Polynomial-Time Algorithms for Phylogenetic Inference Problems involving duplication and reticulation

TL;DR

This paper introduces polynomial-time algorithms for complex phylogenetic inference problems involving gene duplications and reticulations, revealing their close relationship and providing new methods for species tree and network inference.

Contribution

It demonstrates that two seemingly different phylogenetic inference problems can be solved efficiently using a novel structure called 'beaded trees' and introduces a new polynomial-time variant minimizing duplication episode depth.

Findings

Both problems are solvable in polynomial time.

Optimal species phylogenies have a restricted form.

New polynomial-time variant minimizes duplication episode depth.

Abstract

A common problem in phylogenetics is to try to infer a species phylogeny from gene trees. We consider different variants of this problem. The first variant, called Unrestricted Minimal Episodes Inference, aims at inferring a species tree based on a model with speciation and duplication where duplications are clustered in duplication episodes. The goal is to minimize the number of such episodes. The second variant, Parental Hybridization, aims at inferring a species \emph{network} based on a model with speciation and reticulation. The goal is to minimize the number of reticulation events. It is a variant of the well-studied Hybridization Number problem with a more generous view on which gene trees are consistent with a given species network. We show that these seemingly different problems are in fact closely related and can, surprisingly, both be solved in polynomial time, using a structure we call "beaded trees". However, we also show that methods based on these problems have to be used with care because the optimal species phylogenies always have a restricted form. To mitigate this problem, we introduce a new variant of Unrestricted Minimal Episodes Inference that minimizes the duplication episode depth. We prove that this new variant of the problem can also be solved in polynomial time