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
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
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).
A rooted tree in phylo format.
areaPerPairI returns the area per pair index of the given tree.
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.
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