BACKGROUND The dimensionality of genomic information is limited by the number of independent chromosome segments (Me), which is a function of the effective population size. This dimensionality can be determined approximately by singular value decomposition of the gene content matrix, by eigenvalue decomposition of the genomic relationship matrix (GRM), or by the number of core animals in the algorithm for proven and young (APY) that maximizes the accuracy of genomic prediction. In the latter, core animals act as proxies to linear combinations of Me. Field studies indicate that a moderate accuracy of genomic selection is achieved with a small dataset, but that further improvement of the accuracy requires much more data. When only one quarter of the optimal number of core animals are used in the APY algorithm, the accuracy of genomic selection is only slightly below the optimal value. This suggests that genomic selection works on clusters of Me. RESULTS The simulation included datasets with different population sizes and amounts of phenotypic information. Computations were done by genomic best linear unbiased prediction (GBLUP) with selected eigenvalues and corresponding eigenvectors of the GRM set to zero. About four eigenvalues in the GRM explained 10% of the genomic variation, and less than 2% of the total eigenvalues explained 50% of the genomic variation. With limited phenotypic information, the accuracy of GBLUP was close to the peak where most of the smallest eigenvalues were set to zero. With a large amount of phenotypic information, accuracy increased as smaller eigenvalues were added. CONCLUSIONS A small amount of phenotypic data is sufficient to estimate only the effects of the largest eigenvalues and the associated eigenvectors that contain a large fraction of the genomic information, and a very large amount of data is required to estimate the remaining eigenvalues that account for a limited amount of genomic information. Core animals in the APY algorithm act as proxies of almost the same number of eigenvalues. By using an eigenvalues-based approach, it was possible to explain why the moderate accuracy of genomic selection based on small datasets only increases slowly as more data are added.

中文翻译：

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当考虑基于最大特征值数量的基因组关系矩阵时，基因组BLUP的准确性：模拟研究。

背景技术基因组信息的维度受到独立染色体区段（Me）的数量的限制，独立染色体区段（Me）的数量是有效种群大小的函数。可以通过基因内容矩阵的奇异值分解，基因组关系矩阵（GRM）的特征值分解或通过已验证和年轻的算法（APY）中的核心动物数量来最大程度地确定该维数。基因组预测。在后者中，核心动物充当Me线性组合的代理。现场研究表明，使用较小的数据集可获得中等程度的基因组选择准确度，但是进一步提高准确度需要更多的数据。当APY算法仅使用最佳动物数量的四分之一时，基因组选择的准确性仅略低于最佳值。这表明基因组选择对Me簇起作用。结果模拟包括具有不同种群大小和表型信息量的数据集。通过基因组最佳线性无偏预测（GBLUP）将选定的特征值和GRM的对应特征向量设置为零来进行计算。GRM中约有四个特征值解释了10％的基因组变异，少于总特征值的2％解释了50％的基因组变异。在有限的表型信息下，GBLUP的准确性接近峰值，在该峰值处，大多数最小特征值均设为零。有了大量的表型信息，由于添加了较小的特征值，因此准确性提高了。结论少量的表型数据足以仅估计最大特征值和包含大部分基因组信息的相关特征向量的影响，并且需要非常大量的数据来估计剩下的特征值。数量有限的基因组信息。APY算法中的核心动物充当几乎相同数量的特征值的代理。通过使用基于特征值的方法，可以解释为什么基于小数据集的基因组选择的中等准确性只会随着添加更多数据而缓慢增加。并且需要大量的数据来估计占有限数量的基因组信息的剩余特征值。APY算法中的核心动物充当几乎相同数量的特征值的代理。通过使用基于特征值的方法，可以解释为什么基于小数据集的基因组选择的中等准确性只会随着添加更多数据而缓慢增加。并且需要大量的数据来估计占有限数量的基因组信息的剩余特征值。APY算法中的核心动物充当几乎相同数量的特征值的代理。通过使用基于特征值的方法，可以解释为什么基于小数据集的基因组选择的中等准确性只会随着添加更多数据而缓慢增加。