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Journal of Mathematical Biology

, Volume 73, Issue 6–7, pp 1761–1780

First Online: 23 April 2016Received: 08 June 2015Revised: 16 December 2015


Phylogenetic networks are rooted, labelled directed acyclic graphswhich 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 UN and, conversely, a MUL-tree T can in certain circumstances be -folded- to obtain aphylogenetic network FT 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 FUN 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 UN. To do this, we develop aphylogenetic analogue of graph fibrations. This allows us to view UN as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in UN and reconciling phylogenetic trees with networks.

KeywordsPhylogenetic networks Multi-labelled trees Graph fibrations Tree and network reconciliation Universal cover of a digraph Mathematics Subject Classification05C90 92D15  Download fulltext PDF

Autor: Katharina T. Huber - Vincent Moulton - Mike Steel - Taoyang Wu


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