Rarefaction and extrapolation with Hill numbers: a framework for sampling and estimation in species diversity studies
2013/05/17 by Anne Chao, Nicholas J. Gotelli, T. C. Hsieh +5 · 162 citations
Environmental Science · Agricultural and Biological Sciences · #Ecology and Vegetation Dynamics Studies #Plant and animal studies #Species Distribution and Climate Change
paper · doi:10.1890/13-0133.1
Abstract
Quantifying and assessing changes in biological diversity are central aspects of many ecological studies, yet accurate methods of estimating biological diversity from sampling data have been elusive. Hill numbers, or the effective number of species, are increasingly used to characterize the taxonomic, phylogenetic, or functional diversity of an assemblage. However, empirical estimates of Hill numbers, including species richness, tend to be an increasing function of sampling effort and, thus, tend to increase with sample completeness. Integrated curves based on sampling theory that smoothly link rarefaction (interpolation) and prediction (extrapolation) standardize samples on the basis of sample size or sample completeness and facilitate the comparison of biodiversity data. Here we extended previous rarefaction and extrapolation models for species richness (Hill number q D , where q = 0) to measures of taxon diversity incorporating relative abundance (i.e., for any Hill number q D , q > 0) and present a unified approach for both individual‐based (abundance) data and sample‐based (incidence) data. Using this unified sampling framework, we derive both theoretical formulas and analytic estimators for seamless rarefaction and extrapolation based on Hill numbers. Detailed examples are provided for the first three Hill numbers: q = 0 (species richness), q = 1 (the exponential of Shannon's entropy index), and q = 2 (the inverse of Simpson's concentration index). We developed a bootstrap method for constructing confidence intervals around Hill numbers, facilitating the comparison of multiple assemblages of both rarefied and extrapolated samples. The proposed estimators are accurate for both rarefaction and short‐range extrapolation. For long‐range extrapolation, the performance of the estimators depends on both the value of q and on the extrapolation range. We tested our methods on simulated data generated from species abundance models and on data from large species inventories. We also illustrate the formulas and estimators using empirical data sets from biodiversity surveys of temperate forest spiders and tropical ants.
Citations
Cited by
- Biodiversity resilience in a tropical rainforest
- Temporal changes in the dietary niche of sympatric seals provides insight into the role of competition in population declines
- Agricultural disturbance reduces arbuscular mycorrhizal fungal diversity and biomass by excluding specialist species
- Does Participatory Bird Monitoring Provide Accurate Data for Ecological Research? An Experience in Rural Southwestern Mexico
- Multiple disturbances, multiple legacies: Fire, canopy gaps and deer jointly change the forest seed bank
- Habitat and land‐use intensity shape moth community structure across temperate forest and grassland
- How much sampling is enough? Four decades of understorey bird mist‐netting across Amazonia define the minimum effort to uncover species assemblage structure
- The genus Andrena Fabricius, 1775 (Hymenoptera, Andrenidae) in a Mediterranean biodiversity hotspot: community-wide relationships with plants and description of three new species
- Temporal dynamics of parasite populations and communities of blue sea catfish Ariopsis guatemalensis (Günther, 1864), in a eutrophic coastal lagoon from Mexican Pacific
- Consumer biodiversity increases organic nutrient availability across aquatic and terrestrial ecosystems
- Managed forests are a stronghold of non‐native beetles in Europe
- Species turnover does not rescue biodiversity in fragmented landscapes
- Dynamics of Near‐Coastal Fish Assemblages following the Deepwater Horizon Oil Spill in the Northern Gulf of Mexico
- Urban areas have lower species richness, but maintain functional diversity: insights from the African Bird Atlas Project
- Forest clear‐cuts support diverse moth fauna but lack common grassland species
- Life at the (h)edge—Multidiversity in shrub ecotones is driven by habitat quality and shrub foliage cover
- Continental‐scale interactions of Australian showy mistletoes and their hosts
- The impact of tree mortality and post‐disturbance management on insect diversity in temperate forests: Insights from a replicated experiment
- Urbanization of seed dispersal networks
- Linear anthropogenic disturbances increase butterfly abundance, species richness, and cross-corridor movements
- Differential predation patterns of free‐ranging cats among continents
- Fire frequency shapes diversity in multi‐guild communities through direct and indirect pathways
