\title{Continuous Character Simulation}
\usage{
rTraitCont(phy, model = "BM", sigma = 0.1, alpha = 1, theta = 0,
- ancestor = FALSE, root.value = 0, linear = TRUE, ...)
+ ancestor = FALSE, root.value = 0, ...)
}
\arguments{
\item{phy}{an object of class \code{"phylo"}.}
values at the nodes as well (by default, only the values at the tips
are returned).}
\item{root.value}{a numeric giving the value at the root.}
- \item{linear}{a logical indicating which parameterisation of the OU
- model to use (see details).}
\item{\dots}{further arguments passed to \code{model} if it is a
function.}
}
\item{\code{"OU"}:}{an Ornstein-Uhlenbeck model is used. The above
indexing rule is used for the three parameters \code{sigma},
- \code{alpha}, and \code{theta}. This may be more interesting for the
- last one to model varying phenotypic optima.
-
- By default the following formula is used:
-
- \deqn{x_{t''} = x_{t'} - \alpha l (x_{t'} - \theta) + \sigma
- l \epsilon}{x(t'') = x(t') - alpha l (x(t') - theta) + sigma
- l epsilon}
-
- where \eqn{l (= t'' - t')} is the branch length, and \eqn{\epsilon
- \sim N(0, 1)}{\epsilon ~ N(0, 1)}. If \eqn{\alpha > 1}{alpha > 1},
- this may lead to chaotic oscillations. Thus an alternative
- parameterisation is used if \code{linear = FALSE}:
-
- \deqn{x_{t''} = x_{t'} - (1 - exp(-\alpha l)) * (x_{t'} - \theta) +
- \sigma l \epsilon}{x(t'') = x(t') - (1 - exp(-alpha l)) * (x(t') -
- theta) + sigma l epsilon}}
+ \code{alpha}, and \code{theta}. This may be interesting for the last
+ one to model varying phenotypic optima. The exact updating formula
+ from Gillespie (1996) are used which are reduced to BM formula if
+ \code{alpha = 0}.
\item{A function:}{it must be of the form \code{foo(x, l)} where
\code{x} is the trait of the ancestor and \code{l} is the branch
present, otherwise, ``Node1'', ``Node2'', etc.
}
\references{
+ Gillespie, D. T. (1996) Exact numerical simulation of the
+ Ornstein-Uhlenbeck process and its integral. \emph{Physical Review E},
+ \bold{54}, 2084--2091.
+
Paradis, E. (2006) \emph{Analyses of Phylogenetics and Evolution with
R.} New York: Springer.
}
\author{Emmanuel Paradis}
\seealso{
- \code{\link{rTraitDisc}}, \code{\link{ace}}
+ \code{\link{rTraitDisc}}, \code{\link{rTraitMult}}, \code{\link{ace}}
}
\examples{
data(bird.orders)