Abstract
In 2007, Eickmeyer et al. showed that the tree topologies outputted by the Neighbor-Joining (NJ) algorithm and the balanced minimum evolution (BME) method for phylogenetic reconstruction are each determined by a polyhedral subdivision of the space of dissimilarity maps \({\mathbb R}^{n \choose 2}\), where n is the number of taxa. In this paper, we will analyze the behavior of the Neighbor-Joining algorithm on five and six taxa and study the geometry and combinatorics of the polyhedral subdivision of the space of dissimilarity maps for six taxa as well as hyperplane representations of each polyhedral subdivision. We also study simulations for one of the questions stated by Eickmeyer et al., that is, the robustness of the NJ algorithm to small perturbations of tree metrics, with tree models which are known to be hard to be reconstructed via the NJ algorithm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Atteson, K.: The performance of neighbor-joining methods of phylogenetic reconstruction. Algorithmica 25, 251–278 (1999)
Bryant, D.: On the uniqueness of the selection criterion in neighbor-joining. J. Classif. 22, 3–15 (2005)
Eickmeyer, K., Huggins, P., Pachter, L., Yoshida, R.: On the optimality of the neighbor-joining algorithm. Algorithms in Molecular Biology 3 (2008)
Felsenstein, J.: Evolutionary trees from DNA sequences: a maximum likelihood approach. Journal of Molecular Evolution 17, 368–376 (1981)
Galtier, N., Gascuel, O., Jean-Marie, A.: Markov models in molecular evolution. In: Nielsen, R. (ed.) Statistical Methods in Molecular Evolution, pp. 3–24 (2005)
Gawrilow, E., Joswig, M.: Polymake: a framework for analyzing convex polytopes. In: Kalai, G., Ziegler, G.M. (eds.) Polytopes — Combinatorics and Computation, pp. 43–74 (2000)
Kimura, M.: A simple method for estimating evolutionary rates of base substitution through comparative studies of nucleotide sequences. Journal of Molecular Evolution 16, 111–120 (1980)
Neyman, J.: Molecular studies of evolution: a source of novel statistical problems. In: Gupta, S., Yackel, J. (eds.) Statistical decision theory and related topics, pp. 1–27. New York Academic Press, London (1971)
Jukes, H.T., Cantor, C.: Evolution of protein molecules. In: Munro, H.N. (ed.) Mammalian Protein Metabolism, pp. 21–32. New York Academic Press, London (1969)
Levy, D., Yoshida, R., Pachter, L.: Neighbor-joining with phylogenetic diversity estimates. Molecular Biology and Evolution 23, 491–498 (2006)
Mihaescu, R., Levy, D., Pachter, L.: Why Neighbor-Joining Works. Algorithmica (2008)
Olsen, G.J., Matsuda, H., Hagstrom, R., Overbeek, R.: fastDNAml: A tool for construction of phylogenetic trees of DNA sequences using maximum likelihood. Comput. Appl. Biosci. 10, 41–48 (1994)
Ota, S., Li, W.H.: NJML: A Hybrid algorithm for the neighbor-joining and maximum likelihood methods. Molecular Biology and Evolution 17(9), 1401–1409 (2000)
Saitou, N., Nei, M.: The neighbor joining method: a new method for reconstructing phylogenetic trees. Molecular Biology and Evolution 4, 406–425 (1987)
Gascuel, O., Steel, M.: Neighbor-joining revealed. Molecular Biology and Evolution 23, 1997–2000 (2006)
Studier, J.A., Keppler, K.J.: A note on the neighbor-joining method of Saitou and Nei. Molecular Biology and Evolution 5, 729–731 (1988)
Yang, Z.: PAML: A program package for phylogenetic analysis by maximum likelihood. CABIOS 15, 555–556 (1997)
Yang, Z.: Complexity of the simplest phylogenetic estimation problem. Proceedings of the Royal Society B: Biological Sciences 267, 109–116 (2000)
Ziegler, G.: Lectures on Polytopes. Springer, Heidelberg (1995)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Eickmeyer, K., Yoshida, R. (2008). The Geometry of the Neighbor-Joining Algorithm for Small Trees. In: Horimoto, K., Regensburger, G., Rosenkranz, M., Yoshida, H. (eds) Algebraic Biology. AB 2008. Lecture Notes in Computer Science, vol 5147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85101-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-85101-1_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85100-4
Online ISBN: 978-3-540-85101-1
eBook Packages: Computer ScienceComputer Science (R0)