发表机构
Columbia University（哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过嵌入随机游走的精确渐近分析，提出非参数方法估计系统发育树Fréchet均值中三叉分支未来分叉的概率，并应用于灵长类等物种树的多叉性检验。
AI 中文摘要
在 Billera-Holmes-Vogtmann 空间中对系统发育树群体进行统计分析时，一个众所周知的现象是 Fréchet 均值树的拓扑结构可能包含多叉分支（即内部节点具有两个以上子节点），这引发了实际问题：这是否反映了群体层面的分支结构（硬多叉）或仅仅是数据中的抽样变异性（软多叉）。这是非欧几里得统计中“粘性”这一更普遍现象的一个实例，即样本 Fréchet 均值在某些非正曲率分层空间中会永久被困在较低维度的分层中。在本工作中，我们识别了嵌入在 Fréchet 均值过程中的一个特定多维随机游走，并证明粘性发生的时间由该随机游走坐标在零以上的最大最后通过时间决定。利用这一表示，我们开发了一种完全非参数的程序，用于估计在收集更多观测数据后，样本 Fréchet 均值树中的三叉分支在未来某个时刻发生分叉的概率。最后，我们将我们的方法应用于系统发育学中的一个问题，即考虑灵长类、啮齿类和树鼩物种树中观察到的三叉分支在群体层面是否真正三叉。
英文摘要
A well-known phenomenon in statistical analyses of populations of phylogenetic trees in the Billera-Holmes-Vogtmann space is that the topology of the Fréchet mean tree can contain multifurcations (i.e., internal nodes with more than two children), which raises the practical question of whether this reflects a population-level branching structure (hard polytomy) or merely sampling variability in the data (soft polytomy). This is an instance of the more general phenomenon of "stickiness" in non-Euclidean statistics, whereby the sample Fréchet mean in certain non-positively curved stratified spaces becomes permanently trapped in a lower-dimensional stratum. In this work, we identify a particular multidimensional random walk embedded within the Fréchet mean process, and we show that the time at which stickiness occurs is determined by the largest last-passage time above zero of the coordinates of this random walk. Using this representation, we develop a fully nonparametric procedure for estimating the probability that trifurcations in a sample Fréchet mean tree will bifurcate at some future time if more observations are collected. Lastly, we apply our methodology to a problem in phylogenetics where we consider whether an observed trifurcation in the species tree of primates, glires, and tree shrews is genuinely trifurcated at the population level.
Comments27 pages, 6 figures. Comments welcome!
