Plots species accumulation curves for samples or individuals (D.A. Murray).

### Options

`PRINT` = string token |
Controls printed output (`summary` ); default `summ` |
---|---|

`CURVE` = string token |
Controls the type of species accumulation curve (`collector` , `random` , `coleman` ); default `coll` |

`PLOT` = string token |
Controls plot type (`sac` ); default `sac` |

`METHOD` = string token |
Controls collector curve when data supplied in variate or factor with groups (`individual` , `sample` ); default `samp` |

`GROUPS` = factor |
Grouping factor for samples when data are supplied in variate or factor of individuals |

`NPERMUTATIONS` = scalar |
A scalar defining the number of permutations to be performed for the random method; default 100 |

`SEED` = scalar |
Seed for random number generator; default 0 |

`SCREEN` = string token |
Whether to clear screen before displaying the graph (`keep` , `clear` ); defaul `clea` |

`WINDOW` = scalar |
Window for the graph; default 1 |

`KEYWINDOW` = scalar |
Window number for the key (zero for no key); default 2 |

`PEN` = scalar |
Pen number to draw the curve; default 1 |

### Parameters

`DATA` = variates, factors, matrices or pointers |
For individual-based collector curves, a variate or factor containing the individuals in the order they were collected; for sample-based species accumulation curves, a pointer or matrix specifying the number of individuals for each species for different sites/samples |
---|---|

`RICHNESS` = variates |
Saves the observed number of species for the collector method and the average or expected number of species at each sample size for the Coleman and random methods |

`VARIANCE` = variates |
Saves the variance for the richness (Coleman and random methods only) |

### Description

Species accumulation curves show the rate at which new species are found within a community, and can be extrapolated to provide an estimate of species richness. The simplest type of species accumulation curve is the *collectors* curve. This plots the cumulative number of species recorded as a function of sampling effort (i.e. number of individuals collected or cumulative number of samples). The order in which samples are included in a species accumulation curve will influence the overall shape. A smooth accumulation curve can be produced by repeating a process of randomly adding the samples to the accumulation curve and then plotting the mean of these permutations. `ECACCUMULATION`

can be used to produce these types of species accumulation curves, and can plot a *Coleman* curve of the expected number of species based on the method of Coleman *et al.* (1982); see *Method*.

For sample-based species accumulation curves, the data can be supplied using the `DATA`

parameter, either as a matrix where the rows contain the number of individuals for each species and the columns specify the different samples or sites, or as a pointer to variates containing samples for the individuals for each species. Alternatively, the individual species numbers or labels can be supplied in either a variate or factor using the `DATA`

parameter while the samples are identified by supplying a grouping factor using the `GROUPS`

option. Individual-based species accumulation curves can be formed using the collector method, where the individual species numbers or labels are specifed in either a variate or factor using the `DATA`

parameter. The species numbers or labels must be specified in the order in which they were collected within the variate or factor. Different samples of individuals can be plotted on the same graph by supplying a grouping factor using the `GROUPS`

option and specifying the individual setting of the `METHOD`

option. For the collector curve the observed number of species can be saved using the `RICHNESS`

parameter. For the random and Coleman curves the average and expected number of species and associated variance can be saved using the `RICHNESS`

and `VARIANCE`

parameters respectively. The type of species accumulation curve (collector, random or Coleman) is specified using the `CURVE`

option. If the collector curve is chosen and the data have been supplied using the individual values with a grouping factor, the `METHOD`

option can be used to choose whether to produce a sample-based plot or a plot of the individual-based curves. The number of permutations used for the random method can be supplied using the `NPERMUTATIONS`

option, by default 100 permutations are used. The `SEED`

option specifies the seed to use for the sub-sampling without replacements. The default value of zero continues an existing sequence of random numbers or, if the generator has not yet been used in this run of Genstat, initializes the generator automatically.

