\name{yule}
\alias{yule}
\title{Fits Yule Model to a Phylogenetic Tree}
\usage{
yule(phy)
}
\arguments{
  \item{phy}{an object of class \code{"phylo"}.}
}
\description{
  This function fits by maximum likelihood a Yule model, i.e. a
  birth-only model to the branching times computed from a phylogenetic
  tree.
}
\details{
  The tree must be fully dichotomous.

  The maximum likelihood estimate of the speciation rate is obtained by
  the ratio of the number of speciation events on the cumulative number
  of species through time; these two quantities are obtained with the
  number of nodes in the tree, and the sum of the branch lengths,
  respectively.

  If there is a `root.edge' element in the phylogenetic tree, then it is
  assumed that it has a biological meaning and is counted as a branch
  length, and the root is counted as a speciation event; otherwise the
  number of speciation events is the number of nodes - 1.

  The standard-error of lambda is computed with the second derivative of
  the log-likelihood function.
}
\value{
  An object of class "yule" which is a list with the following
  components:
  \item{lambda}{the maximum likelihood estimate of the speciation
    (birth) rate.}
  \item{se}{the standard-error of lambda.}
  \item{loglik}{the log-likelihood at its maximum.}
}
\author{Emmanuel Paradis \email{Emmanuel.Paradis@mpl.ird.fr}}
\seealso{
  \code{\link{branching.times}}, \code{\link{diversi.gof}},
  \code{\link{diversi.time}}, \code{\link{ltt.plot}},
  \code{\link{birthdeath}}, \code{\link{bd.ext}}, \code{\link{yule.cov}}
}
\keyword{models}