Across sample rarefaction
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This method estimates the species richness of every sample in you data set for a standard number of individuals. By standardising on a constant number of individuals it is possible to compare the samples for a standardised effort and thus determine if species richness varies between samples. This approach is particularly useful when it is clear from the species accumulation curve that species sampling for one or more samples is far from complete.
Species Diversity and Richness uses as the standard number of individuals the minimum number observed in any one of the samples in the data set. It is therefore essential to ensure that you do not apply this approach to a data set that includes samples comprising only one or a few individuals!
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:
This method estimates the species richness of each sample if they all contained the same number of individuals. It is therefore a way of allowing for different sampling effort if the total number of individuals in each sample can be assumed be give a measure of effort. All of the selected samples must come from the same habitat or community.