title: An ILP solution for the gene duplication problem.
abstract: BACKGROUND
  The gene duplication (GD) problem seeks a species tree that implies the fewest gene duplication events across a given collection of gene trees. Solving this problem makes it possible to use large gene families with complex histories of duplication and loss to infer phylogenetic trees. However, the GD problem is NP-hard, and therefore, most analyses use heuristics that lack any performance guarantee.
  
  
  RESULTS
  We describe the first integer linear programming (ILP) formulation to solve instances of the gene duplication problem exactly. With simulations, we demonstrate that the ILP solution can solve problem instances with up to 14 taxa. Furthermore, we apply the new ILP solution to solve the gene duplication problem for the seed plant phylogeny using a 12-taxon, 6,084-gene data set. The unique, optimal solution, which places Gnetales sister to the conifers, represents a new, large-scale genomic perspective on one of the most puzzling questions in plant systematics.
  
  
  CONCLUSIONS
  Although the GD problem is NP-hard, our novel ILP solution for it can solve instances with data sets consisting of as many as 14 taxa and 1,000 genes in a few hours. These are the largest instances that have been solved to optimally to date. Thus, this work can provide large-scale genomic perspectives on phylogenetic questions that previously could only be addressed by heuristic estimates.
authors.affiliation: Department of Computer Science, Iowa State University, Ames 50011, USA. wcchang@iastate.edu
authors.forename: Wen-Chieh
authors.initials: WC
authors.lastname: Chang
authors.forename: Gordon J
authors.initials: GJ
authors.lastname: Burleigh
authors.forename: David F
authors.initials: DF
authors.lastname: Fernández-Baca
authors.forename: Oliver
authors.initials: O
authors.lastname: Eulenstein
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D020440:Gene Duplication; D018745:Genome, Plant; D023281:Genomics / Q000379:methods; D010802:Phylogeny; D010944:Plants / Q000235:genetics*; D011382:Programming, Linear