Derivation of equivalent computing algorithms for genomic predictions and reliabilities of animal merit
Derivation of equivalent computing algorithms for genomic predictions and reliabilities of animal merit
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DOI：
10.3168/jds.2008-1929
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发表时间：
2009-06-01
影响因子：
3.5
通讯作者：
Garrick, D. J.
中科院分区：
文献类型：
--
作者：
Stranden, I.;Garrick, D. J.
传统的奶牛价值预测包括建立和求解线性方程，其中未知的数量是动物的数量，通常是数百万，乘以同时评估的特征数量。系数矩阵很大且稀疏，选择对数据进行迭代，这样系数矩阵不存储，而是根据需要重新创建。相比之下，基因组预测涉及评估以单核苷酸多态性基因型为特征的基因组片段的优点，目前约有50,000个，然后可以根据它们遗传的片段来预测单个动物的优点。染色体片段的预测方程通常有少于10万个未知数，但用于预测片段效应的观察数量可以是片段数量的十分之一。系数矩阵趋于密集，由此产生的方程组可能表现不佳。推导了基因组预测的等效计算算法。等效系统中的未知数量随着基因型动物（通常是公牛）的数量而增加，而不是染色体片段效应的数量。在基因型动物比单核苷酸多态性基因型动物少的情况下，这些等效的计算允许求解一个更小的方程组，在数值上表现得更好。比较了3种求解策略：1种方法在内存中形成并存储系数矩阵，2种方法对数据进行迭代。最后，提出了基因组预测的可靠性公式。
Conventional prediction of dairy cattle merit involves setting up and solving linear equations with the number of unknowns being the number of animals, typically millions, multiplied by the number of traits being simultaneously assessed. The coefficient matrix has been large and sparse and iteration on data has been the method of choice, whereby the coefficient matrix is not stored but recreated as needed. In contrast, genomic prediction involves assessment of the merit of genome fragments characterized by single nucleotide polymorphism genotypes, currently some 50,000, which can then be used to predict the merit of individual animals according to the fragments they have inherited. The prediction equations for chromosome fragments typically have fewer than 100,000 unknowns, but the number of observations used to predict the fragment effects can be one-tenth the number of fragments. The coefficient matrix tends to be dense and the resulting system of equations can be ill behaved. Equivalent computing algorithms for genomic prediction were derived. The number of unknowns in the equivalent system grows with number of genotyped animals, usually bulls, rather than the number of chromosome fragment effects. In circumstances with fewer genotyped animals than single nucleotide polymorphism genotypes, these equivalent computations allow the solving of a smaller system of equations that behaves numerically better. There were 3 solving strategies compared: 1 method that formed and stored the coefficient matrix in memory and 2 methods that iterate on data. Finally, formulas for reliabilities of genomic predictions of merit were developed.