Description Usage Arguments Value Author(s) References Examples

This function calculates the area per pair index *APP(T)* for a given rooted
tree *T*. The tree must not necessarily be binary. *APP(T)* is defined as

*
APP(T)=2/(n(n-1))*∑_{1<=i<j<=n} d_T(i,j)*

in which *n* denotes the
number of leaves in *T*, and
*d_T(i,j)* denotes the number of edges on the path between the two
leaves *i* and *j*. Note that *APP(T)* can also be
computed from the Sackin index *S(T)* and the total cophenetic
index *TCI(T)* of *T* as
*APP(T)=2/n*S(T)-4/(n(n-1))*TCI(T)*
enabling efficient computation.

The area per pair index does not fulfill the definition of an (im)balance
index given in "Tree balance indices: a comprehensive survey" (Fischer et al., 2021).

1 | ```
areaPerPairI(tree)
``` |

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

`areaPerPairI`

returns the area per pair index of the given tree.

Luise Kuehn

T. Araújo Lima, F. M. D. Marquitti, and M. A. M. de Aguiar. Measuring Tree Balance with Normalized Tree Area. arXiv e-prints, art. arXiv:2008.12867, 2020.

1 2 | ```
tree <- ape::read.tree(text="((((,),),(,)),(((,),),(,)));")
areaPerPairI(tree)
``` |

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