Nodal distances for rooted phylogenetic trees.
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 M(n)(R) of real-valued n x n matrices. We conclude this paper by establishing some basic facts about the metrics for non-weighted phylogenetic trees defined in this way using L(p) metrics on M(n)(R), with p [epsilon] R(>0).
Cardona
Gabriel
G
Department of Mathematics and Computer Science, University of the Balearic Islands, 07122, Palma de Mallorca, Spain.
Llabrés
Mercè
M
Department of Mathematics and Computer Science, University of the Balearic Islands, 07122, Palma de Mallorca, Spain.|Research Institute of Health Science (IUNICS), 07122, Palma de Mallorca, Spain.
Rosselló
Francesc
F
Department of Mathematics and Computer Science, University of the Balearic Islands, 07122, Palma de Mallorca, Spain. cesc.rossello@uib.es.|Research Institute of Health Science (IUNICS), 07122, Palma de Mallorca, Spain. cesc.rossello@uib.es.
Valiente
Gabriel
G
Research Institute of Health Science (IUNICS), 07122, Palma de Mallorca, Spain.|Algorithms, Bioinformatics, Complexity and Formal Methods Research Group, Technical University of Catalonia, 08034, Barcelona, Spain.
D000465:Algorithms; D008957:Models, Genetic; D010802:Phylogeny; D016008:Statistical Distributions