In breeding programmes, the observed genetic change is a sum of the contributions of different selection paths represented by groups of individuals. Quantifying these sources of genetic change is essential for identifying the key breeding actions and optimizing breeding programmes. However, it is difficult to disentangle the contribution of individual paths due to the inherent complexity of breeding programmes. Here we extend the previously developed method for partitioning genetic mean by paths of selection to work both with the mean and variance of breeding values. First, we extended the partitioning method to quantify the contribution of different paths to genetic variance assuming that the breeding values are known. Second, we combined the partitioning method with the Markov Chain Monte Carlo approach to draw samples from the posterior distribution of breeding values and use these samples for computing the point and interval estimates of partitions for the genetic mean and variance. We implemented the method in the R package AlphaPart. We demonstrated the method with a simulated cattle breeding programme. We show how to quantify the contribution of different groups of individuals to genetic mean and variance and that the contributions of different selection paths to genetic variance are not necessarily independent. Finally, we observed that the partitioning method under the pedigree-based model has some limitations, which suggests the need for a genomic extension. We presented a partitioning method to quantify sources of change in genetic mean and variance in breeding programmes. The method can help breeders and researchers understand the dynamics in genetic mean and variance in a breeding programme. The developed method for partitioning genetic mean and variance is a powerful method for understanding how different selection paths interact within a breeding programme and how they can be optimised.

中文翻译：

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一种划分遗传均值和方差趋势以了解育种实践的方法

在育种计划中，观察到的遗传变化是由个体群体代表的不同选择路径的贡献的总和。量化这些遗传变化的来源对于确定关键育种行为和优化育种计划至关重要。然而，由于育种计划的内在复杂性，很难区分各个路径的贡献。在这里，我们扩展了先前开发的通过选择路径划分遗传均值的方法，以同时处理育种值的均值和方差。首先，假设育种值已知，我们扩展了分区方法以量化不同路径对遗传方差的贡献。第二，我们将分区方法与马尔可夫链蒙特卡罗方法相结合，从育种值的后验分布中抽取样本，并使用这些样本计算遗传均值和方差的分区的点估计和区间估计。我们在 R 包 AlphaPart 中实现了该方法。我们通过模拟牛育种程序演示了该方法。我们展示了如何量化不同群体的个体对遗传均值和方差的贡献，以及不同选择路径对遗传方差的贡献不一定是独立的。最后，我们观察到基于谱系模型下的分区方法有一些局限性，这表明需要进行基因组扩展。我们提出了一种分区方法来量化育种计划中遗传均值和方差的变化来源。该方法可以帮助育种者和研究人员了解育种计划中遗传均值和方差的动态变化。用于划分遗传均值和方差的开发方法是了解不同选择路径如何在育种计划中相互作用以及如何优化它们的有效方法。