- Does pollen-assemblage richness reflect floristic richness? A review of recent developments and future challenges
- Fungal Spore Richness and Abundance of Allergenic Taxa: Comparing a Portable Impactor and Passive Trap Indoors and Outdoors in an Urban Setting
- Key concepts and a world‐wide look at plant recruitment networks
- Pollinator gardening is constrained by income but not lot size in urban front yards
- Constructing a lower-bound estimate of the global number of insect species on a hyperdiverse empirical foundation
- Estimating global bee species richness and taxonomic gaps
- Metacommunity structural changes of Antarctic benthic invertebrates over the late Maastrichtian
- Macro‐ and microclimate interactively shape species diversity of multiple taxa in mountain landscapes
- Recent community warming of moths in Finland is driven by extinction in the north and colonisation in the south
- Uniform bathymetric zonation of marine benthos on a Pan-Arctic scale
- A case study on the application of spore sampling for the monitoring of macrofungi
- Big data approaches reveal large-scale spatial patterns in marine epifauna
- Arctic Ocean virus communities and their seasonality, bipolarity, and prokaryotic associations
- Dietary Breadth Predicts Toxin Expression Complexity in the Venoms of North American Gartersnakes
- Connection over creation: hydrological connectivity drives post-restoration community assembly in coastal ponds
- Contrasting effects of protected areas on understory plant diversity in broadleaved deciduous forests
- Forest Heterogeneity by Chain Saw: How Between‐Patch Variation in Old Growth Attributes Changes the Metacommunities of Beetles
- Herpetofaunal diversity of the disturbed and isolated Bukit Maras in Terengganu, Peninsular Malaysia
- Eyeing <scp>DNA</scp> barcoding for species identification of fish larvae
- Exploring elasmobranch biodiversity in the western Mediterranean and Alboran Sea through eDNA-Based monitoring
- Pollination effectiveness affects the level of generalisation of a plant species with phenotypically plastic flowers
- Citizen science helps reveal how urban land management shapes butterfly communities
- How Should Beta-Diversity Inform Biodiversity Conservation?
- Detecting diversity: emerging methods to estimate species diversity
- <scp>GUBIC</scp>: The global urban biological invasions compendium for plants
- Sampling biases shape our view of the natural world
- Back to the roots: Uncovering ectomycorrhizal communities across three major African vegetation types
- Cross‐scale scaling‐law analyses for the heterogeneity and diversity of animal gut microbiomes from community to landscape
- Metabarcoding reveals that mixed forests mitigate negative effects of non‐native trees on canopy arthropod diversity
- Measuring biological diversity
- Testing the potential of pollen assemblages to capture composition, diversity and ecological gradients of surrounding vegetation in two biogeographical regions of southeastern Europe
- Metagenomic analyses of gut microbiome composition and function with age in a wild bird; little change, except increased transposase gene abundance
- Moult is associated with higher diversity of food items in the diet of Common Bulbuls (<i>Pycnonotus barbatus</i>) in Cameroon
- Spatial and temporal comparisons of salt marsh soil fungal communities following the deepwater horizon spill
- The potential of farmer-managed small-scale grazing exclusions as an adaptive management to restore degraded lands in arid regions
- Global phylogeny of the family Gomphillaceae (Ascomycota, Graphidales) sheds light on the origin, diversification and endemism in foliicolous lineages
- Higher trophic levels and species with poorer dispersal traits are more susceptible to habitat loss on island fragments
- Solar parks provide heterogeneous habitats for winter‐active ground‐dwelling predatory arthropods
- Mild HIV-specific selective forces overlaying natural CD4+ T cell dynamics explain the clonality and decay dynamics of HIV reservoir cells
- Frugivore-mediated seed dispersal in fragmented landscapes: Compositional and functional turnover from forest to matrix
- Harmonising digitised herbarium data to enhance biodiversity knowledge: Major steps towards an updated checklist for the flora of Greenland
- Diversity and structure of the deep-sea sponge microbiome in the equatorial Atlantic Ocean
- Silent changes in taxonomic, functional and phylogenetic diversity of birds in Qiyunshan National Nature Reserve, south China
- Revealing Elasmobranch Distributions in Turbid Coastal Waters: Insights From Environmental <scp>DNA</scp> and Particle Tracking
- Effects of agricultural land conversion and interstitial sediment on Tasmanian stream macroinvertebrate communities
- Distance-decay reveals contrasting effects of land-use types on arthropod community homogenisation
