Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthurerstrasse 190, Zurich, Switzerland.
Department of Biostatistics, Epidemiology, Biostatistics and Prevention Institute, University of Zurich, Hirschengraben 84, Zurich, Switzerland.
Genet Sel Evol. 2019 Feb 28;51(1):7. doi: 10.1186/s12711-019-0449-7.
The animal model is a key tool in quantitative genetics and has been used extensively to estimate fundamental parameters, such as additive genetic variance or heritability. An implicit assumption of animal models is that all founder individuals derive from a single population. This assumption is commonly violated, for instance in crossbred livestock or when a meta-population is split into genetically differentiated subpopulations. Ignoring that base populations are genetically heterogeneous and thus split into different 'genetic groups' may lead to biased parameter estimates, especially for additive genetic variance. To avoid such biases, genetic group animal models, which account for the presence of more than one genetic group, have been proposed. Unfortunately, the method to date is only computationally feasible when the breeding values of the groups are allowed to differ in their means, but not in their variances.
We present an extension of the animal model that permits estimation of group-specific additive genetic variances. This is achieved by employing group-specific relatedness matrices for the breeding value components to different genetic groups. We derive these matrices by decomposing the full relatedness matrix via the generalized Cholesky decomposition, and by scaling the respective matrix components for each group. We propose a computationally convenient approximation for the matrix component that encodes for the Mendelian sampling variance, and show that this approximation is not critical. In addition, we explain why segregation variances are often negligible when analyzing the complex polygenic traits that are frequently the focus of evolutionary ecologists and animal breeders. Simulations and an example from an insular meta-population of house sparrows in Norway with three distinct genetic groups illustrate that the method is successful in estimating group-specific additive genetic variances, and that segregation variances are indeed negligible in the empirical example.
Quantifying differences in additive genetic variance within and among populations is of major biological interest in ecology, evolution, and animal and plant breeding. The proposed method allows to estimate such differences for subpopulations that form a connected set of populations, and may thus also be useful to study temporal or spatial variation of additive genetic variances.
动物模型是数量遗传学的关键工具，已广泛用于估计基本参数，如加性遗传方差或遗传力。动物模型的一个隐含假设是所有的基础个体都来自于一个单一的群体。这种假设通常是违反的，例如在杂交牲畜中，或者当一个复合种群被分裂成遗传分化的亚种群时。忽略基础群体是遗传异质的，因此被分为不同的“遗传群体”，可能会导致参数估计的偏差，特别是对于加性遗传方差。为了避免这种偏差，已经提出了考虑到存在多个遗传群体的遗传群体动物模型。不幸的是，迄今为止，该方法仅在允许组间的育种值在均值上有所不同，但方差上没有差异的情况下在计算上才可行。
我们提出了一种动物模型的扩展，允许估计特定群体的加性遗传方差。这是通过为不同遗传群体的育种值分量使用特定群体的亲缘关系矩阵来实现的。我们通过广义 Cholesky 分解来分解完整的亲缘关系矩阵，并对每个群体的相应矩阵分量进行缩放，从而得到这些矩阵。我们提出了一个用于矩阵分量的计算上方便的近似值，该分量用于编码孟德尔抽样方差，并表明该近似值并不关键。此外，我们解释了为什么在分析经常是生态学家和动物饲养者关注焦点的复杂多基因性状时，分离方差通常可以忽略不计。模拟和挪威一个有三个不同遗传群体的岛屿麻雀复合种群的实例表明，该方法成功地估计了特定群体的加性遗传方差，并且在实际例子中分离方差确实可以忽略不计。
在生态学、进化学以及动植物育种中，量化群体内和群体间的加性遗传方差差异具有重要的生物学意义。所提出的方法允许对形成一个连通种群集合的亚种群进行这种差异的估计，因此也可能对研究加性遗传方差的时间或空间变化有用。
