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).
Usage
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)Arguments
- tree1
A phylogenetic tree (class
phylo) or vector of trees (an object of classmultiPhylo). See details- tree2
A phylogenetic tree.
- check.labels
compares labels of the trees.
- normalize
compute normalized RF-distance, see details.
- rooted
take bipartitions for rooted trees into account, default is unrooting the trees.
- use.weight
use edge.length argument or just count number of edges on the path (default)
Value
treedist returns a vector containing the following tree
distance methods
- symmetric.difference
symmetric.difference or Robinson-Foulds distance
- branch.score.difference
branch.score.difference
- path.difference
path.difference
- weighted.path.difference
weighted.path.difference
Details
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!
References
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
Author
Klaus P. Schliep klaus.schliep@gmail.com, Leonardo de Oliveira Martins
Examples
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