Polyhedral geometry of Phylogenetic Rogue Taxa

TL;DR

This paper investigates how adding a rogue taxon affects phylogenetic trees under the BME method, using polyhedral geometry to characterize and predict these effects, and provides computational tools for small datasets.

Contribution

It characterizes the behavior of rogue taxa in BME phylogenetics using polyhedral geometry and develops computational cones for small datasets.

Findings

Existence of rogue taxon distances that alter tree topology

Restrictions on BME-optimal tree topologies with rogue taxa

Polyhedral cones for small datasets (4-6 taxa)

Abstract

It is well known among phylogeneticists that adding an extra taxon (e.g. species) to a data set can alter the structure of the optimal phylogenetic tree in surprising ways. However, little is known about this "rogue taxon" effect. In this paper we characterize the behavior of balanced minimum evolution (BME) phylogenetics on data sets of this type using tools from polyhedral geometry. First we show that for any distance matrix there exist distances to a "rogue taxon" such that the BME-optimal tree for the data set with the new taxon does not contain any nontrivial splits (bipartitions) of the optimal tree for the original data. Second, we prove a theorem which restricts the topology of BME-optimal trees for data sets of this type, thus showing that a rogue taxon cannot have an arbitrary effect on the optimal tree. Third, we construct polyhedral cones computationally which give complete answers for BME rogue taxon behavior when our original data fits a tree on four, five, and six taxa. We use these cones to derive sufficient conditions for rogue taxon behavior for four taxa, and to understand the frequency of the rogue taxon effect via simulation.