Data from: Robustness of compound Dirichlet priors for Bayesian inference of branch lengths

We modified the phylogenetic program MrBayes 3.1.2 to incorporate the compound Dirichlet priors for branch lengths proposed recently by Rannala, Zhu, and Yang (2012. Tail paradox, partial identifiability and influential priors in Bayesian branch length inference. Mol. Biol. Evol. 29:325-335.) as a solution to the problem of branch-length overestimation in Bayesian phylogenetic inference. The compound Dirichlet prior specifies a fairly diffuse prior on the tree length (the sum of branch lengths) and uses a Dirichlet distribution to partition the tree length into branch lengths. Six problematic data sets originally analyzed by Brown, Hedtke, Lemmon, and Lemmon (2010. When trees grow too long: investigating the causes of highly inaccurate Bayesian branch-length estimates. Syst. Biol. 59:145-161) are reanalyzed using the modified version of MrBayes to investigate properties of Bayesian branch-length estimation using the new priors. While the default exponential priors for branch lengths produced extremely long trees, the compound Dirichlet priors produced posterior estimates that are much closer to the maximum likelihood estimates. Furthermore, the posterior tree lengths were quite robust to changes in the parameter values in the compound Dirichlet priors, for example, when the prior mean of tree length changed over several orders of magnitude. Our results suggest that the compound Dirichlet priors may be useful for correcting branch-length overestimation in phylogenetic analyses of empirical data sets.

本研究对系统发育程序MrBayes 3.1.2进行了修改，将Rannala、Zhu与Yang（2012年，《贝叶斯分支长度推断中的尾悖论、部分可识别性与影响先验》，《分子生物学与进化》29卷：325-335）新近提出的复合Dirichlet先验（compound Dirichlet priors）引入其中，以此解决贝叶斯系统发育推断中分支长度高估的问题。该复合Dirichlet先验对树长（即各分支长度之和）设定了较为弥散的先验分布，并通过Dirichlet分布将树长拆解为各分支长度。本研究使用修改后的MrBayes程序，对Brown、Hedtke、Lemmon与Lemmon（2010年，《树长过长：探究贝叶斯分支长度推断严重不准的成因》，《系统生物学》59卷：145-161）最初分析过的6组存在问题的数据集进行重分析，以探究新先验下贝叶斯分支长度推断的特性。结果显示，默认的分支长度指数先验会生成过长的系统发育树，而复合Dirichlet先验得到的后验估计值与最大似然估计值更为接近。此外，即使复合Dirichlet先验中的参数值发生变化（例如树长先验均值跨越数个数量级调整），后验树长仍表现出较强的稳健性。本研究结果表明，复合Dirichlet先验或可用于校正实证数据集系统发育分析中的分支长度高估问题。