# Two-species model of the storage effect

### Description

Simulates a fluctuating environment over time, and two species' responses to the environment, after Chesson (1994).

### Usage

1 2 3 |

### Arguments

`alpha` |
a vector of length 2; the negative effects of all individuals (of both species) on each population – typically different among species. |

`d` |
disturbance rate; the proportion of all individuals killed at each time step. |

`years` |
numbers of time steps |

`N0` |
vector of length 2; initial abundances. |

`w` |
vector of length 2; average fitnesses for each species. |

`env.var` |
degree of environmental variability. |

`specialization` |
determines the narrowness of each species fitness response. |

`spread` |
determines how far apart the peak fitness responses are. |

`type` |
determines the form of |

### Details

The argument `type`

controls the value of *e^C*, the effect of competition on
reproduction, where the annual finite rate of increase is *R=e^(E-C)*. `type = 1`

causes *e^C
= alpha[i] N[J,i]*, that is, a
species-specific fixed fraction of juveniles that depends on each
species response to competition. This is illustrated in a for-loop in Stevens (2009,
*Ch. 9, Storage Effect, Simulating Dynamics*). Any other value for `type`

results
in the same negative effect on both species that depends on the number
of juveniles and the disturbance rate.

### Value

Returns a list of length one, for use with `ode`

in the `deSolve`

package.

`Component 1 ` |
vector of the state variables, y. |

### Author(s)

Hank Stevens <HStevens@muohio.edu>

### References

Chesson, P.L. (1994) Multispecies competition in variable
environments. *Theoretical Population Biology*, **45**, 227–276.

Stevens. M.H.H. (2009) *A Primer of Ecology with R*. Use R! Series. Springer.

### See Also

`succniche`

### Examples

1 2 3 4 5 6 7 8 9 10 | ```
out <- chesson(years=50)
layout(matrix(1:4, nc=2))
matplot(out[["time"]], out[["Ns"]], type='l', lty=c(1:3),
xlab="Time", ylab="N", log="y")
plot(out[["time"]][-1], out[["env"]], type='l',
xlab="Time", ylab="Environment")
matplot(out[["env"]], out[["Es"]], xlab="Environment",
ylab="Density-independent reproduction")
matplot(out[["env"]], out[["Rs"]], xlab="Environment",
ylab="Annual growth rate")
``` |