A key feature of life's diversity is that some species are common but many more are rare. Nonetheless, at global scales, we do not know what fraction of biodiversity consists of rare species. Here, we present the largest compilation of global plant diversity to quantify the fraction of Earth's plant biodiversity that are rare. A large fraction, ~36.5% of Earth's ~435,000 plant species, are exceedingly rare. Sampling biases and prominent models, such as neutral theory and the k-niche model, cannot account for the observed prevalence of rarity. Our results indicate that (i) climatically more stable regions have harbored rare species and hence a large fraction of Earth's plant species via reduced extinction risk but that (ii) climate change and human land use are now disproportionately impacting rare species. Estimates of global species abundance distributions have important implications for risk assessments and conservation planning in this era of rapid global change.

AMAP IRD CIRAD CNRS INRA Université Montpellier Montpellier France

Betty and Gordon Moore Center for Science Conservation International 2011 Crystal Dr Arlington VA 22202 USA

Cape Research Centre South African National Parks Tokai 7947 Cape Town South Africa

Center for Biodiversity Dynamics in a Changing World and Section for Ecoinformatics and Biodiversity Department of Bioscience Aarhus University Ny Munkegade 114 DK 8000 Aarhus C Denmark

Center for Macroecology Evolution and University of Copenhagen Universitetsparken 15 Building 3 DK 2100 Copenhagen Ø Denmark

Centre for Integrative Conservation Xishuangbanna Tropical Botanical Garden and Center of Conservation Biology Core Botanical Gardens Chinese Academy of Sciences Menglun Yunnan China

Centre for Theoretical Study Charles University Prague 1 Czech Republic

Departamento de Ecología Facultad de Ciencias Biológicas Pontificia Universidad Católica de Chile CP 8331150 Santiago Chile

Department of Biology Santa Clara University Santa Clara CA 95053 USA

Department of Biology University of North Carolina NC 27599 USA

Department of Botany and Zoology Stellenbosch University Stellenbosch South Africa

Department of Botany Federal University of Minas Gerais Belo Horizonte 31270 901 Minas Gerais Brazil

Department of Ecology and Evolutionary Biology University of Arizona Tucson AZ 85721 USA

Department of Ecology and Evolutionary Biology University of California Los Angeles Los Angeles CA 90095 USA

Department of Ecology and Evolutionary Biology University of Connecticut CT 06269 USA

Department of Ecology Faculty of Sciences Charles University Czech Republic

Department of Organismic and Evolutionary Biology Harvard University MA 02138 USA

DIADE IRD Université Montpellier Montpellier France

Institute of the Environment University of Arizona Tucson AZ 85721 USA

Instituto de Ecología y Biodiversidad Laboratorio Internacional de Cambio Global and Centro de Cambio Global UC Chile

Manaaki Whenua Landcare Research Lincoln New Zealand

Missouri Botanical Garden St Louis MO 63110 USA

National Center for Ecological Analysis and Synthesis Santa Barbara CA 93101 USA

Naturalis Biodiversity Center Darwinweg 2 Leiden Netherlands

New York Botanical Garden 2900 Southern Blvd Bronx NY 10348 USA

Rincon Consultants Inc Ventura CA 93003 USA

Royal Botanic Gardens Kew Richmond Surrey UK

Santa Fe Institute 1399 Hyde Park Rd Santa Fe NM 87501 USA

School of Biology and Ecology and Senator George J Mitchell Center of Sustainability Solutions University of Maine Orono ME 04469 USA

School of Geography University of Leeds Leeds UK

Université de Lorraine AgroParisTech INRA Silva 54000 Nancy France

Université Montpellier CNRS EPHE IRD Université Paul Valéry Montpellier 3 Montpellier France

See more in PubMed

Preston F. W., The canonical distribution of commonness and rarity: Part I. Ecology 43, 185–215 (1962).

Hanski I., Dynamics of regional distribution: The core and satellite species hypothesis. Oikos 38, 210–221 (1982).

C. Darwin, On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life (John Murray, 1859), 502 pp. PubMed PMC

J. M. Diamond, “Normal” extinctions of isolated populations, in Extinctions, M. H. Nitecki, Ed. (University of Chicago Press, 1984), pp. 191–246.

