Centre for Research in Mathematics, Western Sydney University, NSW, Australia.
Math Biosci. 2018 Aug;302:131-138. doi: 10.1016/j.mbs.2018.06.005. Epub 2018 Jun 19.
Phylogenetic networks are a generalisation of phylogenetic trees that allow for more complex evolutionary histories that include hybridisation-like processes. It is of considerable interest whether a network can be considered 'tree-like' or not, which leads to the introduction of tree-based networks in the rooted, binary context. Tree-based networks are those networks which can be constructed by adding additional edges into a phylogenetic tree, called the base tree. Previous extensions have considered extending to the binary, unrooted case and the nonbinary, rooted case. In this paper, we extend tree-based networks to the context of unrooted, nonbinary networks in three ways, depending on the types of additional edges that are permitted. Further, we study fully tree-based networks which are phylogenetic networks in which every embedded tree is a base tree. We also extend this concept to unrooted, nonbinary, phylogenetic networks and classify the resulting networks. Finally, we derive some results on the colourability of tree-based networks, which can be useful to determine whether a network is tree-based.
系统发生网络是系统发生树的一种推广，它允许更复杂的进化历史，包括类似于杂交的过程。网络是否可以被认为是“树状的”，这是一个非常有趣的问题，这导致了基于树的网络在有根的、二叉的背景下的引入。基于树的网络是那些可以通过向系统发生树（称为基础树）添加额外的边来构建的网络。以前的扩展已经考虑了扩展到二叉无根和非二叉有根的情况。在本文中，我们通过三种方式将基于树的网络扩展到无根非二叉网络的情况，具体取决于允许的附加边的类型。此外，我们研究了完全基于树的网络，即每个嵌入的树都是基础树的系统发生网络。我们还将这个概念扩展到无根非二叉的系统发生网络，并对生成的网络进行分类。最后，我们得出了一些关于基于树的网络可着色性的结果，这对于确定一个网络是否基于树是有用的。
