B2I | R Documentation |

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).

```
B2I(tree, logbase = 2)
```

`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. |

`B2I`

returns the B2 index of the given tree.

Sophie Kersting, Luise Kuehn

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.

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

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