Rarefaction and extrapolation with beta diversity under a framework of Hill numbers: The iNEXT.beta3D standardization
Journal
Ecological Monographs
Journal Volume
93
Journal Issue
4
ISSN
1557-7015
0012-9615
Date Issued
2023-11-01
Author(s)
Anne Chao
Simon Thorn
Faye Moyes
Kai‐Hsiang Hu
Robin L. Chazdon
Jessie Wu
Luiz Fernando S. Magnago
Maria Dornelas
Robert K. Colwell
Anne E. Magurran
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. 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.
Subjects
alpha diversity
assemblage differentiation
beta diversity
extrapolation
gamma diversity
Hill numbers
rarefaction
replication invariance
replication principle
sample coverage
Type
journal article