Pimm S. L., Jones H. L., Diamond J., On the risk of extinction. Am. Nat. 132, 757–785 (1988).

S. P. Hubbell, R. B. Foster, in Conservation Biology: The Science of Scarcity and Diversity, M. E. Soulé, Ed. (Sinauer Associates, 1986), pp. 205–231.

M. E. Soulé, Conservation Biology: The Science of Scarcity and Diversity (Sinauer Associates, 1986).

Ter Steege H., Pitman N. C. A., Killeen T. J., Laurance W. F., Peres C. A., Guevara J. E., Salomão R. P., Castilho C. V., Amaral I. L., de Almeida Matos F. D., de Souza Coelho L., Magnusson W. E., Phillips O. L., de Andrade Lima Filho D., de Jesus Veiga Carim M., Irume M. V., Martins M. P., Molino J.-F., Sabatier D., Wittmann F., López D. C., da Silva Guimarães J. R., Mendoza A. M., Vargas P. N., Manzatto A. G., Reis N. F. C., Terborgh J., Casula K. R., Montero J. C., Feldpausch T. R., Coronado E. N. H., Montoya A. J. D., Zartman C. E., Mostacedo B., Vasquez R., Assis R. L., Medeiros M. B., Simon M. F., Andrade A., Camargo J. L., Laurance S. G. W., Nascimento H. E. M., Marimon B. S., Marimon B.-H. Jr., Costa F., Targhetta N., Vieira I. C. G., Brienen R., Castellanos H., Duivenvoorden J. F., Mogollón H. F., Piedade M. T. F., Aymard G. A. C., Comiskey J. A., Damasco G., Dávila N., García-Villacorta R., Diaz P. R. S., Vincentini A., Emilio T., Levis C., Schietti J., Souza P., Alonso A., Dallmeier F., Ferreira L. V., Neill D., Araujo-Murakami A., Arroyo L., Carvalho F. A., Souza F. C., do Amaral D. D., Gribel R., Luize B. G., Pansonato M. P., Venticinque E., Fine P., Toledo M., Baraloto C., Cerón C., Engel J., Henkel T. W., Jimenez E. M., Maas P., Mora M. C. P., Petronelli P., Revilla J. D. C., Silveira M., Stropp J., Thomas-Caesar R., Baker T. R., Daly D., Paredes M. R., da Silva N. F., Fuentes A., Jørgensen P. M., Schöngart J., Silman M. R., Arboleda N. C., Cintra B. B. L., Valverde F. C., Di Fiore A., Phillips J. F., van Andel T. R., von Hildebrand P., Barbosa E. M., de Matos Bonates L. C., de Castro D., de Sousa Farias E., Gonzales T., Guillaumet J.-L., Hoffman B., Malhi Y., de Andrade Miranda I. P., Prieto A., Rudas A., Ruschell A. R., Silva N., Vela C. I. A., Vos V. A., Zent E. L., Zent S., Cano A., Nascimento M. T., Oliveira A. A., Ramirez-Angulo H., Ramos J. F., Sierra R., Tirado M., Medina M. N. U., van der Heijden G., Torre E. V., Vriesendorp C., Wang O., Young K. R., Baider C., Balslev H., de Castro N., Farfan-Rios W., Ferreira C., Mendoza C., Mesones I., Torres-Lezama A., Giraldo L. E. U., Villarroel D., Zagt R., Alexiades M. N., Garcia-Cabrera K., Hernandez L., Huamantupa-Chuquimaco I., Milliken W., Cuenca W. P., Pansini S., Pauletto D., Arevalo F. R., Sampaio A. F., Valderrama Sandoval E. H., Gamarra L. V., Estimating the global conservation status of more than 15,000 Amazonian tree species. Sci Adv. 1, e1500936 (2015). PubMed PMC

Zizka A., Ter Steege H., Pessoa M. d. C. R., Antonelli A., Finding needles in the haystack: Where to look for rare species in the American tropics. Ecography 41, 321–330 (2018).

Ter Steege H., Vaessen R. W., Cárdenas-López D., Sabatier D., Antonelli A., de Oliveira S. M., Pitman N. C. A., Jørgensen P. M., Salomão R. P., The discovery of the Amazonian tree flora with an updated checklist of all known tree taxa. Sci. Rep. 6, 29549 (2016). PubMed PMC

Brown J. H., Mehlman D. W., Stevens G. C., Spatial variation in abundance. Ecology 76, 2028–2043 (1995).

