`Lassoing' a phylogenetic tree I: Basic properties, shellings, and covers
Abstract
A classical result, fundamental to evolutionary biology, states that an edge-weighted tree with leaf set , positive edge weights, and no vertices of degree 2 can be uniquely reconstructed from the set of leaf-to-leaf distances between any two elements of . In biology, corresponds to a set of taxa (e.g. extant species), the tree 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') a tree 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.
Cite
@article{arxiv.1102.0309,
title = {`Lassoing' a phylogenetic tree I: Basic properties, shellings, and covers},
author = {A. W. M. Dress and K. T. Huber and M. Steel},
journal= {arXiv preprint arXiv:1102.0309},
year = {2011}
}