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## Formula

Since we do not know how many species there were in either community we do not know if any more species would have been found if our second survey had observed more individuals than it actually did. But, using the hypergeometric model, we can estimate how many species we would expect to observe among a subsample, of m observations, from our larger survey of n observations (so n > m).

#### Algebraically speaking -

E(sm) = Σ[1 - a/b]
Where:
• E(sm) is the expected (mean) number of species to be found in a random sample of m individuals from your larger survey.
• a is the number of combinations of m individuals that can be taken from a set of n - ni individuals, or n-niCm or [n - ni]!/[m!({n - ni}-m)!]
• b is the number of combinations of m individuals that can be taken from a set of n individuals, or nCm or or n!/[m!(n-m!)].
• ni is the number of individuals observed which belong to the ith species, so the summation is for all the species observed in the larger survey.

Notice that this only enables us to estimate the number of species we expect to observe if we know how many organisms represented each species in our larger survey.

Also the model only applies for individual-based rarefaction. If samples are taken randomly rather than individuals, then one must use Monte-Carlo resampling to produce the rarefaction curves (See Gotelli & Colwell (2001))

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