Distance-based phylogenetic methods around a polytomy

TL;DR

This paper uses polyhedral geometry to analyze how distance-based phylogenetic methods like UPGMA and Neighbor-Joining perform around polytomies, revealing limitations in their accuracy compared to least squares phylogeny.

Contribution

It introduces a geometric framework to compare phylogenetic algorithms and highlights their shortcomings near polytomies.

Findings

UPGMA and Neighbor-Joining poorly match least squares phylogeny with polytomies

The geometric approach reveals differences in local subdivision regions of dissimilarity space

The study provides insights into the limitations of common distance-based methods

Abstract

Distance-based phylogenetic algorithms attempt to solve the NP-hard least squares phylogeny problem by mapping an arbitrary dissimilarity map representing biological data to a tree metric. The set of all dissimilarity maps is a Euclidean space properly containing the space of all tree metrics as a polyhedral fan. Outputs of distance-based tree reconstruction algorithms such as UPGMA and Neighbor-Joining are points in the maximal cones in the fan. Tree metrics with polytomies lie at the intersections of maximal cones. A phylogenetic algorithm divides the space of all dissimilarity maps into regions based upon which combinatorial tree is reconstructed by the algorithm. Comparison of phylogenetic methods can be done by comparing the geometry of these regions. We use polyhedral geometry to compare the local nature of the subdivisions induced by least squares phylogeny, UPGMA, and Neighbor-Joining. Our results suggest that in some circumstances, UPGMA and Neighbor-Joining poorly match least squares phylogeny when the true tree has a polytomy.