Research Institute of Health Science IUNICS

Palma, Spain

Research Institute of Health Science IUNICS

Palma, Spain
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Cardona G.,University of the Balearic Islands | Llabres M.,University of the Balearic Islands | Llabres M.,Research Institute of Health Science IUNICS | Rossello F.,University of the Balearic Islands | And 3 more authors.
Journal of Mathematical Biology | Year: 2010

Dissimilarity measures for (possibly weighted) phylogenetic trees based on the comparison of their vectors of path lengths between pairs of taxa, have been present in the systematics literature since the early seventies. For rooted phylogenetic trees, however, these vectors can only separate non-weighted binary trees, and therefore these dissimilarity measures are metrics only on this class of rooted phylogenetic trees. In this paper we overcome this problem, by splitting in a suitable way each path length between two taxa into two lengths. We prove that the resulting splitted path lengths matrices single out arbitrary rooted phylogenetic trees with nested taxa and arcs weighted in the set of positive real numbers. This allows the definition of metrics on this general class of rooted phylogenetic trees by comparing these matrices through metrics in spaces Mn(ℝ) of real-valued n × n matrices. We conclude this paper by establishing some basic facts about the metrics for non-weighted phylogenetic trees defined in this way using Lp metrics on Mn(ℝ), with p∈ℝ>0. © 2009 Springer-Verlag.


Cardona G.,University of the Balearic Islands | Llabres M.,University of the Balearic Islands | Llabres M.,Research Institute of Health Science IUNICS | Rossello F.,University of the Balearic Islands | And 3 more authors.
Information Sciences | Year: 2010

Hybridization networks are representations of evolutionary histories that allow for the inclusion of reticulate events like recombinations, hybridizations, or lateral gene transfers. The recent growth in the number of hybridization network reconstruction algorithms has led to an increasing interest in the definition of metrics for their comparison that can be used to assess the accuracy or robustness of these methods. In this paper we establish some basic results that make it possible the generalization to tree-child time consistent (TCTC) hybridization networks of some of the oldest known metrics for phylogenetic trees: those based on the comparison of the vectors of path lengths between leaves. More specifically, we associate to each hybridization network a suitably defined vector of 'splitted' path lengths between its leaves, and we prove that if two TCTC hybridization networks have the same such vectors, then they must be isomorphic. Thus, comparing these vectors by means of a metric for real-valued vectors defines a metric for TCTC hybridization networks. We also consider the case of fully resolved hybridization networks, where we prove that simpler, 'non-splitted' vectors can be used. © 2009 Elsevier Inc. All rights reserved.

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