saddle_node_ibm: Individual based simulation of a saddle node bifurcation Uses...

In cboettig/populationdynamics: Tools to simulate various population dynamics models in ecology

Description

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.

Usage

  saddle_node_ibm(pars = c(Xo = 570, e = 0.5, a = 160, K = 1000, h = 200, i = 0, Da = 1, Dt = 100, p = 2),
    times = seq(0, 150, length = 50), reps = 1)

Arguments

pars	a list of parameters for the saddle-node model
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.
reps	how many replicate simulations should we run?

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

Value

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.

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)

cboettig/populationdynamics documentation built on May 13, 2019, 2:11 p.m.