Genomic relationship matrices are used to obtain genomic inbreeding coefficients. However, there are several methodologies to compute these matrices and there is still an unresolved debate on which one provides the best estimate of inbreeding. In this study, we investigated measures of inbreeding obtained from five genomic matrices, including the Nejati-Javaremi allelic relationship matrix (FNEJ), the Li and Horvitz matrix based on excess of homozygosity (FL&H), and the VanRaden (methods 1, FVR1, and 2, FVR2) and Yang (FYAN) genomic relationship matrices. We derived expectations for each inbreeding coefficient, assuming a single locus model, and used these expectations to explain the patterns of the coefficients that were computed from thousands of single nucleotide polymorphism genotypes in a population of Iberian pigs. Except for FNEJ, the evaluated measures of inbreeding do not match with the original definitions of inbreeding coefficient of Wright (correlation) or Malécot (probability). When inbreeding coefficients are interpreted as indicators of variability (heterozygosity) that was gained or lost relative to a base population, both FNEJ and FL&H led to sensible results but this was not the case for FVR1, FVR2 and FYAN. When variability has increased relative to the base, FVR1, FVR2 and FYAN can indicate that it decreased. In fact, based on FYAN, variability is not expected to increase. When variability has decreased, FVR1 and FVR2 can indicate that it has increased. Finally, these three coefficients can indicate that more variability than that present in the base population can be lost, which is also unreasonable. The patterns for these coefficients observed in the pig population were very different, following the derived expectations. As a consequence, the rate of inbreeding depression estimated based on these inbreeding coefficients differed not only in magnitude but also in sign. Genomic inbreeding coefficients obtained from the diagonal elements of genomic matrices can lead to inconsistent results in terms of gain and loss of genetic variability and inbreeding depression estimates, and thus to misleading interpretations. Although these matrices have proven to be very efficient in increasing the accuracy of genomic predictions, they do not always provide a useful measure of inbreeding.

中文翻译：

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基因组关系矩阵对于估计近亲繁殖水平的价值


基因组关系矩阵用于获得基因组近交系数。然而，有多种方法可以计算这些矩阵，并且关于哪种方法可以提供近亲繁殖的最佳估计仍然存在未决的争论。在本研究中，我们研究了从五个基因组矩阵获得的近交测量，包括 Nejati-Javaremi 等位基因关系矩阵 (FNEJ)、基于纯合性过剩的 Li 和 Horvitz 矩阵 (FL&H) 以及 VanRaden（方法 1、FVR1、 2，FVR2）和Yang（FYAN）基因组关系矩阵。我们假设单基因座模型，得出每个近交系数的期望值，并使用这些期望值来解释根据伊比利亚猪群体中数千个单核苷酸多态性基因型计算得出的系数模式。除FNEJ外，近亲繁殖的评估指标与Wright（相关性）或Malécot（概率）的近亲繁殖系数的原始定义不符。当近交系数被解释为相对于基础群体获得或丧失的变异性（杂合性）指标时，FNEJ 和 FL&H 都得出了合理的结果，但 FVR1、FVR2 和 FYAN 的情况并非如此。当变异性相对于基础增加时，FVR1、FVR2 和 FYAN 可以表明变异性下降。事实上，根据 FYAN，变异性预计不会增加。当变异性降低时，FVR1 和 FVR2 可以表明变异性已增加。最后，这三个系数可以表明可能会丢失比基础总体中存在的更多的变异性，这也是不合理的。根据推导的预期，在猪群中观察到的这些系数的模式非常不同。 因此，根据这些近交系数估计的近交衰退率不仅在大小上不同，而且在符号上也不同。从基因组矩阵的对角线元素获得的基因组近交系数可能导致遗传变异性的增益和损失以及近交抑制估计结果不一致，从而导致误导性的解释。尽管这些矩阵已被证明在提高基因组预测的准确性方面非常有效，但它们并不总是提供近亲繁殖的有用测量。