Journal of Mathematical Biology

, Volume 65, Issue 2, pp 293–308

Non-hereditary Maximum Parsimony trees


DOI: 10.1007/s00285-011-0458-9

Cite this article as:
Fischer, M. J. Math. Biol. (2012) 65: 293. doi:10.1007/s00285-011-0458-9


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 

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

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