Oikawa Takuro, Yasuda Kazuhiro
Graduate School of Natural Science and Technology, Okayama University, Okayama-shi, Japan.
Genet Sel Evol. 2009 Mar 3;41(1):25. doi: 10.1186/1297-9686-41-25.
In the field of animal breeding, estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix (NRM) into a mixed model has made these analyses possible. However, a method including a genetically identical animal (GIA) in NRM if genetic relationships between pairs of GIAs are not perfect, is still lacking. Here, we describe a method to incorporate GIAs into NRM using a K matrix in which diagonal elements are set to 1.0, off-diagonal elements between pairs of GIAs to (1-x) and the other elements to 0, where x is a constant less than 0.05. The inverse of the K matrix is then calculated directly by a simple formula. Thus, the inverse of the NRM is calculated by the products of the lower triangular matrix that identifies the parents of each individual, its transpose matrix, the inverse of the K matrix and the inverse of diagonal matrix D, in which the diagonal elements comprise a number of known parents and their inbreeding coefficients. The computing method is adaptable to the analysis of a data set including pairs of GIAs with imperfect relationships.
在动物育种领域，通过分析数量性状来常规地进行遗传参数估计和育种值预测。使用动物模型并将分子关系矩阵（NRM）的直接逆矩阵纳入混合模型使得这些分析成为可能。然而，如果基因相同动物（GIA）对之间的遗传关系不完美，在NRM中纳入GIA的方法仍然缺乏。在此，我们描述一种使用K矩阵将GIA纳入NRM的方法，其中对角元素设为1.0，GIA对之间的非对角元素设为(1 - x)，其他元素设为0，这里x是小于0.05的常数。然后通过一个简单公式直接计算K矩阵的逆矩阵。因此，NRM的逆矩阵通过识别每个个体亲本的下三角矩阵、其转置矩阵、K矩阵的逆矩阵以及对角矩阵D的逆矩阵的乘积来计算，其中对角元素包含一些已知亲本及其近交系数。该计算方法适用于分析包含关系不完美的GIA对的数据集。
