avgLeafDepI {treebalance}

Calculation of the average leaf depth index for rooted trees

Description

This function calculates the average leaf depth N(T) for a given rooted tree T. The tree must not necessarily be binary. N(T) is defined as

N(T)=\frac{1}{n}\cdot\sum_{u\in V_{in}(T)} n_u

in which n denotes the number of leaves in T, V_{in}(T) denotes the set of inner nodes of T and n_u denotes the number of leaves in the pending subtree that is rooted at the inner node u. Note that N(T) can also be computed from the Sackin index S(T) as N(T)=\frac{1}{n}\cdot S(T). The average leaf depth is an imbalance index.

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

For details on the average leaf depth, see also Chapter 6 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_6).

Usage

avgLeafDepI(tree)

Arguments

tree

A rooted tree in phylo format.

Value

avgLeafDepI returns the average leaf depth of the given tree.

Author(s)

Luise Kuehn

References

M. J. Sackin. "Good" and "Bad" Phenograms. Systematic Biology, 21(2):225-226, 1972. doi: 10.1093/sysbio/21.2.225.

K.-T. Shao and R. R. Sokal. Tree Balance. Systematic Zoology, 39(3):266, 1990.
doi: 10.2307/2992186.

Examples

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