Anne Chao

National Tsing Hua University | NTHU · Institute of Statistics

Gentry’s forest transect data have been frequently used to assess global patterns of plant diversity and plant species compositional changes along environmental and geographical gradients. Based on the worldwide woody plant abundance records from Gentry’s 197 localities/plots (each consisting of ten 2 m × 50 m subplots/transects), we apply a recent...

Based on sampling data, we propose a rigorous standardization method to measure and compare beta diversity across datasets. Here beta diversity, which quantifies the extent of among‐assemblage differentiation, relies on Whittaker's original multiplicative decomposition scheme, but we use Hill numbers for any diversity order q ≥ 0. Richness‐based be...

An ecological network refers to the ecological interactions among sets of species. Quantification of ecological network diversity and related sampling/estimation challenges have explicit analogues in species diversity research. A unified framework based on Hill numbers and their generalizations was developed to quantify taxonomic, phylogenetic and...

Incomplete sampling of species' geographic distributions has challenged biogeographers for many years to precisely quantify global-scale biodiversity patterns. After correcting for the spatial inequality of sample completeness, we generated a global species diversity map for woody angiosperms (82,974 species, 13,959,780 occurrence records). The est...

We investigated the biogeography of benthic foraminifera in a highly urbanized tropical seascape, i.e., Hong Kong, in order to assess their utility as bioindicators relative to other marine fauna. Hong Kong is one of the largest coastal cities on the planet and studies of other benthic fauna in the region are available for comparison. We found that...

Intensification of land use by humans has led to a homogenization of landscapes and decreasing resilience of ecosystems globally due to a loss of biodiversity, including the majority of forests. Biodiversity-ecosystem functioning (BEF) research has provided compelling evidence for a positive effect of biodiversity on ecosystem functions and service...

Hotspots of tropical marine biodiversity are areas that harbour disproportionately large numbers of species compared to surrounding regions. The richness and location of these hotspots have changed throughout the Cenozoic. Here, we review the global dynamics of Cenozoic tropical marine biodiversity hotspots, including the four major hotspots of the...

Given the importance of species diversity as a tool for assessing recovery during forest regeneration and active restoration, robust approaches for assessing changes in tree species diversity over time are urgently needed. We assessed changes in tree species diversity during natural regeneration over 12–20 years in eight 1-ha monitoring plots in NE...

Species richness is a key ecological characteristic that influences numerous ecosystem functions. Here we analyse the patterns and possible causes of phytoplankton taxon richness in seasonal datasets from twenty contrasting lakes in the English Lake District over six years and near-weekly datasets over 33 years from Windermere. Taxon richness was l...

Disturbances alter biodiversity via their specific characteristics, including severity and extent in the landscape, which act at different temporal and spatial scales. Biodiversity response to disturbance also depends on the community characteristics and habitat requirements of species. Untangling the mechanistic interplay of these factors has guid...

Invertebrates constitute the majority of animal species and are critical for ecosystem functioning and services. Nonetheless, global invertebrate biodiversity patterns and their congruences with vertebrates remain largely unknown. We resolve the first high-resolution (~20-km) global diversity map for a major invertebrate clade, ants, using biodiver...

The study of ancient cultures is hindered by the incomplete survival of material artifacts, so we commonly underestimate the diversity of cultural production in historic societies. To correct this survivorship bias, we applied unseen species models from ecology to gauge the loss of narratives from medieval Europe, such as the romances about King Ar...

This chapter focuses on quantifying biodiversity and its spatial/temporal change under a unified framework. It reviews a continuum of species/taxonomic diversity (TD) measures based on the concept of the effective number of species. TD includes two components – species richness and evenness among species abundances. The chapter introduces a class o...

Probability models for Zipf's law; asymptotic theories in urn models; optimal stopping‐time theories in urn models; and inter‐disciplinary collaboration.

Anne Chao and Liza Levina reflect on an “extraordinarily brilliant student”.

Hong Kong is one of the most urbanized coastal cities in the world. Yet, despite extensive anthropogenic impacts, adjacent marine environments harbour tremendous biodiversity. We investigated how the diversity, taxonomic composition, and biogeography of meiobenthic ostracods in Hong Kong's coastal waters vary in response to natural and anthropogeni...

