‘TreeDist’ implements a suite of metrics that quantify the topological distance between pairs of unweighted phylogenetic trees. The metrics generally fall in the category of ‘generalized Robinson-Foulds distances’: they are based on comparing partitions between trees, and thus reflect the relationship data within trees, with no reference to branch lengths.

The Robinson-Foulds distance simply tallies the number of non-trivial splits (sometimes inaccurately termed clades, nodes or edges) that occur in both trees – any splits that are not perfectly identical contributes one point to the distance score of zero, however similar or different they are. By overlooking potential similarities between almost-identical splits, this conservative approach has undesirable properties.

‘Generalized’ RF metrics generate matchings that pair each split in one tree with a similar split in the other. Each pair of splits is assigned a similarity score; the sum of these scores in the optimal matching then quantifies the similarity between two trees.

Different ways of calculating the the similarity between a pair of splits lead to different tree distance metrics, implemented in the functions below:

  • MutualClusteringInfo(), SharedPhylogeneticInfo()

    Smith (2020) scores matchings based on the amount of information that one partition contains about the other. The Mutual Phylogenetic Information assigns zero similarity to split pairs that cannot both exist on a single tree; The Mutual Clustering Information metric is more forgiving, and exhibits more desirable behaviour; it is the recommended metric for tree comparison. (Its complement, ClusteringInfoDistance(), returns a tree distance.)

  • NyeSimilarity()

    Nye et al. (2006) score matchings according to the size of the largest split that is consistent with both of them, normalized against the Jaccard index. This approach is extended by Böcker et al. (2013) with the Jaccard-Robinson-Foulds metric (function JaccardRobinsonFoulds()).

  • MatchingSplitDistance()

    Bogdanowicz and Giaro (2012) and Lin et al. (2012) independently proposed counting the number of ‘mismatched’ leaves in a pair of splits. MatchingSplitInfoDistance() provides an information-based equivalent (Smith 2020).

The package also implements the variation of the path distance proposed by Kendal and Colijn (2016) (function KendallColijn()), approximations of the Nearest-Neighbour Interchange (NNI) distance (function NNIDist(); following Li et al. (1996)), and calculates the size (function MASTSize()) and information content (function MASTInfo()) of the Maximum Agreement Subtree.

For an implementation of the Tree Bisection and Reconnection (TBR) distance, see the package ‘TBRDist’.


Install and load the library from CRAN as follows:

You can install the development version of the package with:

if (!require(devtools)) install.packages("devtools")

See also

Other R packages implementing tree distance functions include:

  • ape:
    • cophenetic.phylo(): Cophenetic distance
    • dist.topo(): Path (topological) distance, Robinson-Foulds distance.
  • phangorn
    • treedist(): Path, Robinson-Foulds and approximate SPR distances.
  • Quartet: Triplet and Quartet distances, using the tqDist algorithm.
  • TBRDist: TBR and SPR distances on unrooted trees, using the ‘uspr’ C library.
  • distory (unmaintained): Geodesic distance


Please note that the ‘TreeDist’ project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.