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\name{bd.ext}
\alias{bd.ext}
\title{Extended Version of the Birth-Death Models to Estimate Speciation
and Extinction Rates}
\usage{
bd.ext(phy, S, conditional = TRUE)
}
\arguments{
\item{phy}{an object of class \code{"phylo"}.}
\item{S}{a numeric vector giving the number of species for each tip.}
\item{conditional}{whether probabilities should be conditioned on no
extinction (mainly to compare results with previous analyses; see
details).}
}
\description{
This function fits by maximum likelihood a birth-death model to the
combined phylogenetic and taxonomic data of a given clade. The
phylogenetic data are given by a tree, and the taxonomic data by the
number of species for the its tips.
}
\details{
A re-parametrization of the birth-death model studied by Kendall
(1948) so that the likelihood has to be maximized over \emph{d/b} and
\emph{b - d}, where \emph{b} is the birth rate, and \emph{d} the death
rate.
The standard-errors of the estimated parameters are computed using a
normal approximation of the maximum likelihood estimates.
If the argument \code{S} has names, then they are matched to the tip
labels of \code{phy}. The user must be careful here since the function
requires that both series of names perfectly match, so this operation
may fail if there is a typing or syntax error. If both series of names
do not match, the values \code{S} are taken to be in the same order
than the tip labels of \code{phy}, and a warning message is issued.
Note that the function does not check that the tree is effectively
ultrametric, so if it is not, the returned result may not be
meaningful.
If \code{conditional = TRUE}, the probabilities of the taxonomic data
are calculated conditioned on no extinction (Rabosky et al. 2007). In
previous versions of the present function (until ape 2.6-1),
unconditional probabilities were used resulting in underestimated
extinction rate. Though it does not make much sense to use
\code{conditional = FALSE}, this option is provided to compare results
from previous analyses: if the species richnesses are relatively low,
both versions will give similar results (see examples).
}
\references{
Paradis, E. (2003) Analysis of diversification: combining phylogenetic
and taxonomic data. \emph{Proceedings of the Royal Society of
London. Series B. Biological Sciences}, \bold{270}, 2499--2505.
Rabosky, D. L., Donnellan, S. C., Talaba, A. L. and Lovette,
I. J. (2007) Exceptional among-lineage variation in diversification
rates during the radiation of Australia's most diverse vertebrate
clade. \emph{Proceedings of the Royal Society of London. Series
B. Biological Sciences}, \bold{274}, 2915--2923.
}
\author{Emmanuel Paradis}
\seealso{
\code{\link{birthdeath}}, \code{\link{branching.times}},
\code{\link{diversi.gof}}, \code{\link{diversi.time}},
\code{\link{ltt.plot}}, \code{\link{yule}}, \code{\link{yule.cov}},
\code{\link{bd.time}}
}
\examples{
### An example from Paradis (2003) using the avian orders:
data(bird.orders)
### Number of species in each order from Sibley and Monroe (1990):
S <- c(10, 47, 69, 214, 161, 17, 355, 51, 56, 10, 39, 152,
6, 143, 358, 103, 319, 23, 291, 313, 196, 1027, 5712)
bd.ext(bird.orders, S)
bd.ext(bird.orders, S, FALSE) # same than older versions
}
\keyword{models}
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