# @file: ind_based_models.R
# @author: Carl Boettiger, <cboettig@gmail.com>
# @section DESCRIPTION wrapper to the C code containing the gillespie simulation for individual-based models.
## Some example parameters to try:
## In the C code
# Pars = {n, e, a, K, h, i, Da, Dt}
# inits[8] = {572, .5, 160, 1000, 200, 0, 1, 100};
# in the R code
#pars = c(Xo = 730, e = 0.5, a = 100, K = 1000, h = 200,
# i = 0, Da = .09, Dt = 0, p = 2)
#' @title Individual based simulation of a saddle node bifurcation
#'
#' Uses the Gillespie algorithm to simulate an individual birth-death process
#' for the saddle node bifurcation. The system gradually approaches the bifurcation
#' at the specified rate.
#'
#' @param pars a list of parameters for the saddle-node model
#' @param times a sequence of times at which we sample the system state
#' (note that the dynamics of the system itself are continuous and independent
#' of this sampling process.
#' @param reps how many replicate simulations should we run?
#' @return a list with the observed values in the matrix as "x1" (columns are reps, if desired),
#' mean values "m1" across replicates, "v1" variance across replicates, "parameters" is
#' the input list of pars, and "time" is the input list of times.
#'
#' @details
#'
#' If given replicates, this produces some summary statistics of the replicates as well.
#'
#' pars contains a named list of these elements, in this order:
#' Xo is initial population size
#' e is the natural per-capita death-rate
#' a is the environmental toxin level
#' K scales the birth rate (hence the equilibrium size)
#' h is the half-max growth rate
#' i is a place-holder for an internal counter, not real parameter
#' Da is the rate of environmental degradation
#' Dt is the time at which environmental degradation begins
#'
#' @examples
#' pars = c(Xo = 730, e = 0.5, a = 100, K = 1000, h = 200, i = 0, Da = .09, Dt = 0, p = 2)
#' time=seq(0,500, length=500)
#' sn <- saddle_node_ibm(pars,time)
#' X <- data.frame(time=time, value=sn$x1)
#'
#' @useDynLib populationdynamics
#' @export
saddle_node_ibm <- function(
pars=c("Xo" = 570, "e" = .5, "a" = 160, "K" = 1000, "h" = 200,
"i" = 0, "Da" = 1, "Dt" = 100, "p"=2),
times = seq(0,150,length=50),
reps=1)
{
samples <- length(times)
N <- reps*samples
maxtime <- max(times)
o <- .C("saddle_node_direct", double(N), as.double(pars), as.integer(samples), as.integer(reps), as.double(maxtime) )
x1 <- matrix(o[[1]], samples, reps)
m1 <- sapply(1:samples, function(i) mean(x1[i,]))
v1 <- sapply(1:samples, function(i) var(x1[i,]))
list(x1 = x1, m1=m1, v1=v1, parameters = pars, Xo = pars[1], time=times)
}
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