Pedigree information is often missing for some animals in a breeding program. Unknown-parent groups (UPGs) are assigned to the missing parents to avoid biased genetic evaluations. Although the use of UPGs is well established for the pedigree model, it is unclear how UPGs are integrated into the inverse of the unified relationship matrix (H-inverse) required for single-step genomic best linear unbiased prediction. A generalization of the UPG model is the metafounder (MF) model. The objectives of this study were to derive 3 H-inverses and to compare genetic trends among models with UPG and MF H-inverses using a simulated purebred population. All inverses were derived using the joint density function of the random breeding values and genetic groups. The breeding values of genotyped animals (u2) were assumed to be adjusted for UPG effects (g) using matrix Q2 as u2∗=u2+Q2g before incorporating genomic information. The Quaas–Pollak-transformed (QP) H-inverse was derived using a joint density function of u2∗ and g updated with genomic information and assuming nonzero cov(u2∗,g′). The modified QP (altered) H-inverse also assumes that the genomic information updates u2∗ and g, but cov(u2∗,g′)=0. The UPG-encapsulated (EUPG) H-inverse assumed genomic information updates the distribution of u2∗. The EUPG H-inverse had the same structure as the MF H-inverse. Fifty percent of the genotyped females in the simulation had a missing dam, and missing parents were replaced with UPGs by generation. The simulation study indicated that u2∗ and g in models using the QP and altered H-inverses may be inseparable leading to potential biases in genetic trends. Models using the EUPG and MF H-inverses showed no genetic trend biases. These 2 H-inverses yielded the same genomic EBV (GEBV). The predictive ability and inflation of GEBVs from young genotyped animals were nearly identical among models using the QP, altered, EUPG, and MF H-inverses. Although the choice of H-inverse in real applications with enough data may not result in biased genetic trends, the EUPG and MF H-inverses are to be preferred because of theoretical justification and possibility to reduce biases.

中文翻译：

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单步基因组预测中缺失谱系模型的比较

在育种计划中，某些动物经常缺少谱系信息。未知父母组（UPG）被分配给失踪的父母，以避免有偏见的遗传评估。尽管 UPG 的使用已经很好地用于谱系模型，但尚不清楚如何将 UPG 集成到单步基因组最佳线性无偏预测所需的统一关系矩阵（H 逆）的逆矩阵中。UPG 模型的推广是元创始人 (MF) 模型。本研究的目的是推导出 3 个 H 逆，并使用模拟纯种种群比较具有 UPG 和 MF H 逆的模型之间的遗传趋势。所有的逆都是使用随机育种值和遗传组的联合密度函数得出的。假设基因分型动物 (u2) 的育种值在合并基因组信息之前使用矩阵 Q2 作为 u2∗=u2+Q2g 针对 UPG 效应 (g) 进行调整。Quaas-Pollak-transformed (QP) H-inverse 是使用 u2* 和 g 的联合密度函数推导出来的，用基因组信息更新并假设非零 cov(u2*,g')。修改后的 QP（改变的）H-inverse 还假设基因组信息更新 u2* 和 g，但 cov(u2*,g')=0。UPG 封装（EUPG）H 逆假设基因组信息更新了 u2* 的分布。EUPG H-inverse 与 MF H-inverse 具有相同的结构。模拟中 50% 的基因分型雌性有一个失踪的大坝，失踪的父母被一代代的 UPG 取代。模拟研究表明，使用 QP 和改变的 H 逆的模型中的 u2* 和 g 可能是不可分割的，导致遗传趋势的潜在偏差。使用 EUPG 和 MF H-inverses 的模型没有显示出遗传趋势偏差。这 2 个 H 逆产生了相同的基因组 EBV (GEBV)。来自年轻基因型动物的 GEBV 的预测能力和膨胀在使用 QP、改变、EUPG 和 MF H 逆的模型中几乎相同。尽管在具有足够数据的实际应用中选择 H-inverse 可能不会导致有偏差的遗传趋势，但 EUPG 和 MF H-inverses 是首选，因为理论上的合理性和减少偏差的可能性。来自年轻基因型动物的 GEBV 的预测能力和膨胀在使用 QP、改变、EUPG 和 MF H 逆的模型中几乎相同。尽管在具有足够数据的实际应用中选择 H-inverse 可能不会导致有偏差的遗传趋势，但 EUPG 和 MF H-inverses 是首选，因为理论上的合理性和减少偏差的可能性。来自年轻基因型动物的 GEBV 的预测能力和膨胀在使用 QP、改变、EUPG 和 MF H 逆的模型中几乎相同。尽管在具有足够数据的实际应用中选择 H-inverse 可能不会导致有偏差的遗传趋势，但 EUPG 和 MF H-inverses 是首选，因为理论上的合理性和减少偏差的可能性。