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```
#' Partitioning of the temporal CV of ecological communities
#'
#' `PartitionR()` is a function used to partition the temporal coefficient of variation of a community
#' into the variability of the average species and three stabilizing effects: the dominance, asynchrony and averaging effects
#' (see Details).
#'
#' @usage partitionR(z, ny = 1)
#'
#' @param z A `matrix` containing repeated measurements of species abundances.
#' The `matrix` must contain numerical values only, with years in rows and species in
#' columns. Remove any extra column.
#' @param ny Only species appearing more than `ny` years (`integer`, defaults to 1) are used in the calculations.
#'
#' @return Returns an object of class `'comstab'`.
#' @return An object of class `'comstab'` is a list containing the following components:
#' * `'CVs'` a named vector of calculated coefficient of variations. `CVe` is the CV of an average species,
#' `CVtilde` is the mean of species CVs weighted by their relative abundances, `CVa` is the expected community CV if
#' the community was stabilized by species asynchrony only, and `CVc` is the observed community CV.
#' * `'Stabilization'` a named vector of the stabilizing effects. `tau` is the total stabilization, `Delta` is
#' the dominance effect, `Psi` is the asynchrony effect, and `omega` is the averaging effect.
#' * `'Relative'` a named vector of the relative contributions of each stabilizing effect to the total stabilization.
#' `Delta_cont`, `Psi_cont`, and `omega_cont` are the relative contribution of respectively, the dominance, asynchrony, and averaging effects to the total stabilization.
#' Returns a vector of NAs if any Stabilizing effect is higher than 1.
#'
#' @details The analytic framework is described in details in Segrestin *et al.* (2024).
#' In short, the partitioning relies on the following equation: \deqn{CV_{com} = CV_e \Delta \Psi \omega}
#' where \eqn{CV_{com}} is the community coefficient of variation (reciprocal of community stability),
#' \eqn{CV_e} is the expected community CV when controlling for the dominance structure and species temporal synchrony,
#' \eqn{ \Delta} is the dominance effect, \eqn{ \Psi} is the asynchrony effect, and \eqn{ \omega} is the averaging effect.
#'
#' @references Segrestin *et al.* (2024) A unified framework for partitioning the drivers of stability of ecological communities. Global Ecology and Biogeography, 33(5), e13828. https://doi.org/10.1111/geb.13828
#'
#' @examples
#' require(stats)
#'
#' # Simulates a custom community time series using 'comTS()':
#' z <- comTS(nsp = 10, ny = 30, even = 0.6, mvs = 1.5, sync = "0")
#'
#' # Runs the partitioning of the community coefficient of variation:
#' partitionR(z)
#'
#' @importFrom stats var coef lm cor.test setNames
#'
#' @author Jules Segrestin, \email{jsegrestin@@gmail.com}
#'
#' @export
partitionR <- function(z, ny = 1){
if(!is.matrix(z)) stop("Error: z is not a matrix")
if(!is.numeric(z)) stop("Error: non-numerical values in z")
if(any(z < 0)) stop("Error: negative values in z")
if(dim(z)[1] == 1) stop("Error: single-row matrix")
if(!is.numeric(ny)) stop("ny must be numeric")
# Replace Nas with zeros
z[is.na(z)] <- 0
# Remove absent species
z <- z[, colSums(z) > 0, drop = FALSE]
# Remove non-fluctuating species
z <- z[, apply(X = z, MARGIN = 2, FUN = min) != apply(X = z, MARGIN = 2, FUN = max), drop = FALSE]
# Remove transient species appearing only ny years
nyi <- apply(X = z, MARGIN = 2, FUN = function(x) sum(x > 0))
z <- z[, nyi > ny, drop = FALSE]
n <- ncol(z)
# Total CV
varsum <- stats::var(rowSums(z))
meansum <- mean(rowSums(z))
CV <- sqrt(varsum)/meansum
if(CV == 0) stop("The community CV is zero. This analysis does not apply to
perfectly stable communities.")
if(dim(z)[2] == 1) {
warning("This analysis is not relevant for single-species communities.
