# Environmental fit for a single dataset

### Description

`all_environmental_fit`

calculates the best expressions for colonization
and extinction rates given their dependency on environmental variables.

`greedy_environmental_fit`

calculates expressions for colonization and
extinction rates given their dependency on environmental variables using a
greedy algorithm.

`custom_environmental_fit`

calculates the m.l.e.
of the parameters describing the relationship between colonization and
extinction rates and environmental variables.

### Usage

1 2 3 4 5 | ```
all_environmental_fit(dataset, vector, env, c, e, aic)
custom_environmental_fit(dataset, vector, params, exp1, exp2)
greedy_environmental_fit(dataset, vector, env, c, e, aic)
``` |

### Arguments

`dataset` |
A single dataset. |

`vector` |
A vector indicating the columns with presence-absence data. |

`env` |
The names of the environmental variables to be considered. |

`c` |
Tentative colonization rate. |

`e` |
Tentative extinction rate. |

`aic` |
Tentative AIC to be improved by the optimizer. |

`params` |
A vector with priors of the parameters in exp1 and exp2. |

`exp1` |
Expression for colonization. |

`exp2` |
Expression for extinction. |

### Details

`all_environmental_fit`

calculates all the combinations of
parameters, that increase exponentially with the number of parameters. We
advise to keep low the number of parameters.

`greedy_environmental_fit`

adds sequentially environmental variables
to the expressions of colonization and extinction rates and fix one at a
time until termination, when only adding one variable does not improve the
AIC of the last accepted model.

### Value

A list with three components: a expression for colonization, a expression for extinction and the output of the optimization function, or the output of the optimization function in the custom environmental fit.

### Note

AIC is recomended to be higher than the AIC of the most simple model (i.e. not including environmental variables).

### See Also

`rates_calculator`

### Examples

1 2 3 4 5 6 7 8 9 10 | ```
## Not run:
all_environmental_fit(idaho[[1]],3:23,c("idaho[[2]]$TOTAL.ppt",
"idaho[[2]]$ANNUAL.temp"),0.13,0.19,100000)
greedy_environmental_fit(idaho[[1]],3:23,c("idaho[[2]]$TOTAL.ppt",
"idaho[[2]]$ANNUAL.temp"),0.13,0.19,100000)
## End(Not run)
custom_environmental_fit(idaho[[1]], 3:23, c(-0.00497925, -0.01729602,
0.19006501, 0.93486956), expression(params[1] * idaho[[2]]$TOTAL.ppt[i] +
params[3]), expression(params[2] * idaho[[2]]$ANNUAL.temp[i] + params[4]))
``` |