R/elasticity.R

In popbio: Construction and Analysis of Matrix Population Models

#' Elasticity analysis of a projection matrix
#'
#' Calculate the elasticities of eigenvalues to changes in the projection matrix
#' elements
#'
#' see section 9.2 in Caswell (2001)
#'
#' @param A A projection matrix
#'
#' @return An elasticity matrix
#'
#' @references Caswell, H. 2001. Matrix population models: construction,
#' analysis, and interpretation, Second edition. Sinauer, Sunderland,
#' Massachusetts, USA.
#'
#' @seealso  \code{\link{sensitivity}}
#'
#' @author Chris Stubben
#'
#' @examples
#' elas <- elasticity(teasel)
#' image2(elas, mar=c(1,3.5,5,1) )
#'  title("Teasel elasticity matrix", line=2.5)
#' # Summed elasticities for teasel.
#' # fertility in last column, stasis P on diagonal, and growth in bottom-left triangle
#' c(F=sum(elas[,6]), P=sum(diag(elas)), G=sum(elas[row(elas)>col(elas)]))
#' 
#' elas <- elasticity(tortoise[["med.high"]])
#' image2(elas, mar=c(1,3.5,5,1),  log=FALSE)
#'  title("Tortoise elasticity matrix", line=2.5)
#' # Summed elasticities for tortoise (see example 9.4)
#' # fertility in top row, stasis on diagonal, and growth on subdiagonal
#' c(F=sum(elas[1,]), P=sum(diag(elas)), G=sum(elas[row(elas)==col(elas)+1]))
#'
#' @export

elasticity <- function(A) {
  s <- sensitivity(A)
  lambda <- lambda(A)
  e <- s * A / lambda
  e
}