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#' @title Relationship between mean metabolic rate (\eqn{\bar{\epsilon}}) and abundance
#'
#' @description \code{ebar} calculates the relationship between average metabolic rate of a species and that species' abundance. Also known as the Damuth relationship
#' @details
#' See examples.
#'
#' @param x an object of class meteESF.
#' @keywords lagrange multiplier, METE, MaxEnt, ecosystem structure function
#' @export
#'
#' @examples
#' data(arth)
#' esf1 <- meteESF(spp=arth$spp,
#' abund=arth$count,
#' power=arth$mass^(.75),
#' minE=min(arth$mass^(.75)))
#' damuth <- ebar(esf1)
#'
#' @return An object of class \code{meteRelaT}. The object contains a list with the following elements.
#' \describe{
#' \item{\code{pred}}{predicted relationship}
#' \item{\code{obs}}{observed relationship}
#' }
#'
#' @author Andy Rominger <ajrominger@@gmail.com>, Cory Merow
#' @seealso meteDist, sad.meteESF, metePsi
#' @references Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
#' @importFrom stats aggregate
ebar <- function(x) {
if(is.na(x$state.var[3])) stop('must provide metabolic rate data or E0 to calculate power distributions')
dat <- x$data$e
if(is.null(dat)) {
X <- NULL
} else {
X <- aggregate(list(n=x$data$n, e=x$data$e), list(s=x$data$s), sum)
X$e <- X$e/X$n
X <- X[, c('n', 'e')]
}
thr <- data.frame(n=1:min(x$state.var['N0'], max(X$n)), e=1 + 1/(1:min(x$state.var['N0'], max(X$n)) * x$La[2]))
attr(X, 'source') <- 'empirical'
attr(X, 'type') <- 'damuth'
class(X) <- 'damuth'
attr(thr, 'source') <- 'theoretical'
attr(thr, 'type') <- 'damuth'
class(thr) <- 'damuth'
out <- list(obs=X, pred=thr)
class(out) <- 'meteRelat'
return(out)
}
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