AI 中文总结
研究数学系统发育学中如何识别单系群性状，给出通用公式及针对二元性状和特定树形的简单公式，还通过线性时间算法探讨单系性与最大简约法的关系。
AI 中文摘要
根据系统发育关系对物种进行分组，往往与根据共享特征分组的结果不同。单系群在这方面起着重要作用，因为它们是共享相同特征且由联合系统发育子树唯一界定的物种组。这就引出了如何在性状中识别可能的单系群的问题，性状通常用于系统发育树重建。本文提供了一个通用公式来量化在任何给定树上有多少不同性状是单系的，并给出了二元性状和某些树形的简单公式。还通过提供一种线性时间算法来研究单系性与著名的系统发育树重建标准最大简约法之间的关系，该算法可确定树上一个性状的简约得分和单系类型。
英文摘要
Grouping species according to their phylogenetic relationships often results in different groups than grouping them according to their shared traits. Monophyletic groups play an important role in this regard, as they are groups of species sharing the same trait and being uniquely defined by a joint phylogenetic subtree. This immediately leads to the question of how to identify possible monophyletic groups in characters, which assign each present-day species a certain trait and which are typically used for phylogenetic tree reconstruction. In our manuscript, we provide a general formula to quantify how many different characters are monophyletic on any given tree and provide simple formulae for binary characters and for certain tree shapes. We also investigate relations between monophyly and the well-known phylogenetic tree reconstruction criterion maximum parsimony by providing a linear-time algorithm which determines the parsimony score together with the monophyly type of a character on a tree.
Comments23 pages, 5 figures