Abades S. R., Marquet P. A., Finite size scaling in the local abundances of geographic populations. Biol. Res. 44, 107–112 (2011). PubMed

He F., Gaston K. J., Occupancy-abundance relationships and sampling scales. Ecography 23, 503–511 (2000).

J. H. Brown, Macroecology (University of Chicago Press, 1995).

McGill B. J., Does Mother Nature really prefer rare species or are log-left-skewed SADs a sampling artefact? Ecol. Lett. 6, 766–773 (2003).

Jenkins C. N., Pimm S. L., Joppa L. N., Global patterns of terrestrial vertebrate diversity and conservation. Proc. Natl. Acad. Sci. U.S.A. 110, E2602–E2610 (2013). PubMed PMC

Daru B. H., Park D. S., Primack R. B., Willis C. G., Barrington D. S., Whitfeld T. J. S., Seidler T. G., Sweeney P. W., Foster D. R., Ellison A. M., Davis C. C., Widespread sampling biases in herbaria revealed from large-scale digitization. New Phytol. 217, 939–955 (2018). PubMed

Meyer C., Weigelt P., Kreft H., Multidimensional biases, gaps and uncertainties in global plant occurrence information. Ecol. Lett. 19, 992–1006 (2016). PubMed

B. J. Enquist, R. Condit, R. K. Peet, M. Schildhauer, B. M. Thiers, “Cyber in frastructure for an integrated botanical information network to investigate the ecological impacts of global climate change on plant biodiversity” (PeerJ Preprints, 2016); https://peerj.com/preprints/2615.pdf.

Thomas C., Biodiversity databases spread, prompting unification call. Science 324, 1632–1633 (2009). PubMed

D. Rabinowitz, Seven forms of rarity, in The Biological Aspects of Rare Plant Conservation, H. Synge, Ed. (Wiley, 1981), pp. 205–217.

Yu J., Dobson F. S., Seven forms of rarity in mammals. J. Biogeogr. 27, 131–139 (2000).

IUCN, The IUCN Red List of Threatened Species (2019);www.iucnredlist.org.

Magurran A. E., Henderson P. A., Explaining the excess of rare species in natural species abundance distributions. Nature 422, 714–716 (2003). PubMed

S. P. Hubbell, The Unified Neutral Theory of Biodiversity and Biogeography (Princeton Univ. Press, 2001). PubMed

Chisholm R. A., Pacala S. W., Niche and neutral models predict asymptotically equivalent species abundance distributions in high-diversity ecological communities. Proc. Nat. Acad. Sci. U.S.A. 107, 15821–15825 (2010). PubMed PMC

Fisher R. A., Corbet A. S., Williams C. B., The relation between the number of species and the number of individuals in a random sample of an animal population. J. Anim. Ecol. 12, 42–58 (1943).

Pueyo S., Diversity: Between neutrality and structure. Oikos 112, 392–405 (2006).

White E. P., Enquist B. J., Green J. L., On estimating the exponent of power-law frequency distributions. Ecology 89, 905–912 (2008). PubMed

Zillio T., Condit R., The impact of neutrality, niche differentiation and species input on diversity and abundance distributions. Methods 116, 931–940 (2007).

J. Aitchison, J. A. C. Brown, The Lognormal Distribution with Special Reference to Its Uses in Economics (Cambridge Univ. Press, 1957); http://cds.cern.ch/record/109563.

McGill B., Strong and weak tests of macroecological theory. Oikos 102, 679–685 (2003).

Williamson M., Gaston K. J., The lognormal distribution is not an appropriate null hypothesis for the species-abundance distribution. J. Anim. Ecol. 74, 409–422 (2005).

R. May, Patterns of species abundance and diversity, in Ecology and Evolution of Communities, M. L. Cody, J. M. Diamond, Eds. (Harvard Univ. Press, 1975), pp. 81–120.

MacArthur R. H., On the relative abundance of species. Am. Nat. 94, 25–36 (1960).

