Journal
ADVANCES IN APPLIED MATHEMATICS
Volume 105, Issue -, Pages 102-129Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aam.2019.01.004
Keywords
Agreement forest; Cherry-picking sequence; Minimum hybridisation; Phylogenetic networks; Reticulation; Tree-child networks
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Funding
- New Zealand Marsden Fund
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Throughout the last decade, we have seen much progress towards characterising and computing the minimum hybridisation number for a set P of rooted phylogenetic trees. Roughly speaking, this minimum quantifies the number of hybridisation events needed to explain a set of phylogenetic trees by simultaneously embedding them into a phylogenetic network. From a mathematical viewpoint, the notion of agreement forests is the underpinning concept for almost all results that are related to calculating the minimum hybridisation number for when vertical bar P vertical bar = 2. However, despite various attempts, characterising this number in terms of agreement forests for vertical bar P vertical bar > 2 remains elusive. In this paper, we characterise the minimum hybridisation number for when P is of arbitrary size and consists of not necessarily binary trees. Building on our previous work on cherry-picking sequences, we first establish a new characterisation to compute the minimum hybridisation number in the space of tree-child networks. Subsequently, we show how this characterisation extends to the space of all rooted phylogenetic networks. Moreover, we establish a particular hardness result that gives new insight into some of the limitations of agreement forests. (C) 2019 Elsevier Inc. All rights reserved.
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