International audienceThree important and related measures for summarizing the dissimilarity in phylogenetic trees are the minimum number of hybridization events required to fit two phylogenetic trees onto a single phylogenetic network (the hybridization number), the (rooted) subtree prune and regraft distance (the rSPR distance) and the tree bisection and reconnection distance (the TBR distance) between two phylogenetic trees. The respective problems of computing these measures are known to be NP-hard, but also fixed-parameter tractable in their respective natural parameters. This means that, while they are hard to compute in general, for cases in which a parameter (here the hybridization number and rSPR/TBR distance, respectively) is small, the problem can be solved efficiently even for large input trees. Here, we present new analyses showing that the use of the “cluster reduction” rule—already defined for the hybridization number and the rSPR distance and introduced here for the TBR distance—can transform any O(f(p)⋅n) -time algorithm for any of these problems into an O(f(k)⋅n) -time one, where n is the number of leaves of the phylogenetic trees, p is the natural parameter and k is a much stronger (that is, smaller) parameter: the minimum level of a phylogenetic network displaying both trees
Nihan (2017) 'Constructing tree-child networks from distance matrices. ', Algorithmica., 80 (8). pp. 2240-2259. Further information on publisher's website:https://doi.org/10.1007/s00453-017-0320-6Publisher's copyright statement:The nal publication is available at Springer via https://doi.org/10.1007/s00453-017-0320-6Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract A tree-child network is a phylogenetic network with the property that each non-leaf vertex is the parent of a tree vertex or a leaf. In this paper, we show that a tree-child network on taxa (leaf) set X with an outgroup and a positive real-valued weighting of its edges is essentially determined by the multi-set of all path-length distances between elements in X provided, for each reticulation, the edges directed into it have equal weight. Furthermore, we give a polynomial-time algorithm for reconstructing such a network from this inter-taxa distance information. Such constructions are of central importance in evolutionary biology where phylogenetic networks represent the ancestral history of a collection of present-day taxa.
Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractTraditional "distance based methods" reconstruct a phylogenetic tree from a matrix of pair-wise distances between taxa. A phylogenetic network is a generalization of a phylogenetic tree that can describe evolutionary events such as reticulation and hybridization that are not tree-like. Although evolution has been known to be more accurately modelled by a network than a tree for some time, only recently have efforts been made to directly reconstruct a phylogenetic network from sequence data, as opposed to reconstructing several trees first and then trying to combine them into a single coherent network. In this work we present a generalisation of the UPGMA algorithm for ultrametric tree reconstruction which can accurately reconstruct ultrametric tree-child networks from the set of distinct distances between each pair of taxa.
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