Pooled rarefaction
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Species Diversity and Richness offers a number of rarefaction methods. If you select Pooled Rarefaction the program undertakes individual-based rarefaction on the pooled data for all of the samples within the data set. First all of the samples are summed to form a grand sample. Then the average number of individuals in a single sample is calculated. The standard method for both the finite and infinite versions of the rarefaction curve of Heck et al. (1975) is then used to calculate the species number as the number of individuals increases. This procedure of calculating from the sum of all the samples only makes sense if it is assumed that all the samples selected for inclusion are from the same community.
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:
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. The above equations are are for sampling without replacement.
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