Although single-step GBLUP (ssGBLUP) is an animal model, SNP effects can be backsolved from genomic estimated breeding values (GEBV). Predicted SNP effects allow to compute indirect prediction (IP) per individual as the sum of the SNP effects multiplied by its gene content, which is helpful when the number of genotyped animals is large, for genotyped animals not in the official evaluations, and when interim evaluations are needed. Typically, IP are obtained for new batches of genotyped individuals, all of them young and without phenotypes. Individual (theoretical) accuracies for IP are rarely reported, but they are nevertheless of interest. Our first objective was to present equations to compute individual accuracy of IP, based on prediction error covariance (PEC) of SNP effects, and in turn, are obtained from PEC of GEBV in ssGBLUP. The second objective was to test the algorithm for proven and young (APY) in PEC computations. With large datasets, it is impossible to handle the full PEC matrix, thus the third objective was to examine the minimum number of genotyped animals needed in PEC computations to achieve IP accuracies that are equivalent to GEBV accuracies. Correlations between GEBV and IP for the validation animals using SNP effects from ssGBLUP evaluations were ≥ 0.99. When all available genotyped animals were used for PEC computations, correlations between GEBV and IP accuracy were ≥ 0.99. In addition, IP accuracies were compatible with GEBV accuracies either with direct inversion of the genomic relationship matrix (G) or using the algorithm for proven and young (APY) to obtain the inverse of G. As the number of genotyped animals included in the PEC computations decreased from around 55,000 to 15,000, correlations were still ≥ 0.96, but IP accuracies were biased downwards. Theoretical accuracy of indirect prediction can be successfully obtained by computing SNP PEC out of GEBV PEC from ssGBLUP equations using direct or APY G inverse. It is possible to reduce the number of genotyped animals in PEC computations, but accuracies may be underestimated. Further research is needed to approximate SNP PEC from ssGBLUP to limit the computational requirements with many genotyped animals.

中文翻译：

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基于单步 GBLUP 的 SNP 效应的间接预测的理论准确性

尽管单步 GBLUP (ssGBLUP) 是一种动物模型，但 SNP 效应可以从基因组估计育种值 (GEBV) 反演。预测的 SNP 效应允许将每个个体的间接预测 (IP) 计算为 SNP 效应乘以其基因含量的总和，这在基因分型动物的数量很大、对于未在官方评估中的基因分型动物以及中期时很有帮助需要评估。通常情况下，IP 是为新批次的基因分型个体获得的，这些个体都很年轻且没有表型。IP 的个别（理论）准确性很少被报道，但它们仍然很有趣。我们的第一个目标是根据 SNP 效应的预测误差协方差 (PEC) 提出方程来计算 IP 的个体精度，反过来，从 ssGBLUP 中的 GEBV 的 PEC 获得。第二个目标是在 PEC 计算中测试 proven and young (APY) 的算法。对于大型数据集，不可能处理完整的 PEC 矩阵，因此第三个目标是检查 PEC 计算中实现与 GEBV 准确度相当的 IP 准确度所需的最少基因分型动物数量。使用来自 ssGBLUP 评估的 SNP 效应的验证动物的 GEBV 和 IP 之间的相关性≥ 0.99。当所有可用的基因分型动物都用于 PEC 计算时，GEBV 和 IP 准确性之间的相关性≥ 0.99。此外，IP 准确度与 GEBV 准确度兼容，无论是直接反转基因组关系矩阵 (G) 还是使用 proven and young (APY) 算法来获得 G 的逆矩阵。由于 PEC 计算中包含的基因分型动物数量从大约 55,000 只减少到 15,000 只，相关性仍≥ 0.96，但 IP 准确度向下偏斜。通过使用直接或 APY G 逆从 ssGBLUP 方程从 GEBV PEC 计算 SNP PEC，可以成功获得间接预测的理论准确性。可以减少 PEC 计算中基因分型动物的数量，但准确性可能被低估。需要进一步研究从 ssGBLUP 近似 SNP PEC，以限制许多基因分型动物的计算要求。通过使用直接或 APY G 逆从 ssGBLUP 方程从 GEBV PEC 计算 SNP PEC，可以成功获得间接预测的理论准确性。可以减少 PEC 计算中基因分型动物的数量，但准确性可能被低估。需要进一步研究从 ssGBLUP 近似 SNP PEC，以限制许多基因分型动物的计算要求。通过使用直接或 APY G 逆从 ssGBLUP 方程从 GEBV PEC 计算 SNP PEC，可以成功获得间接预测的理论准确性。可以减少 PEC 计算中基因分型动物的数量，但准确性可能被低估。需要进一步研究从 ssGBLUP 近似 SNP PEC，以限制许多基因分型动物的计算要求。