Species Richness Calculator

Species richness S is the raw count of species detected in a defined area or sample, and it weights every species equally regardless of abundance. Because rare species are found only with effort, raw S rises with the number of individuals examined, so comparisons between samples of unequal size are meaningless without correction. Margalef's index, D = (S-1)/ln(N), divides by the natural log of individual count, the form implied by a log-series abundance distribution; typical field values run from about 1 in depauperate sites to 6 or more in species-rich tropical plots. Menhinick's index, D = S/sqrt(N), assumes instead that species accumulate with the square root of sampling effort and usually falls between roughly 0.5 and 5. Neither index fully removes sample-size dependence, because each is exact only under the abundance distribution it assumes. Rarefaction is the more defensible correction: it computes the expected number of species in a random subsample of n individuals drawn from the observed community, so two samples can be compared at a common n. Hurlbert's exact expression uses hypergeometric probabilities that a species is missed; the closed form used here is an approximation that effectively treats species as equally abundant and will overstate richness in communities dominated by a few species. Rarefaction also cannot extrapolate beyond the observed sample, which is why nonparametric estimators such as Chao1, built from counts of singletons and doubletons, are usually reported alongside it.

Counting species is as old as floristic survey work, but the sample-size problem was formalized only in the mid twentieth century. Ramon Margalef, the Catalan ecologist who shaped modern Mediterranean plankton ecology, proposed the (S-1)/ln(N) form in 1958 while adapting Shannon's information theory to phytoplankton communities. Edward Menhinick published the square-root alternative in Ecology in 1964 from work on insects sampled in herbaceous vegetation, arguing that the square root tracked observed accumulation better than the logarithm for his data. Both were quick to compute by hand, which mattered a great deal before ecologists had routine access to computing. Rarefaction came out of deep-sea benthic ecology. Howard Sanders introduced it in 1968 to compare dredge hauls of wildly different size, though his original formulation was biased. Stuart Hurlbert corrected it in 1971 with the exact hypergeometric expectation, and Daniel Simberloff derived the same result independently at about that time. Anne Chao published her singleton-and-doubleton lower-bound estimator in 1984, and the 2001 review by Nicholas Gotelli and Robert Colwell separated individual-based from sample-based accumulation curves and became the standard methodological reference. Chao and Lou Jost extended the framework in 2012 to compare samples at equal coverage rather than equal size, now the preferred practice for uneven sampling.