‘Lassoing’ a phylogenetic tree I: basic properties, shellings, and covers

A classical result, fundamental to evolutionary biology, states that an edge-weighted tree T with leaf set X , positive edge weights, and no vertices of degree 2 can be uniquely reconstructed from the leaf-to-leaf distances between any two elements of X . In biology, X corresponds to a set of taxa (...

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Bibliographic Details
Published in:Journal of mathematical biology 2012-07, Vol.65 (1), p.77-105
Main Authors: Dress, Andreas W. M., Huber, Katharina T., Steel, Mike
Format: Article
Language:English
Subjects:
Applications of Mathematics
Biological Evolution
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Models, Genetic
Phylogeny
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Summary:A classical result, fundamental to evolutionary biology, states that an edge-weighted tree T with leaf set X , positive edge weights, and no vertices of degree 2 can be uniquely reconstructed from the leaf-to-leaf distances between any two elements of X . In biology, X corresponds to a set of taxa (e.g. extant species), the tree T describes their phylogenetic relationships, the edges correspond to earlier species evolving for a time until splitting in two or more species by some speciation/bifurcation event, and their length corresponds to the genetic change accumulating over that time in such a species. In this paper, we investigate which subsets of suffice to determine (‘lasso’) the tree T from the leaf-to-leaf distances induced by that tree. The question is particularly topical since reliable estimates of genetic distance—even (if not in particular) by modern mass-sequencing methods—are, in general, available only for certain combinations of taxa.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-011-0450-4