The genetic correlation between purebred (PB) and crossbred (CB) performances ( $${r}_{pc}$$ ) partially determines the response in CB when selection is on PB performance in the parental lines. An earlier study has derived expressions for an upper and lower bound of $${r}_{pc}$$ , using the variance components of the parental purebred lines, including e.g. the additive genetic variance in the sire line for the trait expressed in one of the dam lines. How to estimate these variance components is not obvious, because animals from one parental line do not have phenotypes for the trait expressed in the other line. Thus, the aim of this study was to propose and compare three methods for approximating the required variance components. The first two methods are based on (co)variances of genomic estimated breeding values (GEBV) in the line of interest, either accounting for shrinkage (VCGEBV-S) or not (VCGEBV). The third method uses restricted maximum likelihood (REML) estimates directly from univariate and bivariate analyses (VCREML) by ignoring that the variance components should refer to the line of interest, rather than to the line in which the trait is expressed. We validated these methods by comparing the resulting predicted bounds of $${r}_{pc}$$ with the $${r}_{pc}$$ estimated from PB and CB data for five traits in a three-way cross in pigs. With both VCGEBV and VCREML, the estimated $${r}_{pc}$$ (plus or minus one standard error) was between the upper and lower bounds in 14 out of 15 cases. However, the range between the bounds was much smaller with VCREML (0.15–0.22) than with VCGEBV (0.44–0.57). With VCGEBV-S, the estimated $${r}_{pc}$$ was between the upper and lower bounds in only six out of 15 cases, with the bounds ranging from 0.21 to 0.44. We conclude that using REML estimates of variance components within and between parental lines to predict the bounds of $${r}_{pc}$$ resulted in better predictions than methods based on GEBV. Thus, we recommend that the studies that estimate $${r}_{pc}$$ with genotype data also report estimated genetic variance components within and between the parental lines.

中文翻译：

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从亲本品系的表型和基因型标记数据预测基因型与基因型相互作用对纯种-杂交遗传相关性的影响

The genetic correlation between purebred (PB) and crossbred (CB) performances ( $${r}_{pc}$$ ) partially determines the response in CB when selection is on PB performance in the parental lines. 一项较早的研究使用亲本纯种品系的方差分量导出了 $${r}_{pc}$$ 的上限和下限的表达式，包括例如父系中表达的性状的加性遗传方差大坝线之一。如何估计这些方差分量并不明显，因为来自一个亲本系的动物不具有在另一系中表达的性状的表型。因此，本研究的目的是提出并比较三种近似所需方差分量的方法。前两种方法基于感兴趣的基因组估计育种值 (GEBV) 的（协）方差，考虑收缩 (VCGEBV-S) 或不考虑 (VCGEBV)。第三种方法使用直接来自单变量和双变量分析 (VCREML) 的受限最大似然 (REML) 估计，忽略方差分量应指的是感兴趣的线，而不是表达特征的线。我们通过比较 $${r}_{pc}$$ 的预测边界与从 PB 和 CB 数据估计的三向杂交中的五个性状的 $${r}_{pc}$$ 来验证这些方法在猪中。对于 VCGEBV 和 VCREML，在 15 个案例中有 14 个案例的估计 $${r}_{pc}$$（加上或减去一个标准误差）在上限和下限之间。但是，VCREML (0.15–0.22) 的界限之间的范围比 VCGEBV (0.44–0.57) 小得多。使用 VCGEBV-S，在 15 个案例中，估计的 $${r}_{pc}$$ 只有 6 个在上限和下限之间，范围从 0.21 到 0.44。我们得出结论，与基于 GEBV 的方法相比，使用 REML 估计父母系内和父母系之间的方差分量来预测 $${r}_{pc}$$ 的边界会产生更好的预测。因此，我们建议使用基因型数据估计 $${r}_{pc}$$ 的研究也报告了亲本系内和亲本系之间的估计遗传方差成分。