Naturally and artificially selected populations usually exhibit some degree of stratification. In Genome-Wide Association Studies and in Whole-Genome Regressions (WGR) analyses, population stratification has been either ignored or dealt with as a potential confounder. However, systematic differences in allele frequency and in patterns of linkage disequilibrium can induce sub-population-specific effects. From this perspective, structure acts as an effect modifier rather than as a confounder. In this article, we extend WGR models commonly used in plant and animal breeding to allow for sub-population-specific effects. This is achieved by decomposing marker effects into main effects and interaction components that describe group-specific deviations. The model can be used both with variable selection and shrinkage methods and can be implemented using existing software for genomic selection. Using a wheat and a pig breeding data set, we compare parameter estimates and the prediction accuracy of the interaction WGR model with WGR analysis ignoring population stratification (across-group analysis) and with a stratified (i.e., within-sub-population) WGR analysis. The interaction model renders trait-specific estimates of the average correlation of effects between sub-populations; we find that such correlation not only depends on the extent of genetic differentiation in allele frequencies between groups but also varies among traits. The evaluation of prediction accuracy shows a modest superiority of the interaction model relative to the other two approaches. This superiority is the result of better stability in performance of the interaction models across data sets and traits; indeed, in almost all cases, the interaction model was either the best performing model or it performed close to the best performing model. ELECTRONIC SUPPLEMENTARY MATERIAL Supplementary materials for this article are available at 10.1007/s13253-015-0222-5.

中文翻译：

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使用相互作用将遗传异质性纳入全基因组回归中。

自然和人工选择的种群通常表现出一定程度的分层。在全基因组关联研究和全基因组回归（WGR）分析中，人口分层被忽略或被视为潜在的混杂因素。但是，等位基因频率和连锁不平衡模式的系统性差异可能会诱导亚群特异性效应。从这个角度来看，结构是一种效果修饰符，而不是混杂因素。在本文中，我们扩展了动植物育种中常用的WGR模型，以实现特定于亚种群的效果。这是通过将标记效果分解为描述特定于组的偏差的主要效果和交互组件来实现的。该模型可与变量选择和收缩方法一起使用，并可使用用于基因组选择的现有软件来实现。使用小麦和猪的繁殖数据集，我们将交互WGR模型的参数估计值和预测准确性与忽略人口分层（跨组分析）的WGR分析和分层（即亚种群内）WGR分析进行比较。相互作用模型给出了亚群之间效应的平均相关性的特定于性状的估计。我们发现，这种相关性不仅取决于群体之间等位基因频率的遗传分化程度，而且还取决于性状。相对于其他两种方法，对预测准确性的评估显示了交互模型的适度优势。这种优势是跨数据集和特征的交互模型的性能更好的稳定性的结果。实际上，在几乎所有情况下，交互模型要么是性能最佳的模型，要么是性能接近最佳性能的模型。电子补充材料本文的补充材料位于10.1007 / s13253-015-0222-5。