ewCollessI {treebalance}

Calculation of the equal weights Colless index for rooted binary trees

Description

This function calculates the equal weights Colless index I_2(T) for a given rooted binary tree T. I_2(T) is defined as

I_2(T)=\frac{1}{n-2}\cdot\sum_{u\in V_{in}(T), n_u>2} \frac{|n_{u_a}-n_{u_b}|}{n_u-2}

in which V_{in}(T) denotes the set of all inner vertices of T, and in which n_u, n_{u_a} and n_{u_b} denote the number of leaves in the pending subtrees that are rooted at u and the two direct descendants of u. The equal weights Colless index is an imbalance index.

For n=1 and n=2 the function returns I_2(T)=0 and a warning.

For details on the equal weigths Colless index, see also Chapter 14 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_14).

Usage

ewCollessI(tree)

Arguments

tree

A rooted binary tree in phylo format.

Value

ewCollessI returns the equal weights Colless index of the given tree.

Author(s)

Luise Kuehn

References

A. O. Mooers and S. B. Heard. Inferring Evolutionary Process from Phylogenetic Tree Shape. The Quarterly Review of Biology, 72(1), 1997. doi: 10.1086/419657.

Examples

tree <- ape::read.tree(text="((((,),),(,)),(((,),),(,)));")
ewCollessI(tree)