Combinatorial Scoring of Phylogenetic Networks

TL;DR

This paper introduces a new combinatorial method to measure how well phylogenetic networks capture character relationships among species, providing an enumeration algorithm applicable to complex networks.

Contribution

It proposes a novel measure for the specificity of phylogenetic networks and develops an enumeration algorithm for character state distributions in arbitrary networks.

Findings

Exact formula for binary trees

Enumeration algorithm for complex networks

Applicable to non-binary phylogenetic structures

Abstract

Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for tree/network construction, it becomes important to measure how well the constructed networks capture the given character relationship across the species. In the current study, we propose a novel method for measuring the specificity of a given phylogenetic network in terms of the total number of distributions of character states at the leaves that the network may impose. While for binary phylogenetic trees, this number has an exact formula and depends only on the number of leaves and character states but not on the tree topology, the situation is much more complicated for non-binary trees or networks. Nevertheless, we develop an algorithm for combinatorial enumeration of such distributions, which is applicable for arbitrary trees and networks under some reasonable assumptions.