lv {simecol}

Lotka-Volterra Predator-Prey Model

Description

simecol example: basic Lotka-Volterra predator prey-model.

Usage

data(lv)

Format

An S4 object according to the odeModel specification. The object contains the following slots:

main

Lotka-Volterra equations for predator and prey.

parms

Vector with the named parameters of the model:

k1

growth rate of the prey population,

k2

encounter rate of predator and prey,

k3

death rate of the predator population.

times

Simulation time and integration interval.

init

Vector with start values for predator and prey.

Details

To see all details, please have a look into the implementation.

References

Lotka, A. J. 1925. Elements of physical biology. Williams and Wilkins, Baltimore.

Volterra, V. (1926). Variazionie fluttuazioni del numero d'individui in specie animali conviventi. Mem. Acad.Lincei, 2, 31-113.

See Also

simecol-package, sim, parms, init, times.

Examples

##============================================
## Basic Usage:
##   explore the example
##============================================
data(lv)
print(lv)
plot(sim(lv))

parms(lv) <- c(k1=0.5, k2=0.5, k3=0.5)
plot(sim(lv))

##============================================
## Implementation:
##   The code of the Lotka-Volterra-model
##============================================
lv <- new("odeModel",
  main = function (time, init, parms) {
    x <- init
    p <- parms
    dx1 <-   p["k1"] * x[1] - p["k2"] * x[1] * x[2]
    dx2 <- - p["k3"] * x[2] + p["k2"] * x[1] * x[2]
    list(c(dx1, dx2))
  },
  parms  = c(k1=0.2, k2=0.2, k3=0.2),
  times  = c(from=0, to=100, by=0.5),
  init   = c(prey=0.5, predator=1),
  solver = "rk4"
)