Rarefaction

## Usage

```
rarefaction(object, ...)
index_baxter(x, ...)
index_hurlbert(x, ...)
# S4 method for matrix
rarefaction(object, sample = NULL, method = c("hurlbert", "baxter"), step = 1)
# S4 method for data.frame
rarefaction(object, sample = NULL, method = c("hurlbert", "baxter"), step = 1)
# S4 method for numeric
index_baxter(x, sample, ...)
# S4 method for numeric
index_hurlbert(x, sample, ...)
```

## Arguments

- object
A \(m \times p\)

`numeric`

`matrix`

or`data.frame`

of count data (absolute frequencies giving the number of individuals for each category, i.e. a contingency table). A`data.frame`

will be coerced to a`numeric`

`matrix`

via`data.matrix()`

.- ...
Currently not used.

- x
A

`numeric`

vector of count data (absolute frequencies).- sample
A length-one

`numeric`

vector giving the sub-sample size. The size of sample should be smaller than total community size.- method
A

`character`

string or vector of strings specifying the index to be computed (see details). Any unambiguous substring can be given.- step
An

`integer`

giving the increment of the sample size.

## Value

`rarefaction()`

returns a RarefactionIndex object.`index_*()`

return a`numeric`

vector.

## Rarefaction Measures

The following rarefaction measures are available for count data:

`baxter`

Baxter's rarefaction.

`hurlbert`

Hurlbert's unbiased estimate of Sander's rarefaction.

## Details

The number of different taxa, provides an instantly comprehensible
expression of diversity. While the number of taxa within a sample
is easy to ascertain, as a term, it makes little sense: some taxa
may not have been seen, or there may not be a fixed number of taxa
(e.g. in an open system; Peet 1974). As an alternative, *richness*
(\(S\)) can be used for the concept of taxa number (McIntosh 1967).

It is not always possible to ensure that all sample sizes are equal
and the number of different taxa increases with sample size and
sampling effort (Magurran 1988). Then, *rarefaction*
(\(E(S)\)) is the number of taxa expected if all samples were of a
standard size (i.e. taxa per fixed number of individuals).
Rarefaction assumes that imbalances between taxa are due to sampling and
not to differences in actual abundances.

## References

Baxter, M. J. (2001). Methodological Issues in the Study of Assemblage
Diversity. *American Antiquity*, 66(4), 715-725. doi:10.2307/2694184
.

Hurlbert, S. H. (1971). The Nonconcept of Species Diversity: A Critique and
Alternative Parameters. *Ecology*, 52(4), 577-586.
doi:10.2307/1934145
.

Sander, H. L. (1968). Marine Benthic Diversity: A Comparative Study.
*The American Naturalist*, 102(925), 243-282.

## See also

Other diversity measures:
`heterogeneity()`

,
`occurrence()`

,
`richness()`

,
`similarity()`

,
`simulate()`

,
`turnover()`