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

J Math Biol. 2012 Jul;65(1):77-105. doi: 10.1007/s00285-011-0450-4. Epub 2011 Jul 7.

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 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 [Formula: see text] 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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Biological Evolution*
  • Models, Genetic*
  • Phylogeny*