E. C. Pielou, Ecological Diversity (John Wiley & Sons, 1975).

Engen S., Lande R., Population dynamic models generating the log normal species abundance distribution. Math. Biosci. 132, 169–183 (1996). PubMed

E. C. Pielou, Mathematical Ecology (Wiley, 1977).

Schoenberg F. P., Peng R., Woods J., On the distribution of wildfire sizes. Environmetrics 14, 583–592 (2003).

McGill B. J., Etienne R. S., Gray J. S., Alonso D., Anderson M. J., Benecha H. K., Dornelas M., Enquist B. J., Green J. L., He F., Hurlbert A. H., Magurran A. E., Marquet P. A., Maurer B. A., Ostling A., Soykan C. U., Ugland K. I., White E. P., Species abundance distributions: Moving beyond single prediction theories to integration within an ecological framework. Ecol. Lett. 10, 995–1015 (2007). PubMed

Connolly S. R., Hughes T. P., Bellwood D. R., Karlson R. H., Community structure of corals and reef fishes at multiple scales. Science 309, 1363–1365 (2005). PubMed

Pimm S. L., Raven P. H., The fate of the World’s plants. Trends Ecol. Evol. 32, 317–320 (2017). PubMed

Lughadha E. N., Govaerts R., Belyaeva I., Black N., Lindon H., Allkin R., Magill R. E., Nicolson N., Counting counts: Revised estimates of numbers of accepted species of flowering plants, seed plants, vascular plants and land plants with a review of other recent estimates. Phytotaxa 272, 82–88 (2016).

Pitman N. C. A., Terborgh J. W., Silman M. R., Núñez P. V, Neill D. A., Cerón C. E., Palacios W. A., Aulestia M., Dominance and distribution of tree species in upper Amazonian Terra Firme Forests. Ecology 82, 2101–2117 (2001).

Myers N., Mittermeier R. A., Mittermeier C. G., da Fonseca G. A. B., Kent J., Biodiversity hotspots for conservation priorities. Nature 403, 853–858 (2000). PubMed

Sandel B., Arge L., Dalsgaard B., Davies R. G., Gaston K. J., Sutherland W. J., Svenning J.-C., The influence of late Quaternary climate-change velocity on species endemism. Science 334, 660–664 (2011). PubMed

Sandel B., Monnet A.-C., Govaerts R., Vorontsova M., Late quaternary climate stability and the origins and future of global grass endemism. Ann. Bot. 119, 279–288 (2017). PubMed PMC

Venter O., Sanderson E. W., Magrach A., Allan J. R., Beher J., Jones K. R., Possingham H. P., Laurance W. F., Wood P., Fekete B. M., Levy M. A., Watson J. E. M., Sixteen years of change in the global terrestrial human footprint and implications for biodiversity conservation. Nat. Commun. 7, 12558 (2016). PubMed PMC

Simpson G. G., Species density of North American recent mammals. Syst. Zool. 13, 57–73 (1964).

Janzen D. H., Why mountain passes are higher in the tropics. Am. Nat. 101, 233–249 (1967).

Rahbek C., Borregaard M. K., Antonelli A., Colwell R. K., Holt B. G., Nogues-Bravo D., Rasmussen C. M. Ø., Richardson K., Rosing M. T., Whittaker R. J., Fjeldså J., Building mountain biodiversity: Geological and evolutionary processes. Science 365, 1114–1119 (2019). PubMed

Rahbek C., Borregaard M. K., Colwell R. K., Dalsgaard B., Holt B. G., Morueta-Holme N., Nogues-Bravo D., Whittaker R. J., Fjeldså J., Humboldt’s enigma: What causes global patterns of mountain biodiversity? Science 365, 1108–1113 (2019). PubMed

Hannah L., Midgley G., Andelman S., Araújo M., Hughes G., Martinez-Meyer E., Pearson R., Williams P., Protected area needs in a changing climate. Front. Ecol. Environ. 5, 131–138 (2007).

Dinerstein E., Vynne C., Sala E., Joshi A. R., Fernando S., Lovejoy T. E., Mayorga J., Olson D., Asner G. P., Baillie J. E. M., Burgess N. D., Burkart K., Noss R. F., Zhang Y. P., Baccini A., Birch T., Hahn N., Joppa L. N., Wikramanayake E., A Global Deal For Nature: Guiding principles, milestones, and targets. Sci. Adv. 5, eaaw2869 (2019). PubMed PMC

Intergovernmental Panel on Climate Change, Climate Change 2014—Impacts, Adaptation and Vulnerability: Part A: Global and Sectoral Aspects: Volume 1, Global and Sectoral Aspects: Working Group II Contribution to the IPCC Fifth Assessment Report (Cambridge Univ. Press, 2014).

