[论文解读] Non-binary treebased unrooted phylogenetic networks and their relations to binary and rooted ones

Mareike Fischer, Michelle Galla+3 more|arXiv (Cornell University)|Oct 16, 2018

Evolution and Paleontology Studies被引用 8

一句话总结

本文将树基物种系网络理论扩展至非二叉无根网络，表明尽管二叉无根网络在至多第4级时仍为树基网络，但非二叉网络仅在至多第3级时为树基网络。本文引入了非二叉通用树基网络，并提供了根系非二叉版本的构造方法，进而推广至无根情形。

ABSTRACT

Phylogenetic networks are a generalization of phylogenetic trees allowing for the representation of non-treelike evolutionary events such as hybridization. Typically, such networks have been analyzed based on their `level', i.e. based on the complexity of their 2-edgeconnected components. However, recently the question of how `treelike' a phylogenetic network is has become the center of attention in various studies. This led to the introduction of \emph{treebased networks}, i.e. networks that can be constructed from a phylogenetic tree, called the \emph{base tree}, by adding additional edges. Here, we initially consider unrooted treebased networks and first revisit some established results known for these networks in case they are binary. We consider them from a more graph-theoretical point of view, before we extend these results to treebased unrooted non-binary networks. While it is known that up to level 4 all binary unrooted networks are treebased, we show that in case of non-binary networks, this result only holds up to level 3. Subsequently, we consider the notion of non-binary \emph{universal treebased networks}, i.e. networks on some taxon set which have every phylogenetic tree on the same taxon set as a base tree. Again, our aim is to understand the unrooted case, but here, we first present a construction for a rooted non-binary universal treebased network, because this easily can be generalized to the unrooted case.

研究动机与目标

• 将树基网络的概念从二叉网络扩展至非二叉无根物种系网络。
• 通过分析其层级结构，研究非二叉无根网络的树状特性。
• 确定非二叉无根网络保持树基特性的最大层级。
• 引入并构建非二叉通用树基网络，从根系情形出发。
• 利用图论方法，将根系结果推广至无根非二叉网络。

提出的方法

• 从图论视角重新审视关于二叉无根树基网络的既定结果。
• 通过考虑基树与边添加，将树基网络的定义扩展至非二叉无根网络。
• 通过分析2-边连通分量，定义非二叉无根网络的层级。
• 利用图论构造方法，证明非二叉网络仅在层级3以内为树基网络。
• 构建一个根系非二叉通用树基网络，作为推广至无根情形的基础。
• 通过拓扑变换，将根系构造应用于推导无根非二叉通用树基网络。

实验结果

研究问题

• RQ1 非二叉无根物种系网络在多大层级以内仍为树基网络？
• RQ2 非二叉无根网络的树状特性与二叉无根网络相比有何异同？
• RQ3 能否构建一个根系非二叉通用树基网络？若能，如何推广至无根情形？
• RQ4 何种图论条件可确保非二叉无根网络为树基网络？
• RQ5 在网络层级与非二叉无根情形下树基结构之间的关系如何？

主要发现

• 非二叉无根物种系网络仅在层级3以内为树基网络，而二叉网络可保持至层级4。
• 通过基树与边添加构造，树基网络的概念可自然地从二叉网络推广至非二叉无根网络。
• 可构建一个根系非二叉通用树基网络，作为无根推广的基础。
• 在非二叉情形下，通过将根系网络构造扩展至无根拓扑，实现了通用树基网络的构建。
• 对2-边连通分量的图论分析，证实了非二叉无根网络中层级依赖的树基特性。
• 研究结果揭示了非二叉网络的结构性限制：更高复杂度（层级 > 3）并不保证具有树基结构。