cherry: Number of Cherries and Null Models of Trees
Description
This function calculates the number of cherries (see definition below)
on a phylogenetic tree, and tests the null hypotheses whether this
number agrees with those predicted from two null models of trees (the
Yule model, and the uniform model).
Usage
cherry(phy)
Arguments
phy
an object of class "phylo".
Value
A NULL value is returned, the results are simply printed.
Details
A cherry is a pair of adjacent tips on a tree. The tree can be either
rooted or unrooted, but the present function considers only rooted
trees. The probability distribution function of the number of cherries
on a tree depends on the speciation/extinction model that generated
the tree.
McKenzie and Steel (2000) derived the probability
distribution function of the number of cherries for two models: the
Yule model and the uniform model. Broadly, in the Yule model, each extant
species is equally likely to split into two daughter-species; in the
uniform model, a branch is added to tree on any of the already
existing branches with a uniform probability.
The probabilities are computed using recursive formulae; however, for
both models, the probability density function converges to a normal
law with increasing number of tips in the tree. The function uses
these normal approximations for a number of tips greater than or equal
to 20.
References
McKenzie, A. and Steel, M. (2000) Distributions of cherries for two
models of trees. Mathematical Biosciences, 164, 81--92.