treebalance (version 1.2.0)

mWovermD: Calculation of the maximum width over maximum depth of the tree

Description

This function calculates the maximum width over maximum depth \(mWovermD(T)\) for a given rooted tree \(T\). The tree must not necessarily be binary. For \(n>1\), \(mWovermD(T)\) is defined as $$mWovermD(T)=maxWidth(T) / h(T)$$ in which \(h(T)\) denotes the height of the tree \(T\), which is the same as the maximum depth of any leaf in the tree, and \(maxWidth(T)\) denotes the maximum width of the tree \(T\). The maximum width over maximum depth is a balance index.

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

Usage

mWovermD(tree)

Value

mWovermD returns the maximum width over maximum depth of a tree.

Arguments

tree

A rooted tree in phylo format.

Author

Luise Kuehn

References

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

Examples

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