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treedist computes different tree distance methods and RF.dist the Robinson-Foulds or symmetric distance. The Robinson-Foulds distance only depends on the topology of the trees. If edge weights should be considered wRF.dist calculates the weighted RF distance (Robinson & Foulds 1981). and KF.dist calculates the branch score distance (Kuhner & Felsenstein 1994). path.dist computes the path difference metric as described in Steel and Penny 1993). sprdist computes the approximate SPR distance (Oliveira Martins et al. 2008, de Oliveira Martins 2016).


treedist(tree1, tree2, check.labels = TRUE)

sprdist(tree1, tree2)

SPR.dist(tree1, tree2 = NULL)

RF.dist(tree1, tree2 = NULL, normalize = FALSE, check.labels = TRUE,
  rooted = FALSE)

wRF.dist(tree1, tree2 = NULL, normalize = FALSE, check.labels = TRUE,
  rooted = FALSE)

KF.dist(tree1, tree2 = NULL, check.labels = TRUE, rooted = FALSE)

path.dist(tree1, tree2 = NULL, check.labels = TRUE, use.weight = FALSE)



A phylogenetic tree (class phylo) or vector of trees (an object of class multiPhylo). See details


A phylogenetic tree.


compares labels of the trees.


compute normalized RF-distance, see details.


take bipartitions for rooted trees into account, default is unrooting the trees.


use edge.length argument or just count number of edges on the path (default)


treedist returns a vector containing the following tree distance methods


symmetric.difference or Robinson-Foulds distance








The Robinson-Foulds distance between two trees \(T_1\) and \(T_2\) with \(n\) tips is defined as (following the notation Steel and Penny 1993): $$d(T_1, T_2) = i(T_1) + i(T_2) - 2v_s(T_1, T_2)$$ where \(i(T_1)\) denotes the number of internal edges and \(v_s(T_1, T_2)\) denotes the number of internal splits shared by the two trees. The normalized Robinson-Foulds distance is derived by dividing \(d(T_1, T_2)\) by the maximal possible distance \(i(T_1) + i(T_2)\). If both trees are unrooted and binary this value is \(2n-6\).

Functions like RF.dist returns the Robinson-Foulds distance (Robinson and Foulds 1981) between either 2 trees or computes a matrix of all pairwise distances if a multiPhylo object is given.

For large number of trees the distance functions can use a lot of memory!


de Oliveira Martins L., Leal E., Kishino H. (2008) Phylogenetic Detection of Recombination with a Bayesian Prior on the Distance between Trees. PLoS ONE 3(7). e2651. doi: 10.1371/journal.pone.0002651

de Oliveira Martins L., Mallo D., Posada D. (2016) A Bayesian Supertree Model for Genome-Wide Species Tree Reconstruction. Syst. Biol. 65(3): 397-416, doi:10.1093/sysbio/syu082

Steel M. A. and Penny P. (1993) Distributions of tree comparison metrics - some new results, Syst. Biol., 42(2), 126--141

Kuhner, M. K. and Felsenstein, J. (1994) A simulation comparison of phylogeny algorithms under equal and unequal evolutionary rates, Molecular Biology and Evolution, 11(3), 459--468

D.F. Robinson and L.R. Foulds (1981) Comparison of phylogenetic trees, Mathematical Biosciences, 53(1), 131--147

D.F. Robinson and L.R. Foulds (1979) Comparison of weighted labelled trees. In Horadam, A. F. and Wallis, W. D. (Eds.), Combinatorial Mathematics VI: Proceedings of the Sixth Australian Conference on Combinatorial Mathematics, Armidale, Australia, 119--126

See also


Klaus P. Schliep, Leonardo de Oliveira Martins


tree1 <- rtree(100, rooted=FALSE)
tree2 <- rSPR(tree1, 3)
RF.dist(tree1, tree2)
#> [1] 42
treedist(tree1, tree2)
#>      symmetric.difference   branch.score.difference           path.difference 
#>                 42.000000                  3.803442                246.428489 
#> quadratic.path.difference 
#>                121.432291 
sprdist(tree1, tree2)
#>       spr spr_extra        rf     hdist 
#>         3         0        42        68 
trees <- rSPR(tree1, 1:5)
SPR.dist(tree1, trees)
#> [1] 1 2 3 4 5