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taxondive.Rd
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\name{taxondive}
\alias{taxondive}
\alias{summary.taxondive}
\alias{plot.taxondive}
\alias{taxa2dist}
\title{ Indices of Taxonomic Diversity and Distinctness }
\description{
Function finds indices of taxonomic diversity and distinctness,
which are averaged taxonomic distances among species or individuals in
the community (Clarke & Warwick 1998, 2001)
}
\usage{
taxondive(comm, dis, match.force = FALSE)
taxa2dist(x, varstep = FALSE, check = TRUE, labels)
}
\arguments{
\item{comm}{Community data. }
\item{dis}{Taxonomic distances among taxa in \code{comm}. This should
be a \code{\link{dist}} object or a symmetric square matrix. }
\item{match.force}{Force matching of column names in \code{comm} and
labels in \code{dis}. If \code{FALSE}, matching only happens when
dimensions differ, and in that case the species must be in identical
order in both.}
\item{x}{Classification table with a row for each species or other
basic taxon, and columns
for identifiers of its classification at higher levels.}
\item{varstep}{Vary step lengths between successive levels
relative to proportional loss of the number of distinct classes.}
\item{check}{If \code{TRUE}, remove all redundant levels which are
different for all rows or constant for all rows and regard each row
as a different basal taxon (species). If \code{FALSE} all
levels are retained and basal taxa (species) also must be coded as
variables (columns). You will get a warning if species are not
coded, but you can ignore this if that was your intention.}
\item{labels}{The \code{labels} attribute of taxonomic distances. Row
names will be used if this is not given. Species will be matched by
these labels in \code{comm} and \code{dis} in \code{taxondive} if
these have different dimensions.}
}
\details{
Clarke & Warwick (1998, 2001) suggested several alternative indices of
taxonomic diversity or distinctness. Two basic indices are called
taxonomic diversity (\eqn{\Delta}) and distinctness (\eqn{\Delta^*}):
\tabular{c}{
\eqn{\Delta = (\sum \sum_{i<j} \omega_{ij} x_i x_j)/(n (n-1) / 2)} \cr
\eqn{\Delta^* = (\sum \sum_{i<j} \omega_{ij} x_i x_j)/(\sum \sum_{i<j} x_i x_j) }
}
The equations give the index value for a single site, and summation
goes over species \eqn{i} and \eqn{j}. Here \eqn{\omega} are taxonomic
distances among taxa, and \eqn{x} are species abundances, and \eqn{n}
is the total abundance for a site.
With presence/absence data both indices reduce to the same index
\eqn{\Delta^+}, and for this index Clarke & Warwick (1998) also have
an estimate of its standard deviation. Clarke & Warwick (2001)
presented two new indices: \eqn{s\Delta^+} is the product of species
richness and \eqn{\Delta^+}, and index of variation in
taxonomic distinctness (\eqn{\Lambda^+}) defined as
\tabular{c}{
\eqn{\Lambda^+ = (\sum \sum_{i<j} \omega_{ij}^2)/(n (n-1) / 2) - (\Delta^+)^2}
}
The \code{dis} argument must be species dissimilarities. These must be
similar to dissimilarities produced by \code{\link{dist}}. It is
customary to have integer steps of taxonomic hierarchies, but other
kind of dissimilarities can be used, such as those from phylogenetic
trees or genetic differences. Further, the \code{dis} need not be
taxonomic, but other species classifications can be used.
Function \code{taxa2dist} can produce a suitable \code{dist} object
from a classification table. Each species (or basic taxon) corresponds
to a row of the classification table, and columns give the
classification at different levels. With \code{varstep = FALSE} the
successive levels will be separated by equal steps, and with
\code{varstep = TRUE} the step length is relative to the proportional
decrease in the number of classes (Clarke & Warwick 1999).
With \code{check = TRUE}, the function removes classes which are distinct for all
species or which combine all species into one class, and assumes that
each row presents a distinct basic taxon. The function scales
the distances so that longest path length between
taxa is 100 (not necessarily when \code{check = FALSE}).
Function \code{plot.taxondive} plots \eqn{\Delta^+} against Number of
species, together with expectation and its approximate 2*sd
limits. Function \code{summary.taxondive} finds the \eqn{z} values and
their significances from Normal distribution for \eqn{\Delta^+}.
}
\value{
Function returns an object of class \code{taxondive} with following items:
\item{Species }{Number of species for each site.}
\item{D, Dstar, Dplus, SDplus, Lambda}{\eqn{\Delta}, \eqn{\Delta^*},
\eqn{\Delta^+}, \eqn{s\Delta^+} and \eqn{\Lambda^+}
for each site.}
\item{sd.Dplus}{Standard deviation of \eqn{\Delta^+}.}
\item{ED, EDstar, EDplus}{Expected values of corresponding
statistics.}
Function \code{taxa2dist} returns an object of class \code{"dist"}, with
an attribute \code{"steps"} for the step lengths between successive levels.
}
\references{
Clarke, K.R & Warwick, R.M. (1998) A taxonomic distinctness index and
its statistical properties. \emph{Journal of Applied Ecology} 35,
523--531.
Clarke, K.R. & Warwick, R.M. (1999) The taxonomic distinctness measure
of biodiversity: weighting of step lengths between hierarchical
levels. \emph{Marine Ecology Progress Series} 184: 21--29.
Clarke, K.R. & Warwick, R.M. (2001) A further biodiversity index
applicable to species lists: variation in taxonomic
distinctness. \emph{Marine Ecology Progress Series} 216, 265--278.
}
\author{ Jari Oksanen }
\note{
The function is still preliminary and may change. The scaling of
taxonomic dissimilarities influences the results. If you multiply
taxonomic distances (or step lengths) by a constant, the values of all
Deltas will be multiplied with the same constant, and the value of
\eqn{\Lambda^+} by the square of the constant.
}
\seealso{\code{\link{diversity}}. }
\examples{
## Preliminary: needs better data and some support functions
data(dune)
data(dune.taxon)
# Taxonomic distances from a classification table with variable step lengths.
taxdis <- taxa2dist(dune.taxon, varstep=TRUE)
plot(hclust(taxdis), hang = -1)
# Indices
mod <- taxondive(dune, taxdis)
mod
summary(mod)
plot(mod)
}
\keyword{ univar }