Nonparametric estimation of Shannon's index of diversity when there are unseen species in sample
Nonparametric estimation of Shannon's index of diversity when there are unseen species in sample
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DOI：
10.1023/a:1026096204727
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发表时间：
2003-12-01
影响因子：
3.8
通讯作者：
Shen, TJ
中科院分区：
文献类型：
--
作者：
Chao, A;Shen, TJ
一个生物群落通常有大量的物种，但丰度相对较小。当随机选择个体样本，并根据物种身份对每个个体进行分类时，可能会发现一些稀有物种。本文讨论了在物种数和物种丰度未知的情况下，Shannon多样性指数的估计问题。传统的估计，忽略了失踪的物种低估时，有一个不可忽略的数量看不见的物种。我们提供了一种不同的方法，基于不等概率抽样理论，因为物种在样本中被发现的概率不同。没有参数形式的物种丰度假设。建议的估计程序结合了Horvitz-Thompson（1952）对缺失物种的调整和样本覆盖率的概念，用于正确估计样本中发现的物种的相对丰度。仿真结果表明，所提出的估计工作在各种丰度模型，即使当一个相对较大的比例的物种是失踪。三个真实的数据集，两个来自生物学和另一个来自钱币学，给出了说明。
A biological community usually has a large number of species with relatively small abundances. When a random sample of individuals is selected and each individual is classified according to species identity, some rare species may not be discovered. This paper is concerned with the estimation of Shannon's index of diversity when the number of species and the species abundances are unknown. The traditional estimator that ignores the missing species underestimates when there is a non-negligible number of unseen species. We provide a different approach based on unequal probability sampling theory because species have different probabilities of being discovered in the sample. No parametric forms are assumed for the species abundances. The proposed estimation procedure combines the Horvitz-Thompson (1952) adjustment for missing species and the concept of sample coverage, which is used to properly estimate the relative abundances of species discovered in the sample. Simulation results show that the proposed estimator works well under various abundance models even when a relatively large fraction of the species is missing. Three real data sets, two from biology and the other one from numismatics, are given for illustration.