Single sample rarefaction
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This method estimates how the species number in a selected sample changes with the number of individuals. When selected, a dialog box appears where you select which sample to apply the method to, and whether the Finite or Infinite version of the rarefaction curve is required.
Sampling is assumed to be without replacement for the Finite version, and with replacement for the Infinite version. Generally it is the Finite version which is quoted by authors.
The tabulated output presents the change in estimated species richness with the number of individuals and the standard error of the estimate. The Graph tab shows the output graphically.
Rarefaction is a procedure for analyzing the number of species (species richness) among collections, when all collections are scaled down to the same number of individuals. This scaling procedure was termed 'rarefaction' by Sanders (1968) who used an incorrect equation which was corrected by Hurlbert (1971). The number of species, Sn, that can be expected from a random sample of n individuals, drawn without replacement from N individuals distributed among S species, is given by
where S is the total number of species found in the collection, and Ni is the number of individuals of the i th species.
The formula computes the expected number of species in a random sample of n individuals as the sum of the probabilities that each species will be included in the sample.
The variance of the estimate was given by Heck et al (1975) as:
The standard error is the square root of the variance.
These procedures calculate the number of combinations of the data and thus require a considerable amount of computation for large data sets. In addition to the estimated species richness the output also includes the standard deviation of the estimates.
Sampling is assumed to be without replacement for the Finite version, and with replacement for the Infinite version. Generally it is the Finite version which is quoted by authors.
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