Departamento de Producción Animal, Universidad de Buenos Aires, Argentina.
Genet Sel Evol. 2010 Jun 11;42(1):20. doi: 10.1186/1297-9686-42-20.
It has been argued that multibreed animal models should include a heterogeneous covariance structure. However, the estimation of the (co)variance components is not an easy task, because these parameters can not be factored out from the inverse of the additive genetic covariance matrix. An alternative model, based on the decomposition of the genetic covariance matrix by source of variability, provides a much simpler formulation. In this study, we formalize the equivalence between this alternative model and the one derived from the quantitative genetic theory. Further, we extend the model to include maternal effects and, in order to estimate the (co)variance components, we describe a hierarchical Bayes implementation. Finally, we implement the model to weaning weight data from an Angus x Hereford crossbred experiment.
Our argument is based on redefining the vectors of breeding values by breed origin such that they do not include individuals with null contributions. Next, we define matrices that retrieve the null-row and the null-column pattern and, by means of appropriate algebraic operations, we demonstrate the equivalence. The extension to include maternal effects and the estimation of the (co)variance components through the hierarchical Bayes analysis are then straightforward. A FORTRAN 90 Gibbs sampler was specifically programmed and executed to estimate the (co)variance components of the Angus x Hereford population.
In general, genetic (co)variance components showed marginal posterior densities with a high degree of symmetry, except for the segregation components. Angus and Hereford breeds contributed with 50.26% and 41.73% of the total direct additive variance, and with 23.59% and 59.65% of the total maternal additive variance. In turn, the contribution of the segregation variance was not significant in either case, which suggests that the allelic frequencies in the two parental breeds were similar.
The multibreed maternal animal model introduced in this study simplifies the problem of estimating (co)variance components in the framework of a hierarchical Bayes analysis. Using this approach, we obtained for the first time estimates of the full set of genetic (co)variance components. It would be interesting to assess the performance of the procedure with field data, especially when interbreed information is limited.
有人认为，多品种动物模型应包括异质协方差结构。然而，协方差分量的估计并不是一件容易的事，因为这些参数不能从加性遗传协方差矩阵的逆中分离出来。基于变异来源对遗传协方差矩阵进行分解的替代模型提供了一种更为简单的方法。在这项研究中，我们形式化地证明了这种替代模型与从数量遗传学理论中得出的模型之间的等价性。此外，我们将该模型扩展到包括母本效应，并为了估计协方差分量，我们描述了一个分层贝叶斯实现。最后，我们将该模型应用于 Angus x Hereford 杂交实验的断奶体重数据。
我们的论点是基于通过品种起源重新定义育种值向量，使得它们不包括没有贡献的个体。接下来，我们定义了检索空行和空列模式的矩阵，并通过适当的代数运算证明了等价性。然后，通过分层贝叶斯分析很容易扩展到包括母本效应和估计协方差分量。具体来说，我们专门编写了一个 FORTRAN 90 Gibbs 抽样器来估计 Angus x Hereford 群体的协方差分量。
一般来说，遗传（协）方差分量的边缘后验密度具有高度对称性，除了分离分量。 Angus 和 Hereford 品种分别贡献了总直接加性方差的 50.26%和 41.73%，以及总母本加性方差的 23.59%和 59.65%。反过来，两种情况下的分离方差贡献都不显著，这表明两个亲本品种的等位基因频率相似。
本研究中引入的多品种母本动物模型简化了在分层贝叶斯分析框架下估计协方差分量的问题。使用这种方法，我们首次获得了完整的遗传协方差分量的估计值。用现场数据评估该程序的性能将是很有趣的，特别是当杂交信息有限时。
