lvcomp3 {primer} | R Documentation |
System of ordinary differential equations for three species Lotka-Volterra competition. For use with ode
in the deSolve
package.
lvcomp3(t, n, parms)
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). |
The parameters include r, a
with the usual meanings. Here the a
's are the per capita effects which determine K (a11 = 1/K1
).
Returns a list of length one which is the rate of increase (required by ode
).
Hank Stevens <HStevens@muohio.edu>
Lotka, A.J. Elements of Mathematical Biology. Dover Publications, Inc., 1956.
Stevens. M.H.H. A Primer of Ecology with R. Use R! Series. Springer, 2009.
## 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")