Gene tree reconciliation including transfers with replacement is hard and FPT

TL;DR

This paper studies the computational complexity of gene tree reconciliation models that include gene transfer with replacement, proving NP-hardness and fixed-parameter tractability under certain conditions.

Contribution

It introduces a new reconciliation model with gene transfer and replacement, proving NP-hardness and FPT results, extending to the dated SPR problem.

Findings

Reconciliation with transfer and replacement is NP-hard.

Reconciliation with speciations and transfers with replacement is FPT.

Results extend to the dated SPR problem.

Abstract

Phylogenetic trees illustrate the evolutionary history of genes and species. In most cases, although genes evolve along with the species they belong to, a species tree and gene tree are not identical, because of evolutionary events at the gene level like duplication or transfer. These differences are handled by phylogenetic reconciliation, which formally is a mapping between gene tree nodes and species tree nodes and branches. We investigate models of reconciliation with a gene transfer that replaces existing gene, which is a biological important event but never included in reconciliation models. Also the problem is close to a dated version of the classical subtree prune and regraft (SPR) distance problem, where a pruned subtree has to be regrafted only on a branch closer to the root. We prove that the reconciliation problem including transfer and replacement is NP-hard, and that if speciations and transfers with replacement are the only allowed evolutionary events, then it is fixed-parameter tractable (FPT) with respect to the reconciliation's weight. We prove that the results extend to the dated SPR problem.