rogersI: Calculation of the Rogers J index for rooted binary trees

In treebalance: Computation of Tree (Im)Balance Indices

Calculation of the Rogers J index for rooted binary trees

Description

This function calculates the Rogers J index J(T) for a given rooted binary tree T. It is defined as the number of inner vertices whose balance value is unequal to zero, more precisely

J(T)=\sum_{u \in V_{in}(T)} (1-I(n_{u_a}=n_{u_b}))

in which V_{in}(T) denotes the set of all inner vertices of T, and in which n_{u_a} and n_{u_b} denote the number of leaves in the two pending subtrees that are rooted at the direct descendants of u.
Special cases: For n=1, the function returns J(T)=0 and a warning.

For details on the Rogers J index, see also Chapter 19 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_19).

Usage

rogersI(tree)

Arguments

tree	A rooted binary tree in phylo format.

Value

rogersI returns the Rogers J index of the given tree.

Author(s)

Sophie Kersting

References

J. S. Rogers. Central Moments and Probability Distributions of Three Measures of Phylogenetic Tree Imbalance. Systematic Biology, 45(1):99-110, 1996. doi: 10.1093/sysbio/45.1.99.

Examples

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

treebalance documentation built on May 29, 2024, 1:15 a.m.