Gianola Daniel, Sorensen Daniel
Departments of Animal Sciences, Dairy Science and Biostatistics and Medical Informatics, University of Wisconsin, Madison, Wisconsin 53706, USA.
Genetics. 2004 Jul;167(3):1407-24. doi: 10.1534/genetics.103.025734.
Multivariate models are of great importance in theoretical and applied quantitative genetics. We extend quantitative genetic theory to accommodate situations in which there is linear feedback or recursiveness between the phenotypes involved in a multivariate system, assuming an infinitesimal, additive, model of inheritance. It is shown that structural parameters defining a simultaneous or recursive system have a bearing on the interpretation of quantitative genetic parameter estimates (e.g., heritability, offspring-parent regression, genetic correlation) when such features are ignored. Matrix representations are given for treating a plethora of feedback-recursive situations. The likelihood function is derived, assuming multivariate normality, and results from econometric theory for parameter identification are adapted to a quantitative genetic setting. A Bayesian treatment with a Markov chain Monte Carlo implementation is suggested for inference and developed. When the system is fully recursive, all conditional posterior distributions are in closed form, so Gibbs sampling is straightforward. If there is feedback, a Metropolis step may be embedded for sampling the structural parameters, since their conditional distributions are unknown. Extensions of the model to discrete random variables and to nonlinear relationships between phenotypes are discussed.
多变量模型在理论和应用数量遗传学中具有重要意义。我们扩展数量遗传理论，以适应多变量系统中所涉及的表型之间存在线性反馈或递归性的情况，假设遗传模型为无穷小、加性模型。结果表明，当忽略这些特征时，定义同步或递归系统的结构参数会影响数量遗传参数估计值（如遗传力、亲子回归、遗传相关性）的解释。给出了用于处理大量反馈 - 递归情况的矩阵表示。在假设多变量正态性的情况下推导似然函数，并将计量经济学理论中用于参数识别的结果应用于数量遗传环境。建议采用马尔可夫链蒙特卡罗实现的贝叶斯方法进行推断并展开研究。当系统完全递归时，所有条件后验分布都具有封闭形式，因此吉布斯抽样很直接。如果存在反馈，则可能需要嵌入一个梅特罗波利斯步骤来对结构参数进行抽样，因为它们的条件分布是未知的。还讨论了将该模型扩展到离散随机变量以及表型之间的非线性关系。
