仰觀宇宙之大，俯察品類之盛: How to quantify and estimate biodiversity
报告人：趙蓮菊 (Anne Chao) 清華大學統計研究所
主持人：何芳良教授
时间：2017.9.6 10:30-11:30
地点：闵行校区资环楼148报告厅
报告摘要：
The biological diversity and compositional complexity of an assemblage is not expressible as a single number; standard measures such as species diversities (Hill numbers) and entropies (Rényi entropies and Tsallis entropies) vary in their order q which determines the measures’ emphasis on rare or common species. Rather than selecting one or a few measures to describe an assemblage, it is preferable to convey the complete story by presenting a continuous profile, a plot of diversity or entropy as a function of the order q ≥ 0. Based on sampling data, the empirical profile typically depends strongly on sample size and underestimates the true profile for low values of q, because samples usually miss some of the assemblage’s species due to under-sampling. In this talk, analytic estimators of species richness estimators (q = 0) and Shannon entropy (q = 1) are first reviewed, followed by the generalized method of obtaining continuous diversity and entropy profiles. The generalized approach is based on reformulating the diversity and entropy of any order q in terms of the successive discovery rates of new species with respect to sample size, i.e., the successive slopes of the species accumulation curve. Turing’s statistical work, originally developed in his cryptographic analysis during World War II, is then applied to estimate the slopes of any sample size. A bootstrap method is used to obtain approximate variances of the profiles and to construct the associated confidence intervals. Real examples are presented for illustrating the use of the online software SpadeR (Species-richness prediction and diversity estimation in R) to compute and plot diversity/entropy profiles. The extension to a phylogenetic version is briefly discussed.
Main References
Chao, A., Chiu, C.-H. and Jost, L. (2014) Unifying species diversity, phylogenetic diversity, functional diversity, and related similarity and differentiation measures through Hill numbers. Annual Review of Ecology, Evolution, and Systematics 45:297−324.
Chao, A. and Jost, L. (2015). Estimating diversity and entropy profiles via discovery rates of new species. Methods in Ecology and Evolution, 6, 873-882.
Chao, A. (2016) My Entropy ‘Pearl’: Using Turing’s insight to find an optimal estimator for Shannon entropy. https://methodsblog.wordpress.com/2016/03/04/entropy-pearl/
报告人简介：
Anne Chao (趙蓮菊) received her BS in mathematics from National Tsing Hua University, Taiwan, in 1973, and her PhD in statistics from the University of Wisconsin-Madison in 1977. Since 1978, she has been with the Institute of Statistics, National Tsing Hua University, Taiwan, where she is currently a Tsing Hua Distinguished Chair Professor. She is a Fellow of the Institute of Mathematical Statistics, and held a Taiwan National Chair Professorship from 2005-2008. Chao has long been fascinated with mathematical and statistical issues arising in ecology and related sciences; her major research interests include ecological statistics, statistical inferences of biodiversity measures, and statistical analysis of ecological and environmental survey data. She and her collaborators have published more than 120 papers. These have (i) developed several biodiversity measures/estimators including Chao1, Chao2, ACE, and ICE for species richness, as well as some novel methods to infer entropy, diversity and related similarity/differentiation measures, (ii) established a unified mathematical/statistical framework for taxonomic, phylogenetic and functional diversities, and (iii) generalized the classic sample-size-based rarefaction method to sample-coverage-based rarefaction and extrapolation, to standardize biodiversity samples. To implement their methodologies, Chao and her colleagues/students have also developed statistical software including CARE (CApture-REcapture), SPADE (Species Prediction And Diversity Estimation), iNEXT (iNterpolation/EXTrapolation), and PhD (Phylogenetic Diversity). For the past 20 years, Chao served in the editorial boards of four major statistical journals, and currently serves as an Associate Editor for Methods in Ecology and Evolution.