Extrapolating the species accumulation curve for incomplete samplings: how to estimate accurately the number of missing species and reliably forecast the extra sampling effort required to reduce this number

While approaching or even reaching total completeness remains the ideal goal of any species inventory, incomplete samplings are deemed to become more often the rule, as multiple priorities of investigations accumulate and new taxonomic groups are addressed that are significantly more difficult to cope with (such as (micro-) invertebrates, for example). However, once post-operated appropriately, incomplete samplings may provide far more data than it would seem and it is indeed possible to obtain valuable extra information from a reliable mode of extrapolation of the so-called Species Accumulation Curve. In fact, numerous tools designed for the exploitation of incomplete samplings have already been proposed in the literature but the concern, with these numerous different tools, is precisely the disparity of the results they provide respectively. Fortunately, the recent derivation of a specific mathematical relationship strongly constrains and restricts the range of relevant formulations of the Species Accumulation Curve. This, in turn, allows for efficient selection among the various tools proposed, thus highlighting the more reliable type of extrapolation of the Species Accumulation Curve beyond the ongoing sampling. Accordingly, this makes it possible: (i) to estimate, with fairly good accuracy, the number of missing species that escaped sampling and hence the total species richness of the sampled assemblage; `` (ii) to extrapolate the (gradually slowing) pace at which new species are expected to add progressively to the list of already recorded species, according to the level of additional sampling effort and, thus, to objectively gauge the expected gain in terms of newly collected species according to the degree of additional sampling effort required. All these are essential information to help making a rational decision about the opportunity either to continue or to stop sampling operation, given (i) the ratio between the expected gain in new species and the required additional sampling effort, (ii) the degree of completeness of the current sample (with respect to the estimated total species richness), (iii) the usual co -occurrence of several other competing priorities of investigations, involving either other sites and/or other taxonomic groups to be further surveyed. Hereafter, I illustrate the implementation of the suggested procedure, aiming at reliably extrapolating the Species Accumulation Curve so as to ``extend'' numerically already achieved samplings. For this purpose, I consider a recent survey of the gall -forming fauna of the ``Ecrins National Park'', located in south-west French Alps, including partial samplings of each of the four main orders of gall -forming arthropods: Acari-Trombidiformes, Hemiptera, Diptera and Hymenoptera.