1. Biodiversity is a multifaceted concept covering different levels of organization from genes to ecosystems. Biodiversity has at least three dimensions: (a) Taxonomic diversity (TD): a measure that is sensitive to the number and abundances of species. (b) Phylogenetic diversity (PD): a measure that incorporates not only species abundances but also species evolutionary histories. (c) 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.

中文翻译：

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测量 alpha 多样性的时间变化：整合分类、系统发育和功能多样性以及 iNEXT.3D 标准化的框架

1. 生物多样性是一个多方面的概念，涵盖从基因到生态系统的不同组织层次。生物多样性至少有三个维度： (a) 分类多样性 (TD)：一种对物种数量和丰度敏感的衡量标准。(b) 系统发育多样性 (PD)：一种不仅包含物种丰度而且还包含物种进化历史的度量。(c) 功能多样性（FD）：一种不仅考虑物种丰度而且考虑物种特征的措施。
2. 我们在希尔数及其概括的统一框架下整合了多样性的三个维度。我们的 TD 量化了等丰度物种的有效数量，PD 量化了有效的总分支长度，平均 PD（PD 除以树深度）量化了同样不同的谱系的有效数量，而 FD 量化了同样不同的虚拟功能群的有效数量（或功能“物种”）。因此，TD、平均 PD 和 FD 都在相同的物种/谱系等效单位中，可以进行有意义的比较。
3. 与物种丰富度一样，基于采样数据的经验 TD、PD 和 FD 取决于采样工作量和样本完整性。对于 TD（希尔数），开发了 iNEXT（内插和外推）标准化，用于标准化样本大小或样本完整性（通过样本覆盖率衡量，属于观察物种的个体比例），以便在研究之间进行客观比较。本文将 iNEXT 方法扩展到 iNEXT.3D 标准化，以在统一框架下通过基于样本大小和样本覆盖率的稀疏和外推涵盖多样性的所有三个维度。渐近多样性估计（即样本量趋于无穷大，样本覆盖趋向于统一）也被推导出来。除了基于个体的丰度数据，建议的 iNEXT.
4. 我们应用综合框架和提议的 iNEXT.3D 标准化来测量跨越四个十年的河口鱼类组合数据的时间 alpha 多样性变化。还评估了环境驱动因素对多样性变化的影响。我们的分析提供了对多样性三个维度中生物多样性变化的机械解释。在该项目期间开发的随附免费软件 iNEXT.3D 促进了所有计算和图形。