Nodal distances for rooted phylogenetic trees |
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Authors: | Gabriel Cardona Mercè Llabrés Francesc Rosselló Gabriel Valiente |
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Institution: | (1) Electronics Laboratory, Department of Physics, University of Patras, Patras, 26500, Greece;; |
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Abstract: | 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(\mathbb R){\mathcal{M}_n(\mathbb {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 L
p
metrics on
Mn(\mathbb R){\mathcal{M}_n(\mathbb {R})}, with ${p \in \mathbb {R}_{ >0 }}${p \in \mathbb {R}_{ >0 }}. |
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Keywords: | |
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