3 \title{Number of Cherries and Null Models of Trees}
8 \item{phy}{an object of class \code{"phylo"}.}
11 This function calculates the number of cherries (see definition below)
12 on a phylogenetic tree, and tests the null hypotheses whether this
13 number agrees with those predicted from two null models of trees (the
14 Yule model, and the uniform model).
17 A NULL value is returned, the results are simply printed.
20 A cherry is a pair of adjacent tips on a tree. The tree can be either
21 rooted or unrooted, but the present function considers only rooted
22 trees. The probability distribution function of the number of cherries
23 on a tree depends on the speciation/extinction model that generated
26 McKenzie and Steel (2000) derived the probability
27 distribution function of the number of cherries for two models: the
28 Yule model and the uniform model. Broadly, in the Yule model, each extant
29 species is equally likely to split into two daughter-species; in the
30 uniform model, a branch is added to tree on any of the already
31 existing branches with a uniform probability.
33 The probabilities are computed using recursive formulae; however, for
34 both models, the probability density function converges to a normal
35 law with increasing number of tips in the tree. The function uses
36 these normal approximations for a number of tips greater than or equal
40 McKenzie, A. and Steel, M. (2000) Distributions of cherries for two
41 models of trees. \emph{Mathematical Biosciences}, \bold{164}, 81--92.
43 \author{Emmanuel Paradis \email{Emmanuel.Paradis@mpl.ird.fr}}
45 \code{\link{gammaStat}}