Estimating total species richness: Fitting rarefaction by asymptotic approximation

Estimating the number of species in a community is important for assessments of biodiversity. Previous species richness estimators are mainly based on nonparametric approaches. Although parametric asymptotic models have been applied, they received limited attention due to specific limitations. Here, we introduce parametric models fitting the probability-based rarefied species richness curve that allow us to estimate the "Total Expected Species" (TES) in a community based on species' abundance data. We develop two approaches to calculate TES (termed "TESa" and "TESb"), based on two slightly different mathematical assumptions regarding Expected Species (ES) models. We provide R functions to calculate both these estimation approaches and their standard deviation. The function also enables users to visualize the estimation. We test the performance of TESa, TESb, and their average (TESab) across simulated and empirical data, and compare their bias, precision, and accuracy with other commonly used, nonparametric species richness estimators: the bias-corrected (bc-)Chao1 and the abundance-based coverage estimator (ACE). Simulation reveals that in small samples TESa shows a tendency to overestimate and TESb to underestimate overall species richness. TESab performs well in bias, precision, and accuracy when compared with (bc-)Chao1 and ACE estimators. Results from empirical data show that the variance generated from TES estimates is comparable with that for (bc-)Chao1 and ACE. Our study demonstrates that rarefaction theory in combination with parametric approximation models provides a valuable new approach to estimate the species richness of incompletely sampled communities. Robust estimates are likely to be obtained where the observed number of species is greater than half of the TES estimation. When the ratio of TESa to the observed richness is >> 2, we suggest the use of TESb or TESab. Although more comprehensive comparisons with other estimators are suggested, we encourage researchers to consider the TES approach in their biodiversity studies as a complement to current existing estimators.