On General Mathematical Constraints Applying to the Kinetics of Species Discovery during Progressive Sampling: Consequences on the Theoretical Expression of the Species Accumulation Curve

The “Species Accumulation Curve” accounts for the rate of increase of the number of recorded species during progressive sampling of an assemblage of species. Due to the usual incompleteness of samplings, the accurate extrapolation of the Species Accumulation Curve has become an essential tool to estimate the total species richness of a sampled assemblage and to predict the additional sampling effort required to obtain a given increase of sample completeness. In this perspective, important efforts have been devoted to improve the accuracy of the extrapolation of the Species Accumulation Curves. Substantial progress in this respect was achieved recently by considering a general mathematical relationship that constrains the theoretical expression of any kind of Species Accumulation Curves. Moreover, this general relationship proves having interesting corollaries applying specifically to the detailed process of species accumulation during progressive sampling.

Hereafter, I first derive these correlative relationships and then I show how they link together the variations of the numbers of species respectively recorded 1-, 2-, 3- …, x- times and their cumulative contributions to the Species Accumulation Curve. This, in turn, provides suggestive insights regarding the remarkably regulated mechanism of species discovery and accumulation during progressive sampling effort.