Bulletin of Mathematical Biology

, Volume 79, Issue 12, pp 2865–2886 | Cite as

Ancestral Sequence Reconstruction with Maximum Parsimony

  • Lina Herbst
  • Mareike Fischer
Original Article


One of the main aims in phylogenetics is the estimation of ancestral sequences based on present-day data like, for instance, DNA alignments. One way to estimate the data of the last common ancestor of a given set of species is to first reconstruct a phylogenetic tree with some tree inference method and then to use some method of ancestral state inference based on that tree. One of the best-known methods both for tree inference and for ancestral sequence inference is Maximum Parsimony (MP). In this manuscript, we focus on this method and on ancestral state inference for fully bifurcating trees. In particular, we investigate a conjecture published by Charleston and Steel in 1995 concerning the number of species which need to have a particular state, say a, at a particular site in order for MP to unambiguously return a as an estimate for the state of the last common ancestor. We prove the conjecture for all even numbers of character states, which is the most relevant case in biology. We also show that the conjecture does not hold in general for odd numbers of character states, but also present some positive results for this case.


Maximum Parsimony Fitch algorithm Ancestral sequence reconstruction 



We thank Mike Steel for bringing this topic to our attention. Moreover, we thank two anonymous reviewers for their helpful comments on an earlier version of this manuscript. The first author also thanks the Ernst-Moritz-Arndt-University Greifswald for the Landesgraduiertenförderung studentship, under which this work was conducted.


  1. Cai W, Pei J, Grishin NV (2004) Reconstruction of ancestral protein sequences and its applications. BMC Evolut Biol 4:33CrossRefGoogle Scholar
  2. Felsenstein J (2004) Inferring phylogenies. Sinauer Associates, Inc., SunderlandGoogle Scholar
  3. Fischer M, Liebscher V (2015) On the balance of unrooted trees. Preprint. arXiv:1510.07882
  4. Fitch WM (1971) Toward defining the course of evolution: minimum change for a specific tree topology. Syst Zool 20:406–416CrossRefGoogle Scholar
  5. Gascuel O, Steel M (2010) Inferring ancestral sequences in taxon-rich phylogenies. Math Biosci 227:125–153MathSciNetCrossRefzbMATHGoogle Scholar
  6. Gascuel O, Steel M (2014) Predicting the ancestral character changes in a tree is typically easier than predicting the root state. Syst Biol 63:421–435CrossRefGoogle Scholar
  7. Goulden IP, Jackson DM (1983) Combinatorial enumeration. Wiley, New YorkzbMATHGoogle Scholar
  8. Griffith OW, Blackburn DG, Brandley MC, Van Dyke JU, Whittington CM, Thompson MB (2015) Ancestral state reconstructions require biological evidence to test evolutionary hypotheses: a case study examining the evolution of reproductive mode in squamate reptiles. J Exp Zool 324:493–503CrossRefGoogle Scholar
  9. Li G, Steel M, Zhang L (2008) More taxa are not necessarily better for the reconstruction of ancestral character states. Syst Biol 57:647–653CrossRefGoogle Scholar
  10. Liberles DA (ed) (2007) Ancestral sequence reconstruction. Oxford University Press, New YorkGoogle Scholar
  11. Semple C, Steel M (2003) Phylogenetics. Oxford University Press, New YorkzbMATHGoogle Scholar
  12. Steel M, Charleston M (1995) Five surprising properties of parsimoniously colored trees. Bull Math Biol 57:367–375CrossRefzbMATHGoogle Scholar

Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  1. 1.Institute for Mathematics and Computer ScienceGreifswald UniversityGreifswaldGermany

Personalised recommendations