Title: Statistical summaries of unlabelled evolutionary trees and ranked hierarchical clustering trees Show Chinese title

Title: 无标签进化树和排名分层聚类树的统计摘要

Abstract: Rooted and ranked binary trees are mathematical objects of great importance used to model hierarchical data and evolutionary relationships with applications in many fields including evolutionary biology and genetic epidemiology. Bayesian phylogenetic inference usually explore the posterior distribution of trees via Markov Chain Monte Carlo methods, however assessing uncertainty and summarizing distributions or samples of such trees remains challenging. While labelled phylogenetic trees have been extensively studied, relatively less literature exists for unlabelled trees which are increasingly useful, for example when one seeks to summarize samples of trees obtained with different methods, or from different samples and environments, and wishes to assess stability and generalizability of these summaries. In our paper, we exploit recently proposed distance metrics of unlabelled ranked binary trees and unlabelled ranked genealogies (equipped with branch lengths) to define the Frechet mean and variance as summaries of these tree distributions. We provide an efficient combinatorial optimization algorithm for computing the Frechet mean from a sample of or distribution on unlabelled ranked tree shapes and unlabelled ranked genealogies. We show the applicability of our summary statistics for studying popular tree distributions and for comparing the SARS-CoV-2 evolutionary trees across different locations during the COVID-19 epidemic in 2020. Show Chinese abstract

Abstract: 带根且有序的二叉树是具有重要意义的数学对象，用于建模层次数据和进化关系，在包括进化生物学和遗传流行病学在内的许多领域都有应用。 贝叶斯系统发育推断通常通过马尔可夫链蒙特卡罗方法探索树的后验分布，然而评估不确定性以及总结或汇总此类树的分布或样本仍然具有挑战性。 虽然标记的系统发育树已被广泛研究，但对于无标记树的文献相对较少，而无标记树正变得越来越有用，例如当需要总结用不同方法或从不同样本和环境中获得的树样本，并希望评估这些总结的稳定性和泛化能力时。 在我们的论文中，我们利用最近提出的无标记有序二叉树和无标记有序系谱（带有分支长度）的距离度量来定义弗雷歇均值和方差作为这些树分布的总结。 我们提供了一个高效的组合优化算法，用于计算来自无标记有序树形状或无标记有序系谱样本或分布的弗雷歇均值。 我们展示了我们的总结统计量在研究流行树分布以及比较2020年COVID-19疫情期间不同地点的SARS-CoV-2进化树方面的适用性。