Hijmans R. J., Cameron S. E., Parra J. L., Jones P. G., Jarvis A., Very high resolution interpolated climate surfaces for global land areas. Int. J. Climatol. 25, 1965–1978 (2005).

Riahi K., Rao S., Krey V., Cho C., Chirkov V., Fischer G., Kindermann G., Nakicenovic N., Rafaj P., RCP 8.5—A scenario of comparatively high greenhouse gas emissions. Clim. Change 109, 33 (2011).

Loarie S. R., Duffy P. B., Hamilton H., Asner G. P., Field C. B., Ackerly D. D., The velocity of climate change. Nature 462, 1052–1055 (2009). PubMed

Wieczorek J., Bloom D., Guralnick R., Blum S., Döring M., Giovanni R., Robertson T., Vieglais D., Darwin Core: An evolving community-developed biodiversity data standard. PLOS ONE 7, e29715 (2012). PubMed PMC

Boyle B., Hopkins N., Lu Z., Raygoza Garay J. A., Mozzherin D., Rees T., Matasci N., Narro M. L., Piel W. H., McKay S. J., Lowry S., Freeland C., Peet R. K., Enquist B. J., The taxonomic name resolution service: An online tool for automated standardization of plant names. BMC Bioinf. 14, 16 (2013). PubMed PMC

Maitner B. S., Boyle B., Casler N., Condit R., Donoghue J., Durán S. M., Guaderrama D., Hinchliff C. E., Jørgensen P. M., Kraft N. J. B., McGill B., Merow C., Morueta-Holme N., Peet R. K., Sandel B., Schildhauer M., Smith S. A., Svenning J.-C., Thiers B., Violle C., Wiser S., Enquist B. J., The BIEN R package: A tool to access the Botanical Information and Ecology Network (BIEN) database. Methods Ecol. Evol. 9, 373–379 (2018).

Goldsmith G. R., Morueta-Holme N., Sandel B., Fitz E. D., Fitz S. D., Boyle B., Casler N., Engemann K., Jørgensen P. M., Kraft N. J. B., McGill B., Peet R. K., Piel W. H., Spencer N., Svenning J. C., Thiers B. M., Violle C., Wiser S. K., Enquist B. J., Plant-O-Matic: A dynamic and mobile guide to all plants of the Americas. Methods Ecol. Evol. 7, 960–965 (2016).

McFadden I. R., Sandel B., Tsirogiannis C., Morueta-Holme N., Svenning J.-C., Enquist B. J., Kraft N. J. B., Temperature shapes opposing latitudinal gradients of plant taxonomic and phylogenetic β diversity. Ecol. Lett. 22, 1126–1135 (2019). PubMed

Fegraus E., Tropical Ecology Assessment and Monitoring Network (TEAM Network). Biodivers. Ecol. 4, 287 (2012).

Peet R. K., Lee M. T., Jennings M. D., Faber-Langendoen D., VegBank: A permanent, open-access archive for vegetation plot data. Biodivers. Ecol. 4, 233–241 (2012).

DeWalt S. J., Bourdy G., Chávez de Michel L. R., Quenevo C., Ethnobotany of the Tacana: Quantitative inventories of two permanent plots of Northwestern Bolivia. Econ. Bot. 53, 237–260 (1999).

Forest Inventory and Analysis National Program (2013); www.fia.fs.fed.us/.

Wiser S. K., Bellingham P. J., Burrows L. E., Managing biodiversity information: Development of New Zealand’s National Vegetation Survey databank. N. Z. J. Ecol. 25, 1–17 (2001).

