The Exploration of Phylogenetic Tree Space through Combinatorics, Statistics and Geometry

通过组合学、统计学和几何学探索系统发育树空间

• 批准号: 9973891
• 负责人: Susan Holmes
• 金额: $ 7.5万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-01 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9973891&HistoricalAwards=false
• 关键词: Exploration; Phylogenetic; Tree; Space; through

The research proposal I am developing aims to help biologists understand the properties of the space ofall phylogenetic trees. I propose to combine three approaches to tackle this problem,combinatorial, statistical and geometrical.I have already made some good progress through a combinatorial approach to the problem that I have started with Persi Diaconis. We have built a bijection between the space of all phylogenetic trees and the space of perfect matchings. This has provided new distances between trees, ways of doing random walks on tree space, and a new approach to the $NP$ complete optimization procedures involved in building phylogenetic trees.The embedding of tree estimation in a statistical framework allows one to see trees as a special type of parameter to be estimated. The next step needed is the ability to construct confidence regions. My first work on this subject was done with Brad Efron and Betz Halloran a few years ago and started me on this project.Currently biologists validate the tree estimated by perturbing the data and then summarizing this simplyby associating p-values to the branches of the tree. Communication between statisticians and biologistshas a difficult history in this field. One school of taxonomists has been encouraging the use of maximum likelihood for the estimation of the tree.Other taxonomists have been using parsimony as their criterion, and have been highly critical ofwhat they called the `statistical approach'. In fact their own method is statistical also, but the parsimony method is a nonparametric approach, whereas the Maximum Likelihood is a parametric one. The MLE model is finite dimensional, however, statisticians know that if one allows the number of parameters to increase as this number becomes larger than the amount of information contained in the data, the method becomes nonparametric. Making this interpretation known to biologists would be a worthwhile enterprise, the consequence would be that nonparametric-parametric discussion in statistics could enlighten the parsimony-MLE debate.Understanding the geometry of the tree-space would help understand how to combine trees obtained from perturbed data or different genes on the same set of species. I hope to continue a collaboration I have started with a combinatorialist, Louis Billera and a topologist, Karen Vogtmann on a more mathematical understanding of tree space that would allow for a more natural definition of distances between points in the `tree polytope'. This topological study of tree space is crucial in the definition of a notion of neighborhood that would then allow a definition of continuity in the estimation function.The notion of confidence region could then be defined, and it would also be possible to combine trees from built from different datasets or to combine trees with other data (biogeographic, for instance). Finally I will diffuse my matlab tree analysis programs and preliminary results through a web site `Geometry of Tree Space'. This POWRE project is supported by the MPS Office of Multidisciplinary Activities (OMA).

我正在开发的研究计划旨在帮助生物学家理解所有系统发育树的空间属性。 我建议联合收割机三种方法来解决这个问题，组合，统计和几何。我已经取得了一些很好的进展，通过组合的方法来解决这个问题，我已经开始与波斯Diaconis。 我们在所有系统发育树的空间和完美匹配的空间之间建立了一个双射。 这提供了树之间的新距离，在树空间上进行随机游走的方法，以及构建系统发育树所涉及的$NP$完全优化过程的新方法。 下一步需要的是构建置信区域的能力。 几年前，我和布拉德埃夫隆（Brad Efron）和贝茨哈洛伦（Betz Halloran）一起完成了这个课题的第一项工作，并开始了这个项目。目前，生物学家通过扰动数据来验证估计的树，然后简单地通过将p值与树的分支联系起来来总结。 统计学家和生物学家之间的交流在这个领域是一段艰难的历史。 有一派分类学家一直鼓励使用最大似然法来估计树木，其他分类学家则一直使用简约法作为他们的标准，并对他们所谓的“统计方法”持高度批评态度。 事实上，他们自己的方法也是统计方法，但简约法是一种非参数方法，而最大似然法是一种参数方法。 MLE模型是有限维的，但是，统计学家知道，如果允许参数的数量增加，因为这个数量大于数据中包含的信息量，则该方法变为非参数。 让生物学家了解这种解释是一项有价值的事业，其结果是统计学中的非参数-参数讨论可以启发简约-极大似然估计的争论，理解树空间的几何结构将有助于理解如何将从扰动数据或同一物种集合上的不同基因获得的联合收割机树组合起来。 我希望继续合作，我已经开始与combinatorialist，路易斯Billera和拓扑学家，卡伦Vogtmann对一个更数学的理解树空间，将允许一个更自然的定义之间的距离点的“树多面体”。树空间的这种拓扑研究对于定义邻域的概念至关重要，邻域的概念可以定义估计函数的连续性，置信区域的概念可以定义，也可以将不同数据集构建的树联合收割机组合起来，或者将树与其他数据（例如地理数据）联合收割机组合。 最后，我将通过一个网站“树空间几何”传播我的matlab树分析程序和初步结果。 该项目由MPS多学科活动办公室（OMA）支持。