Calculate the Robinson–Foulds distance (Robinson and Foulds 1981) , or the equivalent similarity measure, with options to (i) annotate matched splits; (ii) weight splits according to their phylogenetic information content (Smith 2020) .

InfoRobinsonFoulds(
tree1,
tree2 = NULL,
similarity = FALSE,
normalize = FALSE,
reportMatching = FALSE
)

InfoRobinsonFouldsSplits(
splits1,
splits2,
nTip = attr(splits1, "nTip"),
reportMatching = FALSE
)

RobinsonFoulds(
tree1,
tree2 = NULL,
similarity = FALSE,
normalize = FALSE,
reportMatching = FALSE
)

RobinsonFouldsMatching(
tree1,
tree2,
similarity = FALSE,
normalize = FALSE,
...
)

RobinsonFouldsSplits(
splits1,
splits2,
nTip = attr(splits1, "nTip"),
reportMatching = FALSE
)

## Arguments

tree1, tree2

Trees of class phylo, with leaves labelled identically, or lists of such trees to undergo pairwise comparison. Where implemented, tree2 = NULL will compute distances between each pair of trees in the list tree1 using a fast algorithm based on Day (1985).

similarity

Logical specifying whether to report the result as a tree similarity, rather than a difference.

normalize

If a numeric value is provided, this will be used as a maximum value against which to rescale results. If TRUE, results will be rescaled against a maximum value calculated from the specified tree sizes and topology, as specified in the 'Normalization' section below. If FALSE, results will not be rescaled.

reportMatching

Logical specifying whether to return the clade matchings as an attribute of the score.

splits1, splits2

Logical matrices where each row corresponds to a leaf, either listed in the same order or bearing identical names (in any sequence), and each column corresponds to a split, such that each leaf is identified as a member of the ingroup (TRUE) or outgroup (FALSE) of the respective split.

nTip

(Optional) Integer specifying the number of leaves in each split.

...

Not used.

## Value

RobinsonFoulds() and InfoRobinsonFoulds() return an array of numerics providing the distances between each pair of trees in tree1 and tree2, or splits1 and splits2.

## Details

Note that if reportMatching = TRUE, the pairScores attribute returns a logical matrix specifying whether each pair of splits is identical.

InfoRobinsonFoulds() calculates the tree similarity or distance by summing the phylogenetic information content of all splits that are (or are not) identical in both trees. Consequently, splits that are more likely to be identical by chance alone make a smaller contribution to overall tree distance, because their similarity is less remarkable.

Rapid comparison between multiple pairs of trees employs the Day Day (1985) linear-time algorithm.

## Functions

• RobinsonFouldsMatching(): Matched splits, intended for use with VisualizeMatching().

## Normalization

• RobinsonFoulds() is normalized against the total number of splits that are present.

• InfoRobinsonFoulds() is normalized against the sum of the phylogenetic information of all splits in both trees, treated independently.

## References

Day WHE (1985). “Optimal algorithms for comparing trees with labeled leaves.” Journal of Classification, 2(1), 7--28. doi:10.1007/BF01908061 .

Robinson DF, Foulds LR (1981). “Comparison of phylogenetic trees.” Mathematical Biosciences, 53(1-2), 131--147. doi:10.1016/0025-5564(81)90043-2 .

Smith MR (2020). “Information theoretic Generalized Robinson-Foulds metrics for comparing phylogenetic trees.” Bioinformatics, 36(20), 5007--5013. doi:10.1093/bioinformatics/btaa614 .

Display paired splits: VisualizeMatching()

Other tree distances: JaccardRobinsonFoulds(), KendallColijn(), MASTSize(), MatchingSplitDistance(), NNIDist(), NyeSimilarity(), PathDist(), SPRDist(), TreeDistance()

## Examples

 # For BalancedTree, PectinateTree, as.phylo:
library('TreeTools', quietly = TRUE, warn.conflicts = FALSE)
balanced7 <- BalancedTree(7)
pectinate7 <- PectinateTree(7)
RobinsonFoulds(balanced7, pectinate7)
#> [1] 4
RobinsonFoulds(balanced7, pectinate7, normalize = TRUE)
#> [1] 0.5
VisualizeMatching(RobinsonFouldsMatching, balanced7, pectinate7)

InfoRobinsonFoulds(balanced7, pectinate7)
#> [1] 13.90209
VisualizeMatching(InfoRobinsonFoulds, balanced7, pectinate7)