A hierarchical Bayesian model for calibrating estimates of species divergence times

In Bayesian divergence time estimation methods, incorporating calibrating information from the fossil record is commonly done by assigning prior densities to ancestral nodes in the tree. Calibration prior densities are typically parametric distributions offset by minimum age estimates provided by the fossil record. Specification of the parameters of calibration densities requires the user to quantify his or her prior knowledge of the age of the ancestral node relative to the age of its calibrating fossil. The values of these parameters can, potentially, result in biased estimates of node ages if they lead to overly informative or excessively vague prior distributions. Accordingly, determining parameter values that lead to adequate prior densities is not straightforward. In this study, I present a hierarchical Bayesian model for calibrating divergence time analyses with multiple fossil age constraints. This approach applies a Dirichlet process prior as a hyperprior on the parameters of calibration prior densities. Specifically, this model assumes that the rate-parameters of exponential prior distributions on calibrated nodes are distributed according to a Dirichlet process, whereby the rate-parameters are clustered into distinct parameter categories. Both simulated and biological data are analyzed to evaluate the performance of the Dirichlet process hyperprior. Compared to fixed exponential prior densities, the hierarchical Bayesian approach results in more accurate and precise estimates of internal node ages. When this hyperprior is applied using Markov chain Monte Carlo methods, the ages of calibrated nodes are sampled from mixtures of exponential distributions and uncertainty in the values of calibration density parameters is taken into account.

在贝叶斯分歧时间估计方法中，通常通过为系统发育树的祖先节点分配先验密度，以整合来自化石记录的校准信息。校准先验密度通常为以化石记录提供的最小年代估计值为偏移基准的参数化分布。校准密度的参数设定要求研究者量化其针对祖先节点年代相对于其校准化石年代的先验认知。若这些参数值使得先验分布过度信息化或过度模糊，则可能会导致节点年代估计产生偏倚。因此，确定能够生成适宜先验密度的参数值并非易事。本研究提出了一种针对带有多化石年代约束的分歧时间分析进行校准的分层贝叶斯模型。该方法将狄利克雷过程先验（Dirichlet Process Prior）作为校准先验密度参数的超先验。具体而言，该模型假设校准节点上的指数先验分布的速率参数服从狄利克雷过程分布，由此将速率参数聚类为不同的参数类别。本研究通过模拟数据与生物实测数据开展分析，以评估该狄利克雷过程超先验的性能表现。相较于固定指数先验密度，该分层贝叶斯方法能够得到更准确且精度更高的内部节点年代估计结果。当采用马尔可夫链蒙特卡洛（Markov Chain Monte Carlo）方法应用该超先验时，校准节点的年代将从指数分布的混合分布中采样，同时校准密度参数值的不确定性也会被纳入考量范围。