Phylogenetic networks are used to represent evolutionary relationships between species in biology. Such networks are often categorized into classes by their topological features, which stem from both biological and computational motivations. We study two network classes in this paper: tree-based networks and orchard networks. Tree-based networks are those that can be obtained by inserting edges between the edges of an underlying tree. Orchard networks are a recently introduced generalization of the class of tree-child networks. Structural characterizations have already been discovered for tree-based networks; this is not the case for orchard networks. In this paper, we introduce cherry covers—a unifying characterization of both network classes—in which we decompose the edges of the networks into so-called cherry shapes and reticulated cherry shapes. We show that cherry covers can be used to characterize the class of tree-based networks as well as the class of orchard networks. Moreover, we also generalize these results to non-binary networks.

系统发育网络用于表示生物学中物种之间的进化关系。此类网络通常根据其拓扑特征分类，这些拓扑特征来自生物学和计算动机。在本文中，我们研究了两个网络类：基于树的网络和果园网络。基于树的网络是可以通过在基础树的边缘之间插入边缘来获得的网络。Orchard网络是最近引入的树状网络类别的概括。已经发现了基于树的网络的结构特征。果园网络不是这种情况。在本文中，我们介绍了樱桃套（这是两个网络类的统一表征），其中我们将网络的边缘分解为所谓的樱桃形状和网状樱桃形状。我们显示出樱桃覆盖物可用于表征基于树的网络以及果园网络的类别。此外，我们还将这些结果推广到非二进制网络。