All stabilizing effects were fixed to 1.")
# outputs
CVs <- stats::setNames(object = c(CV, CV, CV, CV),
nm = c("CVe", "CVtilde", "CVa", "CVc"))
Stabilization <- stats::setNames(object = c(1, 1, 1, 1),
nm = c("tau", "Delta", "Psi", "omega"))
Relative <- stats::setNames(object = rep(NA, 3),
nm = c("Delta_cont", "Psi_cont", "omega_cont"))
res <- list(CVs = CVs, Stabilization = Stabilization, Relative = Relative)
class(res) <- "comstab"
return(res)
}
if(dim(z)[2] > 1) {
# Expected community CV if all species had even abundances
vari <- apply(X = z, MARGIN = 2, FUN = stats::var)
meani <- colMeans(z)
CVi <- sqrt(vari) / meani
if (any(CVi == 0)) warning("Non-fluctuating species found in the data.")
CV0 <- which(CVi > 0)
TPL <- stats::coef(stats::lm(log10(CVi[CV0]) ~ log10(meani[CV0])))
CVe <- 10^TPL[1] * (meansum / n) ^ TPL[2]
if(sum(CV0) > 5){
testcor <- stats::cor.test(log10(CVi[CV0]), log10(meani[CV0]))$p.value > 0.05
if (testcor) warning("No significant power law between species CVs and abundances.")
} else {
warning("Low number of species. The power law between species CVs and abundances cannot be tested.")
}
# Dominance effect
sumsd <- sum(sqrt(vari))
CVtilde <- sumsd / meansum
Delta <- CVtilde / CVe
if(Delta > 1) warning("Destabilizing effect of dominants. Relative effects cannot be computed.")
# Compensatory dynamics
sdsum <- sqrt(varsum)
rootPhi <- sdsum / sumsd
# Asynchrony effect
sumvar <- sum(vari)
beta <- log10(1/2) / (log10(sumvar / (sumsd^2)))
Psi <- rootPhi^beta
# averaging effect
omega <- rootPhi / Psi
if(omega > 1) warning("Community diversity is lower than the null diversity. Relative effects cannot be computed.")
# total stabilization
tau <- Delta * Psi * omega
# outputs
CVs <- stats::setNames(object = c(CVe, CVtilde, CVtilde * Psi, CV),
nm = c("CVe", "CVtilde", "CVa", "CVc"))
Stabilization <- stats::setNames(object = c(tau, Delta, Psi, omega),
nm = c("tau", "Delta", "Psi", "omega"))
if(any(Stabilization > 1)){
Relative <- stats::setNames(object = rep(NA, 3),
nm = c("Delta_cont", "Psi_cont", "omega_cont"))
} else {
Relative <- stats::setNames(object = c(log10(Delta)/log10(tau), log10(Psi)/log10(tau), log10(omega)/log10(tau)),
nm = c("Delta_cont", "Psi_cont", "omega_cont"))
}
res <- list(CVs = CVs, Stabilization = Stabilization, Relative = Relative)
class(res) <- "comstab"
return(res)
}
}
#' @export
print.comstab <- function(x, ...){
cat("\nPartitionning of the community temporal variability (CV)")
cat("\n")
cat(paste0("Community CV = ", round(x$CVs["CVc"], 2),
"\nTotal stabilization = ", round(x$Stabilization["tau"], 2),
"\nDominance effect = ", round(x$Stabilization["Delta"], 2),
"\nAsynchrony effect = ", round(x$Stabilization["Psi"], 2),
"\nAveraging effect = ", round(x$Stabilization["omega"], 2)))
cat("\n")
cat("\nRelatives contributions:")
cat(paste0("\n% Dominance = ", round(x$Relative["Delta_cont"], 2)),
paste0("\n% Asynchrony = ", round(x$Relative["Psi_cont"], 2)),
paste0("\n% Averaging = ", round(x$Relative["omega_cont"], 2)))
}
```

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