R/levins.R

In primer: Functions and Data for the Book, a Primer of Ecology with R

#' Classic Metapopulation Model
#'
#' A function for the classic metaapopulation dynamics, for use with \code{ode}
#' in the \code{deSolve} package.
#'
#'
#' @param t Argument for time
#' @param y A scalar for the population variable
#' @param parms Vector or list of parameters
#' @return Returns a list of length one, for use with \code{ode} in the
#' \code{deSolve} package.  \item{Component 1 }{vector of the state variable (a
#' scalar for the proportion of sites occupied).}
#' @author Hank Stevens <HStevens@@muohio.edu>
#' @seealso \code{\link{gotelli}}, \code{\link{hanski}},\code{\link{lande}},
#' \code{\link{MetaSim}}, \code{\link{clogistic}}
#' @references Levins, R. (1969) Some demographic and genetic consequences of
#' environmental heterogeneity for biological control. \emph{Bulletin of the
#' Entomological Society of America}, \bold{15}, 237--240.
#'
#' Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R!  Series. Springer.
#' @keywords methods
#' @export
#' @examples
#'
#' ## The function is currently defined as
#' function (t, y, parms)
#' {
#'     p <- y[1]
#'     with(as.list(parms), {
#'         dp <- ci * p * (1 - p) - e * p
#'         return(list(dp))
#'     })
#'   }
#' library(deSolve)
#' p <- c(ci=.1, e=.01)
#' time <- 1:10
#' initialN <- .3
#' out <- ode(y=initialN, times=time, func=levins, parms=p)
#' plot(time, out[,-1], type='l')
#'
`levins` <-
function (t, y, parms)
{
    p <- y[1]
    with(as.list(parms), {
        dp <- ci * p * (1 - p) - e * p
        return(list(dp))
    })
}