动物对应的方程。未表型测定的祖先动物通常会被纳入分析，因为它们有助于形成逆分子关系矩阵。然而，简化模型可以排除这些动物，并获得感兴趣动物育种值的相同解。与未表型测定动物对应的解可以从表型测定动物的解和逆关系矩阵的特定块中反推出来。这一想法被扩展到其他形式的动物模型，每个简化模型（以及反推）的结果与相应完整模型的结果相同。以往的研究主要集中在吸收对应非亲本方程并仅求解表型测定动物亲本方程的简化动物模型。这两种类型的简化动物模型可以结合起来，仅构建与表型测定后代的表型测定亲本对应的方程。
