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\name{reconstruct}
\alias{reconstruct}
\title{Continuous Ancestral Character Estimation}
\description{
This function estimates ancestral character states, and the associated
uncertainty, for continuous characters. It mainly works as the ace
function, from which it differs, first, in the fact that computations
are not performed by numerical optimisation but through matrix
calculus. Second, besides classical Brownian-based reconstruction
methods, it reconstructs ancestral states under Arithmetic Brownian
Motion (ABM, i.e. Brownian with linear trend) and Ornstein-Uhlenbeck
process (OU, i.e. Brownian with an attractive optimum).
}
\usage{
reconstruct(x, phyInit, method = "ML", alpha = NULL,
low_alpha = 0.0001, up_alpha = 1, CI = TRUE)
}
\arguments{
\item{x}{a numerical vector.}
\item{phyInit}{an object of class \code{"phylo"}.}
\item{method}{a character specifying the method used for
estimation. Six choices are possible: \code{"ML"}, \code{"REML"}, \code{"GLS"}, \code{"GLS_ABM"}, \code{"GLS_OU"} or \code{"GLS_OUS"}.}
\item{alpha}{a numerical value which accounts for the attractive strength parameter of \code{"GLS_OU"} or \code{"GLS_OUS"} (used only in these cases). If alpha = NULL (the default), then it is estimated by maximum likelihood using \code{optim}, with \code{low_alpha} (resp. \code{up_alpha}) as lower value (resp. upper value), which may lead to convergence issue.}
\item{low_alpha}{a lower bound for alpha, used only with methods \code{"GLS_OU"} or \code{"GLS_OUS"}. It has to be positive.}
\item{up_alpha}{an upper bound for alpha, used only with methods \code{"GLS_OU"} or \code{"GLS_OUS"}. It has to be positive.}
\item{CI}{a logical specifying whether to return the 95\% confidence
intervals of the ancestral state estimates.}
}
\details{
For \code{"ML"}, \code{"REML"} and \code{"GLS"}, the default model is Brownian motion. This model
can be fitted by maximum
likelihood (\code{method = "ML"}, Felsenstein 1973, Schluter et al. 1997) - the default, residual maximum likelihood (\code{method = "REML"}), or generalized least
squares (\code{method = "GLS"}, Martins and Hansen 1997, Garland T and Ives AR 2000).
\code{"GLS_ABM"} is based on Brownian motion with trend model. Both \code{"GLS_OU"} and \code{"GLS_OUS"} are based on Ornstein-Uhlenbeck model.
\code{"GLS_OU"} and \code{"GLS_OUS"} differs in the fact that \code{"GLS_OUS"} assume that the process starts from the optimum, while the root state has to be estimated for \code{"GLS_OU"}, which may rise some issues (see Royer-Carenzi and Didier, 2016). Users may provide the attractive strength parameter \code{alpha}, for these two models.
\code{"GLS_ABM"}, \code{"GLS_OU"} and \code{"GLS_OUS"} are all fitted by generalized least squares (Royer-Carenzi and Didier, 2016).
}
\value{
an object of class \code{"ace"} with the following elements:
\item{ace}{the estimates of the
ancestral character values.}
\item{CI95}{the estimated 95\%
confidence intervals.}
\item{sigma2}{if
\code{method = "ML"}, the maximum likelihood estimate of the
Brownian parameter.}
\item{loglik}{if \code{method = "ML"}, the maximum log-likelihood.}
}
\references{
Felsenstein, J. (1973) Maximum likelihood estimation of evolutionary
trees from continuous characters. \emph{American Journal of Human
Genetics}, \bold{25}, 471--492.
Garland T. and Ives A.R. (2000) Using the past to predict the present:
confidence intervals for regression equations in phylogenetic
comparative methods. \emph{American Naturalist}, \bold{155},
346--364.
Martins, E. P. and Hansen, T. F. (1997) Phylogenies and the
comparative method: a general approach to incorporating phylogenetic
information into the analysis of interspecific data. \emph{American
Naturalist}, \bold{149}, 646--667.
Royer-Carenzi, M. and Didier, G. (2016) A comparison of ancestral
state reconstruction methods for quantitative
characters. \emph{Journal of Theoretical Biology}, \bold{404},
126--142.
Schluter, D., Price, T., Mooers, A. O. and Ludwig, D. (1997)
Likelihood of ancestor states in adaptive radiation. \emph{Evolution},
\bold{51}, 1699--1711.
Yang, Z. (2006) \emph{Computational Molecular Evolution}. Oxford:
Oxford University Press.
}
\author{Manuela Royer-Carenzi, Gilles Didier}
\seealso{
\code{\link{MPR}}, \code{\link{corBrownian}}, \code{\link{compar.ou}}
Reconstruction of ancestral sequences can be done with the package
\pkg{phangorn} (see function \code{?ancestral.pml}).
}
\note{
\code{GLS_ABM} should not be used on ultrametric tree.
\code{GLS_OU} may lead to aberrant reconstructions.
}
\examples{
### Some random data...
data(bird.orders)
x <- rnorm(23, m=100)
### Reconstruct ancestral quantitative characters:
reconstruct(x, bird.orders)
reconstruct(x, bird.orders, method = "GLS_OUS", alpha=NULL)
}
\keyword{models}
|
