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\name{cherry}
\alias{cherry}
\title{Number of Cherries and Null Models of Trees}
\usage{
cherry(phy)
}
\arguments{
\item{phy}{an object of class \code{"phylo"}.}
}
\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).
}
\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. \emph{Mathematical Biosciences}, \bold{164}, 81--92.
}
\author{Emmanuel Paradis}
\seealso{
\code{\link{gammaStat}}
}
\keyword{univar}
|
