Efficient Quartet Representations of Trees and Applications to Supertree and Summary Methods

TL;DR

This paper introduces an Efficient Quartet System (EQS) that compactly represents phylogenetic trees, enabling effective species and supertree reconstruction with reduced computational load while maintaining high accuracy.

Contribution

The paper proposes the EQS concept, mathematically proves it preserves all tree information, and demonstrates its practical effectiveness in reducing computational complexity.

Findings

EQS retains all combinatorial information of the original tree.

Using EQS reduces the number of quartets needed in inference pipelines.

EQS-based methods show only minor accuracy loss in simulations.

Abstract

Quartet trees displayed by larger phylogenetic trees have long been used as inputs for species tree and supertree reconstruction. Computational constraints prevent the use of all displayed quartets in many practical problems due to the number of taxa. We introduce the notion of an Efficient Quartet System (EQS) to represent a phylogenetic tree with a subset of the quartets displayed by the tree. We show mathematically that the set of quartets obtained from a tree via an EQS contains all of the combinatorial information of the tree itself. Using performance tests on simulated datasets, we also demonstrate that using an EQS to reduce the number of quartets in pipelines for summary methods of species tree inference and supertree inference results in only small reductions in accuracy.