Estimating total species richness: Fitting rarefaction by asymptotic approximation

Abstract

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.

rarestR: An R package using rarefaction metrics to estimate α-diversity (species richness) and β-diversity (species shared) for incomplete samples

“…The tes()function calculates the total expected species based on asymptotic parametric curve fittings. Unlike traditional curvefitting approaches that depend on specific species abundance distributions (Walther and Moore 2005), TES provides flexibility and robust applicability across various species abundance distribution models (Zou et al 2023). TES is hence comparable with nonparametric estimators such as Chao 1 and ACE (e.g., in vegan package) (Chao 1984, Chao andLee 1992).…”

“…Zou et al (2023) proposed curve-fitting for the relationship between the rarefaction curve (ES) and the standardized sample size (m), either based on a 4-parameter Weibull model (eq. 7) or a 3-parameter logistic model (eq.…”

Wild pollinator communities benefit from mixed cultivation of oilseed rape and milk vetch

“…All statistical analysis was conducted in R 4.2.2 (R Core Team, 2022). We calculated rarefied species using the ‘vegan’ package (Oksanen et al., 2019) and the total expected species richness using the R function “TES()” (Zou et al., 2023). Models were selected using the “dredge()” function in the ‘MuMIn’ package (Barton, 2019).…”

“…In addition, we calculated the total expected species richness (TES) to evaluate sampling completeness. TES is based on the asymptotic parametric approximation models for the extrapolation of individual-based rarefaction that were recently developed by Zou et al (2023), which are robust in estimating the species richness of incompletely sampled communities (Zou et al, 2023). The total number of expected species (TES) for this region was 77.54 ± 34.10.…”

divraster: an R package to calculate taxonomic, functional and phylogenetic diversity from rasters

“…alpha diversity). It plays a crucial role in the effective assessment and conservation of biodiversity as monitoring species across different spatial scales helps define highly diverse places as priority areas (Scott et al 1987, Weber et al 2004, Jenkins et al 2013, Zou et al 2023). Besides alpha diversity, knowing species composition variation (i.e.…”