Data from: Quantifying MCMC exploration of phylogenetic tree space

In order to gain an understanding of the effectiveness of phylogenetic Markov chain Monte Carlo (MCMC), it is important to understand how quickly the empirical distribution of the MCMC converges to the posterior distribution. In this paper we investigate this problem on phylogenetic tree topologies with a metric that is especially well suited to the task: the subtree prune-and-regraft (SPR) metric. This metric directly corresponds to the minimum number of MCMC rearrangements required to move between trees in common phylogenetic MCMC implementations. We develop a novel graph-based approach to analyze tree posteriors and find that the SPR metric is much more informative than simpler metrics that are unrelated to MCMC moves. In doing so we show conclusively that topological peaks do occur in Bayesian phylogenetic posteriors from real data sets as sampled with standard MCMC approaches, investigate the efficiency of Metropolis-coupled MCMC (MCMCMC) in traversing the valleys between peaks, and show that conditional clade distribution (CCD) can have systematic problems when there are multiple peaks.

为了明晰系统发育马尔可夫链蒙特卡洛（phylogenetic Markov Chain Monte Carlo, MCMC）的应用效能，探究其经验分布收敛至后验分布的速率至关重要。本文针对系统发育树拓扑结构，采用适配性极佳的度量指标——子树剪枝与重接（subtree prune-and-regraft, SPR）度量，对该问题展开研究。该度量指标直接对应于常见系统发育MCMC实现中，两棵树拓扑之间进行构型转换所需的最少MCMC重排次数。我们提出了一种全新的基于图论的树后验分布分析方法，研究发现SPR度量相较于与MCMC转换无关的简单度量指标，具备更强的信息阐释能力。通过该研究路径，我们确凿证明了采用标准MCMC方法采样得到的真实数据集的贝叶斯系统发育后验分布中，确实存在拓扑峰；同时探究了Metropolis耦合马尔可夫链蒙特卡洛（Metropolis-coupled MCMC, MCMCMC）在峰间谷地遍历过程中的效率，并证实了当存在多个拓扑峰时，条件支系分布（conditional clade distribution, CCD）可能存在系统性缺陷。