Information or entropy analysis of diversity is used extensively in community ecology, and has recently been exploited for prediction and analysis in molecular ecology and evolution. Information measures belong to a spectrum (or ‘q-profile’) of measures whose contrasting properties provide a rich summary of diversity, including allelic richness (q=...

Biodiversity is a multifaceted concept covering different levels of organization from genes to ecosystems. Biodiversity has at least three dimensions: (a) Taxonomic diversity (TD): a measure that is sensitive to the number and abundances of species. (b) Phylogenetic diversity (PD): a measure that incorporates not only species abundances but also sp...

Natural and anthropogenic factors shape present-day benthic marine ecosystems. Understanding their combined influence on benthic communities is limited, however, by a lack of biological monitoring. Using a conservation paleobiology approach, this study establishes biological baselines and assesses the effects of natural and anthropogenic environmen...

Biodiversity keeps our planet stable. Each species, no matter how small, plays an important role in this global balancing act. That’s why the current pace of biodiversity loss is so alarming. Unfortunately, slowing that pace is extremely difficult. Scientists must first take on the virtually impossible task of measuring the richness and variety of...

Forests are increasingly affected by natural disturbances. Subsequent salvage logging, a widespread management practice conducted predominantly to recover economic capital, produces further disturbance and impacts biodiversity worldwide. Hence, naturally disturbed forests are among the most threatened habitats in the world, with consequences for th...

Forests are increasingly affected by natural disturbances. Subsequent salvage logging, a widespread management practice conducted predominantly to recover economic capital, produces further disturbance and impacts biodiversity worldwide. Hence, naturally disturbed forests are among the most threatened habitats in the world, with consequences for th...

The evolutionary split between gymnosperms and angiosperms has far‐reaching implications for the current communities colonizing trees. The inherent characteristics of dead wood include its role as a spatially scattered habitat of plant tissue, transient in time. Thus, local assemblages in deadwood forming a food web in a necrobiome should be affect...

Biodiversity knowledge shortfalls, especially incomplete information on species distributions, can lead to false conclusions about global biodiversity patterns. Diversity estimation theory statistically uses species occurrence records and sampling completeness (coverage) to predict diversity in terms of species richness, dominance and evenness. We...

We develop a novel class of measures to quantify sample completeness of a biological survey. The class of measures is parameterized by an order q ≥ 0 to control for sensitivity to species relative abundances. When q = 0, species abundances are disregarded and our measure reduces to the conventional measure of completeness, that is, the ratio of the...

Salvage logging following natural disturbances may alter the natural successional trajectories of biological communities by affecting the occurrences of species, functional groups and evolutionary lineages. However, few studies have examined whether dissimilarities between bird communities of salvaged and unsalvaged forests are more pronounced for...

Following natural disturbances, additional anthropogenic disturbance may alter community recovery by affecting the occurrences of species, functional groups and evolutionary lineages. However, our understanding is limited of whether rare, common, or dominant species, functional groups, or evolutionary lineages are most strongly affected by an addit...

Ecological restoration can re-establish plant species populations, enhance forested habitats extension, improve landscape connectivity, and enable biodiversity persistence within a landscape. However, the potential benefits of ecological restoration on beta diversity have never been explored. Here we use field data to investigate, for the first tim...

Progressive habitat transformation causes global changes in landscape biodiversity patterns, but can be hard to quantify. Rarefaction/extrapolation approaches can quantify within‐habitat biodiversity, but may not be useful for cases in which one habitat type is progressively transformed into another habitat type. To quantify biodiversity patterns i...

An enormous number of measures based on different criteria have been proposed to quantify evenness or unevenness among species relative abundances in an assemblage. However, a unified approach that can encompass most of the widely‐used indices is still lacking. Here we first present some basic requirements for an evenness measure. We then propose t...

Ratio-like approaches for estimating global species richness have been criticised for their unjustified extrapolation from regional to global patterns. Here we explore the use of cumulative percentages of ‘new’ (i.e., not formally described) species over large geographic areas (‘megatransects’) as a means to overcome this problem. In addition, we t...

