Rarefaction and extrapolation with beta diversity under a framework of Hill numbers : the iNEXT.beta3D standardization
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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. Under independent sampling, 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, that is, 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 simulation-based 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 spatiotemporal datasets, while the freeware iNEXT.beta3D facilitates all computations and graphics.
Chao , A , Thorn , S , Chiu , C-H , Moyes , F , Hu , K-H , Chazdon , R L , Wu , J , Magnago , L F S , Dornelas , M , Zelený , D , Colwell , R K & Magurran , A E 2023 , ' Rarefaction and extrapolation with beta diversity under a framework of Hill numbers : the iNEXT.beta3D standardization ' , Ecological Monographs , vol. Early View , e1588 . https://doi.org/10.1002/ecm.1588
Copyright © 2023 The Authors. Ecological Monographs published by Wiley Periodicals LLC on behalf of The Ecological Society of America. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
DescriptionThis work isjointly supported by the Natural Environment Research Council, UK and the Taiwan Ministry of Science and Technology under Contracts NERC-MOST 108-2923-M-007-003 and NE/T004487/1. AEM also acknowledges the Leverhulme Trust (RPG-2019-402). Support for the establishment and monitoring of permanent plots in Costa Rican forests was provided by grants from the Andrew W. Mellon Foundation, the US National Science Foundation (NSF DEB-0424767, NSF DEB-0639393 and NSF DEB-1147429), US NASA Terrestrial Ecology Program, and the University of Connecticut Research Foundation. MD is supported by a Leverhulme Trust Research Centre - the Leverhulme Centre for Anthropocene Biodiversity (RC-2018-021). L.F.S.M. was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) grant 307984/2022-2.
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