IEEE/ACM Trans Comput Biol Bioinform. 2018 Jan-Feb;15(1):205-217. doi: 10.1109/TCBB.2016.2615918. Epub 2016 Oct 7.
Rooted phylogenetic networks are used to describe evolutionary histories that contain non-treelike evolutionary events such as hybridization and horizontal gene transfer. In some cases, such histories can be described by a phylogenetic base-tree with additional linking arcs, which can, for example, represent gene transfer events. Such phylogenetic networks are called tree-based. Here, we consider two possible generalizations of this concept to nonbinary networks, which we call tree-based and strictly-tree-based nonbinary phylogenetic networks. We give simple graph-theoretic characterizations of tree-based and strictly-tree-based nonbinary phylogenetic networks. Moreover, we show for each of these two classes that it can be decided in polynomial time whether a given network is contained in the class. Our approach also provides a new view on tree-based binary phylogenetic networks. Finally, we discuss two examples of nonbinary phylogenetic networks in biology and show how our results can be applied to them.
有根进化网络被用来描述包含非树状进化事件（如杂交和水平基因转移）的进化历史。在某些情况下，可以使用具有附加连接弧的系统发生基础树来描述这样的历史，这些弧例如可以表示基因转移事件。这样的进化网络称为基于树的。在这里，我们考虑了将此概念推广到非二进制网络的两种可能情况，我们称之为基于树的和严格基于树的非二进制系统发生网络。我们给出了基于树的和严格基于树的非二进制系统发生网络的简单图论特征。此外，对于这两个类别中的每一个，我们都表明可以在多项式时间内确定给定网络是否包含在该类别中。我们的方法还为基于树的二进制系统发生网络提供了新的视角。最后，我们讨论了生物学中两个非二进制系统发生网络的示例，并展示了如何将我们的结果应用于它们。
