Bruckner C M, Slanger W D
J Anim Sci. 1986 Dec;63(6):1779-93. doi: 10.2527/jas1986.6361779x.
Analysis of variance (ANOVA) and symmetric differences squared (SDS) methods for estimating genetic and environmental variances and covariances associated with beef cattle weaning weight were compared via simulation. Simulation was based on the pedigree and record structure of 503 beef weaning weights collected over 19 yr from a university herd. The SDS methodology was used with four models. The simplest model included direct (g) and maternal (gm) additive genetic effects, genetic covariance between direct and maternal additive genetic effects (sigma ggm), permanent maternal environmental effects (m) and temporary environmental effects (e). The second model also allowed for a nonzero environmental covariance (sigma mem) between dam and offspring weaning weights. Models 3 and 4 were models 1 and 2, respectively, expanded to include a grandmaternal genetic effect (gn) and covariances sigma ggn and sigma gmgn. Two ANOVA solution sets for the parameters of model 4 were obtained using sire, dam, maternal grandsire, maternal grandam and phenotypic variances and offspring-dam (covOD), offspring-sire (covOS), offspring-grandam (covOGD), and offspring-maternal half-aunt or uncle (covOMH) covariances. Four ANOVA solution sets for the parameters of model 2 were obtained using sire, dam, within dam and maternal grandsire variances, covOD and either covOS or covOGD. Two sets of 1,000 replicates of the data were simulated. These data were used to compare precision and accuracy of SDS and ANOVA estimators, to estimate correlations among SDS and ANOVA estimators, and to study the importance of taking inbreeding into account with SDS methodology. All ANOVA estimators for rho ggm were biased downward. The SDS procedure had a clear advantage over ANOVA. Averages of SDS estimates were closer to parameter values used to simulate the data and their standard deviations were generally smaller. The standard deviations of both SDS and ANOVA estimates of rho ggm were very large. It is important to allow for a nonzero sigma mem (at least when it is negative) when using SDS methods; otherwise estimators of sigma 2gm and sigma ggm are biased upward and downward, respectively.
通过模拟比较了用于估计与肉牛断奶体重相关的遗传和环境方差及协方差的方差分析（ANOVA）和对称差平方（SDS）方法。模拟基于从一所大学畜群19年收集的503个肉牛断奶体重的系谱和记录结构。SDS方法用于四个模型。最简单的模型包括直接（g）和母体（gm）加性遗传效应、直接和母体加性遗传效应之间的遗传协方差（sigma ggm）、永久母体环境效应（m）和临时环境效应（e）。第二个模型还允许母畜和后代断奶体重之间存在非零环境协方差（sigma mem）。模型3和4分别是模型1和2的扩展，包括一个祖母遗传效应（gn）以及协方差sigma ggn和sigma gmgn。使用父本、母本、母系祖父、母系祖母和表型方差以及后代 - 母本（covOD）、后代 - 父本（covOS）、后代 - 祖母（covOGD）和后代 - 母系半姑母或叔父（covOMH）协方差获得模型4参数的两个ANOVA解集。使用父本、母本、母本内和母系祖父方差、covOD以及covOS或covOGD获得模型2参数的四个ANOVA解集。模拟了两组各1000次重复的数据。这些数据用于比较SDS和ANOVA估计量的精度和准确性，估计SDS和ANOVA估计量之间的相关性，并研究在SDS方法中考虑近亲繁殖的重要性。所有ANOVA对rho ggm的估计量都向下有偏差。SDS程序相对于ANOVA具有明显优势。SDS估计值的平均值更接近用于模拟数据的参数值，并且其标准差通常更小。rho ggm的SDS和ANOVA估计值的标准差都非常大。使用SDS方法时允许sigma mem非零（至少当它为负时）很重要；否则，sigma 2gm和sigma ggm的估计量将分别向上和向下有偏差。
