rmprey: Rosenzweig-MacArthur Predator-Prey Model

rmpreyR Documentation

Rosenzweig-MacArthur Predator-Prey Model

Description

The function sets up a Rosenzweig-MacArthur model of predator-prey relationship. The prey has density-dependent control, and predator has type II functional response.

Usage

rmprey(b, K, w, D, e, s)
## S3 method for class 'rmprey'
plot(x, xlim, ylim, arrows = 5, ...)
## S3 method for class 'rmprey'
lines(x, N, P, time = 100, step = 0.2, ...)
## S3 method for class 'rmprey'
traj(x, N, P, time = 100, step = 1, ...)

Arguments

b, K, w, D, e, s

Model parameters: see Details.

x

An rmprey result object.

xlim, ylim

Axis limits.

arrows

Number of trend arrows displayed in the graphs.

N, P

Initial prey and predator densities.

time, step

Total time span and time step for which trajectories are found.

...

Other parameters passed to graphical functions.

Details

The prey N and predator P population changes are given by equations:

dN/dt = b*N(1-N/K) - w*(N/(D+N))*P

dP/dt = e*w*(N/(D+N))*P - s*P

where b is the prey population growth rate, K is the prey carrying capacity, w is the attack rate, D is the handling time in in type II functional response, e is the production efficiency of the predator, and s is the predator mortality rate. Except for parameters K and D these are the same parameters as in the Lotka-Volterra predator-prey model (lotkaprey).

The current implementation is based on Stevens (2009). This is the main predator–prey model in Krebs (2009, p. 191–195). However, it seems that his graphics are conceptual rather than produced by rigorous mathematics, and cannot be exactly reproduced with the used functional response models.

Function rmprey set ups the model, and plot draws the phase diagram.

Value

Function rmprey returns an object of class "rmprey" with following items:

preyfun

A quadratic function giving the prey isocline.

invpreyfun

The inverse of preyfun that gives the (two) roots for given predator density, or NA if the roots are not real.

preyopt, preytop, preylimits

Descriptive statistics for the prey isocline: the location of the peak, the height of the peak, and the limits of the prey isocline. The limits are the real roots of rmprey or zero if the roots are negative.

prediso

The predator isocline.

b, K, w, s, e, D

Model parameters.

call

The function call.

Author(s)

Jari Oksanen

References

Krebs, C. J. (2009) Ecology. Benjamin Cummings. 6 ed., 655 p.

Stevens, M.H.H. (2009) A Primer of Ecology with R. Springer.

See Also

lotkaprey, lotkapreyK.

Examples

mod <- rmprey(0.8, 1000, 5, 400, 0.07, 0.2)
mod
op <- par(no.readonly = TRUE)
layout(matrix(c(1,1, 1,1, 2,2), ncol = 2, byrow=TRUE))
plot(mod)
lines(mod, 1000, 100)
plot(traj(mod, 1000, 100))
par(op)

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