collessI {treebalance} | R Documentation |
Calculation of the Colless index for rooted binary trees
Description
This function calculates variants of the Colless index for a given rooted
binary tree . All of them are imbalance indices.
The original Colless index is defined as
in which denotes the set of all inner vertices
of
, and in which
and
denote the number of leaves in the two pending subtrees that are
rooted at the direct descendants of
.
The corrected Colless index of
is defined as
for
and
and for
as
in which denotes the
total number of leaves in
.
The quadratic Colless index of
is defined as
Special cases: For the function returns
and a warning.
For details on the original, corrected and quadratic Colless indices, see
also Chapters 12, 13 and 15 in "Tree balance indices: a comprehensive survey"
(https://doi.org/10.1007/978-3-031-39800-1_12, https://doi.org/10.1007/978-3-031-39800-1_13,
https://doi.org/10.1007/978-3-031-39800-1_15).
Usage
collessI(tree, method = "original")
Arguments
tree |
A rooted binary tree in phylo format. |
method |
A character string specifying the version that shall be computed. It can be one of the following: "original", "corrected", "quadratic". |
Value
collessI
returns the Colless index of the given tree according to the chosen method.
Author(s)
Luise Kuehn and Sophie Kersting
References
D. Colless. Review of Phylogenetics: the theory and practice of phylogenetic systematics. Systematic Zoology, 1982. ISSN 00397989.
T. M. Coronado, M. Fischer, L. Herbst, F. Rossello, and K. Wicke. On the minimum value of the Colless index and the bifurcating trees that achieve it. Journal of Mathematical Biology, 2020.doi: 10.1007/s00285-020-01488-9.
S. B. Heard. Patterns in tree balance among cladistic, phenetic, and randomly generated phylogenetic trees. Evolution, 1992. doi: 10.1111/j.1558-5646.1992.tb01171.x.
K. Bartoszek, T. M. Coronado, A. Mir, and F. Rossello. Squaring within the Colless index yields a better balance index. Mathematical Biosciences, 331:108503, 2021. doi: 10.1016/j.mbs.2020.108503.
Examples
tree <- ape::read.tree(text="((((,),),(,)),(((,),),(,)));")
collessI(tree, method="original")
collessI(tree, method="corrected")
collessI(tree, method="quadratic")