ewCollessI {treebalance}R Documentation

Calculation of the equal weights Colless index for rooted binary trees

Description

This function calculates the equal weights Colless index I2(T)I_2(T) for a given rooted binary tree TT. I2(T)I_2(T) is defined as

I2(T)=1n2uVin(T),nu>2nuanubnu2I_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 Vin(T)V_{in}(T) denotes the set of all inner vertices of TT, and in which nun_u, nuan_{u_a} and nubn_{u_b} denote the number of leaves in the pending subtrees that are rooted at uu and the two direct descendants of uu. The equal weights Colless index is an imbalance index.

For n=1n=1 and n=2n=2 the function returns I2(T)=0I_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)


[Package treebalance version 1.2.0 Index]