# weighL1dist: Calculation of weighted l1 distance index for rooted binary... In treebalance: Computation of Tree (Im)Balance Indices

 weighL1dist R Documentation

## 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.

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.