Limitations of the concept of identity by descent in the presence of stratification within a breeding population may lead to an incomplete formulation of the conventional numerator relationship matrix ( $$\mathbf{A}$$ ). Combining $$\mathbf{A}$$ with the genomic relationship matrix ( $$\mathbf{G}$$ ) in a single-step approach for genetic evaluation may cause inconsistencies that can be a source of bias in the resulting predictions. The objective of this study was to identify stratification using genomic data and to transfer this information to matrix $$\mathbf{A}$$ , to improve the compatibility of $$\mathbf{A}$$ and $$\mathbf{G}$$ . Using software to detect population stratification (ADMIXTURE), we developed an iterative approach. First, we identified 2 to 40 strata ( $$k$$ ) with ADMIXTURE, which we then introduced in a stepwise manner into matrix $$\mathbf{A}$$ , to generate matrix $${\mathbf{A}}^{{\varvec{\Gamma}}}$$ using the metafounder methodology. Improvements in consistency between matrix $$\mathbf{G}$$ and $${\mathbf{A}}^{{\varvec{\Gamma}}}$$ were evaluated by regression analysis and through the comparison of the overall mean and mean diagonal values of both matrices. The approach was tested on genotype and pedigree information of European and North American Brown Swiss animals (85,249). Analyses with ADMIXTURE were initially performed on the full set of genotypes (S1). In addition, we used an alternative dataset where we avoided sampling of closely related animals (S2). Results of the regression analyses of standard $$\mathbf{A}$$ on $$\mathbf{G}$$ were – 0.489, 0.780 and 0.647 for intercept, slope and fit of the regression. When analysing S1 data results of the regression for $${\mathbf{A}}^{{\varvec{\Gamma}}}$$ on $$\mathbf{G}$$ corresponding values were – 0.028, 1.087 and 0.807 for $$k$$ =7, while there was no clear optimum $$k$$ . Analyses of S2 gave a clear optimal $$k$$ =24, with − 0.020, 0.998 and 0.817 as results of the regression. For this $$k$$ differences in mean and mean diagonal values between both matrices were negligible. The derivation of hidden stratification information based on genotyped animals and its integration into $$\mathbf{A}$$ improved compatibility of the resulting $${\mathbf{A}}^{{\varvec{\Gamma}}}$$ and $$\mathbf{G}$$ considerably compared to the initial situation. In dairy breeding populations with large half-sib families as sub-structures it is necessary to balance the data when applying population structure analysis to obtain meaningful results.

中文翻译：

---

基于人群结构分析的元创始人定义


在繁殖群体内存在分层的情况下，血统同一性概念的局限性可能会导致传统分子关系矩阵 ( $$\mathbf{A}$$ ) 的不完整表述。在遗传评估的单步方法中将 $$\mathbf{A}$$ 与基因组关系矩阵 ( $$\mathbf{G}$$ ) 相结合可能会导致不一致，从而成为结果预测中的偏差来源。本研究的目的是使用基因组数据识别分层并将此信息传输到矩阵 $$\mathbf{A}$$ ，以提高 $$\mathbf{A}$$ 和 $$\mathbf{G 的兼容性}$$ 。使用软件检测群体分层 (ADMIXTURE)，我们开发了一种迭代方法。首先，我们使用 ADMIXTURE 识别出 2 到 40 个层（ $$k$$ ），然后将其逐步引入矩阵 $$\mathbf{A}$$ 中，以生成矩阵 $${\mathbf{A}} ^{{\varvec{\Gamma}}}$$ 使用元创建者方法。通过回归分析和总体平均值的比较来评估矩阵 $$\mathbf{G}$$ 和 $${\mathbf{A}}^{{\varvec{\Gamma}}}$$ 之间一致性的改进以及两个矩阵的平均对角线值。该方法针对欧洲和北美棕色瑞士动物 (85,249) 的基因型和谱系信息进行了测试。最初对全套基因型 (S1) 进行了 ADMIXTURE 分析。此外，我们使用了替代数据集，避免对密切相关的动物进行采样（S2）。标准 $$\mathbf{A}$$ 对 $$\mathbf{G}$$ 的回归分析结果为 – 0.489、0.780 和 0.647 的截距、斜率和回归拟合。 分析 $$\mathbf{G}$$ 上 $${\mathbf{A}}^{{\varvec{\Gamma}}}$$ 回归的 S1 数据结果时，相应值为 – 0.028、1.087 和 0.807对于 $$k$$ =7，而没有明确的最佳 $$k$$ 。 S2 的分析给出了明确的最佳 $$k$$ =24，回归结果为 −0.020、0.998 和 0.817。对于这个 $$k$$ 两个矩阵之间的平均值和平均对角线值的差异可以忽略不计。基于基因型动物的隐藏分层信息的推导及其与 $$\mathbf{A}$$ 的整合提高了所得 $${\mathbf{A}}^{{\varvec{\Gamma}}}$$ 的兼容性与初始情况相比，$$\mathbf{G}$$ 显着增加。在以大型同父异母家族为子结构的奶牛育种群体中，在应用群体结构分析时必须平衡数据以获得有意义的结果。