weighL1dist: Calculation of weighted l1 distance index for rooted binary...

In treebalance: Computation of Tree (Im)Balance Indices

Calculation of weighted l1 distance index for rooted binary trees

Description

This function calculates the weighted l1 distance index D_{l1}(T) for a given rooted binary tree T. D_{l1}(T) is defined as

D_{l1}(T)=\sum_{z=2}^n z \cdot |f_n(z)-p_n(z)|

in which n denotes the number of leaves of T, f_n(z) denotes the frequency of pending subtrees of size z in T and p_n(z) is the expected number of pending subtrees of size z under the Yule model, i.e. p_n(z)=\frac{1}{n-1} if z=n and otherwise \frac{n}{n-1}\cdot\frac{2}{z\cdot(z+1)}.

For n=1 the function returns D_{l1}(T)=0.

For details on the weighted l1 distance index, see also Chapter 24 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_24).

Usage

weighL1dist(tree)

Arguments

tree	A rooted binary tree in phylo format.

Value

weighL1distI returns the weighted l1 distance index of the given tree.

Author(s)

Sophie Kersting

References

M. G. Blum and O. Francois. On statistical tests of phylogenetic tree imbalance: The Sackin and other indices revisited. Mathematical Biosciences, 195(2):141-153, 2005. doi: 10.1016/j.mbs.2005.03.003.

Examples

tree <- ape::read.tree(text="((((,),),(,)),(((,),),(,)));")
weighL1dist(tree)

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