On the Maximum Parsimony Distance Between Phylogenetic Trees

Mareike Fischer*, Steven Kelk*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


Within the field of phylogenetics there is great interest in distance measures to quantify the dissimilarity of two trees. Here, based on an idea of Bruen and Bryant, we propose and analyze a new distance measure: theMaximum Parsimony (MP) distance. This is based on the difference of the parsimony scores of a single character on both trees under consideration, and the goal is to find the character which maximizes this difference. In this article we show that this new distance is a metric and provides a lower bound to the well-known Subtree Prune and Regraft (SPR) distance. We also show that to compute the MP distance it is sufficient to consider only characters that are convex on one of the trees, and prove several additional structural properties of the distance. On the complexity side, we prove that calculating the MP distance is in general NP-hard, and identify an interesting island of tractability in which the distance can be calculated in polynomial time.

Original languageEnglish
Pages (from-to)87-113
Number of pages27
JournalAnnals of Combinatorics
Issue number1
Publication statusPublished - 1 Mar 2016


  • HARD
  • maximum parsimony
  • subtree prune and regraft (SPR)
  • tree metric

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