stairs2 | R Documentation |

This function calculates the stairs2 value `st2(T)`

for a given rooted
binary tree `T`

. It is defined as the mean ratio between the leaf
numbers of the smaller and larger pending subtree over all inner vertices, more precisely

`st2(T)=\frac{1}{n-1}\cdot\sum_{u \in V_{in}(T)} \frac{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}\geq n_{u_b}`

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

. The stairs2 value is an imbalance index.

Special cases: For `n=1`

, the function returns `st2(T)=0`

and a warning.

For details on the stairs2 value, see
also Chapter 23 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_23).

```
stairs2(tree)
```

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

`stairs2`

returns the stairs2 value of the given tree.

Sophie Kersting

C. Colijn, J. Gardy. Phylogenetic tree shapes resolve disease transmission patterns. Evolution, Medicine, and Public Health, 2014(1):96-108, 2014. ISSN 2050-6201. doi: 10.1093/emph/eou018.

```
tree <- ape::read.tree(text="((((,),),(,)),(((,),),(,)));")
stairs2(tree)
```

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