On the optimality of the neighbor-joining algorithm

Kord Eickmeyer¹ , Peter Huggins² , Lior Pachter² and Ruriko Yoshida³

¹Department of Computer Science, Humboldt University, Unter den Linden 6, 10099 Berlin, Germany

²Department of Mathematics, University of California at Berkeley Berkeley, CA 94720-3840, USA

³Department of Statistics, University of Kentucky Lexington, KY 40506, USA

author email corresponding author email

Algorithms for Molecular Biology 2008, 3:5doi:10.1186/1748-7188-3-5


Published:	30 April 2008

Abstract

The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy algorithm for finding the balanced minimum evolution (BME) tree associated to a dissimilarity map. From this point of view, NJ is "optimal" when the algorithm outputs the tree which minimizes the balanced minimum evolution criterion. We use the fact that the NJ tree topology and the BME tree topology are determined by polyhedral subdivisions of the spaces of dissimilarity maps to study the optimality of the neighbor-joining algorithm. In particular, we investigate and compare the polyhedral subdivisions for n ≤ 8. This requires the measurement of volumes of spherical polytopes in high dimension, which we obtain using a combination of Monte Carlo methods and polyhedral algorithms. Our results include a demonstration that highly unrelated trees can be co-optimal in BME reconstruction, and that NJ regions are not convex. We obtain the l₂radius for neighbor-joining for n = 5 and we conjecture that the ability of the neighbor-joining algorithm to recover the BME tree depends on the diameter of the BME tree.