Phylogenetic comparative analyses use trees of evolutionary relationships between species to understand their evolution and ecology. A phylogenetic tree of n taxa can be algebraically transformed into an n by n squared symmetric phylogenetic covariance matrix C where each element $c_{\mathrm{ij}}$ in C represents the affinity between extant species i and extant species j. This matrix C 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 $\kappa$, defined by the ratio of the maximum eigenvalue of C to the minimum eigenvalue of C, 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.

系统发育比较分析使用物种之间的进化关系树来了解其进化和生态学。的系统发生树Ñ类群可代数变换成Ñ通过Ñ平方对称亲缘协方差矩阵C ^的每个元素，其中$C_{\mathrm{ij}}$C中的C表示现存物种i和现存物种j之间的亲和力。该矩阵C在几种比较方法中内部使用：例如，经常将其反转以计算模型下数据的可能性。但是，如果矩阵条件不佳（即$\kappa$通过的最大特征值之比定义Ç到的最小特征值Ç，太高），此反转可能并不稳定，并且因此既不将是基于优化的可能性的可能性或参数估计值的计算中。我们调查了此潜在问题，并提出了几种方法来尝试纠正此问题。