primer (version 1.1.1)

LVCompGames: Lotka-Volterra Competition Games

Description

A pedagogical tool for learning about isoclines and stable equilibria.

Usage

LVCompGames(Alpha=NULL, r1=.1, r2=.1, num=20, time=10, step=1)

Arguments

Alpha

a 2 x 2 matrix of coefficients; if NULL, then a sensible random matrix will be generated - fun for games.

r1

the intrinsic rate of increase for species 1 (isocline -- a solid line).

r2

the intrinsic rate of increase for species 2 (isocline -- a dashed line).

num

the desired number of random starting points for trajectories.

time

the number of time steps for each trajectory.

step

the number of time steps for which the integration is estimated (has no effect on accuracy, merely the smoothness of the line).

Value

First generates a plot of isoclines and initial points; the user is then prompted to "Hit <return>" in the console to see the trajectories. These will indicate the rate and path the trajectories, demonstrating, among other things, whether the equilibrium is stable.

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

# NOT RUN {
LVCompGames() # Hit return in the console to see the trajectories.
# }