R/lvcomp3.R

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

#' Three Species Lotka-Volterra Competition
#'
#' System of ordinary differential equations for three species Lotka-Volterra
#' competition. For use with \code{ode} in the \code{deSolve} package.
#'
#' The parameters include \code{r, a} with the usual meanings. Here the
#' \code{a}'s are the per capita effects which determine K (\code{a11 = 1/K1}).
#'
#' @param t the time for each integration.
#' @param n a vector of length three 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{lvcomp2}}, \code{\link{lvcompg}},
#' \code{\link{clogistic}}
#' @references Lotka, A.J. (1956) \emph{Elements of Mathematical Biology}.
#' Dover Publications, Inc.
#'
#' Stevens. M.H.H. (2009) \emph{A Primer of 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] - a13 *
#'             n[3])
#'         dn2dt <- r2 * n[2] * (1 - a22 * n[2] - a21 * n[1] - a23 *
#'             n[3])
#'         dn3dt <- r3 * n[3] * (1 - a33 * n[3] - a31 * n[1] - a32 *
#'             n[2])
#'         list(c(dn1dt, dn2dt, dn3dt))
#'     })
#'   }
#'
#' library(deSolve)
#' parms <- c(r1 = 0.1, r2 = 0.2, r3 = 0.3,
#' a11 = 0.1, a12 = 0.01, a13 = 0.01,
#' a21 = 0.01, a22 = 0.15, a23 = 0.01,
#' a31 = 0.01, a32 = 0.01, a33 = 0.2)
#' initialN <- c(1, 1, 1)
#' out <- ode(y = initialN, times = 1:100, func = lvcomp3, parms = parms)
#' matplot(out[, 1], out[, -1], type = "l")
#'
`lvcomp3` <-
function (t, n, parms)
{
    with(as.list(parms), {
        dn1dt <- r1 * n[1] * (1 - a11 * n[1] - a12 * n[2] - a13 *
            n[3])
        dn2dt <- r2 * n[2] * (1 - a22 * n[2] - a21 * n[1] - a23 *
            n[3])
        dn3dt <- r3 * n[3] * (1 - a33 * n[3] - a31 * n[1] - a32 *
            n[2])
        list(c(dn1dt, dn2dt, dn3dt))
    })
}