lv {simecol} | R Documentation

## 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"
    )

[Package simecol version 0.6-9 Index]