Abstract

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.

Highlights

  • 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

  • Phylogenetic trees and networks are used to represent the evolutionary history of species in biology and languages in linguistics

  • In this paper we have provided a unifying structural characterization for tree-based networks and orchard networks using cherry covers

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Summary

Introduction

Phylogenetic trees and networks are used to represent the evolutionary history of species in biology and languages in linguistics. Hatched from an ongoing debate on whether evolutionary histories should or should not be viewed as tree-like with reticulate events sprinkled in (e.g., in the context of horizontal gene transfer within prokaryotes [9]), tree-based networks were introduced as those that can be obtained from trees by inserting new reticulate edges between the edges of the tree [3] In their seminal paper, Francis and Steel explored the mathematical properties of these tree-based networks and provided a linear time algorithm to check whether a binary network was tree-based. We prove that a network is orchard precisely if it has an acyclic cherry cover (Theorem 4.3) This shows that the class of non-binary orchard networks are contained in the class of non-binary tree-based networks (Corollary 4.5)

Preliminaries
Cherry cover
Binary networks
Network classes
Reducing shapes
Tree-based networks
Orchard networks
Discussion
Full Text
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