The objectives of this study were to develop an efficient algorithm for calculating prediction error variances (PEVs) for genomic best linear unbiased prediction (GBLUP) models using the Algorithm for Proven and Young (APY), extend it to single-step GBLUP (ssGBLUP), and apply this algorithm for approximating the theoretical reliabilities for single- and multiple-trait models in ssGBLUP. The PEV with APY was calculated by block sparse inversion, efficiently exploiting the sparse structure of the inverse of the genomic relationship matrix with APY. Single-step GBLUP reliabilities were approximated by combining reliabilities with and without genomic information in terms of effective record contributions. Multi-trait reliabilities relied on single-trait results adjusted using the genetic and residual covariance matrices among traits. Tests involved two datasets provided by the American Angus Association. A small dataset (Data1) was used for comparing the approximated reliabilities with the reliabilities obtained by the inversion of the left-hand side of the mixed model equations. A large dataset (Data2) was used for evaluating the computational performance of the algorithm. Analyses with both datasets used single-trait and three-trait models. The number of animals in the pedigree ranged from 167,951 in Data1 to 10,213,401 in Data2, with 50,000 and 20,000 genotyped animals for single-trait and multiple-trait analysis, respectively, in Data1 and 335,325 in Data2. Correlations between estimated and exact reliabilities obtained by inversion ranged from 0.97 to 0.99, whereas the intercept and slope of the regression of the exact on the approximated reliabilities ranged from 0.00 to 0.04 and from 0.93 to 1.05, respectively. For the three-trait model with the largest dataset (Data2), the elapsed time for the reliability estimation was 11 min. The computational complexity of the proposed algorithm increased linearly with the number of genotyped animals and with the number of traits in the model. This algorithm can efficiently approximate the theoretical reliability of genomic estimated breeding values in ssGBLUP with APY for large numbers of genotyped animals at a low cost.

中文翻译：

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使用 Proven and Young 算法有效逼近单步基因组最佳线性无偏预测模型的可靠性


本研究的目标是开发一种有效的算法，使用 Proven and Young 算法 (APY) 计算基因组最佳线性无偏预测 (GBLUP) 模型的预测误差方差 (PEV)，并将其扩展到单步 GBLUP (ssGBLUP) ，并应用该算法来近似 ssGBLUP 中单性状和多性状模型的理论可靠性。 APY的PEV通过块稀疏求逆计算，有效地利用了APY基因组关系矩阵逆的稀疏结构。单步 GBLUP 可靠性是通过根据有效记录贡献结合有和没有基因组信息的可靠性来近似的。多性状可靠性依赖于使用性状之间的遗传和残差协方差矩阵调整的单性状结果。测试涉及美国安格斯协会提供的两个数据集。使用小型数据集 (Data1) 将近似可靠性与通过混合模型方程左侧反演获得的可靠性进行比较。使用大型数据集（Data2）来评估算法的计算性能。对两个数据集的分析均使用单性状和三性状模型。谱系中的动物数量范围从 Data1 中的 167,951 只到 Data2 中的 10,213,401 只，其中 Data1 中分别有 50,000 只和 20,000 只基因分型动物用于单性状和多性状分析，Data2 中分别有 335,325 只。通过反演获得的估计可靠性和精确可靠性之间的相关性范围为 0.97 至 0.99，而精确可靠性对近似可靠性的回归的截距和斜率分别为 0.00 至 0.04 和 0.93 至 1.05。 对于具有最大数据集（Data2）的三性状模型，可靠性估计所用时间为 11 分钟。该算法的计算复杂度随着基因分型动物的数量和模型中性状的数量线性增加。该算法可以以较低的成本有效地近似大量基因分型动物的 ssGBLUP 和 APY 中基因组估计育种值的理论可靠性。