| weighL1dist {treebalance} | 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.
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)