Diversity partitioning, which decomposes gamma diversity into alpha and beta components, is commonly used to obtain measures that quantify spatial/temporal diversity and compositional similarity or dissimilarity among assemblages. We focus on the decomposition of diversity as measured by Hill numbers (parameterized by a diversity order q ≥ 0). At l...

Based on the framework of attribute diversity (a generalization of Hill numbers of order q), we develop a class of functional diversity measures sensitive not only to species abundances but also to trait‐based species‐pairwise functional distances. The new method refines and improves on the conventional species‐equivalent approach in three areas: (...

Biological diversity is a key concept in the life sciences and plays a fundamental role in many ecological and evolutionary processes. Although biodiversity is inherently a hierarchical concept covering different levels of organisation (genes, population, species, ecological communities and ecosystems), a diversity index that behaves consistently a...

Information or entropy analysis of diversity is used extensively in community ecology, and has recently been exploited for prediction and analysis in molecular ecology and evolution. Information measures belong to a spectrum (or q profile) of measures whose contrasting properties provide a rich summary of diversity, including allelic richness (q=0)...

Estimating the species, phylogenetic, and functional diversity of a community is challenging because rare species are often undetected, even with intensive sampling. The Good-Turing frequency formula, originally developed for cryptography, estimates in an ecological context the true frequencies of rare species in a single assemblage based on an inc...

Whether successional forests converge towards an equilibrium in species composition remains an elusive question, hampered by high idiosyncrasy in successional dynamics. Based on long-term tree monitoring in second-growth (SG) and old-growth (OG) forests in Costa Rica, we show that patterns of convergence between pairs of forest stands depend upon t...

Due to sampling limitations, almost every biodiversity survey misses species that are present, but not detected, so that empirical species counts underestimate species richness. A wide range of species richness estimators has been proposed in the literature to reduce undersampling bias. We focus on nonparametric estimators, which make no assumption...

The weaponry technology associated with Clovis and related Early Paleoindians represents the earliest well-defined evidence of humans in Pleistocene North America. We assess the technological diversity of these fluted stone points found at archaeological sites in the western and eastern halves of North America by employing statistical tools used in...

In the context of capture-recapture studies, Chao (1987) derived an inequality among capture frequency counts to obtain a lower bound for the size of a population based on individuals' capture/non-capture records for multiple capture occasions. The inequality has been applied to obtain a non-parametric lower bound of species richness of an assembla...

iNEXT (iNterpolation and EXTrapolation) Online is the R-based interactive online version of iNEXT available via the link https://chao.shinyapps.io/iNEXTOnline/ or http://chao.stat.nthu.edu.tw/wordpress/software_download/. Clicking these links, you will be directed to the online interface window. Users do not need to learn/understand R to run iNEXT...

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...

On the basis of the sampling data from an assemblage, estimation of species richness (observed plus undetected) is statistically difficult especially for highly diverse assemblages with many rare species. Simple counts of species richness in samples typically underestimate and strongly depend on sampling effort and sample completeness. There are tw...

The program SpadeR is the R-based online version of SPADE available via the link http://chao.stat.nthu.edu.tw/wordpress/software_download/ or https://chao.shinyapps.io/SpadeR/. Clicking these links, you will be directed to the online interface window. Users do not need to learn/understand R to run SpadeR. The interactive web application was built u...

The program SpadeR is the R-based online version of SPADE available via the link http://chao.stat.nthu.edu.tw/wordpress/software_download/ or https://chao.shinyapps.io/SpadeR/. Clicking these links, you will be directed to the online interface window. Users do not need to learn/understand R to run SpadeR. The interactive web application was built u...

Hill numbers (or the effective number of species) have been increasingly used to quantify the species/taxonomic diversity of an assemblage. The sample‐size‐ and coverage‐based integrations of rarefaction (interpolation) and extrapolation (prediction) of H ill numbers represent a unified standardization method for quantifying and comparing species d...

The repertoire of IgG antibody responses to infection and vaccination varies depending on the characteristics of the immunogen and the ability of the host to mount a protective immune response. Chronic hepatitis B virus (HBV) infections are marked by persistent infection and immune tolerance to vaccination. This disease offers a unique opportunity...

Ibanez et al. (Journal of Vegetation Science, this issue) applied sample size- and coverage-based rarefaction to analyse the elevational richness pattern in New Caledonian tree communities. We comment on the statistical assumptions behind rarefaction/extrapolation and suggest pooling small plot data to effectively assess/detect the diversity patter...

