\encoding{UTF-8}
\name{contribdiv}
\alias{contribdiv}
\alias{plot.contribdiv}
\title{Contribution Diversity Approach}
\description{
The contribution diversity approach is based in the differentiation of 
within-unit and among-unit diversity by using additive diversity 
partitioning and unit distinctiveness.
}
\usage{
contribdiv(comm, index = c("richness", "simpson"),
     relative = FALSE, scaled = TRUE, drop.zero = FALSE)
\method{plot}{contribdiv}(x, sub, xlab, ylab, ylim, col, ...)
}
\arguments{
  \item{comm}{The community data matrix with samples as rows and species as column.}
  \item{index}{Character, the diversity index to be calculated.}
  \item{relative}{Logical, if \code{TRUE} then contribution diversity 
    values are expressed as their signed deviation from their mean. See details.}
  \item{scaled}{Logical, if \code{TRUE} then relative contribution diversity 
    values are scaled by the sum of gamma values (if \code{index = "richness"}) 
    or by sum of gamma values times the number of rows in \code{comm} 
    (if \code{index = "simpson"}). See details.}
  \item{drop.zero}{Logical, should empty rows dropped from the result? 
    If empty rows are not dropped, their corresponding results will be \code{NA}s.}
  \item{x}{An object of class \code{"contribdiv"}.}
  \item{sub, xlab, ylab, ylim, col}{Graphical arguments passed to plot.}
  \item{\dots}{Other arguments passed to plot.}
}
\details{
This approach was proposed by Lu et al. (2007). 
Additive diversity partitioning (see \code{\link{adipart}} for more references) 
deals with the relation of mean alpha and the total (gamma) diversity. Although 
alpha diversity values often vary considerably. Thus, contributions of the sites 
to the total diversity are uneven. This site specific contribution is measured by 
contribution diversity components. A unit that has e.g. many unique species will 
contribute more to the higher level (gamma) diversity than another unit with the 
same number of species, but all of which common.

Distinctiveness of species \eqn{j} can be defined as the number of sites where it 
occurs (\eqn{n_j}), or the sum of its relative frequencies (\eqn{p_j}). Relative 
frequencies are computed sitewise and \eqn{sum_j{p_ij}}s at site \eqn{i} sum up 
to \eqn{1}.

The contribution of site \eqn{i} to the total diversity is given by 
\eqn{alpha_i = sum_j(1 / n_ij)} when dealing with richness and 
\eqn{alpha_i = sum(p_{ij} * (1 - p_{ij}))} for the Simpson index.

The unit distinctiveness of site \eqn{i} is the average of the species 
distinctiveness, averaging only those species which occur at site \eqn{i}. 
For species richness: \eqn{alpha_i = mean(n_i)} (in the paper, the second 
equation contains a typo, \eqn{n} is without index). For the Simpson index: 
\eqn{alpha_i = mean(n_i)}.

The Lu et al. (2007) gives an in-depth description of the different indices.
}
\value{
An object of class \code{"contribdiv"} in heriting from data frame.

Returned values are alpha, beta and gamma components for each sites (rows)
of the community matrix. The \code{"diff.coef"} attribute gives the
differentiation coefficient (see Examples).
}
\references{
Lu, H. P., Wagner, H. H. and Chen, X. Y. 2007. A contribution diversity 
approach to evaluate species diversity.
\emph{Basic and Applied Ecology}, 8, 1--12.
}
\author{\enc{Péter Sólymos}{Peter Solymos}, \email{solymos@ualberta.ca}}
\seealso{\code{\link{adipart}}, \code{\link{diversity}}}
\examples{
## Artificial example given in
## Table 2 in Lu et al. 2007
x <- matrix(c(
1/3,1/3,1/3,0,0,0,
0,0,1/3,1/3,1/3,0,
0,0,0,1/3,1/3,1/3),
3, 6, byrow = TRUE,
dimnames = list(LETTERS[1:3],letters[1:6]))
x
## Compare results with Table 2
contribdiv(x, "richness")
contribdiv(x, "simpson")
## Relative contribution (C values), compare with Table 2
(cd1 <- contribdiv(x, "richness", relative = TRUE, scaled = FALSE))
(cd2 <- contribdiv(x, "simpson", relative = TRUE, scaled = FALSE))
## Differentiation coefficients
attr(cd1, "diff.coef") # D_ST
attr(cd2, "diff.coef") # D_DT
## BCI data set
data(BCI)
opar <- par(mfrow=c(2,2))
plot(contribdiv(BCI, "richness"), main = "Absolute")
plot(contribdiv(BCI, "richness", relative = TRUE), main = "Relative")
plot(contribdiv(BCI, "simpson"))
plot(contribdiv(BCI, "simpson", relative = TRUE))
par(opar)
}
\keyword{multivariate}
