Path lengths in tree-child time consistent hybridization networks

Authors:
Gabriel Cardona;Mercè Llabrés;Francesc Rosselló;Gabriel Valiente
Affiliations:
Department of Mathematics and Computer Science, University of the Balearic Islands, E-07122 Palma de Mallorca, Spain;Department of Mathematics and Computer Science, University of the Balearic Islands, E-07122 Palma de Mallorca, Spain and Research Institute of Health Science (IUNICS), E-07122 Palma de Mallorca, S ...;Department of Mathematics and Computer Science, University of the Balearic Islands, E-07122 Palma de Mallorca, Spain and Research Institute of Health Science (IUNICS), E-07122 Palma de Mallorca, S ...;Algorithms, Bioinformatics, Complexity and Formal Methods Research Group, Technical University of Catalonia, E-08034 Barcelona, Spain and Research Institute of Health Science (IUNICS), E-07122 Pal ...
Venue:
Information Sciences: an International Journal
Year:
2010

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Abstract

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.