# Lotka-Volterra Competition Games

### Description

A pedagogical tool for learning about isoclines and stable equilibria.

### Usage

1 | ```
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.

### 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

1 | ```
LVCompGames() # Hit return in the console to see the trajectories.
``` |