Bulletin of Mathematical Biology

, Volume 81, Issue 4, pp 1173–1200 | Cite as

Statistical Inconsistency of Maximum Parsimony for k-Tuple-Site Data

  • Michelle Galla
  • Kristina Wicke
  • Mareike FischerEmail author


One of the main aims of phylogenetics is to reconstruct the “Tree of Life.” In this respect, different methods and criteria are used to analyze DNA sequences of different species and to compare them in order to derive the evolutionary relationships of these species. Maximum parsimony is one such criterion for tree reconstruction, and it is the one which we will use in this paper. However, it is well known that tree reconstruction methods can lead to wrong relationship estimates. One typical problem of maximum parsimony is long branch attraction, which can lead to statistical inconsistency. In this work, we will consider a blockwise approach to alignment analysis, namely the so-called k-tuple analyses. For four taxa, it has already been shown that k-tuple-based analyses are statistically inconsistent if and only if the standard character-based (site-based) analyses are statistically inconsistent. So, in the four-taxon case, going from individual sites to k-tuples does not lead to any improvement. However, real biological analyses often consider more than only four taxa. Therefore, we analyze the case of five taxa for 2- and 3-tuple-site data and consider alphabets with two and four elements. We show that the equivalence of single-site data and k-tuple-site data then no longer holds. Even so, we can show that maximum parsimony is statistically inconsistent for k-tuple-site data and five taxa.


Maximum parsimony Statistical inconsistency Codons Long branch attraction Felsenstein zone 



The first and second authors thank the University of Greifswald for the Bogislaw studentship and the Landesgraduiertenförderung studentship, respectively, under which this work was conducted. Moreover, we wish to thank two anonymous reviewers for very helpful suggestions on an earlier version of this manuscript.


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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceUniversity of GreifswaldGreifswaldGermany

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