Journal of Mathematical Biology

, Volume 65, Issue 2, pp 293–308 | Cite as

Non-hereditary Maximum Parsimony trees

  • Mareike Fischer


In this paper, we investigate a conjecture by Arndt von Haeseler concerning the Maximum Parsimony method for phylogenetic estimation, which was published by the Newton Institute in Cambridge on a list of open phylogenetic problems in 2007. This conjecture deals with the question whether Maximum Parsimony trees are hereditary. The conjecture suggests that a Maximum Parsimony tree for a particular (DNA) alignment necessarily has subtrees of all possible sizes which are most parsimonious for the corresponding subalignments. We answer the conjecture affirmatively for binary alignments on 5 taxa but also show how to construct examples for which Maximum Parsimony trees are not hereditary. Apart from showing that a most parsimonious tree cannot generally be reduced to a most parsimonious tree on fewer taxa, we also show that compatible most parsimonious quartets do not have to provide a most parsimonious supertree. Last, we show that our results can be generalized to Maximum Likelihood for certain nucleotide substitution models.


Phylogenetics Maximum Parsimony Maximum Likelihood Jukes-Cantor model 

Mathematics Subject Classification (2000)

90C35 92E99 94C15 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bandelt HJ, Dress A (1986) Reconstructing the shape of a tree from observed dissimilarity data. Adv Appl Math 7: 309–343MathSciNetzbMATHCrossRefGoogle Scholar
  2. Chor B, Tuller T (2006) Finding a maximum likelihood tree is hard. J ACM 53: 722–744MathSciNetCrossRefGoogle Scholar
  3. Felsenstein J (1978) Cases in which parsimony or compatibility will be positively misleading. Syst Zool 27: 401–410CrossRefGoogle Scholar
  4. Felsenstein J (2004) Inferring phylogenies. Sinauer Associates, MassachusettsGoogle Scholar
  5. Felsenstein J (2005) Phylip (phylogeny inference package version 3.6. Distributed by the author, Department of Genome Sciences. University of Washington, SeattleGoogle Scholar
  6. Felsenstein J, Archie J, Day W, Maddison W, Meacham C, Rohlf F, Swofford D (2000) The newick tree format.
  7. Fitch W (1971) Toward defining the course of evolution: minimum change for a specific tree topology. Syst Zool 20(4): 406–416CrossRefGoogle Scholar
  8. Foulds L, Graham R (1982) The steiner problem in phylogeny is np-complete. Adv Appl Math 3: 43–49MathSciNetzbMATHCrossRefGoogle Scholar
  9. Jukes T, Cantor C (1969) Evolution of protein molecules. In: Mammalian Protein Metabolism. Academic Press, New York, pp 21–132Google Scholar
  10. Neyman J (1971) Molecular studies of evolution: A source of novel statistical problems. In:Statistical Decision Theory and Related Topics. Academic Press, New York, pp 1–27Google Scholar
  11. Roch S (2006) A short proof that phylogenetic tree reconstruction by maximum likelihood is hard. IEEE/ACM Trans Comp Biol Bioinform 3: 92–94CrossRefGoogle Scholar
  12. Semple C, Steel, M (2003) Phylogenetics. Oxford University PressGoogle Scholar
  13. Tuffley C, Steel M (1997) Links between maximum likelihood and maximum parsimony under a simple model of site substitution. Bull Math Biol 59: 581–607zbMATHCrossRefGoogle Scholar
  14. von Haeseler A (2007) Hereditary maximum parsimony trees. In: Steel M (ed) Phylogenetics: challenges and conjectures, Isaac Newton Institute for Mathematical Sciences.
  15. von Haeseler A (2009) Hereditary maximum parsimony trees. In: Steel M (ed) Penny Ante List of open problems in phylogenetics, Biomathematics Research Centre of the Allan Wilson Centre for Molecular Ecology and Evolution.
  16. Yang Z (2006) Computational Molecular Evolution. Oxford University Press, OxfordCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Center for Integrative Bioinformatics Vienna, Max F. Perutz LaboratoriesUniversity of Vienna, Medical University of Vienna, University of Veterinary Medicine ViennaViennaAustria

Personalised recommendations