A Universal Key to Rationally Select Which, Among Nonparametric Species Richness Estimators, Performs Best According to Each Particular Incomplete Sampling

Since most samplings of local species communities are bound to remain substantially incomplete for practical reasons, a wide variety of nonparametric estimators of the number of unrecorded species have been proposed over the past fifty years. Unfortunately, the distinct formulations of each of these estimators naturally lead to substantially divergent estimates. The will to try to select, in each case, the estimator expected to be the more accurate has long been carried out only on a purely empirical, even arbitrary, basis (as is evident from the extensive consultation of much of the past literature on estimating species richness of incompletely sampled communities). So that extrapolating the true species richness of a community from its incomplete survey has long remained quite unsatisfactory. Indeed, the definition of a truly rational procedure for selecting the most accurate (least-biased) estimator actually requires a solidly established theoretical framework, involving to conform, as best as possible, to the general mathematical characteristics of the Species Accumulation Function. Accordingly, unveiling, first of all, these mathematical characteristics of the Species Accumulation Function was a decisive step forward in this perspective. Thereby making it now possible to propose an objective key to rationally select the one, within the series of various estimators, which, depending on each particular sampling, happens to be the least biased in this particular case, thus providing the most accurate estimate of the number of still unrecorded species. And, consequently, making it possible, now, to deliver the best estimate of the true species richness of a local community, despite its being incompletely surveyed.