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\name{bioenv}
\alias{bioenv}
\alias{bioenv.default}
\alias{bioenv.formula}
\alias{summary.bioenv}
\alias{bioenvdist}
\title{Best Subset of Environmental Variables with
Maximum (Rank) Correlation with Community Dissimilarities }
\description{
Function finds the best subset of environmental variables, so that
the Euclidean distances of scaled environmental variables have the
maximum (rank) correlation with community dissimilarities.
}
\usage{
\method{bioenv}{default}(comm, env, method = "spearman", index = "bray",
upto = ncol(env), trace = FALSE, partial = NULL,
metric = c("euclidean", "mahalanobis", "manhattan", "gower"),
parallel = getOption("mc.cores"), ...)
\method{bioenv}{formula}(formula, data, ...)
bioenvdist(x, which = "best")
}
\arguments{
\item{comm}{Community data frame or a dissimilarity object or a square
matrix that can be interpreted as dissimilarities. }
\item{env}{Data frame of continuous environmental variables. }
\item{method}{The correlation method used in \code{\link{cor}}.}
\item{index}{The dissimilarity index used for community data (\code{comm})
in \code{\link{vegdist}}. This is ignored if \code{comm} are dissimilarities.}
\item{upto}{Maximum number of parameters in studied subsets.}
\item{formula, data}{Model \code{\link{formula}} and data.}
\item{trace}{Trace the calculations }
\item{partial}{Dissimilarities partialled out when inspecting
variables in \code{env}.}
\item{metric}{Metric used for distances of environmental distances. See
Details.}
\item{parallel}{Number of parallel processes or a predefined socket
cluster. With \code{parallel = 1} uses ordinary, non-parallel
processing. The parallel processing is done with \pkg{parallel}
package.}
\item{x}{\code{bioenv} result object.}
\item{which}{The number of the model for which the environmental
distances are evaluated, or the \code{"best"} model.}
\item{...}{Other arguments passed to \code{\link{cor}}.}
}
\details{
The function calculates a community dissimilarity matrix using
\code{\link{vegdist}}. Then it selects all possible subsets of
environmental variables, \code{\link{scale}}s the variables, and
calculates Euclidean distances for this subset using
\code{\link{dist}}. The function finds the correlation between
community dissimilarities and environmental distances, and for each
size of subsets, saves the best result. There are \eqn{2^p-1}
subsets of \eqn{p} variables, and an exhaustive search may take a
very, very, very long time (parameter \code{upto} offers a partial
relief).
The argument \code{metric} defines distances in the given set of
environmental variables. With \code{metric = "euclidean"}, the
variables are scaled to unit variance and Euclidean distances are
calculated. With \code{metric = "mahalanobis"}, the Mahalanobis
distances are calculated: in addition to scaling to unit variance,
the matrix of the current set of environmental variables is also
made orthogonal (uncorrelated). With \code{metric = "manhanttan"},
the variables are scaled to unit range and Manhattan distances are
calculated, so that the distances are sums of differences of
environmental variables. With \code{metric = "gower"}, the Gower
distances are calculated using function
\code{\link[cluster]{daisy}}. This allows also using factor
variables, but with continuous variables the results are equal to
\code{metric = "manhattan"}.
The function can be called with a model \code{\link{formula}} where
the LHS is the data matrix and RHS lists the environmental variables.
The formula interface is practical in selecting or transforming
environmental variables.
With argument \code{partial} you can perform \dQuote{partial}
analysis. The partializing item must be a dissimilarity object of
class \code{\link{dist}}. The
\code{partial} item can be used with any correlation \code{method},
but it is strictly correct only for Pearson.
Function \code{bioenvdist} recalculates the environmental distances
used within the function. The default is to calculate distances for
the best model, but the number of any model can be given.
Clarke & Ainsworth (1993) suggested this method to be used for
selecting the best subset of environmental variables in interpreting
results of nonmetric multidimensional scaling (NMDS). They recommended a
parallel display of NMDS of community dissimilarities and NMDS of
Euclidean distances from the best subset of scaled environmental
variables. They warned against the use of Procrustes analysis, but
to me this looks like a good way of comparing these two ordinations.
Clarke & Ainsworth wrote a computer program BIO-ENV giving the name to
the current function. Presumably BIO-ENV
was later incorporated in Clarke's PRIMER software (available for
Windows). In addition, Clarke & Ainsworth suggested a novel method of
rank correlation which is not available in the current function.
}
\value{
The function returns an object of class \code{bioenv} with a
\code{summary} method.
}
\references{
Clarke, K. R & Ainsworth, M. 1993. A method of linking multivariate
community structure to environmental variables. \emph{Marine Ecology
Progress Series}, 92, 205--219.
}
\author{ Jari Oksanen }
\note{ If you want to study the \sQuote{significance} of \code{bioenv}
results, you can use function \code{\link{mantel}} or
\code{\link{mantel.partial}} which use the same definition of
correlation. However, \code{bioenv} standardizes environmental
variables depending on the used metric, and you must do the same in
\code{\link{mantel}} for comparable results (the standardized data are
returned as item \code{x} in the result object). It is safest to use
\code{bioenvdist} to extract the environmental distances that really
were used within \code{bioenv}. NB., \code{bioenv} selects variables
to maximize the Mantel correlation, and significance tests based on
\emph{a priori} selection of variables are biased. }
\seealso{\code{\link{vegdist}}, \code{\link{dist}}, \code{\link{cor}}
for underlying routines, \code{\link{monoMDS}} and
\code{\link{metaMDS}} for ordination, \code{\link{procrustes}} for
Procrustes analysis, \code{\link{protest}} for an alternative, and
\code{\link{rankindex}} for studying alternatives to the default
Bray-Curtis index.}
\examples{
# The method is very slow for large number of possible subsets.
# Therefore only 6 variables in this example.
data(varespec)
data(varechem)
sol <- bioenv(wisconsin(varespec) ~ log(N) + P + K + Ca + pH + Al, varechem)
sol
summary(sol)
}
\keyword{ multivariate }
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