Kendall–Colijn distance
Calculate the Kendall–Colijn tree distance, a measure related to the path difference. UTF-8
KendallColijn(tree1, tree2 = NULL, Vector = KCVector) KCVector(tree) PathVector(tree) SplitVector(tree) KCDiameter(tree)
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 \insertCite Day1985;textualTreeDist.
Vector: Function converting a tree to a numeric vector.
KCVector, the default, returns the number of edges between the common ancestor of each pair of leaves and the root of the tree \insertCite @per @Kendall2016TreeDist.
PathVector returns the number of edges between each pair of leaves \insertCite @per @Steel1993TreeDist.
SplitVector returns the size of the smallest split that contains each pair of leaves (per \insertCite SmithSpace;nobracketsTreeDist).
tree: A tree of class phylo.
KendallColijn() returns an array of numerics providing the distances between each pair of trees in tree1 and tree2, or splits1 and splits2.
KCDiameter() returns the value of the Kendall & Colijn's (2016) metric distance between two pectinate trees with n leaves ordered in the opposite direction, which I suggest (without any attempt at a proof) may be a useful proxy for the diameter (i.e. maximum value) of the K–C metric.
The Kendall–Colijn distance works by measuring, for each pair of leaves, the distance from the most recent common ancestor of those leaves and the root node. For a given tree, this produces a vector of values recording the distance-from-the-root of each most recent common ancestor of each pair of leaves.
Two trees are compared by taking the Euclidean distance between the respective vectors. This is calculated by taking the square root of the sum of the squares of the differences between the vectors.
An analogous distance can be created from any vector representation of a tree. The split size vector metric \insertCite SmithSpaceTreeDist is an attempt to mimic the Kendall Colijn metric in situations where the position of the root should not be afforded special significance; and the path distance \insertCite Steel1993TreeDist is a familiar alternative whose underlying vector measures the distance of the last common ancestor of each pair of leaves from the leaves themselves, i.e. the length of the path from one leaf to another.
None of these vector-based methods performs as well as other tree distances in measuring similarities in the relationships implied by a pair of trees \insertCite SmithDistTreeDist; in particular, the Kendall Colijn metric is strongly influenced by tree balance, and may not be appropriate for a suite of common applications \insertCite SmithSpaceTreeDist.
KCVector(): Creates a vector that characterises a rooted tree, as described in \insertCite Kendall2016;textualTreeDist.PathVector(): Creates a vector reporting the number of edges between each pair of leaves, per the path metric of \insertCite Steel1993;textualTreeDist.SplitVector(): Creates a vector reporting the smallest split containing each pair of leaves, per the metric proposed in \insertCite SmithSpace;textualTreeDist.KendallColijn(TreeTools::BalancedTree(8), TreeTools::PectinateTree(8)) set.seed(0) KendallColijn(TreeTools::BalancedTree(8), lapply(rep(8, 3), ape::rtree)) KendallColijn(lapply(rep(8, 4), ape::rtree)) KendallColijn(lapply(rep(8, 4), ape::rtree), Vector = SplitVector) # Notice that changing tree shape close to the root results in much # larger differences tree1 <- ape::read.tree(text = "(a, (b, (c, (d, (e, (f, (g, h)))))));") tree2 <- ape::read.tree(text = "(a, ((b, c), (d, (e, (f, (g, h))))));") tree3 <- ape::read.tree(text = "(a, (b, (c, (d, (e, ((f, g), h))))));") trees <- c(tree1, tree2, tree3) KendallColijn(trees) KendallColijn(trees, Vector = SplitVector) KCDiameter(4) KCDiameter(trees)
\insertAllCited
is a more sophisticated, if more cumbersome, implementation that supports lambda > 0, i.e. use of edge lengths in tree comparison.
Other tree distances: JaccardRobinsonFoulds(), MASTSize(), MatchingSplitDistance(), NNIDist(), NyeSimilarity(), PathDist(), Robinson-Foulds, SPRDist(), TreeDistance()
Useful links