The Most Parsimonious Reconciliation Problem in the Presence of Incomplete Lineage Sorting and Hybridization is NP-Hard

Abstract

The maximum parsimony phylogenetic reconciliation problem seeks to explain incongruity between a gene phylogeny and a species phylogeny with respect to a set of evolutionary events. While the reconciliation problem is well-studied for species and gene trees subject to events such as duplication, transfer, loss, and deep coalescence, recent work has examined species phylogenies that incorporate hybridization and are thus represented by networks rather than trees. In this paper, we show that the problem of computing a maximum parsimony reconciliation for a gene tree and species network is NP-hard even when only considering deep coalescence. This result suggests that future work on maximum parsimony reconciliation for species networks should explore approximation algorithms and heuristics.

A Polynomial-Time Algorithm for Minimizing the Deep Coalescence Cost for Level-1 Species Networks

“…Finally, theoretical analysis has shown that the MPR problem under a hybridization and ILS model is NP-hard in general, e.g. for level-k species networks for arbitrary values of k [38]. Similar analysis might address whether there exist approximation algorithms or fixed-parameter tractable algorithms.…”