title: 'Lassoing' a phylogenetic tree I: basic properties, shellings, and covers.
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.
authors: CAS-MPG Partner Institute and Key Lab for Computational Biology, Shanghai, China. andreas.dress@infinity-3.de
authors: Andreas W M
authors: AW
authors: Dress
authors: Katharina T
authors: KT
authors: Huber
authors: Mike
authors: M
authors: Steel
mesh_terms: D005075:Biological Evolution; D008957:Models, Genetic; D010802:Phylogeny