Time：2017.9.6 10:30-11:30
Place：资环楼148室
仰觀宇宙之大，俯察品類之盛: How to quantify and estimate biodiversity
趙蓮菊 (Anne Chao) 清華大學統計研究所
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/