Extracting Conflict-free Information from Multi-labeled Trees

TL;DR

This paper introduces a method to extract conflict-free information from multi-labeled phylogenetic trees, defining a reduced form that preserves this information and enabling efficient comparison of such trees.

Contribution

It defines the information content of MUL-trees, introduces the maximal reduced form, and provides an efficient algorithm for reduction and comparison.

Findings

Algorithm effectively reduces MUL-trees while preserving information.

Empirical evaluation shows significant data reduction without loss of conflict-free info.

Reduced forms enable comparison of MUL-trees based on their information content.

Abstract

A multi-labeled tree, or MUL-tree, is a phylogenetic tree where two or more leaves share a label, e.g., a species name. A MUL-tree can imply multiple conflicting phylogenetic relationships for the same set of taxa, but can also contain conflict-free information that is of interest and yet is not obvious. We define the information content of a MUL-tree T as the set of all conflict-free quartet topologies implied by T, and define the maximal reduced form of T as the smallest tree that can be obtained from T by pruning leaves and contracting edges while retaining the same information content. We show that any two MUL-trees with the same information content exhibit the same reduced form. This introduces an equivalence relation in MUL-trees with potential applications to comparing MUL-trees. We present an efficient algorithm to reduce a MUL-tree to its maximally reduced form and evaluate its performance on empirical datasets in terms of both quality of the reduced tree and the degree of data reduction achieved.