# B2I: Calculation of the B2 index for rooted trees In treebalance: Computation of Tree (Im)Balance Indices

 B2I R Documentation

## Calculation of the B2 index for rooted trees

### Description

This function calculates the B2 index B2(T) for a given rooted tree T. The tree must not necessarily be binary. B2(T) is defined as

B2(T)=-\sum_{x\in V_L(T)} p_x\cdot log(p_x)

in which V_L(T) denotes the leaf set of T, and in which

p_x=\prod_{v\in anc(x)} \frac{1}{|child(v)|}

denotes the probability of reaching leaf x when starting at the root and assuming equiprobable branching at each vertex v\in anc(x) with anc(x) denoting the set of ancestors of x excluding x. child(v) denotes the set of children of the inner vertex v.
The B2 index is a balance index.

For n=1 the function returns B2(T)=0 and a warning.

For details on the B2 index, see also Chapter 11 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_11).

### Usage

B2I(tree, logbase = 2)


### Arguments

 tree A rooted tree in phylo format. logbase The base that shall be used for the logarithm. For binary trees it is common to use base 2.

### Value

B2I returns the B2 index of the given tree.

### Author(s)

Sophie Kersting, Luise Kuehn

### References

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

P.-M. Agapow and A. Purvis. Power of Eight Tree Shape Statistics to Detect Nonrandom Diversification: A Comparison by Simulation of Two Models of Cladogenesis. Systematic Biology, 51(6):866-872, 2002.doi: 10.1080/10635150290102564.
URL https://doi.org/10.1080/10635150290102564.

M. Hayati, B. Shadgar, and L. Chindelevitch. A new resolution function to evaluate tree shape statistics. PLOS ONE, 14(11):e0224197, 2019. doi: 10.1371/journal.pone.0224197.
URL https://doi.org/10.1371/journal.pone.0224197.

M. Kirkpatrick and M. Slatkin. Searching for evolutionary patterns in the shape of a phylogenetic tree. Evolution, 47(4):1171-1181, 1993. doi: 10.1111/j.1558-5646.1993.tb02144.x.

### Examples

tree <- ape::read.tree(text="((((,),),(,)),(((,),),(,)));")
B2I(tree)



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