Computing procedures for genetic evaluation including phenotypic, full pedigree, and genomic information
Computing procedures for genetic evaluation including phenotypic, full pedigree, and genomic information
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DOI：
10.3168/jds.2009-2064
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发表时间：
2009-09-01
影响因子：
3.5
通讯作者：
Aguilar, I.
中科院分区：
文献类型：
--
作者：
Misztal, I.;Legarra, A.;Aguilar, I.
目前，基因组评估使用多步骤程序，这容易产生偏差和错误。当可以通过将分子关系矩阵A修改为H = A + A（Delta）来获得基因组预测时，单步程序可以是适用的，其中A（Delta）包括与预期关系的偏差。然而，传统的混合模型方程需要H-1，这通常是很难获得的大谱系。当混合模型方程以同样适用于奇异H的替代形式表示时，以及当这些方程通过共轭梯度技术求解时，用H的计算是可行的。那么涉及H的唯一计算是Aq或A（Delta q）的形式，其中q是向量。替代方程的左侧是非对称的。当A（Delta）中的非零数很小时，计算A（Delta q）是不昂贵的，并且可以使用间接算法在线性时间内有效地计算乘积Aq。提出了更复杂的模型的推广。这些数据包括620万荷斯坦牛的1020万个最终得分，并通过重复性模型进行分析。比较涉及定期和替代方程。第二种情况的模型包括模拟A（Delta）。通过预条件共轭梯度算法和双共轭梯度稳定算法分别得到了解，预条件共轭梯度算法只适用于对称矩阵，双共轭梯度稳定算法也适用于非对称矩阵。与非对称解算器相关的收敛速度略好于原始方程的对称解算器，尽管非对称解算器的每轮时间是其两倍。与替代方程相关的收敛速度范围从没有A（Delta）的2倍降低到最大模拟A（Delta）的3倍降低。当可归因于基因组学的信息可以表示为对分子关系矩阵的修改时，所提出的方法可以允许现有评价的升级以并入基因组学信息。
Currently, genomic evaluations use multiple-step procedures, which are prone to biases and errors. A single-step procedure may be applicable when genomic predictions can be obtained by modifying the numerator relationship matrix A to H = A + A(Delta), where A(Delta) includes deviations from expected relationships. However, the traditional mixed model equations require H-1, which is usually difficult to obtain for large pedigrees. The computations with H are feasible when the mixed model equations are expressed in an alternate form that also applies for singular H and when those equations are solved by the conjugate gradient techniques. Then the only computations involving H are in the form of Aq or A(Delta q), where q is a vector. The alternative equations have a nonsymmetric left-hand side. Computing A(Delta q) is inexpensive when the number of nonzeros in A(Delta) is small, and the product Aq can be calculated efficiently in linear time using an indirect algorithm. Generalizations to more complicated models are proposed. The data included 10.2 million final scores on 6.2 million Holsteins and were analyzed by a repeatability model. Comparisons involved the regular and the alternative equations. The model for the second case included simulated A(Delta). Solutions were obtained by the preconditioned conjugate gradient algorithm, which works only with symmetric matrices, and by the bi-conjugate gradient stabilized algorithm, which also works with nonsymmetric matrices. The convergence rate associated with the nonsymmetric solvers was slightly better than that with the symmetric solver for the original equations, although the time per round was twice as much for the nonsymmetric solvers. The convergence rate associated with the alternative equations ranged from 2 times lower without A(Delta) to 3 times lower for the largest simulated A(Delta). When the information attributable to genomics can be expressed as modifications to the numerator relationship matrix, the proposed methodology may allow the upgrading of an existing evaluation to incorporate the genomic information.