Species richness (the number of species) in an assemblage is a key metric in many research fields of ecology. Simple counts of species in samples typically underestimate the true species richness and strongly depend on sampling effort and sample completeness. Based on possibly unequal-sampling effort and incomplete samples that miss many species, t...

1. There are many concepts and measures of beta diversity and related similarity/differentiation indices. The variance framework (derived from the total variance of a community species abundance matrix) and diversity decomposition (based on partitioning gamma diversity into alpha and beta components) are two major approaches. 2. There have been no...

Estimating and comparing microbial diversity are statistically challenging due to limited sampling and possible sequencing errors for low-frequency counts, producing spurious singletons. The inflated singleton count seriously affects statistical analysis and inferences about microbial diversity. Previous statistical approaches to tackle the sequenc...

R codes. R codes for obtaining estimators of Hill numbers.

Simulation results. Simulation results based on six species abundance models.

Diversity analysis. Diversity analyses for the data sets in Allen et al. (2013).

Ronald Mason's hypothesis from the 1960s that the southeastern United States possesses greater Paleoindian projectile-point diversity than other regions is regularly cited, and often assumed to be true, but in fact has never been quantitatively tested. Even if valid, however, the evolutionary meaning of this diversity is contested. Point diversity...

Conservation biologists need robust, intuitive mathematical tools to quantify and assess patterns and changes in biodiversity. Here we review some commonly used abundance-based species diversity measures and their phylogenetic generalizations. Most of the previous abundance-sensitive measures and their phylogenetic generalizations lack an essential...

Estimating and comparing microbial diversity are statistically challenging due to limited sampling and possible sequencing errors for low-frequency counts, producing spurious singletons. The inflated singleton count seriously affects statistical analysis and inferences about microbial diversity. Previous statistical approaches to tackle the sequenc...

Estimating and comparing microbial diversity are statistically challenging due to limited sampling and possible sequencing errors for low-frequency counts, producing spurious singletons. The inflated singleton count seriously affects statistical analysis and inferences about microbial diversity. Previous statistical approaches to tackle the sequenc...

Capture?recapture methods, originally developed for estimating demographic parameters of animal populations, have been applied to human populations. In epidemiology and health sciences, most surveillance studies and prevalence surveys based on multiple records of incomplete lists are likely to miss some cases, and thus the number of ascertained cas...

Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in...

Based on a sample of individuals, we focus on inferring the vector of species relative abundance of an entire assemblage and propose a novel estimator of the complete species-rank abundance distribution (RAD). Nearly all previous estimators of the RAD use the conventional "plug-in" estimator Pi (sample relative abundance) of the true relative abund...

The compositional complexity of an assemblage is not expressible as a single number; standard measures such as 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. Ranking and comparing assemblages depend on the choice of q . Rather...

Hill numbers or the effective number of species are increasingly used to quantify species diversity of an assemblage. Hill numbers were recently extended to phylogenetic diversity, which incorporates species evolutionary history, as well as to functional diversity, which considers the differences among species traits. We review these extensions and...

Capture–recapture methods are used to estimate population sizes and related parameters such as survival rates, birth rates, and migration rates. A typical capture–recapture experiment places traps in the study area and samples the population several times. At each trapping sample, one records and attaches a unique tag to every unmarked animal, reco...

Traditional species diversity measures do not make distinctions among species. Faith's phylogenetic diversity ( PD ), which is defined as the sum of the branch lengths of a phylogenetic tree connecting all species, takes into account phylogenetic differences among species and has found many applications in various research fields. In this paper, we...

Hill numbers (or the "effective number of species") are increasingly used to characterize species diversity of an assemblage. This work extends Hill numbers to incorporate species pairwise functional distances calculated from species traits. We derive a parametric class of functional Hill numbers, which quantify "the effective number of equally abu...

It is difficult to accurately estimate species richness if there are many almost undetectable species in a hyper-diverse community. Practically, an accurate lower bound for species richness is preferable to an inaccurate point estimator. The traditional nonparametric lower bound developed by Chao (1984, Scandinavian Journal of Statistics 11, 265-27...