lotkapreyK: Lotka-Volterra Predator-Prey Model with Density Dependent...

In jarioksa/ecostudy: Ecology Teaching Package

Lotka-Volterra Predator-Prey Model with Density Dependent Prey

Description

Function implements Lotka-Volterra predator-prey model.

Usage

lotkapreyK(a, b, c, d, K)
## S3 method for class 'lotkapreyK'
plot(x, xlim, ylim, arrows = 5, ...)
## S3 method for class 'lotkapreyK'
lines(x, N, P, time = 100, step = 0.2, ...)
## S3 method for class 'lotkapreyK'
traj(x, N, P, time = 100, step = 1, ...)

Arguments

a, b, c, d, K	Lotka-Volterra model parameters: see Details.
x	"lotkaprey" result object.
xlim, ylim	Axis ranges.
arrows	Number of trend arrows displayed in the graph.
N, P	Initial prey and predator densities
time, step	Total time span and time step for which trajectories are found.
...	Other arguments passed to functions.

Details

The model is identical to lotkaprey except that the prey N is density-dependent following the logistic population growth model with carrying capacity K, prey growth rate a, attack rate b and predator density P:

dN/dt = a*N*(1-N/K) - b*N*P

Other parameters and the predator model are identical to the basic Lotka-Volterra model (lotkaprey). The Rosenzweig-MacArtur model uses the same prey model as this function, but applies type II functional response for the predator. The density-dependent Lotka-Volterra model is not commonly represented in ecology textbooks, but it is an educating step between basic Lotka-Volterra and Rosenzweig-MacArthur models. The predator isocline is identical to the basic model, but the prey isocline is a line reaching P = 0 at carrying capacity K, and the intercept at N is equal to the prey isocline of the basic Lotka-Volterra model. The density dependent Lotka-Volterra model always has a stable equilibrium point.

Function lotkapreyK set ups the model, plot displays the phase diagram and isoclines, and lines adds trajectories. The trajectories can be generated with traj.

Value

The function returns a "lotkapreyK" result object which contains the input parameters and isocline values. Function traj returns trajectories with given starting values.

Note

The parametrization vary: the one in this function is the same as used in my lectures for the basic Lotka-Volterra model.

Author(s)

Jari Oksanen

See Also

lotkacomp, lotkaprey, rmprey.

Examples

mod <- lotkapreyK(0.5, 0.01, 0.2, 0.1, K = 1000)
mod
op <- par(no.readonly = TRUE)
layout(matrix(c(1,1, 1, 1, 2, 2), ncol=2, byrow = TRUE))
plot(mod)
lines(mod, 200, 20)
plot(traj(mod, 200, 20))
par(op)

jarioksa/ecostudy documentation built on June 27, 2022, 6:03 a.m.