  Phylogenetic networks are used to study 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.
