Jhwueng Dwueng-Chwuan, O'Meara Brian C
Department of Statistics, Feng Chia University, Taichung, Taiwan R.O.C.
Department of Ecology and Evolutionary Biology, The University of Tennessee, Knoxville, Knoxville, TN, USA.
Evol Bioinform Online. 2020 Feb 12;16:1176934320901721. doi: 10.1177/1176934320901721. eCollection 2020.
Phylogenetic comparative analyses use trees of evolutionary relationships between species to understand their evolution and ecology. A phylogenetic tree of taxa can be algebraically transformed into an by squared symmetric phylogenetic covariance matrix where each element in represents the affinity between extant species and extant species . This matrix is used internally in several comparative methods: for example, it is often inverted to compute the likelihood of the data under a model. However, if the matrix is ill-conditioned (ie, if , defined by the ratio of the maximum eigenvalue of to the minimum eigenvalue of , is too high), this inversion may not be stable, and thus neither will be the calculation of the likelihood or parameter estimates that are based on optimizing the likelihood. We investigate this potential issue and propose several methods to attempt to remedy this issue.
系统发育比较分析利用物种间进化关系的树来理解它们的进化和生态。分类单元的系统发育树可以代数转换为一个由平方对称系统发育协方差矩阵组成的矩阵，其中矩阵中的每个元素代表现存物种 和现存物种 之间的亲缘关系。这个矩阵在几种比较方法中内部使用：例如，它经常被求逆以计算模型下数据的似然性。然而，如果矩阵是病态的（即，如果由 的最大特征值与 的最小特征值之比定义的 太高），这种求逆可能不稳定，因此基于优化似然性的似然性计算或参数估计也不稳定。我们研究了这个潜在问题，并提出了几种方法来试图解决这个问题。
