Three Species Lotka-Volterra Competition

Description

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

Usage

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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 <HStevens@muohio.edu>

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

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## 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") 

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