Theoretical Derivation of a Bias-reduced Expression for the Extrapolation of the Species Accumulation Curve and the Associated Estimation of Total Species Richness

Abstract

Under-sampling becomes the current situation for an increasing part of biodiversity surveys, as more and more speciose assemblages and increasingly complex taxonomic groups are progressively addressed. Accordingly, (i) extrapolating the Species Accumulation Curve and (ii) estimating the total species richness of partially-sampled species assemblages (or taxonomic-groups) both become major issues for many naturalists nowadays. Numerous different solutions have been proposed to address these issues. Yet, no general consensus has been reached regarding which particular solution among them should be preferred according to each case. This unsatisfactory situation follows from the empirical nature of traditional approaches, especially regarding the extrapolation of the Species Accumulation Curve. Fortunately, reconsidering the problem on decidedly more theoretical basis, including the consideration of general mathematical relationships universally constraining the expression of any theoretical (or rarefied) Species Accumulation Curves, allows a more relevant modeling for the extrapolation of species accumulation. In turn, this theoretical approach provides a rational key to select the more appropriate, less biased type of species-richness estimator and the associated, less biased expression for the extrapolation of the Species Accumulation Curve, according to the context of sampling. In particular, the wide relevance of the series of ‘Jackknife-type’ estimators is highlighted (as had been already argued for specific cases, on semi-empirical basis). In practice, selecting the less biased extrapolation of the Species Accumulation Curve allows to forecast the supplementary sampling effort necessary to reach a given increase of sampling completeness more accurately than the usual procedures, involving arbitrarily chosen empirical models.