Reliabilities of best linear unbiased predictions (BLUP) of breeding values are defined as the squared correlation between true and estimated breeding values and are helpful in assessing risk and genetic gain. Reliabilities can be computed from the prediction error variances for models with a single base population but are undefined for models that include several base populations and when unknown parent groups are modeled as fixed effects. In such a case, the use of metafounders in principle enables reliabilities to be derived. We propose to compute the reliability of the contrast of an individual’s estimated breeding value with that of a metafounder based on the prediction error variances of the individual and the metafounder, their prediction error covariance, and their genetic relationship. Computation of the required terms demands only little extra work once the sparse inverse of the mixed model equations is obtained, or they can be approximated. This also allows the reliabilities of the metafounders to be obtained. We studied the reliabilities for both BLUP and single-step genomic BLUP (ssGBLUP), using several definitions of reliability in a large dataset with 1,961,687 dairy sheep and rams, most of which had phenotypes and among which 27,000 rams were genotyped with a 50K single nucleotide polymorphism (SNP) chip. There were 23 metafounders with progeny sizes between 100,000 and 2000 individuals. In models with metafounders, directly using the prediction error variance instead of the contrast with a metafounder leads to artificially low reliabilities because they refer to a population with maximum heterozygosity. When only one metafounder is fitted in the model, the reliability of the contrast is shown to be equivalent to the reliability of the individual in a model without metafounders. When there are several metafounders in the model, using a contrast with the oldest metafounder yields reliabilities that are on a meaningful scale and very close to reliabilities obtained from models without metafounders. The reliabilities using contrasts with ssGBLUP also resulted in meaningful values. This work provides a general method to obtain reliabilities for both BLUP and ssGBLUP when several base populations are included through metafounders.

中文翻译：

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具有元创始人的模型中估计育种值的可靠性

育种值的最佳线性无偏预测 (BLUP) 的可靠性被定义为真实育种值和估计育种值之间的平方相关性，有助于评估风险和遗传增益。可以根据具有单个基本总体的模型的预测误差方差计算可靠性，但对于包含多个基本总体的模型以及未知父组建模为固定效应时，可靠性是不确定的。在这种情况下，原则上使用元创始人可以推导出可靠性。我们建议根据个体和元创始人的预测误差方差、预测误差协方差及其遗传关系来计算个体估计育种值与元创始人的对比的可靠性。一旦获得混合模型方程的稀疏逆，或者它们可以被近似，所需项的计算只需要很少的额外工作。这也允许获得元创始人的可靠性。我们研究了 BLUP 和单步基因组 BLUP (ssGBLUP) 的可靠性，在包含 1,961,687 只奶羊和公羊的大型数据集中使用了几种可靠性定义，其中大部分具有表型，其中 27,000 只公羊用 50K 单核苷酸进行了基因分型多态性（SNP）芯片。有 23 位元创始人的后代规模在 100,000 到 2000 人之间。在具有元创始人的模型中，直接使用预测误差方差而不是与元创始人的对比会导致人为地降低可靠性，因为它们指的是具有最大杂合性的人群。当模型中只有一个元创始人时，对比的可靠性显示等同于没有元创始人的模型中个体的可靠性。当模型中有多个元创始人时，与最老的元创始人进行对比会产生有意义的可靠性，并且非常接近从没有元创始人的模型中获得的可靠性。使用与 ssGBLUP 对比的可靠性也产生了有意义的值。当通过 metafounders 包含多个基础人群时，这项工作提供了一种获得 BLUP 和 ssGBLUP 可靠性的通用方法。与最古老的元创始人进行对比会产生有意义的可靠性，并且非常接近从没有元创始人的模型中获得的可靠性。使用与 ssGBLUP 对比的可靠性也产生了有意义的值。当通过 metafounders 包含多个基础人群时，这项工作提供了一种获得 BLUP 和 ssGBLUP 可靠性的通用方法。与最古老的元创始人进行对比会产生有意义的可靠性，并且非常接近从没有元创始人的模型中获得的可靠性。使用与 ssGBLUP 对比的可靠性也产生了有意义的值。当通过 metafounders 包含多个基础人群时，这项工作提供了一种获得 BLUP 和 ssGBLUP 可靠性的通用方法。