Measuring temporal change in alpha diversity: a framework integrating taxonomic, phylogenetic and functional diversity and the iNEXT.3D standardization

1. Biodiversity is a multifaceted concept covering different levels of organisation from genes to ecosystems. Biodiversity has at least three dimensions: (i) Taxonomic diversity (TD): a measure that is sensitive to the number and abundances of species. (ii) Phylogenetic diversity (PD): a measure that incorporates not only species abundances but also species evolutionary histories. (iii) Functional diversity (FD): a measure that considers not only species abundances but also species? traits.
2. We integrate the three dimensions of diversity under a unified framework of Hill numbers and their generalizations. Our TD quantifies the effective number of equally-abundant species, PD quantifies the effective total branch length, mean-PD (PD divided by tree depth) quantifies the effective number of equally-divergent lineages, and FD quantifies the effective number of equally-distinct virtual functional groups (or functional ?species?). Thus, TD, mean-PD and FD are all in the same units of species/lineage equivalents and can be meaningfully compared.
3. Like species richness, empirical TD, PD and FD based on sampling data, depend on sampling effort and sample completeness. For TD (Hill numbers), the iNEXT (interpolation and extrapolation) standardization was developed for standardizing sample size or sample completeness (as measured by sample coverage, the fraction of individuals that belong to the observed species) to make objective comparisons across studies. This paper extends the iNEXT method to the iNEXT.3D standardization to encompass all three dimensions of diversity via sample-size- and sample-coverage-based rarefaction and extrapolation under the unified framework. The asymptotic diversity estimates (i.e., sample size tends to infinity and sample coverage tends to unity) are also derived. In addition to individual-based abundance data, the proposed iNEXT.3D standardization is adapted to deal with incidence-based occurrence data.
4. We apply the integrative framework and the proposed iNEXT.3D standardization to measure temporal alpha-diversity changes for estuarine fish assemblage data spanning four decades. The influence of environmental drivers on diversity change are also assessed. Our analysis informs a mechanistic interpretation of biodiversity change in the three dimensions of diversity. The accompanying freeware, iNEXT.3D, developed during this project, facilitates all computation and graphics.