R/lvcomp2.R

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

#' Two Species Lotka-Volterra Competition
#'
#' System of ordinary differential equations for two species Lotka-Volterra
#' competition. For use with \code{ode} in the \code{deSolve} package.
#'
#' The parameters include \code{r1, r2, a11, a12, a21, a22} with the usual
#' meanings. Here the a's are the per capita effects which determine K
#' (\code{a11 = 1/K}).
#'
#' @param t Times points that will return N.
#' @param n a vector of length two for the population sizes at time = t.
#' @param parms vector or list of model parameters (see details below).
#' @return Returns a list of length one which is the rate of increase (required
#' by \code{ode}).
#' @author Hank Stevens <HStevens@@muohio.edu>
#' @seealso \code{\link{lvcomp3}}, \code{\link{lvcompg}},
#' \code{\link{clogistic}}
#' @references Lotka, A.J. (1956) \emph{Elements of Mathematical Biology}.
#' Dover Publications, Inc.
#'
#' Stevens. M.H.H. (2009) A Primer of Theoretical Population Ecology with R.
#' Use R! Series. Springer.
#' @keywords methods
#' @export
#' @examples
#'
#' ## The function is currently defined as
#' function (t, n, parms)
#' {
#'     with(as.list(parms), {
#'         dn1dt <- r1 * n[1] * (1 - a11 * n[1] - a12 * n[2])
#'         dn2dt <- r2 * n[2] * (1 - a22 * n[2] - a21 * n[1])
#'         list(c(dn1dt, dn2dt))
#'     })
#'   }
#' library(deSolve)
#' parms <- c(r1 = 1, r2 = 0.1, a11 = 0.2, a21 = 0.1, a22 = 0.02, a12 = 0.01)
#' initialN <- c(1, 1)
#' out <- ode(y = initialN, times = 1:100, func = lvcomp2, parms = parms)
#' matplot(out[, 1], out[, -1], type = "l")
#'
`lvcomp2` <-
function (t, n, parms)
{
    with(as.list(parms), {
        dn1dt <- r1 * n[1] * (1 - a11 * n[1] - a12 * n[2])
        dn2dt <- r2 * n[2] * (1 - a22 * n[2] - a21 * n[1])
        list(c(dn1dt, dn2dt))
    })
}