- Mathematically and biologically consistent framework for presence–absence pairwise indices
- Asymmetric leading vs. trailing edge shifts since the Last Glacial Maximum underpin the modern bimodal latitudinal diversity gradient in planktonic foraminifera
- Biodiversity dynamics during the initial Devonian radiation of ammonoids
- Unexpected Diversity in Regenerating Sites Stresses the Importance of Baselines: A Case Study With Bats (Order Chiroptera) on the Osa Peninsula, Costa Rica
- Rivers run through it – exploring drivers of aquatic macrozoobenthic diversity in an inner alpine dry valley
- Migratory species strongly affect seabird biomass in seasonal assemblages off northeast Aotearoa/New Zealand
- Historical Lead Contamination Linked to Atmospheric Deposition is Associated With Declines in Ectomycorrhizal Diversity and Shifts in Fungal Community Composition
- Urbanization Shapes Dietary Composition and Snout Morphology of Salamanders
- Threshold responses of birds to agricultural intensification in Mediterranean olive groves
- Comparing <scp>eDNA</scp> and Transect Methods for Aquatic Biodiversity Assessment in Lakes and Ponds
- The invasion of Goldenrod (Solidago canadensis) does not affect the ant communities (Hymenoptera, Formicidae) in central Romania meadows
- The importance of residential vegetation cover for urban birds – linking biodiversity thresholds to standards for human well-being
- Legacies of consecutive summer droughts on soil‐borne plant parasitic protists (Oomycota: Stramenopila and Phytomyxea: Rhizaria) and protistan consumers (Cercozoa: Rhizaria) along an experimental plant diversity gradient
- Seed bank and aboveground vegetation of Atlantic Forest re‐growing on mining tailings in Mariana: Highlighting diversity patterns of functional groups
- Biogeography after Permian/Triassic boundary crisis resulted from a complex combination of functional and dispersal mechanisms
- Global hotspots of mycorrhizal fungal richness are poorly protected
- Landscape context influences local management effects on birds and bats in Amazonian cacao agroforestry systems
- Determining Window Sizes using Species Estimation for Accurate Process Mining over Streams
- Influence of grazing and solar panel installation on tenebrionid beetles (Coleoptera Tenebrionidae) of a central Asian steppe
- Effects of different mycorrhizal types of dispersedly retained trees on the diversity of ectomycorrhizal fungi in neighboring <i>Abies sachalinensis</i> seedlings
- Intrinsic dimensionality as a metric for temporal plant diversity evaluation: Case study from the <scp>SHIFT</scp> campaign
- Contrasting and altitude‐specific temporal trends in functional, phylogenetic, and species diversity in Austrian butterfly communities
- Root-associated ectomycorrhizal fungal communities in and around aggregated retention patches left in logged areas of <i>Abies sachalinensis</i> planted forests
- Habitat transformation reshapes diversity and community structure of amphibians and reptiles in the Eastern Andes
- Context-dependent effects of habitat type and grassland fragment size on bird diversity in European and African grassland-forestry mosaics
- Host immunogenetic variation and gut microbiome functionality in a wild vertebrate population
- Environmental DNA reveals temporal and spatial variability of invertebrate communities in arid-lands ephemeral water bodies
- Paleoecological context of Homo aff. erectus (ATE7-1) at Sima del Elefante (late Early Pleistocene, Atapuerca, Spain) inferred from the herpetofaunal assemblage
- DNA barcodes reveal deeply neglected diversity and numerous invasions of micromoths in Madagascar
- Long-Term Grazing Exclusion Reveals Taxonomic and Functional Reorganization of Plant Communities in an Insular Mediterranean Geopark
- Recovery of tree-related microhabitats in a tropical rainforest after agricultural abandonment
- Bumblebees moving up: shifts in elevation ranges in the Pyrenees over 115 years
- Ant activity and interspecific competition in territories of tropical dominant species are more strongly affected by forest stratum than diel period or bait exposure time
- Trophic ecology of roosterfish (<scp><i>Nematistius pectoralis</i></scp>) inferred from stomach content and stable isotope analyses in the southern part of Baja California peninsula
- Contrasting patterns of land use by resident and migratory bird assemblages in a tropical working landscape
- Species richness and distribution of alien plant species in Kinabalu Park, Malaysia
- Global impoverishment of natural vegetation revealed by dark diversity
- Are plant traits drivers of endophytic communities in seasonally flooded tropical forests?
- Evolutionary consequences of microbiomes for hosts: impacts on host fitness, traits, and heritability
- Evidence of a European seed dispersal crisis
- Does Emerald Ash Borer Infestation Alter Ash Phloem Microbial Communities over Time?
