# lvcomp3: Three Species Lotka-Volterra Competition In primer: Functions and data for A Primer of Ecology with R

## Description

System of ordinary differential equations for three species Lotka-Volterra competition. For use with `ode` in the `deSolve` package.

## Usage

 `1` ```lvcomp3(t, n, parms) ```

## Arguments

 `t` the time for each integration. `n` a vector of length three for the population sizes at time = t. `parms` vector or list of model parameters (see details below).

## Details

The parameters include `r, a` with the usual meanings. Here the `a`'s are the per capita effects which determine K (`a11 = 1/K1`).

## Value

Returns a list of length one which is the rate of increase (required by `ode`).

## Author(s)

Hank Stevens <[email protected]>

## References

Lotka, A.J. (1956) Elements of Mathematical Biology. Dover Publications, Inc.

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

## See Also

`lvcomp2`, `lvcompg`, `clogistic`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```## The function is currently defined as function (t, n, parms) { with(as.list(parms), { dn1dt <- r1 * n[1] * (1 - a11 * n[1] - a12 * n[2] - a13 * n[3]) dn2dt <- r2 * n[2] * (1 - a22 * n[2] - a21 * n[1] - a23 * n[3]) dn3dt <- r3 * n[3] * (1 - a33 * n[3] - a31 * n[1] - a32 * n[2]) list(c(dn1dt, dn2dt, dn3dt)) }) } library(deSolve) parms <- c(r1 = 0.1, r2 = 0.2, r3 = 0.3, a11 = 0.1, a12 = 0.01, a13 = 0.01, a21 = 0.01, a22 = 0.15, a23 = 0.01, a31 = 0.01, a32 = 0.01, a33 = 0.2) initialN <- c(1, 1, 1) out <- ode(y = initialN, times = 1:100, func = lvcomp3, parms = parms) matplot(out[, 1], out[, -1], type = "l") ```

primer documentation built on May 29, 2017, 11:26 p.m.