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arXiv · 1102.0309

`Lassoing' a phylogenetic tree I: Basic properties, shellings, and covers

A. W. M. Dress·K. T. Huber·M. Steel
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Abstract

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 set of 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 $\binom{X}{2}$ 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.

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A. W. M. Dress, K. T. Huber, M. Steel. 2011-07-14. `Lassoing' a phylogenetic tree I: Basic properties, shellings, and covers. https://arxiv.org/abs/1102.0309

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