stairs1 | R Documentation |

This function calculates the stairs1 value `st1(T)`

for a given rooted
binary tree `T`

. It is a modified version of the Rogers J index and is
defined as the fraction of inner vertices whose balance
value is unequal to zero, more precisely

`st1(T)=\frac{1}{n-1}\cdot\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`

. The stairs1 value is an imbalance index.

Special cases: For `n=1`

, the function returns `st1(T)=0`

and a warning.

For details on the stairs1 value, see
also Chapter 23 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_23).

```
stairs1(tree)
```

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

`stairs1`

returns the stairs1 value of the given tree.

Sophie Kersting

M. M. Norstrom, M. C. Prosperi, R. R. Gray, A. C. Karlsson, and M. Salemi. PhyloTempo: A Set of R Scripts for Assessing and Visualizing Temporal Clustering in Genealogies Inferred from Serially Sampled Viral Sequences. Evolutionary Bioinformatics, 8:EBO.S9738, 2012. ISSN 1176-9343, 1176-9343. doi:10.4137/EBO.S9738.

```
tree <- ape::read.tree(text="((((,),),(,)),(((,),),(,)));")
stairs1(tree)
```

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