标题： 表征（多）半定向系统发生网络 显示英文标题

标题： Characterizing (multi-)semi-directed phylogenetic networks

摘要： 在进化生物学中，系统发育网络是图，它们提供了一个灵活的框架，用于表示涉及网状进化事件的复杂进化历史。 最近，系统发育研究开始关注一种特殊的网络类别，称为半定向网络。 这些图被定义为混合图，可以通过对某些根系统发育网络中的弧进行去向化得到，即一个有向无环图，其叶节点对应一组物种，并且有一个单一的源或根顶点。 然而，这种半定向网络的定义本质上是隐式的，因为不清楚一个混合图何时具有这一特性。 在本文中，我们引入了半定向网络和多半定向网络的新颖、显式的数学特征，即可以从可能具有多个根的有向系统发育网络中得到的混合图。 此外，通过将根网络理论中的基础工具扩展到半定向设置——如樱桃采摘序列、全知者和路径划分——我们表征了何时可以由去向化某个包含在已知的树-子节点、果园、树-基于或森林-基于网络类中的根网络得到一个（多）半定向网络。 这些结果涉及（多）半定向网络的结构方面，并为这类网络的改进的理论和计算分析铺平了道路，例如，在基于此类网络的代数进化模型的发展中。 显示英文摘要

摘要： In evolutionary biology, phylogenetic networks are graphs that provide a flexible framework for representing complex evolutionary histories that involve reticulate evolutionary events. Recently phylogenetic studies have started to focus on a special class of such networks called semi-directed networks. These graphs are defined as mixed graphs that can be obtained by de-orienting some of the arcs in some rooted phylogenetic network, that is, a directed acyclic graph whose leaves correspond to a collection of species and that has a single source or root vertex. However, this definition of semi-directed networks is implicit in nature since it is not clear when a mixed-graph enjoys this property or not. In this paper, we introduce novel, explicit mathematical characterizations of semi-directed networks, and also multi-semi-directed networks, that is mixed graphs that can be obtained from directed phylogenetic networks that may have more than one root. In addition, through extending foundational tools from the theory of rooted networks into the semi-directed setting - such as cherry picking sequences, omnians, and path partitions - we characterize when a (multi-)semi-directed network can be obtained by de-orienting some rooted network that is contained in one of the well-known classes of tree-child, orchard, tree-based or forest-based networks. These results address structural aspects of (multi-)semi-directed networks and pave the way to improved theoretical and computational analyses of such networks, for example, within the development of algebraic evolutionary models that are based on such networks.