Abstract
BackgroundPhylogenetic 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.ResultsWe 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.ConclusionsThese intractability results are likely to guide future research on algorithmic aspects of the DLC-reconciliation problem.
Highlights
Phylogenetic tree reconciliation is a widely-used method for inferring the evolutionary histories of genes and species
Phylogenetic tree reconciliation is a fundamental technique in the study of the evolutionary relationships of genes and species
A species tree, and the association between their leaves, we seek to explain the incongruence between the two trees using a set of evolutionary events
Summary
Phylogenetic tree reconciliation is a widely-used method for inferring the evolutionary histories of genes and species. Definition 5 (DCL Decision Problem (DCLDP)) Given gene tree G, species tree S, leaf map Le : L(G) → L(S) , non-negative costs Cd and Cl for duplication and loss events, and non-negative decision parameter k, does there exist a LCT for (G, S, Le) of cost at most k?
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