treebalance:Computation of Tree (Im)Balance Indices

The aim of the 'R' package 'treebalance' is to provide functions for the computation of a large variety of (im)balance indices for rooted trees. The package accompanies the book ''Tree balance indices: a comprehensive survey'' by M. Fischer, L. Herbst, S. Kersting, L. Kuehn and K. Wicke (2023) <ISBN: 978-3-031-39799-8>, <doi:10.1007/978-3-031-39800-1>, which gives a precise definition for the terms 'balance index' and 'imbalance index' (Chapter 4) and provides an overview of the terminology in this manual (Chapter 2). For further information on (im)balance indices, see also Fischer et al. (2021) <https://treebalance.wordpress.com>. Considering both established and new (im)balance indices, 'treebalance' provides (among others) functions for calculating the following 18 established indices and index families: the average leaf depth, the B1 and B2 index, the Colijn-Plazzotta rank, the normal, corrected, quadratic and equal weights Colless index, the family of Colless-like indices, the family of I-based indices, the Rogers J index, the Furnas rank, the rooted quartet index, the s-shape statistic, the Sackin index, the symmetry nodes index, the total cophenetic index and the variance of leaf depths. Additionally, we include 9 tree shape statistics that satisfy the definition of an (im)balance index but have not been thoroughly analyzed in terms of tree balance in the literature yet. These are: the total internal path length, the total path length, the average vertex depth, the maximum width, the modified maximum difference in widths, the maximum depth, the maximum width over maximum depth, the stairs1 and the stairs2 index. As input, most functions of 'treebalance' require a rooted (phylogenetic) tree in 'phylo' format (as introduced in 'ape' 1.9 in November 2006). 'phylo' is used to store (phylogenetic) trees with no vertices of out-degree one. For further information on the format we kindly refer the reader to E. Paradis (2012) <http://ape-package.ird.fr/misc/FormatTreeR_24Oct2012.pdf>.