Hsieh T C, Chao Anne
Institute of Statistics, National Tsing Hua University, Hsin-Chu, Taiwan.
Syst Biol. 2017 Jan 1;66(1):100-111. doi: 10.1093/sysbio/syw073.
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许多系统生物学研究中的基本工具。费思的系统发育多样性（连接所有目标物种的系统发育树分支长度之和）是使用最广泛的系统发育测度。与物种丰富度一样，基于抽样数据的费思系统发育多样性高度依赖于样本大小和样本完整性。最近开发了基于样本大小和样本覆盖度的费思系统发育多样性的稀疏化和外推法，以便在多个集合之间进行公平比较。然而，费思系统发育多样性未考虑物种丰度。基于希尔数框架，费思系统发育多样性被推广到一类纳入物种丰度的系统发育多样性测度。在本文中，我们针对这类对丰度敏感的系统发育测度，开发了用于无缝稀疏化和外推的理论公式和解析估计量，其中包括系统发育熵和二次熵的简单变换。这项工作将之前费思系统发育多样性的稀疏化/外推模型进行了推广，以纳入物种丰度，同时也将之前希尔数的稀疏化/外推模型进行了扩展，以包括物种间的系统发育差异。因此，可以建立一种评估和比较物种/分类多样性与系统发育多样性的统一方法。建议采用自助法构建系统发育多样性的置信区间，便于对多个集合进行比较。我们的公式和估计量可以扩展到从多个抽样单元收集的发生率数据。我们还使用来自人类远端食管的细菌序列数据和来自三个栖息地的叶口蝠数据来说明这些公式和估计量。
