Bulletin of Mathematical Biology

, Volume 73, Issue 6, pp 1398–1411 | Cite as

On the Number of Binary Characters Needed to Recover a Phylogeny Using Maximum Parsimony

  • Juanjuan Chai
  • Elizabeth Ann HousworthEmail author
Original Article


We give an explicit construction to solve a conjecture of Mike Steel and David Penny that any phylogeny involving N taxa can be recovered unambiguously using on the order of log N binary characters and the method of maximum parsimony. Biologically, this means that homoplasy need not be a deterrent to parsimony methods. Some patterns of homoplasy are phylogenetically informative and can exponentially reduce the amount of data needed to resolve a phylogeny.


Phylogeny Maximum parsimony Binary characters Homoplasy One-clustering 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bandelt, H.-J. (2001). In A. Brandstädt & V. B. Le (Eds.), Lecture notes in computer science : Vol. 2204. Median hulls as Steiner hulls in rectilinear and molecular sequence space, graph-theoretic concepts in computer science (pp. 1–7). Berlin: Springer. Google Scholar
  2. Hendy, M. D., Foulds, L. R., & Penny, D. (1980). Proving phylogenetic trees minimal with l-clustering and set partitioning. Math. Biosci., 51, 71–88. MathSciNetzbMATHCrossRefGoogle Scholar
  3. Huber, K. T., Moulton, V., & Steel, M. (2005). Four characters suffice to convexly define a phylogenetic tree. SIAM J. Discrete Math., 18, 835–843. MathSciNetzbMATHCrossRefGoogle Scholar
  4. Kälersjö, M., Albert, V. A., & Farris, J. S. (1999). Homoplasy increases phylogenetic structure. Cladistics, 15, 91–93. Google Scholar
  5. Lipman, R. J., & Tarjan, R. E. (1979). A separator theorem for planar graphs. SIAM J. Appl. Math., 36, 177–189. MathSciNetCrossRefGoogle Scholar
  6. Steel, M., & Penny, D. (2005). In V. Albert (Ed.), Maximum parsimony and the phylogenetic information in multi-state characters, parsimony, phylogeny and genomics (pp. 163–178). London: Oxford University Press. Google Scholar

Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  1. 1.Indiana UniversityBloomingtonUSA

Personalised recommendations