Elzo M A
Animal Science Department, University of Florida, Gainesville 32611.
J Anim Sci. 1994 Dec;72(12):3055-65. doi: 10.2527/1994.72123055x.
Restricted maximum-likelihood procedures were developed to estimate additive and nonadditive genetic and environmental covariances for multiple traits in multibreed populations. The computational procedure follows the expectation-maximization (EM) algorithm, where the set of equations in the maximization step is solved by successive approximations. This computational procedure does not guarantee convergence to a symmetric positive-definite covariance matrix. Thus, computer programs will need to incorporate restrictions in the maximization step to ensure positive definiteness of each covariance matrix. Additive genetic and environmental covariances were modeled in subclass form (zeros and ones in the design matrices). Nonadditive genetic covariances were modeled in regression form (any value between and including zero and one in the design matrices). Computational requirements will be larger than for intrabreed analyses. Appropriate simplifying assumptions and numerical techniques (e.g., sparse and iterative numerical techniques) will be required for the implementation of these multibreed covariance estimation procedures. Number of iterations (5 to 12) and computing times (57 to 113 min) to achieve convergence when estimating 21 genetic and environmental covariances in five small simulated multibreed data sets (two breeds, 25,200 to 50,400 calves, 120 to 135 unrelated bulls) suggest that these procedures are computationally feasible.
限制最大似然法用于估计多品种群体中多个性状的加性和非加性遗传及环境协方差。计算过程遵循期望最大化（EM）算法，其中最大化步骤中的方程组通过逐次逼近求解。此计算过程不能保证收敛到对称正定协方差矩阵。因此，计算机程序需要在最大化步骤中纳入限制条件，以确保每个协方差矩阵的正定。加性遗传和环境协方差以子类形式建模（设计矩阵中的零和一）。非加性遗传协方差以回归形式建模（设计矩阵中的零到一之间包括零和一的任何值）。计算需求将比品种内分析更大。实施这些多品种协方差估计程序需要适当的简化假设和数值技术（例如，稀疏和迭代数值技术）。在五个小型模拟多品种数据集（两个品种，25200至50400头犊牛，120至135头无亲缘关系的公牛）中估计21个遗传和环境协方差时，达到收敛所需的迭代次数（5至12次）和计算时间（57至113分钟）表明这些程序在计算上是可行的。
