Sample interpolation 
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This method estimates the number of species that would be observed for different numbers of samples ranging from zero to the total number of samples in the data set. To use this method all of the samples selected must come from the same community or habitat.
Some authors would refer to this method as a type of rarefaction. In this program we have used rarefaction only for methods based on numbers of individuals rather than samples.
The calculations use the method of Colwell et al (2004) which calculates the species accumulation using a binomial mixture model.
The method is based on the counts of species observed in 1, 2 .. H samples (Sj) where the total number of samples is H.
This method assumes without replacement.
For interpolation, there is an unbiased estimator E(h), the expected number after h samples, that is based on the counts sj, appropriately weighted by combinatorial coefficients.
Now Sobs, the total species number observed, is the sum of the Sj values.
Colwell et al (2004) show that
where the combinatorial coefficients αjk are defined by
or zero for j + h > H.
The standard errors are calculated using the estimated variance equation :
This is a highly conservative estimate of variance which assumes that the total number of unknown species that could eventually be caught is infinite. However, experience shows that conservative approaches to error are wise because of the dynamic and clumped nature of natural systems.
The upper and lower 95% errors are calculated as 1.96 times the standard deviations.
A typical example of the output is shown below:
