Efficient Reconstruction of Phylogenetic Networks with Constrained Recombination

• Authors: Dan Gusfield;Satish Eddhu;Charles Langley
• Venue: CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
• Year: 2003

A phylogenetic network is a generalization of a phylogenetictree, allowing structural properties that are not tree-like.With the growth of genomic data, much of which doesnot fit ideal tree models, there is greater need to understandthe algorithmics and combinatorics of phylogeneticnetworks [10, 11]. However, to date, very little has beenpublished on this, with the notable exception of the paperby Wang et al.[12]. Other related papers include [4, 5, 7]We consider the problem introduced in [12], of determiningwhether the sequences can be derived on a phylogeneticnetwork where the recombination cycles are nodedisjoint. In this paper, we call such a phylogenetic networka "galled-tree". By more deeply analysing the combinatorialconstraints on cycle-disjoint phylogenetic networks, weobtain an efficient algorithm that is guaranteed to be botha necessary and sufficient test for the existence of a galled-treefor the data. If there is a galled-tree, the algorithmconstructs one and obtains an implicit representation of allthe galled trees for the data, and can create these in lineartime for each one. We also note two additional results relatedto galled trees: first, any set of sequences that can bederived on a galled tree can be derived on a true tree (withoutrecombination cycles), where at most one back mutationis allowed per site; second, the site compatibility problem(which is NP-hard in general) can be solved in linear timefor any set of sequences that can be derived on a galled tree.The combinatorial constraints we develop apply (for themost part) to node-disjoint cycles in any phylogenetic network(not just galled-trees), and can be used for exampleto prove that a given site cannot be on a node-disjoint cyclein any phylogenetic network. Perhaps more importantthan the specific results about galled-trees, we introduce anapproach that can be used to study recombination in phylogeneticnetworks that go beyond galled-trees.