Data from: Rarefaction and extrapolation with Hill numbers: a framework for sampling and estimation in species diversity studies

Quantifying and assessing changes in biological diversity are central aspects of many ecological studies, yet accurate methods of estimating biological diversity from sampling data have been elusive. Hill numbers, or the effective number of species, are increasingly used to characterize the taxonomic, phylogenetic, or functional diversity of an assemblage. However, empirical estimates of Hill numbers, including species richness, tend to be an increasing function of sampling effort and, thus, tend to increase with sample completeness. Integrated curves based on sampling theory that smoothly link rarefaction (interpolation) and prediction (extrapolation) standardize samples on the basis of sample size or sample completeness and facilitate the comparison of biodiversity data. Here we extended previous rarefaction and extrapolation models for species richness (Hill number qD, where q = 0) to measures of taxon diversity incorporating relative abundance (i.e., for any Hill number qD, q > 0) and present a unified approach for both individual-based (abundance) data and sample-based (incidence) data. Using this unified sampling framework, we derive both theoretical formulas and analytic estimators for seamless rarefaction and extrapolation based on Hill numbers. Detailed examples are provided for the first three Hill numbers: q = 0 (species richness), q = 1 (the exponential of Shannon's entropy index), and q = 2 (the inverse of Simpson's concentration index). We developed a bootstrap method for constructing confidence intervals around Hill numbers, facilitating the comparison of multiple assemblages of both rarefied and extrapolated samples. The proposed estimators are accurate for both rarefaction and short-range extrapolation. For long-range extrapolation, the performance of the estimators depends on both the value of q and on the extrapolation range. We tested our methods on simulated data generated from species abundance models and on data from large species inventories. We also illustrate the formulas and estimators using empirical data sets from biodiversity surveys of temperate forest spiders and tropical ants.

量化与评估生物多样性变化是诸多生态学研究的核心内容，但从采样数据中精准估算生物多样性的方法始终难以获得。希尔数（Hill numbers），又称有效物种数，正日益广泛地被用于表征群落的分类、系统发育或功能多样性。然而，包括物种丰富度在内的希尔数经验估算值往往随采样投入的增加而升高，因此也会随样本完备度的提升而增大。基于采样理论的整合曲线可将稀疏化（内插法）与预测（外推法）平滑衔接，基于样本量或样本完备度对样本进行标准化处理，进而助力生物多样性数据的跨样本比较。本文将此前针对物种丰富度（希尔数qD，其中q=0）的稀疏化与外推模型，拓展至纳入相对多度的类群多样性测度（即适用于任意阶数q>0的希尔数qD），并提出了一套同时适配基于个体（多度）数据与基于取样（发生）数据的统一分析框架。依托这一统一采样框架，我们推导了基于希尔数的无缝稀疏化与外推的理论公式与解析估计量。针对前三个阶数的希尔数，我们给出了详细示例：q=0对应物种丰富度，q=1对应香农熵指数的指数形式，q=2对应辛普森集中性指数的倒数。我们开发了一种自助法（Bootstrap）以构建希尔数的置信区间，从而便于对经稀疏化与外推处理的多个群落样本进行比较。所提出的估计量在稀疏化与短距离外推场景下均具备优异精度。对于长距离外推，估计量的性能同时取决于q值与外推范围。我们基于物种多度模型生成的模拟数据以及大型物种名录数据集对所提方法进行了实证检验。此外，我们还利用温带森林蜘蛛与热带蚂蚁的生物多样性调查实测数据集，对本文提出的公式与估计量进行了实例演示。