- Influence of traffic‐related pollution and seasonality on tardigrade diversity in urban ecosystems
- Positive response to inoculation with indigenous arbuscular mycorrhizal fungi as modulated by barley genotype
- Elevational Patterns of Plant Species Richness: Insights from Western Himalayas
- Density declines, richness increases, and composition shifts in stream macroinvertebrates
- Forest patches as important bird habitats in Malaysia's large-scale infrastructure development areas
- Contrasting the contributions of <scp>12S eDNA</scp> metabarcoding, visual surveys and anaesthetic collections to the historical regional diversity of cryptobenthic and conspicuous fish
- Metabarcoding arthropods in agroecosystems in Southern Ontario, Canada
- Taxonomic and functional nestedness of bird communities in urban parks of Liuzhou, China
- Arthropod decline in grasslands and forests is associated with landscape-level drivers
- Biodiversity loss in a gradient of urbanization: rodent community structure in a subtropical area of Northern Argentina
- Temporal changes in taxonomic and functional alpha and beta diversity across tree communities in subtropical Atlantic forests
- Set-aside of grassland field margins enhances buckwheat pollination services in small-holder agricultural landscapes
- Using surface environmental <scp>DNA</scp> to assess arthropod biodiversity within a forested ecosystem
- Viticulture abandonment benefits the bird community of the French Mediterranean
- Multiple Disturbances, Multiple Legacies: Fire, Canopy Gaps, and Deer Jointly Change the Forest Seed Bank
- Neglected seed dispersers and research compartmentalisation: how much do we know about what we don't know?
- Acoustic indices can be driven by habitat characteristics rather than bird diversity
- Remote monitoring of snare injuries in great apes
- Seasonal Variation of Butterfly Diversity in Subtropical Urban Forests of Nepal
- Phytochemical diversity of naturally regenerated plants in a biodiversity enrichment experiment
- Advancing Marine Conservation: Metabarcoding and Metaphylogeography for a Multi‐Year Biomonitoring of Benthic Communities of National Parks Across Two Seas
- Performance of Cerrado lizards: a test of the center–periphery hypothesis
- Ecological specialization indices for species of the Czech flora
- Allotaxonometry and rank-turbulence divergence: A universal instrument for comparing complex systems
- Best practices in metabarcoding of fungi: From experimental design to results
- Utility of various genome lengths in diversity and evolution analyses of Hepatitis E virus
- Worldwide occurrence records suggest a global decline in bee species richness
- Deciphering the associations between soil microbial diversity and ecosystem multifunctionality driven by long‐term fertilization management
- In-Depth Assessment of Within-Individual and Inter-Individual Variation in the B Cell Receptor Repertoire. [europepmc]
- Practical guidelines for B-cell receptor repertoire sequencing analysis. [europepmc]
- Impact of demographics on human gut microbial diversity in a US Midwest population. [europepmc]
- Estimating and comparing microbial diversity in the presence of sequencing errors. [europepmc]
- Environmental Viral Genomes Shed New Light on Virus-Host Interactions in the Ocean. [europepmc]
- Diversity, Distribution, and Evolution of Tomato Viruses in China Uncovered by Small RNA Sequencing. [europepmc]
- Shifts among Eukaryota, Bacteria, and Archaea define the vertical organization of a lake sediment. [europepmc]
- Population genomics of virulence genes of Plasmodium falciparum in clinical isolates from Uganda. [europepmc]
- Effects of sampling effort on biodiversity patterns estimated from environmental DNA metabarcoding surveys. [europepmc]
- Multi-marker metabarcoding approach to study mesozooplankton at basin scale. [europepmc]
- Cervicovaginal Fungi and Bacteria Associated With Cervical Intraepithelial Neoplasia and High-Risk Human Papillomavirus Infections in a Hispanic Population. [europepmc]
- Environmental Drivers of Free-Living vs. Particle-Attached Bacterial Community Composition in the Mauritania Upwelling System. [europepmc]
- Diversity-disease relationships and shared species analyses for human microbiome-associated diseases. [europepmc]
- Exploring the Remarkable Diversity of Culturable Escherichia coli Phages in the Danish Wastewater Environment. [europepmc]
- Thousands of reptile species threatened by under-regulated global trade. [europepmc]
- Illuminating an Ecological Blackbox: Using High Throughput Sequencing to Characterize the Plant Virome Across Scales. [europepmc]
- Intratumoral CD103+ CD8+ T cells predict response to PD-L1 blockade. [europepmc]
- Richness estimation in microbiome data obtained from denoising pipelines. [europepmc]
- Influenza A virus undergoes compartmentalized replication in vivo dominated by stochastic bottlenecks. [europepmc]
- Neuroendocrinology of the lung revealed by single-cell RNA sequencing. [europepmc]
- The oral microbiota is a reservoir for antimicrobial resistance: resistome and phenotypic resistance characteristics of oral biofilm in health, caries, and periodontitis. [europepmc]
- Disproportionate declines of formerly abundant species underlie insect loss. [europepmc]
- Rarefaction is currently the best approach to control for uneven sequencing effort in amplicon sequence analyses. [europepmc]
- Long-term lineage commitment in haematopoietic stem cell gene therapy. [europepmc]
- Key features and guidelines for the application of microbial alpha diversity metrics. [europepmc]
Related