RAC {entropart} | R Documentation |

## Fit Distributions to Well-Known Rank Abundance Curves.

### Description

Observed distributions are fitted to classical RAC's.

### Usage

```
RAClnorm(Ns, CheckArguments = TRUE)
RACgeom(Ns, CheckArguments = TRUE)
RAClseries(Ns, CheckArguments = TRUE)
RACbstick(Ns, CheckArguments = TRUE)
```

### Arguments

`Ns` |
A numeric vector containing species abundances. |

`CheckArguments` |
Logical; if |

### Details

`SpeciesDistribution`

or integer vectors can be used to fit classical rank-abundance curves (RAC) of classical distributions: `"RAClnorm"`

for log-normal (Preston, 1948), `"RAClseries"`

for log-series (Fisher *et al.*, 1943), `"RACgeom"`

for geometric (Motomura, 1932) or `"RACbstick"`

for broken stick (MacArthur, 1957).
method returns the estimated parameters of the fitted distribution. The broken stick has no parameter, so the maximum abundance is returned.

### Value

A list (the parameters of distributions are returned only if the distribution has been fit):

`Rank` |
A numeric vector. The ranks of species in the fitted RAC. |

`Abundance` |
The abundance of species in the fitted RAC. |

`mu` |
The expectation of the log-normal distribution |

`sigma` |
The standard deviation of the log-normal distribution |

`alpha` |
Fisher's alpha in the log-series distribution |

`prob` |
The proportion of ressources taken by successive species in the geometric distribution |

`max` |
The maximum abundance in the broken-stick distribution |

### Note

Fisher's alpha is estimated to fit the log-series distribution. The estimation is done by the `fisher.alpha`

function of package `vegan`

. It may differ substantially from the estimation returned by `optimal.theta`

from package `untb`

.

### Author(s)

Eric Marcon <Eric.Marcon@agroparistech.fr>, Bruno Herault <Bruno.Herault@cirad.fr>

### References

Fisher R.A., Corbet A.S., Williams C.B. (1943) The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population. *Journal of Animal Ecology* 12: 42-58.

MacArthur R.H. (1957) On the Relative Abundance of Bird Species. *PNAS* 43(3): 293-295.

Motomura I. (1932) On the statistical treatment of communities. *Zoological Magazine* 44: 379-383.

Preston, F.W. (1948). The commonness, and rarity, of species. *Ecology* 29(3): 254-283.

### See Also

`rgeom`

, `rlnorm`

, `rCommunity`

, `plot.SpeciesDistribution`

### Examples

```
# Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest)
data(Paracou618)
# Ns is the total number of trees per species
Ns <- as.AbdVector(Paracou618.MC$Ns)
# Fitted parameters
RACln <- RAClnorm(Ns)
RACln$mu
RACln$sigma
RACgeom(Ns)$prob
RAClseries(Ns)$alpha
RACbstick(Ns)$max
```

*entropart*version 1.6-13 Index]