Extrapolation of the Species Accumulation Curve for Incomplete Species Samplings: A New Nonparametric Approach to Estimate the Degree of Sample Completeness and Decide when to Stop Sampling

Abstract

Incomplete species samplings are deemed to remain the common practice in those groups of animals, such as small or micro- invertebrates, with numerous species that often are more or less difficult to detect in the field. Thus, extrapolating the Species Accumulation Curve as far as possible beyond the actual sample size may thus serve as a useful (although imperfect) surrogate to the desired, but practically inaccessible, complete samplings. In this context, several kinds of theoretical or empirical models for the Species Accumulation Curve and also a lot of estimators of the asymptotic limit of the Curve (i.e. total species richness) have been proposed. The practical issue is now to select appropriately among these numerous, different propositions. Here, I show that realistic Species Accumulation Curves are constrained to respect a general mathematical relationship, which, in turn, may serve to discriminate and select among the available models of Species Accumulation Curves and, as well, among the different formulations of the estimators of species richness that are commonly referred to. As a result of the application of this screening approach, it follows that, for the generality of cases (i.e. ratio singletons/doubletons larger than 0.6), a specific formulation of the Species Accumulation Curve (bi-hyperbolic with exponents -1 and -2 for sample size) complies at best. Accordingly, the more appropriate estimator of total species richness is Jackknife-2. Only when the ratio singletons/doubletons happens to fall beneath 0.6, Chao estimator may then be preferred. This is the case when samplings closely approach exhaustivity or when they address assemblages with unusually homogeneous abundances of species.