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\name{autoconst}
\alias{autoconst}
\alias{autoreg}
%- Also NEED an `\alias' for EACH other topic documented here.
\title{Spatial autocorrelation parameter estimation}
\description{
Monte Carlo estimation of the disjunction/spatial autocorrelation
parameter \code{pd} for the simulation model used in
\code{randpop.nb}, used for tests for clustering of presence-absence data.
\code{autoconst} is the main function; \code{autoreg} performs the
simulation and is executed within \code{autoconst}.
}
\usage{
autoconst(x, prange = c(0, 1), twostep = TRUE, step1 = 0.1,
step2 = 0.01, plot = TRUE, nperp = 4, ejprob = NULL,
species.fixed = TRUE, pdfnb=FALSE, ignore.richness=FALSE)
autoreg(x, probs, ejprob, plot = TRUE, nperp = 4, species.fixed = TRUE,
pdfnb=FALSE, ignore.richness=FALSE)
}
%- maybe also `usage' for other objects documented here.
\arguments{
\item{x}{object of class \code{prab} as generated by \code{prabinit}.
Presence-absence data to be analyzed.}
\item{prange}{numerical range vector, lower value not smaller than 0, larger
value not larger than 1. Range where the parameter is to be found.}
\item{twostep}{logical. If \code{TRUE}, a first estimation step is
carried out in the whole \code{prange}, and then the final
estimation is determined between the preliminary estimator
\code{-5*step2} and \code{+5*step2}. Else, the first simulation
determines the final estimator.}
\item{step1}{numerical between 0 and 1. Interval length between
subsequent choices of \code{pd} for the first simulation.}
\item{step2}{numerical between 0 and 1. Interval length between
subsequent choices of \code{pd} for the second simulation in case of
\code{twostep=TRUE}.}
\item{plot}{logical. If \code{TRUE}, a scatterplot of \code{pd}-values
against resulting \code{ejprob} values (see below), with regression
line and data value of \code{ejprob} is shown.}
\item{nperp}{integer. Number of simulations per \code{pd}-value.}
\item{ejprob}{numerical between 0 and 1. Observed disjunction
probability for data \code{x}; if not specified in advance,
it will be computed by \code{autoconst}.}
\item{species.fixed}{logical. If \code{TRUE}, sizes of generated
species match the species sizes in \code{x}, else they are generated
from the empirical distribution of species sizes in \code{x}.}
\item{probs}{vector of numericals between 0 and 1. \code{pd} values
for the simulation.}
\item{pdfnb}{logical. If \code{TRUE}, the probabilities of the regions
are modified according to the number of neighboring regions in
\code{randpop.nb}, see Hennig and Hausdorf (2002), p. 5.}
\item{ignore.richness}{logical. If \code{TRUE}, there is no assumption
of species richnesses to differ between regions in the null model.
Regionwise probabilities don't differ in the generation of null
data.}
}
\details{
The spatial autocorrelation parameter \code{pd}
of the model for the generation of
presence-absence data sets used by \code{randpop.nb} can be estimated
by use of the observed disjuction probability \code{ejprob} which is
the sum of
all species' connectivity components minus the number of species
divided by the number of "presence" entries minus the number of
species. This is done by a simulation of artificial data sets with
characteristics of \code{x} and different \code{pd}-values, governed
by \code{prange, step1, step2} and \code{nperp}. \code{ejprob} is then
calculated for all simulated populations. A linear regression of
\code{ejprob} on \code{pd} is performed and the estimator of \code{pd}
is determined by computing the inverse of the regression function for
the \code{ejprob}-value of \code{x}.
}
\value{
\code{autoconst} produces the same list as \code{autoreg} with
additional component \code{ejprob}. The components are
\item{pd}{(eventually) estimated parameter \code{pd}.}
\item{coef}{(eventually) estimated regression coefficients.}
\item{ejprob}{see above.}
}
\references{
Hausdorf, B. and Hennig, C. (2003) Biotic Element Analysis in
Biogeography. To appear in \emph{Systematic Biology}.
Hausdorf, B. and Hennig, C. (2003) Nestedness of north-west European
land snail ranges as a consequence of differential immigration from
Pleistocene glacial refuges. \emph{Oecologia} 135, 102-109.
Hennig, C. and Hausdorf, B. (2004) Distance-based parametric bootstrap
tests for clustering of species ranges. \emph{Computational Statistics
and
Data Analysis} 45, 875-896.
}
\author{Christian Hennig
\email{christian.hennig@unibo.it}
\url{https://www.unibo.it/sitoweb/christian.hennig/en}}
\seealso{
\code{\link{randpop.nb}}, \code{\link{prabinit}}, \code{\link{con.comp}}
}
\examples{
options(digits=4)
data(kykladspecreg)
data(nb)
set.seed(1234)
x <- prabinit(prabmatrix=kykladspecreg, neighborhood=nb)
ax <- autoconst(x,nperp=2,step1=0.3,twostep=FALSE)
}
\keyword{spatial}% at least one, from doc/KEYWORDS
|
