School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom.
CBMA (Centre of Molecular and Environmental Biology), Department of Biology, University of Minho, Campus de Gualtar, Braga, Portugal.
PLoS One. 2019 Feb 19;14(2):e0212311. doi: 10.1371/journal.pone.0212311. eCollection 2019.
When divided by a given mutation rate, the ρ (rho) statistic provides a simple estimator of the age of a clade within a phylogenetic tree by averaging the number of mutations from each sample in the clade to its root. However, a long-standing critique of the use of ρ in genetic dating has been quite often cited. Here we show that the critique is unfounded. We demonstrate by a formal mathematical argument and illustrate with a simulation study that ρ estimates are unbiased and also that ρ and maximum likelihood estimates do not differ in any systematic fashion. We also demonstrate that the claim that the associated confidence intervals commonly estimate the uncertainty inappropriately is flawed since it relies on a means of calculating standard errors that is not used by any other researchers, whereas an established expression for the standard error is largely unproblematic. We conclude that ρ dating, alongside approaches such as maximum likelihood (ML) and Bayesian inference, remains a useful tool for genetic dating.
当通过给定的突变率进行划分时，ρ（rho）统计量通过平均分支中每个样本到其根的突变数量，为系统发育树中的分支提供了一种简单的年龄估计器。然而，遗传约会中使用 ρ 的长期批评经常被引用。在这里，我们表明这种批评是没有根据的。我们通过正式的数学论证进行演示，并通过模拟研究进行说明，表明 ρ 估计是无偏的，并且 ρ 和最大似然估计在任何系统方式上都没有差异。我们还表明，关于相关置信区间通常不适当地估计不确定性的说法是有缺陷的，因为它依赖于一种计算标准误差的方法，而这种方法没有被任何其他研究人员使用，而对于标准误差的既定表达式在很大程度上没有问题。我们得出结论，ρ 约会与最大似然（ML）和贝叶斯推断等方法一样，仍然是遗传约会的有用工具。
