On the Complexity of Optimising Variants of Phylogenetic Diversity on Phylogenetic Networks

TL;DR

This paper investigates the computational complexity of optimizing various variants of Phylogenetic Diversity scores on different classes of rooted phylogenetic networks, extending the classical tree-based measure to more complex network structures.

Contribution

It introduces several variants of PD for taxa related by phylogenetic networks and analyzes their computational complexity for subset selection problems.

Findings

Complexity results vary across network classes.

Some variants are NP-hard to optimize.

Certain network classes admit polynomial-time solutions.

Abstract

Phylogenetic Diversity (PD) is a prominent quantitative measure of the biodiversity of a collection of present-day species (taxa). This measure is based on the evolutionary distance among the species in the collection. Loosely speaking, if $\mathcal{T}$ is a rooted phylogenetic tree whose leaf set $X$ represents a set of species and whose edges have real-valued lengths (weights), then the PD score of a subset $S$ of $X$ is the sum of the weights of the edges of the minimal subtree of $\mathcal{T}$ connecting the species in $S$. In this paper, we define several natural variants of the PD score for a subset of taxa which are related by a known rooted phylogenetic network. Under these variants, we explore, for a positive integer $k$, the computational complexity of determining the maximum PD score over all subsets of taxa of size $k$ when the input is restricted to different classes of rooted phylogenetic networks