varLeafDepI: Calculation of the variance of leaf depths index for rooted...

View source: R/varLeafDepI.R

varLeafDepIR Documentation

Calculation of the variance of leaf depths index for rooted trees


This function calculates the variance of leaf depths index VLD(T) for a given rooted tree T. The tree must not necessarily be binary. VLD(T) is defined as

VLD(T)=\frac{1}{n}\cdot\sum_{x\in V_L(T)} (\delta(x)-N(T))^2

in which n denotes the number of leaves of T, V_L(T) denotes the set of leaves of T, \delta(x) denotes the depth of the leaf x and N(T) denotes the average leaf depth of T.

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

For details on the variance of leaf depths, see also Chapter 7 in "Tree balance indices: a comprehensive survey" (





A rooted tree in phylo format.


varLeafDepI returns the variance of leaf depths index of the given tree.


Sophie Kersting


T. M. Coronado, A. Mir, F. Rossello, and L. Rotger. On Sackin's original proposal: the variance of the leaves' depths as a phylogenetic balance index. BMC Bioinformatics, 21(1), 2020. doi: 10.1186/s12859-020-3405-1. URL

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.


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

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