Bulletin of Mathematical Biology

, Volume 68, Issue 4, pp 919–944 | Cite as

Unique Reconstruction of Tree-Like Phylogenetic Networks from Distances Between Leaves

Original Paper

Abstract

In this paper, a class of rooted acyclic directed graphs (called TOM-networks) is defined that generalizes rooted trees and allows for models including hybridization events. It is argued that the defining properties are biologically plausible. Each TOM-network has a distance defined between each pair of vertices. For a TOM-network N, suppose that the set X consisting of the leaves and the root is known, together with the distances between members of X. It is proved that N is uniquely determined from this information and can be reconstructed in polynomial time. Thus, given exact distance information on the leaves and root, the phylogenetic network can be uniquely recovered, provided that it is a TOM-network. An outgroup can be used instead of a true root.

Keywords

Phylogeny Network Phylogenetic network 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bandelt, H.-J., Dress, A., 1986. Reconstructing the shape of a tree from observed dissimilarity data. Adv. Appl. Math. 7, 309–343.CrossRefMATHMathSciNetGoogle Scholar
  2. Bandelt, H.-J., Dress, A., 1992. Split decomposition: A new and useful approach to phylogenetic analysis of distance data. Mol. Phylogenet. Evol. 1, 242–252.CrossRefPubMedGoogle Scholar
  3. Baroni, M., Semple, C., Steel, M., 2004. A framework for representing reticulate evolution. Anal. Combinat. 8, 391–408.CrossRefMATHMathSciNetGoogle Scholar
  4. Felsenstein, J., 1981. Evolutionary trees from DNA sequences: A maximum likelihood approach. J. Mol. Evol. 17, 368–376.CrossRefPubMedGoogle Scholar
  5. Felsenstein, J., 2004. Inferring Phylogenies. Sinauer, Sunderland, MA.Google Scholar
  6. Fitch, W.M., 1981. A non-sequential method for constructing trees and hierarchical classifications. J. Mol. Evol. 18, 30–37.CrossRefPubMedGoogle Scholar
  7. Dan Gusfield, Gusfield, D., 1991. Efficient algorithms for inferring evolutionary history. Networks 21, 19–28.MATHCrossRefMathSciNetGoogle Scholar
  8. Gusfield, D., Eddhu, S., Langley, C., 2004a. Optimal, efficient reconstruction of phylogenetic networks with constrained recombination. J. Bioinform. Comput. Biol. 2, 173–213.CrossRefGoogle Scholar
  9. Dan Gusfield, Satish Eddhu, and Charles Langley, Gusfield, D., Eddhu, S., Langley, C., 2004b. The fine structure of galls in phylogenetic networks. INFORMS J. Comput. 16(4), 459–469.CrossRefMathSciNetGoogle Scholar
  10. Hasegawa, M., Kishino, H., Yano, K., 1985. Dating of the human-ape splitting by a molecular clock of mitochondrial DNA. J. Mol. Evol. 22, 160–174.CrossRefPubMedGoogle Scholar
  11. Hein, J., 1990. Reconstructing evolution of sequences subject to recombination using parsimony. Math. Biosci. 98, 185–200.CrossRefPubMedMATHMathSciNetGoogle Scholar
  12. Hein, J., 1993. A heuristic method to reconstruct the history of sequences subject to recombination. J. Mol. Evol. 36, 396–405.CrossRefGoogle Scholar
  13. Huson, D.H., 1998. SplitsTree: A program for analyzing and visualizing evolutionary data. Bioinformatics 141, 68–73.CrossRefGoogle Scholar
  14. Jukes, T.H., Cantor, C.R., 1969. Evolution of protein molecules. In: Osawa, S., Honjo, T. (Eds.), Evolution of Life: Fossils, Molecules, and Culture. Springer-Verlag, Tokyo, pp. 79–95.Google Scholar
  15. Kimura, M., 1980. A simple method for estimating evolutionary rate of base substitutions through comparative studies of nucleotide sequences. J. Mol. Evol. 16, 111–120.CrossRefPubMedGoogle Scholar
  16. Li, W.-H., 1981. A simple method for construcing phylogenetic trees from distance matrices. Proc. Natl. Acad. Sci. U.S.A. 78, 1085–1089.PubMedMATHCrossRefGoogle Scholar
  17. Vladamir Makarenkov and Pierre Legendre. Makarenkov, V., Legendre, P., 2004. From a phylogenetic tree to a reticulated network. J. Comput. Biol. 11, 195–212.CrossRefPubMedGoogle Scholar
  18. Moret, B.M.E., Nakhleh, L., Warnow, T., Linder, C.R., Tholse, A., Padolina, A., Sun, J., Timme, R., 2004. Phylogenetic networks: Modeling, reconstructibility, and accuracy. IEEE/ACM Trans. Comput. Biol. Bioinform. 1, 13–23.CrossRefGoogle Scholar
  19. Nakhleh, L., Warnow, T., Randal Linder, C., 2004. Reconstructing reticulate evolution in species—Theory and practice. In: Bourne, P.E., Gusfield, D. (Eds.), Proceedings of the Eighth Annual International Conference on Computational Molecular Biology (RECOMB '04), March 27–31, 2004, San Diego, CA. ACM, New York, pp. 337–346.Google Scholar
  20. Saitou, N., Nei, M., 1987. The neighbor-joining method: A new method for reconstructing phylogenetic trees. Mol. Biol. Evol. 4, 406–425.PubMedGoogle Scholar
  21. Sattath, S., Tversky, A., 1977. Additive similarity trees. Psychometrika 42, 319–345.CrossRefGoogle Scholar
  22. Lusheng Wang, Kaizhong Zhang, and Louxin Zhang. 2001. Wang, L., Zhang, K., Zhang, L., 2001. Perfect phylogenetic networks with recombination. J. Comput. Biol. 8, 69–78.Google Scholar
  23. Willson, S.J., 2006. Unique solvability of certain hybrid networks from their distances. Ann. Combinat.Google Scholar

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  1. 1.Department of MathematicsIowa State UniversityAmesUSA

Personalised recommendations