Multi-trait single step genetic evaluation is increasingly facing the situation of having more individuals with genotypes than markers within each genotype. This creates a situation where the genomic relationship matrix ( $$\mathbf{G }$$ ) is not of full rank and its inversion is algebraically impossible. Recently, the SS-T-BLUP method was proposed as a modified version of the single step equations, providing an elegant way to circumvent the inversion of the $$\mathbf{G }$$ and therefore accommodate the situation described. SS-T-BLUP uses the Woodbury matrix identity, thus it requires an add-on matrix, which is usually the covariance matrix of the residual polygenic effet. In this paper, we examine the application of SS-T-BLUP to a large-scale multi-trait Australian Angus beef cattle dataset using the full BREEDPLAN single step genetic evaluation model and compare the results to the application of two different methods of using $$\mathbf{G }$$ in a single step model. Results clearly show that SS-T-BLUP outperforms other single step formulations in terms of computational speed and avoids approximation of the inverse of $$\mathbf{G }$$ .

中文翻译：

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动物多于标记：单步T-BLUP模型在大规模多性状澳大利亚安格斯肉牛遗传评估中的应用研究

多特征单步遗传评估越来越面临这样的情况，即具有更多基因型的个体比每个基因型中的标记多。这就造成了一种情况，即基因组关系矩阵（$$ \ mathbf {G} $$）的等级不高，其求反在代数上是不可能的。最近，提出了SS-T-BLUP方法作为单步方程的修改版本，它提供了一种优雅的方法来规避$$ \ mathbf {G} $$的反演，从而适应上述情况。SS-T-BLUP使用伍德伯里矩阵恒等式，因此它需要一个附加矩阵，该矩阵通常是残基多基因效应的协方差矩阵。在本文中，我们使用完整的BREEDPLAN单步遗传评估模型研究了SS-T-BLUP在大规模多特征澳大利亚安格斯肉牛数据集上的应用，并将结果与​​两种使用$$ \ mathbf {单步模型中的G} $$。结果清楚地表明，SS-T-BLUP在计算速度方面优于其他单步公式，并且避免了$$ \ mathbf {G} $$的逆数的近似。