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

Michelle Galla, Kristina Wicke, Mareike Fischer

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1173-1200
Number of pages28
JournalBulletin of Mathematical Biology
Issue number4
StatePublished - Apr 15 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


  • Codons
  • Felsenstein zone
  • Long branch attraction
  • Maximum parsimony
  • Statistical inconsistency


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