tree_imbalance {castor}

Calculate various imbalance statistics for a tree.

Description

Given a rooted phylogenetic tree, calculate various "imbalance" statistics of the tree, such as Colless' Index or Sackin's Index.

Usage

tree_imbalance(tree, type)

Arguments

tree

A rooted tree of class "phylo".

type

Character, specifying the statistic to be calculated. Must be one of "Colless" (Shao 1990), "Colless_normalized" (Colless normalized by the maximum possible value in the case of a bifurcating tree), "Sackin" (Sackin 1972) or "Blum" (Blum and Francois 2006, Eq. 5).

Details

The tree may include multifurcations and monofurcations. Note that the Colless Index is traditionally only defined for bifurcating trees. For non-bifurcating trees this function calculates a generalization of the index, by summing over all children pairs at each node.

The Blum statistic is the sum of natural logarithms of the sizes (number of descending tips) of non-monofurcating nodes.

Value

Numeric, the requested imbalance statistic of the tree.

Author(s)

Stilianos Louca

References

M. J. Sackin (1972). "Good" and "Bad" Phenograms. Systematic Biology. 21:225-226.

K.T. Shao, R. R. Sokal (1990). Tree Balance. Systematic Biology. 39:266-276.

M. G. B. Blum and O. Francois (2006). Which random processes describe the Tree of Life? A large-scale study of phylogenetic tree imbalance. Systematic Biology. 55:685-691.

Examples

# generate a random tree
Ntips = 100
tree = generate_random_tree(list(birth_rate_intercept=1),Ntips)$tree

# calculate Colless statistic
colless_index = tree_imbalance(tree, type="Colless")