Rarefaction Calculator

The Calculator

Test data from Simberloff (1978), page 164.
Click "Calculate!" to run this example, or "Clear Inputs" to enter your own data. To enter several subsample sizes, give values for "From", "To" and "By", then hit "Add a Range".

You need a Java-enabled browser to run this program. Perhaps your browser has Java disabled?

How to Read/Write Files on Your Machine

The virtual clipboard was a clunky work around for the security that Java-enabled browsers impose (with good reason!) on web-programs. Provided you trust that you are getting an unmodified copy of this program from our website, you can save a copy on your machine so that data can be read from or written to files directly on your machine, without going through the network and virtual clipboard. This procedure only works for Netscape browsers.

Here's how:

The VC buttons should be replaced by Load and Save buttons which will operate directly on your files. Note: Your browser will ask you to grant permission to this "unsigned" applet, and you'll have to agree to this for it to work.

A Note on Pages

Some browsers limit the size of text windows, so this program allows for bigger input and output using multiple pages. Each page is limited to around 10000 characters. To see if you have filled a page, try typing more characters at the end of the window. When you copy/paste in and out of this program, you have to do so one page at a time; the program has no control over cut/paste, and so can't tell when your input is bigger than one page.

Virtual Clipboard (for large files)

The Virtual Clipboard lets you paste data into or copy data out of multi-page windows. The ---> VC and <--- VC buttons move data to and from the virtual clipboard. If you see a "Browse" button below, then your browser will also let you copy a file on your machine to the Virtual Clipboard. You can then paste it from the V.C. into the calculator's input windows.

Name of file:

Note: if you get a "Save As..." dialog box when viewing the virtual clipboard, it is because the data there is in a binary format (e.g. a PICT file saved from TreeToy). You should specify an appropriate name (e.g. myplot.pict instead of viewclip.php) before saving it.

The Virtual Clipboard is Brainless

Is your window full of garbage after pasting? Unfortunately, the Virtual Clipboard knows nothing about file formats, so cutting and pasting directly from an Excel file will fill your window with junk (ie. raw Excel file bytes). You can, however, copy from the open Excel worksheet to a text editor, then save as text in a new file which you can then copy to the Virtual Clipboard. You can also just save a copy of your Excel file in tab-delimited text format, and copy that file to the VC. The point of the VC is just to help work around the limitations on window size in Netscape, MS Explorer, and probably other browsers.

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What is Rarefaction?

The rarefaction method lets you compare the number of species found in two regions when the sampling effort differed. You would expect that greater sampling effort would yield a larger sample and more species, so you can't just compare the number of species found in each region. Rarefaction uses the data from the larger sample to answers the question "How many species would have been found in a smaller sample?". If you found n organisms in the less-sampled region, rarefaction takes hypothetical subsamples of n organisms from the more-sampled region, and calculates the average number of species in such subsamples. This average can be compared to the number of species actually found in the less-sampled region. (The method computes a variance and standard deviation to help you judge how significant any difference is.)

The program computes the rarefaction estimates for each collection, and for all collections lumped together.

The rarefaction method was proposed by Sanders (1968) , and corrected by Hurlbert (1971) and Simberloff (1972).

There is a full description of rarefaction on p. 330 of Krebs (1989).

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The Chao Estimator

Chao (1984) proposed a non-parametric estimator for species richness that takes the form:


When this formula is applied to a single collection, it is called the Chao-1 estimator (Colwell & Coddington, 1994). When applied to several collections, and "just once/twice" means "observed in just one/two collections", it is called the Chao-2 estimator (Chao 1987). In both cases, a standard deviation is computed using:

The program prints - 1 to indicate that b = 0 and the Chao estimator cannot be computed.

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The rarefaction method requires these inputs:

Kind of Input



number c the number of collections made
list of numbers Ni the number of organisms of each species found in the sampled region. If there is more than one collection, a zero should appear wherever a species was not found in a given collection. The data can be in order either by species within collection, or by collection within species. If the latter (ie. counts are in the order Sp1-Col1, Sp1-Col2, ... Sp1-ColN Sp2-Col1, Sp2-Col2, ... Sp2-ColN, ...) then make sure the "Species Count Order "option is checked.
number(s) n the size(s) of the hypothetical subsample(s) for rarefaction

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Chao, A.1984. Nonparametric estimation of the number of classes in a population. Scandinavian J. Stat. 11:265-270.

Chao, A.1987. Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43:783-791.

Colwell, R.K. & J.A. Coddington. 1994. Estimating terrestrial biodiversity through extrapolation. Phil. Trans. Royal Soc. London (Ser. B) 345:101-118.

Krebs, C. J. 1989. Ecological Methodology. Harper &Row, New York.

Hurlbert, S.H. 1971. The non-concept of species diversity: a critique and alternative parameters. Ecology 52:577-586.

Sanders, H.L. 1968. Marine benthic diversity: a comparative study. Am. Natur. 102:243-282.

Simberloff, D. S. 1978. Use of rarefaction and related methods in ecology. In K.L. Dickson, J. Cairns, Jr., and R.J. Livingston (eds.), Biological Data in Water Pollution Assessment: Quantitative and Statistical Analyses pp. 150-165. American Society for Testing and Materials STP 652, Philadelphia.

Simberloff, D. S. 1972. Properties of the rarefaction diversity measurement. Am. Natur. 106:414-418.

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This calculator is loosely based on the program RAREFACT.FOR, written by Charles J. Krebs

This Java and HTML/PHP web page is by John Brzustowski.

Please send me any comments at: junkjbrzusto@ualberta.cacaca but removing the obvious parts

The source code is available in this .ZIP archive.

To read about why software should be free, see


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