Fits models to species abundance data (D.A. Murray).

### Options

`PRINT` = string tokens |
Controls printed output (`summary` , `estimates` , `fittedvalues` ); default `summ` , `esti` |
---|---|

`MODELTYPE` = string token |
The model or distribution fitted to the data (`logseries` , `plognormal` , `negativebinomial` , `geometric` , `zipf` , `mandelbrotzipf` ); default `logs` |

`GROUPS` = factor |
Defines the groups if there is more than one sample |

`LOGBASE` = string token |
Log base to use to form the octaves for the logseries, Poisson log-Normal and negative binomial distributions (`two` , `ten` ); default `two` |

`PLOT` = string token |
Plots the fitted values (`fittedabundance` , `rankabundance` ); default `fitt` |

### Parameters

`INDIVIDUALS` = variates |
Number of individuals per species |
---|---|

`SPECIES` = variates |
Number of species |

`ESTIMATES` = variates |
Saves the model estimates |

`EGROUPS` = factors |
Saves the grouping of the estimates |

### Description

`ECFIT`

provides a range of distributions and models that can be used to describe species abundance data. For the log series, Poisson log-Normal and negative binomial distributions the species abundance data are grouped into “octaves” using a logarithmic scale. These distributions are then fitted using the `DISTRIBUTION`

directive using the octave classes. The geometric series, Zipf and Zipf-Mandelbrot models are fitted to the observed abundance data using the non-linear regression facilities.

The numbers of individuals per species are specified using the `INDIVIDUALS`

parameter. The `SPECIES`

parameter specifies a variate containing the number of species for the associated number of individuals specified in the corresponding element of `INDIVIDUALS`

. `SPECIES`

can be omitted if each of the values in `INDIVIDUALS`

corresponds to one species. The `GROUPS`

option can be used to fit models for different samples.

The distribution or model to be fitted to the data is specified by the `MODELTYPE`

option. The log base for forming the octaves for the log series, Poisson log-normal and negative binomial distributions can be supplied using the `LOGBASE`

option. The default is to use log base 2, i.e. representing doubling in species abundance. The parameter estimates from the fitted model can be saved using the `ESTIMATES`

parameter. The `EGROUPS`

factor saves a factor indicating the group strucure of the estimates.

The `PRINT`

option controls printed output, with settings:

`summary` |
summary of the analysis, |
---|---|

`estimates` |
the parameter estimates, |

`fittedvalues` |
the fitted values. |

The `PLOT`

option can be used to produce a plot of the fitted model or distribution. For the geometric series, Zipf and Zipf-Mandelbrot models, the fitted model can also be displayed on a rank/abundance plot on the log-scale.

Options: `PRINT`

, `MODELTYPE`

, `GROUPS`

, `LOGBASE`

, `PLOT`

.

Parameters: `INDIVIDUALS`

, `SPECIES`

, `ESTIMATES`

, `EGROUPS`

.

### Method

The log series, negative binomial and poisson log normal are fitted using the `DISTRIBUTION`

directive.

For the geometric series the abundances are ranked from the most to least abundant and fitted using `FITNONLINEAR`

where the series is given by

*a _{i}* =

*N*/ (1 – (1 –

*k*)

^{S}) ×

*k*× (1 –

*k*)

^{i-1}

where *a _{i}* is the total number of individuals in the

*i*th species,

*N*is the total number of individuals,

*k*is the proportion of remaining niche space, and 1 / (1 – (1 –

*k*)

^{S}) is a constant that ensures ∑

_{i}

*a*=

_{i}*N*.

The Zipf and Zipf-Mandelbrot models are fitted using `FITNONLINEAR`

. The Zipf model is given by

*A _{i}* =

*A*

_{1}×

*i*

^{-γ}

where *A*_{1} is the fitted abundance of the most abundant species, and γ is a constant representing the average probability of the appearance of a species.

The Zipf-Mandelbrot is an extension of the Zipf model and is expressed as

*A _{i}* =

*A*

_{1}× (

*i*+ β)

^{-γ}

where *A*_{1} and gamma are as before, and beta is a constant.

### Action with `RESTRICT`

If a parameter is restricted the models will be fitted using only those units included in the restriction.

### References

Kempton, R.A. & Taylor, L.R. (1974). Log-series and log-normal parameters as diversity determinants for the Lepidoptera. *Journal of Animal Ecology*, 43, 381-399

Magurran, A.E. (2003). *Measuring Biological Diversity*. Blackwell, Oxford.

Wilson, J.B. (1991). Methods for fitting dominance/diversity curves. *Journal of Vegetation Science*, 2, 35-46

### See also

Commands for: Ecological data.

### Example

CAPTION 'ECFIT example'; STYLE=meta VARIATE [VALUES=1...18,20...23,25,28,29,33,34,38,39,40,42,48,51,52,53,58,61,\ 64,69,73,75,83,87,88,105,115,131,139,173,200,223,232,294,323,603,\ 1799] Individuals VARIATE [VALUES=37,22,12,12,11,11,6,4,3,5,2,4,2,3,2,2,4,2,4,4,1,1,1,2,\ 2,2,2,1,1,3,2,2,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]\ NumSpecies ECFIT [PRINT=summary,estimates; MODELTYPE=logseries]\ Individuals; SPECIES=NumSpecies ECFIT [PRINT=summary,estimates; MODELTYPE=negativebinomial]\ Individuals; SPECIES=NumSpecies