Cantet R J, Birchmeier A N, Santos-Cristal M G, de Avila V S
Departamento de Producción Animal, Facultad de Agronomía, Universidad de Buenos Aires, Argentina.
J Anim Sci. 2000 Oct;78(10):2554-60. doi: 10.2527/2000.78102554x.
Method R and Restricted Maximum Likelihood (REML) were compared for estimating heritability (h2) and subsequent prediction of breeding values (a) with data subject to selection. A single-trait animal model was used to generate the data and to predict breeding values. The data originated from 10 sires and 100 dams and simulation progressed for 10 overlapping generations. In simulating the data, genetic evaluation used the underlying parameter values and sires and dams were chosen by truncation selection for greatest predicted breeding values. Four alternative pedigree structures were evaluated: complete pedigree information, 50% of phenotypes with sire identities missing, 50% of phenotypes with dam identities missing, and 50% of phenotypes with sire and dams identities missing. Under selection and with complete pedigree data, Method R was a slightly less consistent estimator of h2 than REML. Estimates of h2 by both methods were biased downward when there was selection and loss of pedigree information and were unbiased when no selection was practiced. The empirical mean square error (EMSE) of Method R was several times larger than the EMSE of REML. In a subsequent analysis, different combinations of generations selected and generations sampled were simulated in an effort to disentangle the effects of both factors on Method R estimates of h2. It was observed that Method R overestimated h2 when both the sampling that is intrinsic in the method and the selection occurred in generations 6 to 10. In a final experiment, BLUP(a) were predicted with h2 estimated by either Method R or REML. Subsequently, five more generations of selection were practiced, and the mean square error of prediction (MSEP) of BLUP(a) was calculated with estimated h2 by either method, or the true value of the parameter. The MSEP of empirical BLUP(a) using Method R was greater than the MSEP of empirical BLUP(a) using REML. The latter statistic was closer to prediction error variance of BLUP(a) than the MSEP of empirical BLUP(a) using Method R, indicating that empirical BLUP(a) calculated using REML produced accurate predictions of breeding values under selection. In conclusion, the variability of h2 estimates calculated with Method R was greater than the variability of h2 estimates calculated with REML, with or without selection. Also, the MSEP of EBLUP(a) calculated using estimates of h2 by Method R was larger than MSEP of EBLUP(a) calculated with REML estimates of h2.
对方法R和限制最大似然法（REML）进行了比较，以利用经过选择的数据估计遗传力（h2）并随后预测育种值（a）。使用单性状动物模型生成数据并预测育种值。数据来源于10头公牛和100头母牛，模拟进行了10个重叠世代。在模拟数据时，遗传评估使用潜在参数值，公牛和母牛通过截断选择选出，以获得最大预测育种值。评估了四种不同的系谱结构：完整系谱信息、50%的表型缺失父本身份、50%的表型缺失母本身份以及50%的表型缺失父本和母本身份。在有选择且系谱数据完整的情况下，方法R对h2的估计一致性略低于REML。当存在选择和系谱信息缺失时，两种方法对h2的估计均向下偏倚，而在无选择时则无偏倚。方法R的经验均方误差（EMSE）比REML的EMSE大几倍。在后续分析中，模拟了所选世代和抽样世代的不同组合，以试图厘清这两个因素对方法R估计h2的影响。观察到当方法固有的抽样和选择都发生在第6至10代时，方法R高估了h2。在最后一个实验中，使用方法R或REML估计的h2预测最佳线性无偏预测值（BLUP(a)）。随后，又进行了五代选择，并使用两种方法估计的h2或参数的真实值计算BLUP(a)的预测均方误差（MSEP）。使用方法R的经验BLUP(a)的MSEP大于使用REML的经验BLUP(a)的MSEP。与使用方法R的经验BLUP(a)的MSEP相比，后者的统计量更接近BLUP(a)的预测误差方差，表明使用REML计算的经验BLUP(a)在选择下能准确预测育种值。总之，无论有无选择，使用方法R计算的h2估计值的变异性都大于使用REML计算的h2估计值的变异性。此外，使用方法R估计的h2计算的经验最佳线性无偏预测值（EBLUP(a)）的MSEP大于使用REML估计的h2计算的EBLUP(a)的MSEP。
