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...

量化和评估生物多样性的变化是许多生态学研究的核心内容，但从采样数据中准确估算生物多样性的方法一直难以捉摸。希尔数（或称有效物种数）正越来越多地被用于描述群落的分类学、系统发育或功能多样性。然而，希尔数的经验估计值（包括物种丰富度）往往是采样努力的递增函数，因此会随着样本完整性的提高而增加。基于采样理论的综合曲线可平滑连接稀疏化（插值）和预测（外推），并根据样本量或样本完整性对样本进行标准化，从而促进生物多样性数据的比较。在此，我们将之前针对物种丰富度的稀疏化和外推模型（希尔数qD，其中q=0）扩展到包含相对丰度的分类群多样性测度（即对于任何希尔数qD，q>0...