seem (version 1.0)

Logistic and M3 Model Functions: Functions to define logistic and M3 (Michaelis-Menten-Monod) models for simulation

Description

Functions used as part of argument model to call simulation functions.

Usage

logistic(t,p,x)
logistic.forced(t,p,x)
logistic.var(t,p,x)
logistic.z(t,p,x)
logistic.g(t,p,x,tz)
M3(t,p,x)
monod.batch(t,p,x)

Arguments

t

time

p

parameters, an array

x

state variable

tz

times of sudden disturbance

Value

• Rate of change or derivative of model. Except logistic.z and logistic.g that return disturbance regime.

Details

State variable can be population density (logistic family), or chemical concentration (M3). Two states for monod.batch: chemical concentration and population density.

For logistic, p is dim 2: the intrinsic growth coeff, and the carrying capacity. For logistic.forced, p is dim 4: the intrinsic growth coeff, the carrying capacity, and disturbance parameters. For logistic.var, p is dim 5: mean of the intrinsic growth coeff, the carrying capacity, and, drift coeff, amplitude, and period of sinusoidal variation.

Functions logistic.z and logistic.g define discontinuous disturbance regime. Function logistic.z defines times of discontinuities, and logistic.g applies a linear disturbance at tz times defined by logistic.z.

For function M3, p is dim 2: half-rate concentration and maximum rate. For monod-batch p is dim 4: half-rate concentration, maximum rate, yield coefficient, and death rate.

References

Acevedo M.F. 2012. Simulation of Ecological and Environmental Models. CRC Press.

Hallam, T.G., 1986b. Population dynamics in a homogeneous environment. In Mathetmatical Ecology, eds. T. G. Hallam, and S. A. Levin, 61-94. New York: Springer-Verlag.

Hanson, F.B., and H.C. Tuckwell. 1981. Logistic growth with random density independent disasters. Theoretical Population Biology 19:1-18.

See Also

Simulation functions sim.comp, sim.rnum, sim.mruns, sim, simd Methods euler, RK4

Examples

# logistic
logis <- list(f=logistic)
# single run
t.X <- sim(logis,file="chp6/logistic-inp.csv")
# multiple runs
param <- list(plab="r", pval = seq(0.2,0.6,0.2))
t.X <- sim(logis,"chp6/logistic-inp.csv",param)
# Harvest, multiple runs 
logis.f <- list(f=logistic.forced)
param <- list(plab="Ha",pval=c(0,-0.1,-0.2,-0.3))
t.X <- sim(logis.f,"chp7/logis-harvest-inp.csv",param)
# Seasonality 
logis.v <- list(f=logistic.var)
param <- list(plab="Kd",pval=c(0,-0.5,-0.6))
t.X <- sim(logis.v,"chp7/logis-var-inp.csv",param)
# sudden disturbance
logis.sud <- list(f=logistic,z=logistic.z,g=logistic.g)
t.X <- simd(logis.sud,file="chp7/logis-sud-inp.csv")
# M3 decay multiple runs
m3decay<- list(f=M3)
param <- list(plab="Kmax", pval = seq(-20,-60,-10))
t.X <- sim(m3decay,"chp6/m3decay-inp.csv", param)
# monod batch multiple runs
monod <- list(f=monod.batch)
param <- list(plab="Kmax", pval = seq(0.5,1.5,0.5))
t.X <- sim(monod,"chp6/monod-batch-inp.csv", param)