Folding and unfolding phylogenetic trees and networks

Huber, Katharina, Moulton, Vincent, Steel, Mike and Wu, Taoyang (2016) Folding and unfolding phylogenetic trees and networks. Journal of Mathematical Biology, 73 (6). 1761–1780. ISSN 0303-6812

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Phylogenetic networks are rooted, labelled directed acyclic graphs which are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any phylogenetic network $N$ can be "unfolded" to obtain a MUL-tree $U(N)$ and, conversely, a MUL-tree $T$ can in certain circumstances be "folded" to obtain a phylogenetic network $F(T)$ that exhibits $T$. In this paper, we study properties of the operations $U$ and $F$ in more detail. In particular, we introduce the class of stable networks, phylogenetic networks $N$ for which $F(U(N))$ is isomorphic to $N$, characterise such networks, and show that they are related to the well-known class of tree-sibling networks.We also explore how the concept of displaying a tree in a network $N$ can be related to displaying the tree in the MUL-tree $U(N)$. To do this, we develop a phylogenetic analogue of graph fibrations. This allows us to view $U(N)$ as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in $U(N)$ and reconcilingphylogenetic trees with networks.

Item Type: Article
Additional Information: The paper is published open access under the CC BY license.
Uncontrolled Keywords: phylogenetic networks,multi-labelled trees, graph fibrations,tree and network reconciliation,universal cover of a digraph
Faculty \ School: Faculty of Science > School of Computing Sciences
Depositing User: Pure Connector
Date Deposited: 01 Apr 2016 10:11
Last Modified: 13 Nov 2020 00:48
DOI: 10.1007/s00285-016-0993-5

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