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dc.contributor.authorChao, Anne
dc.contributor.authorGotelli, Nicholas
dc.contributor.authorHsieh, T. C.
dc.contributor.authorSander, Elizabeth
dc.contributor.authorMa, K. H.
dc.contributor.authorColwell, Robert K.
dc.contributor.authorEllison, Aaron M.
dc.date.accessioned2013-10-08T14:55:06Z
dc.date.issued2013-10-08
dc.identifierQuick submit: 2013-05-20T13:52:40-04:00
dc.identifier.citationChao, Anne, Nicholas J. Gotelli, T. C. Hsieh, Elizabeth L. Sander, K. H. Ma, Robert K. Colwell, and Aaron M. Ellison. "Rarefaction and extrapolation with Hill numbers: a framework for sampling and estimation in species diversity studies." Ecological Monographs 84, no. 1 (2014): 45-67.en_US
dc.identifier.issn0012-9615en_US
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:11148822
dc.description.abstractQuantifying 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 extend 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 develop 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 datasets from biodiversity surveys of temperate forest spiders and tropical ants.en_US
dc.description.sponsorshipOrganismic and Evolutionary Biologyen_US
dc.language.isoen_USen_US
dc.publisherEcological Society of Americaen_US
dc.relation.isversionofdoi:10.1890/13-0133.1en_US
dash.licenseLAA
dc.subjectabundance dataen_US
dc.subjectdiversityen_US
dc.subjectextrapolationen_US
dc.subjectHill numbersen_US
dc.subjectincidence dataen_US
dc.subjectinterpolationen_US
dc.subjectpredictionen_US
dc.subjectrarefactionen_US
dc.subjectsample coverageen_US
dc.subjectspecies richnessen_US
dc.titleRarefaction and Extrapolation with Hill Numbers: A Framework for Sampling and Estimation in Species Diversity Studiesen_US
dc.typeJournal Articleen_US
dc.date.updated2013-05-20T17:52:51Z
dc.description.versionAccepted Manuscripten_US
dc.rights.holderA Chao, NJ Gotelli, TC Hsieh, EL Sander, KH Ma, RK Colwell, AM Ellison
dc.relation.journalEcological Monographsen_US
dash.depositing.authorEllison, Aaron M.
dc.date.available2013-10-08T14:55:06Z
dash.affiliation.otherHarvard Foresten_US
dc.identifier.doi10.1890/13-0133.1*
workflow.legacycommentsIn QSDB.en_US
dash.contributor.affiliatedEllison, Aaron
dc.identifier.orcid0000-0003-4151-6081


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