Data from: Rarefaction and extrapolation: making fair comparison of abundance-sensitive phylogenetic diversity among multiple assemblages

Measures of phylogenetic diversity are basic tools in many studies of systematic biology. Faith’s PD (sum of branch lengths of a phylogenetic tree connecting all focal species) is the most widely used phylogenetic measure. Like species richness, Faith’s PD based on sampling data is highly dependent on sample size and sample completeness. The sample-size- and sample-coverage-based integration of rarefaction and extrapolation of Faith’s PD was recently developed to make fair comparison across multiple assemblages. However, species abundances are not considered in Faith’s PD. Based on the framework of Hill numbers, Faith’s PD was generalized to a class of phylogenetic diversity measures that incorporates species abundances. In this article, we develop both theoretical formulae and analytic estimators for seamless rarefaction and extrapolation for this class of abundance-sensitive phylogenetic measures, which includes simple transformations of phylogenetic entropy and of quadratic entropy. This work generalizes the previous rarefaction/extrapolation model of Faith’s PD to incorporate species abundance, and also extends the previous rarefaction/extrapolation model of Hill numbers to include phylogenetic differences among species. Thus a unified approach to assessing and comparing species/taxonomic diversity and phylogenetic diversity can be established. A bootstrap method is suggested for constructing confidence intervals around the phylogenetic diversity, facilitating the comparison of multiple assemblages. Our formulation and estimators can be extended to incidence data collected from multiple sampling units. We also illustrate the formulae and estimators using bacterial sequence data from the human distal esophagus and phyllostomid bat data from three habitats.

系统发育多样性测度是系统生物学诸多研究中的基础工具。费斯系统发育多样性指数（Faith’s PD，即连接所有目标物种的系统发育树的分支长度之和）是目前应用最广泛的系统发育多样性测度指标。与物种丰富度类似，基于采样数据计算的Faith’s PD高度依赖样本量与样本完备性。近年来学界已提出基于样本量与样本覆盖度的Faith’s PD稀疏化与外推整合方法，以实现多个群落间的公平比较。然而，Faith’s PD未考虑物种多度信息。基于希尔数（Hill numbers）框架，现有研究已将Faith’s PD推广至一类纳入物种多度的系统发育多样性测度范畴。本文针对这类纳入物种多度的系统发育多样性测度（涵盖系统发育熵与二次熵的简单变换形式），构建了无缝稀疏化与外推的理论公式与解析估计量。本研究既将此前的Faith’s PD稀疏化/外推模型推广至纳入物种多度的场景，也将希尔数的稀疏化/外推模型拓展至纳入物种间系统发育差异的维度，由此可建立一套统一的方法，用于评估与比较物种/分类多样性及系统发育多样性。本文还提出一种自助法（bootstrap method）以构建系统发育多样性的置信区间，助力多群落间的比较分析。我们所提出的公式与估计量可拓展应用于多采样单元获取的物种发生数据。此外，本文利用人类远端食管的细菌序列数据与三种生境中的叶口蝠数据，对所提公式与估计量进行了实例演示。