treebalance (version 1.2.0)

mCherryI: Calculation of the modified cherry index for rooted binary trees

Description

This function calculates the modified cherry index \(mChI(T)\) for a given rooted binary tree \(T\). Note that compared to the original cherry index \(ChI(T)\), the modified cherry index is defined for binary trees only. \(mChI(T)\) is defined as \(n-2\cdot ChI(T)\), i.e. it counts the number of leaves of the tree which are not in a cherry. A cherry is a pair of leaves that have the same direct ancestor.

The modified cherry index does not fulfill the definition of an (im)balance index given in "Tree balance indices: a comprehensive survey" (Fischer et al., 2023).

For details on the modified cherry index, see also Chapter 24 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_24).

Usage

mCherryI(tree)

Value

mCherryI returns the modified cherry index of the given tree.

Arguments

tree

A rooted binary tree in phylo format.

Author

Luise Kuehn

References

S. J. Kersting, M. Fischer. Measuring tree balance using symmetry nodes — A new balance index and its extremal properties. Mathematical Biosciences, 341:108690, 2021. doi: 10.1016/j.mbs.2021.108690.

Examples

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