Gamma statistic and Colless index of a tree

Computes Pybus and Harvey's (2000) gamma statistic, with ape::gammaStat(), and the Colless index normalized against its expectation under the Yule model, \((I_C - n \log n - n(\gamma_E - 1 - \log 2)) / n\), where \(n\) is the number of tips and \(\gamma_E\) is Euler's constant (the "yule" normalization of treestats::colless()). Both are near zero for Yule trees: gamma is negative when branching times are concentrated near the root, and the normalized Colless index is positive for trees more imbalanced than Yule trees.

Usage

tree_shape(tree)

Arguments

tree

A binary, rooted phylo object with at least three tips. The gamma statistic assumes an ultrametric tree; this is not checked.

Value

A named vector with gamma and colless.

References

Pybus, O. G., & Harvey, P. H. (2000). Testing macro-evolutionary models using incomplete molecular phylogenies. Proceedings of the Royal Society B, 267, 2267–2272. doi:10.1098/rspb.2000.1278

Examples

set.seed(1)
tree_shape(sim_tree_shape(100, beta = -1, c = -1))
#>     gamma   colless 
#> -5.956557  2.440761