stairs2 {treebalance}

Calculation of the stairs2 value for rooted binary trees

Description

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).

Usage

stairs2(tree)

Arguments

tree

A rooted binary tree in phylo format.

Value

stairs2 returns the stairs2 value of the given tree.

Author(s)

Sophie Kersting

References

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.

Examples

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