rogersI | R Documentation |

This function calculates the Rogers J index `J(T)`

for a given rooted
binary tree `T`

. It is defined as the number of inner vertices whose balance
value is unequal to zero, more precisely

`J(T)=\sum_{u \in V_{in}(T)} (1-I(n_{u_a}=n_{u_b}))`

in which `V_{in}(T)`

denotes the set of all inner vertices
of `T`

, and in which `n_{u_a}`

and `n_{u_b}`

denote the number of leaves in the two pending subtrees that are
rooted at the direct descendants of `u`

.

Special cases: For `n=1`

, the function returns `J(T)=0`

and a warning.

For details on the Rogers J index, see
also Chapter 19 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_19).

```
rogersI(tree)
```

`tree` |
A rooted binary tree in phylo format. |

`rogersI`

returns the Rogers J index of the given tree.

Sophie Kersting

J. S. Rogers. Central Moments and Probability Distributions of Three Measures of Phylogenetic Tree Imbalance. Systematic Biology, 45(1):99-110, 1996. doi: 10.1093/sysbio/45.1.99.

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

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