Basic Theoretical Arguments Advocating Jackknife-2 as Usually being the Most Appropriate Nonparametric Estimator of Total Species Richness

A lot of nonparametric estimators of the number of unrecorded species after partial sampling of an assemblage of species, have been proposed in the literature. Unfortunately, these different types of estimators provides substantially divergent predictions. While empirical comparisons have failed to consistently select in favour of one among all these estimators, a new approach, based on more theoretical ground, has proven that among three of the most commonly used nonparametric estimators, Chao, Jackknife-1 and Jackknife-2, the latter was the best choice in most cases while Chao or Jackknife-1 should preferably be restricted to samplings approaching completeness. Here, I propose an alternative approach, aiming also at discriminating between the same three estimators on the basis of another theoretical argument: The necessary compliance with the required “rule of additivity”, according to which, if an assemblage of species is made of several, distinct groups of species, the estimation of species richness for the whole assemblage should be exactly the sum of the estimations of richness for each group of species. Referring to this rule of additivity, the Jackknife series of estimators (and in particular Jackknife-2 when samples remain far from completeness), proves, once again, being satisfactory in full generality. This strengthens the estimators of the Jackknife series as being particularly appropriate to evaluate, in most cases, the number of unrecorded species of a partially sampled assemblage and the corresponding total species richness of the assemblage.