Rarefaction and extrapolation with beta diversity under a framework of Hill numbers: The iNEXT.beta3D standardization

Abstract

Based on sampling data, we propose a rigorous standardization method to measure and compare beta diversity across datasets. Here beta diversity, which quantifies the extent of among‐assemblage differentiation, relies on Whittaker's original multiplicative decomposition scheme, but we use Hill numbers for any diversity order q ≥ 0. Richness‐based beta diversity (q = 0) quantifies the extent of species identity shift, whereas abundance‐based (q > 0) beta diversity also quantifies the extent of difference among assemblages in species abundance. We adopt and define the assumptions of a statistical sampling‐model as the foundation for our approach, treating sampling data as a representative sample taken from an assemblage. The approach makes a clear distinction between the theoretical assemblage level (unknown properties/parameters of the assemblage) and the sampling data level (empirical/observed statistics computed from data). At the assemblage level, beta diversity for N assemblages reflects the interacting effect of the species abundance distribution and spatial/temporal aggregation of individuals in the assemblage. At the data level, observed beta (= gamma/alpha) diversity depends not only on among‐assemblage differentiation but also on sampling effort/completeness, which in turn induces dependence of beta on alpha and gamma diversity. How to remove the dependence of richness‐based beta diversity on its gamma component (species pool) has been intensely debated. Our approach is to standardize gamma and alpha based on sample coverage (an objective measure of sample completeness). For a single assemblage, the iNEXT method was developed, through interpolation (rarefaction) and extrapolation with Hill numbers, to standardize samples by sampling effort/completeness. Here we adapt the iNEXT standardization to alpha and gamma diversity, i.e., alpha and gamma diversity are both assessed at the same level of sample coverage, to formulate standardized, coverage‐based beta diversity. This extension of iNEXT to beta diversity required the development of novel concepts and theories, including a formal proof and empirical demonstration that the resulting standardized beta diversity removes the dependence of beta diversity on both gamma and alpha values, and thus reflects the pure among‐assemblage differentiation. The proposed standardization is illustrated with spatial, temporal and spatio‐temporal datasets, while the freeware iNEXT.beta3D facilitates all computations and graphics.This article is protected by copyright. All rights reserved.

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

“…Generally, β-diversity measures fall into two classes: direct calculation of the ratio between regional (γ) and local (α) diversity, and multivariate measures based on pairwise dissimilarities (Anderson et al 2011). Our ESS-based β-diversity estimate fundamentally differs from the recently developed beta diversity rarefaction and extrapolation methods in the package (Chao et al 2023), as well as from the sample coverage-based rarefaction β-diversity proposed by Engel et al (2021). Both approaches estimate β-diversity based on the ratio between estimated γ- to α-diversity, providing an average (regional) measure of β-diversity across all communities.…”

“…In summary, the package proves valuable for ecologists working on α- and β-diversity, especially when dealing with incomplete and inconsistent sample sizes, which is a prevalent characteristic in samples of ecological communities, but particularly in samples of highly mobile and species-rich taxa. Additionally, it provides visual estimations for species richness and the number of shared species between two communities based on individual samples, offering a complementary approach to non-parametric methods, such as the Chao series of estimators (Chao 1984, Chao et al 2000, Chao et al 2023).…”

Multi‐taxon biodiversity responses to the 2019–2020 Australian megafires

“…Our findings indicated burnt areas which were less urban, showed greater diversity estimates post‐fire than unburnt areas; thus, this bias was either negligible or outweighed by environmental (e.g., fire) drivers (Appendix S4). We also examined whether shifts in diversity estimates more likely reflected species richness or species abundance distribution shifts by estimating beta diversity within the iNEXT framework (Chao et al, 2023; see Appendix S4). Estimates were derived from comparisons of pairs of assemblages (see Appendix S4).…”

Accounting for imperfect detection when estimating species-area relationships and beta-diversity

“…Estimating species richness has been a longstanding issue (Fisher et al 1943, Gwinn et al 2015 and many statistical methods exist to estimate true richness from observed species counts. For instance, the Chao family of non-parametric estimators, including the iNEXT (Hsieh et al 2016) and iNEXT.3D programmes (Chao et al 2021), are widely used to estimate asymptotic species richness based on rarefaction and/or the frequency of rare species within a sample (e.g., Mendenhall et al 2014, Palmeirim et al 2021, and have also been expanded to estimate detection-corrected β-diversity indices (Chao et al 2023). While addressing imperfect detection, the Chao/iNEXT estimators do not consider the influence of covariates on species occurrence or detection (McKenzie 2005).…”

“…Here, we use simulations to explore the impacts of imperfect detection on typical field study designs for SAR and β-diversity estimation, and assess the comparative performance of an abundance-based Chao estimator (iNEXT.3D/iNEXT.beta3D; Chao et al 2021Chao et al , 2023 and MSOMs to 1) estimate Species-Area Relationships (patch-level richness, SAR c-andz-values), and 2) model the relationship between covariates and pairwise β-diversity (pairwise Sørensen similarity, model slopes and intercepts). We test the sensitivity of estimators to variation in species detectabilities, and the sampling design used to assess communities.…”