| rogersI {treebalance} | R Documentation |
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)