Department of Animal and Dairy Science, University of Georgia, Athens, 30602.
Department of Animal and Dairy Science, University of Georgia, Athens, 30602.
J Dairy Sci. 2021 Feb;104(2):2027-2031. doi: 10.3168/jds.2020-18969. Epub 2020 Dec 11.
Single-step genomic BLUP (ssGBLUP) requires compatibility between genomic and pedigree relationships for unbiased and accurate predictions. Scaling the genomic relationship matrix (G) to have the same averages as the pedigree relationship matrix (i.e., scaling by averages) is one way to ensure compatibility. This requires computing both relationship matrices, calculating averages, and changing G, whereas only the inverses of those matrices are needed in the mixed model equations. Therefore, the compatibility process can add extra computing burden. In the single-step Bayesian regression, the scaling is done by including a mean (μ) as a fixed effect in the model. The parameter μ can be interpreted as the average of the breeding values of the genotyped animals. In this study, such scaling, called automatic, was implemented in ssGBLUP via Quaas-Pollak transformation of the inverse of the relationship matrix used in ssGBLUP (H), which combines the inverses of the pedigree and genomic relationship matrices. Comparisons involved a simulated data set, and the genomic relationship matrix was computed using different allele frequencies either from the current population (i.e., realized allele frequencies), equal among all the loci, or from the base population. For all of the scenarios, we computed bias [defined as the average difference between true breeding values (TBV) and genomic estimated breeding values (GEBV)], accuracy (defined as the correlation between TBV and GEBV), and dispersion (defined as the regression coefficient of GEBV on TBV). With no scaling, the bias expressed in terms of genetic standard deviations was 0.86, 0.64, and 0.58 with realized, equal, and base population allele frequencies, respectively. With scaling by averages, which is currently used in ssGBLUP, bias was 0.07, 0.08, and 0.03, respectively. With automatic scaling, bias was 0.18 regardless of allele frequencies. Accuracies were similar among scaling methods, but about 0.1 lower in the scenario without scaling. The GEBV were more inflated without any scaling, whereas the automatic scaling performed similarly to the scaling by averages. The average dispersion for those methods was 0.94. When μ was treated as random, with the variance equal to differences between pedigree and genomic relationships, the bias was the same as with the scaling by averages. The automatic scaling is biased, especially when μ is treated as a fixed effect. The bias may be small in real data with fewer generations, when traits are undergoing weak selection, or when the number of genotyped animals is large.
单步基因组最佳线性无偏预测（ssGBLUP）需要基因组和系谱关系兼容，以实现无偏和准确的预测。通过对基因组关系矩阵（G）进行平均尺度缩放（即按平均值缩放）是确保兼容性的一种方法。这需要计算两个关系矩阵、计算平均值并更改 G，而混合模型方程中只需要这些矩阵的逆。因此，兼容性过程可能会增加额外的计算负担。在单步贝叶斯回归中，通过在模型中包含均值（μ）作为固定效应来进行缩放。参数μ可以解释为基因型动物育种值的平均值。在这项研究中，通过 Quaas-Pollak 变换用于 ssGBLUP 的关系矩阵（H）的逆来实现这种自动缩放，该变换结合了系谱和基因组关系矩阵的逆。比较涉及模拟数据集，并且基因组关系矩阵是使用当前群体（即实现的等位基因频率）中的不同等位基因频率计算的，或者在所有位点上相等，或者从基础群体中计算的。对于所有情况，我们计算了偏差[定义为真实育种值（TBV）和基因组估计育种值（GEBV）之间的平均差异]、准确性（定义为 TBV 和 GEBV 之间的相关性）和分散度（定义为 GEBV 对 TBV 的回归系数）。没有缩放时，以遗传标准差表示的偏差分别为 0.86、0.64 和 0.58，与实现、相等和基础群体等位基因频率相对应。使用平均尺度缩放（目前在 ssGBLUP 中使用）时，偏差分别为 0.07、0.08 和 0.03。使用自动缩放时，无论等位基因频率如何，偏差均为 0.18。在缩放方法之间，准确性相似，但没有缩放的情况下，准确性约低 0.1。没有任何缩放时，GEBV 膨胀更大，而自动缩放与平均缩放效果相似。这些方法的平均分散度为 0.94。当μ被视为随机变量，方差等于系谱和基因组关系之间的差异时，偏差与平均缩放相同。当μ被视为固定效应时，自动缩放存在偏差。在实际数据中，世代较少、性状受到较弱选择或基因型动物数量较大时，偏差可能较小。
