Department of Computer Science, University of Auckland, Auckland, New Zealand.
Syst Biol. 2012 Jan;61(1):138-49. doi: 10.1093/sysbio/syr087. Epub 2011 Aug 18.
The use of fossil evidence to calibrate divergence time estimation has a long history. More recently, Bayesian Markov chain Monte Carlo has become the dominant method of divergence time estimation, and fossil evidence has been reinterpreted as the specification of prior distributions on the divergence times of calibration nodes. These so-called "soft calibrations" have become widely used but the statistical properties of calibrated tree priors in a Bayesian setting hashave not been carefully investigated. Here, we clarify that calibration densities, such as those defined in BEAST 1.5, do not represent the marginal prior distribution of the calibration node. We illustrate this with a number of analytical results on small trees. We also describe an alternative construction for a calibrated Yule prior on trees that allows direct specification of the marginal prior distribution of the calibrated divergence time, with or without the restriction of monophyly. This method requires the computation of the Yule prior conditional on the height of the divergence being calibrated. Unfortunately, a practical solution for multiple calibrations remains elusive. Our results suggest that direct estimation of the prior induced by specifying multiple calibration densities should be a prerequisite of any divergence time dating analysis.
利用化石证据来校准分歧时间估计的方法由来已久。最近，贝叶斯马尔可夫链蒙特卡罗已成为分歧时间估计的主要方法，而化石证据被重新解释为校准节点分歧时间的先验分布的规范。这些所谓的“软校准”已经被广泛使用，但在贝叶斯设置中，校准树先验的统计特性尚未得到仔细研究。在这里，我们澄清了在 BEAST 1.5 中定义的校准密度并不代表校准节点的边缘先验分布。我们通过对小树的一系列分析结果来说明这一点。我们还描述了一种替代的校准尤尔先验的构造方法，该方法允许直接指定校准分歧时间的边缘先验分布，无论是否限制单系性。该方法需要在要校准的分歧高度的条件下计算尤尔先验。不幸的是，对于多个校准的实际解决方案仍然难以捉摸。我们的结果表明，指定多个校准密度所诱导的先验的直接估计应该是任何分歧时间约会分析的前提。
