Daniel Bork1,2, Ricson Cheng3, Jincheng Wang1, Jean Sung1, Ran Libeskind-Hadas1. 1. Department of Computer Science, Harvey Mudd College, Claremont, USA. 2. School of Medicine, University of Pittsburgh, Pittsburgh, USA. 3. School of Computer Science, Carnegie Mellon University, Pittsburgh, USA.
Abstract
BACKGROUND: Phylogenetic tree reconciliation is a widely-used method for inferring the evolutionary histories of genes and species. In the duplication-loss-coalescence (DLC) model, we seek a reconciliation that explains the incongruence between a gene and species tree using gene duplication, loss, and deep coalescence events. In the maximum parsimony framework, costs are associated with these event types and a reconciliation is sought that minimizes the total cost of the events required to map the gene tree onto the species tree. RESULTS: We show that this problem is NP-hard even for the special case of minimizing the number of duplications. We then show that the problem is APX-hard when both duplications and losses are considered, implying that no polynomial-time approximation scheme can exist for the problem unless P = NP. CONCLUSIONS: These intractability results are likely to guide future research on algorithmic aspects of the DLC-reconciliation problem.
BACKGROUND: Phylogenetic tree reconciliation is a widely-used method for inferring the evolutionary histories of genes and species. In the duplication-loss-coalescence (DLC) model, we seek a reconciliation that explains the incongruence between a gene and species tree using gene duplication, loss, and deep coalescence events. In the maximum parsimony framework, costs are associated with these event types and a reconciliation is sought that minimizes the total cost of the events required to map the gene tree onto the species tree. RESULTS: We show that this problem is NP-hard even for the special case of minimizing the number of duplications. We then show that the problem is APX-hard when both duplications and losses are considered, implying that no polynomial-time approximation scheme can exist for the problem unless P = NP. CONCLUSIONS: These intractability results are likely to guide future research on algorithmic aspects of the DLC-reconciliation problem.