s shape statistic of (im)balance.

The s shape statistic of imbalance (also known as the Blum statistic, see blum) calculates the sum of \(log(N-1)\) over all internal nodes, where N represents the total number of extant tips connected to that node. An alternative implementation can be found in the Castor R package.

Usage

sshape(phy, normalization = FALSE)

Arguments

phy

phylogeny or ltable

normalization

because the sshape statistic sums over all nodes, the resulting statistic tends to be correlated with the number of extant tips. Normalization can be performed by dividing by the number of extant tips.

Value

s shape statistic of imbalance

References

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

simulated_tree <- ape::rphylo(n = 10, birth = 1, death = 0)
  balanced_tree <- treestats::create_fully_balanced_tree(simulated_tree)
  unbalanced_tree <- treestats::create_fully_unbalanced_tree(simulated_tree)
  sshape(balanced_tree)
#> [1] 6.291569
  sshape(unbalanced_tree) # should be higher
#> [1] 12.80183