Polyhedral Combinatorics of UPGMA Cones
Populations and Evolution
2012-06-11 v1 Combinatorics
Quantitative Methods
Abstract
Distance-based methods such as UPGMA (Unweighted Pair Group Method with Arithmetic Mean) continue to play a significant role in phylogenetic research. We use polyhedral combinatorics to analyze the natural subdivision of the positive orthant induced by classifying the input vectors according to tree topologies returned by the algorithm. The partition lattice informs the study of UPGMA trees. We give a closed form for the extreme rays of UPGMA cones on n taxa, and compute the normalized volumes of the UPGMA cones for small n. Keywords: phylogenetic trees, polyhedral combinatorics, partition lattice
Keywords
Cite
@article{arxiv.1206.1621,
title = {Polyhedral Combinatorics of UPGMA Cones},
author = {Ruth Davidson and Seth Sullivant},
journal= {arXiv preprint arXiv:1206.1621},
year = {2012}
}