The `PRINT`

option controls printed output, with settings:

`summary` |
the species richness and variance (for Coleman and random methods). |
---|

A plot of the species accumulation curve can be specified using the `sac`

setting of the `PLOT`

option. The graphical display can be controlled using the `SCREEN`

, `WINDOW`

, `KEYWINDOW`

and `PEN`

options. By default the curves are produced in window 1 using pen 1 and drawn on a new screen.

Options: `PRINT`

, `CURVE`

, `PLOT`

, `METHOD`

, `GROUPS`

, `NPERMUTATIONS`

, `SEED`

, `SCREEN`

, `WINDOW`

, `PEN`

.

Parameters: `DATA`

, `RICHNESS`

, `VARIANCE`

.

### Method

For the collector curve the samples or individuals are added in the order they appear in the data. The random method finds the mean number of species and variance from random permutations using sub-sampling without replacement.

For the Coleman curve the expected number of species is calculated by:

*s*_{α} = *S* – ∑_{i=1…S} (1 – α)^{ni}

where *S* is the number of species, *n ^{i}* is the number of individuals belonging to

*i*th species and

*α*is the relative area

α = *a* / ∑*a _{k}*

The variance is estimated by

*v _{α}* = ∑

_{i=1…S}(1 – α)

^{ni}– ∑

_{i=1…S}(1 – α)

^{2 × ni}

Further details of this method are given in Coleman *et al.* (1982).

### Action with `RESTRICT`

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

### References

Coleman, B.D., Mares, M.A. Willig, M.R. & Hsieh, Y,-H. (1982). Randomness, area, and species richess. *Ecology*, 63, 1121-1133.

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

### See also

Commands for Ecological data.

### Example

CAPTION 'ECACCUMULATION examples',\ 'Individual-based collectors curve'; STYLE=meta,minor FACTOR [NVALUES=10; LEVELS=4; LABELS=!t('A','G','X','Y')]\ individuals; VALUES=!T(G,G,A,G,X,Y,G,Y,G,G) ECACCUMULATION [CURVE=collector] individuals CAPTION 'Sample-based random and coleman curves',\ !t('Data from Maguaran (2003).',\ 'Abundance of carabid beetles sampled in hedgerows.');\ STYLE=minor,plain VARIATE [NVALUES=20]\ S1; VALUE=!(0,0,1,0,2,0,6,1,0,0,0,1,1,0,0,1,0,0,0,0) & S2; VALUE=!(0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0) & S3; VALUE=!(6(0),4,13(0)) & S4; VALUE=!(5(0),2,3,3,6(0),2,5(0)) & S5; VALUE=!(6(0),4,4(0),4,0,0,1,5(0)) & S6; VALUE=!(0,0,2,0,1,0,3,2,1,1,4,0,0,1,1,0,1,0,0,0) & S7; VALUE=!(6(0),2,0,0,0,1,9(0)) & S8; VALUE=!(6(0),1,0,1,11(0)) & S9; VALUE=!(16(0),1,0,0,0) & S10; VALUE=!(0,0,2,0,2,0,1,1,0,0,0,1,0,0,0,1,0,0,2,0) & S11; VALUE=!(12,5(0),5,13(0)) & S12; VALUE=!(0,1,1,1,0,0,11,5,0,1,2,9,6(0),1,0) & S13; VALUE=!(32,0,0,1,9(0),1,0,0,0,0,1,0) & S14; VALUE=!(2,0,2,0,0,1,3,0,0,0,1,9(0)) & S15; VALUE=!(4(0),1,0,9,3,0,0,0,1,0,0,0,0,0,1,1,0) & S16; VALUE=!(0,0,0,0,2,1,2,5(0),1,5(0),1,1) POINTER beetle; VALUE=\ !p(S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12,S13,S14,S15,S16) ECACCUMULATION [PRINT=*; CURVE=coleman] beetle ECACCUMULATION [PRINT=*; CURVE=random; SCREEN=keep; PEN=2; SEED=133273] beetle ECACCUMULATION [PRINT=*; CURVE=collector; SCREEN=keep; PEN=3] beetle