Anderson-Teixeira K. J., Davies S. J., Bennett A. C., Gonzalez-Akre E. B., Muller-Landau H. C., Wright S. J., Abu Salim K., Almeyda Zambrano A. M., Alonso A., Baltzer J. L., Basset Y., Bourg N. A., Broadbent E. N., Brockelman W. Y., Bunyavejchewin S., Burslem D. F., Butt N., Cao M., Cardenas D., Chuyong G. B., Clay K., Cordell S., Dattaraja H. S., Deng X., Detto M., Du X., Duque A., Erikson D. L., Ewango C. E., Fischer G. A., Fletcher C., Foster R. B., Giardina C. P., Gilbert G. S., Gunatilleke N., Gunatilleke S., Hao Z., Hargrove W. W., Hart T. B., Hau B. C., He F., Hoffman F. M., Howe R. W., Hubbell S. P., Inman-Narahari F. M., Jansen P. A., Jiang M., Johnson D. J., Kanzaki M., Kassim A. R., Kenfack D., Kibet S., Kinnaird M. F., Korte L., Kral K., Kumar J., Larson A. J., Li Y., Li X., Liu S., Lum S. K., Lutz J. A., Ma K., Maddalena D. M., Makana J. R., Malhi Y., Marthews T., Mat Serudin R., McMahon S. M., McShea W. J., Memiaghe H. R., Mi X., Mizuno T., Morecroft M., Myers J. A., Novotny V., de Oliveira A. A., Ong P. S., Orwig D. A., Ostertag R., den Ouden J., Parker G. G., Phillips R. P., Sack L., Sainge M. N., Sang W., Sri-Ngernyuang K., Sukumar R., Sun I. F., Sungpalee W., Suresh H. S., Tan S., Thomas S. C., Thomas D. W., Thompson J., Turner B. L., Uriarte M., Valencia R., Vallejo M. I., Vicentini A., Vrška T., Wang X., Wang X., Weiblen G., Wolf A., Xu H., Yap S., Zimmerman J., CTFS-ForestGEO: A worldwide network monitoring forests in an era of global change. Glob. Chang. Biol. 21, 528–549 (2015). PubMed

Enquist B., Boyle B., SALVIAS—The SALVIAS vegetation inventory database. Biodivers. Ecol. 4, 288 (2012).

GBIF.org, GBIF Occurrence Download; 10.15468/dl.yubndf. DOI

Dauby G., Zaiss R., Blach-Overgaard A., Catarino L., Damen T., Deblauwe V., Dessein S., Dransfield J., Droissart V., Duarte M. C., Engledow H., Fadeur G., Figueira R., Gereau R. E., Hardy O. J., Harris D. J., de Heij J., Janssens S., Klomberg Y., Ley A. C., Mackinder B. A., Meerts P., van de Poel J. L., Sonké B., Sosef M. S. M., Stévart T., Stoffelen P., Svenning J.-C., Sepulchre P., van der Burgt X., Wieringa J. J., Couvreur T. L. P., RAINBIO: A mega-database of tropical African vascular plants distributions. PhytoKeys , 1–18 (2016). PubMed PMC

Arellano G., Cala V., Fuentes A., Cayola L., Jørgensen P. M., Macía M. J., A standard protocol for woody plant inventories and soil characterisation using temporary 0.1-Ha plots in tropical forests. J. Trop. For. Sci. 28, 508–516 (2016).

B. Crandall-Stotler, R. E. Stotler, D. G. Long, Morphology and classification of the Marchantiophyta, in Bryophyte Biology, A. J. Shaw, Ed. (Cambridge Univ. Press, 2008), pp. 1–54.

E. M. Gifford, A. S. Foster, Morphology and Evolution of Vascular Plants (W. H. Freeman, 1989).

Goffinet B., Buck W., Systematics of the Bryophyta (mosses): From molecules to a revised classification. Monogr. Syst. Botany Missouri Bot. Garden 98, 205–239 (2004).

P. H. Raven, R. F. Evert, S. E. Eichhorn, Biology of Plants (Macmillan, 2005).

Bischler H., Schuster R. M., The Hepaticae and Anthocerotae of North America. Bryologist 96, 281 (1993).

B. J. McGill, Species abundance distributions, in Biological Diversity: Frontiers in Measurement & Assessment, A. E. Magurran, B. J. McGill, Eds. (Oxford Univ. Press, 2011), pp. 105–122.

B. A. Maurer, B. J. McGill, Measurement of species diversity, in Biological Diversity: Frontiers in Measurement and Assessment, A. E. Magurran, B. J. McGill, Eds. (Oxford Univ. Press, 2011), pp. 55–65.

M. Evans, N. Hastings, B. Peacock, Mathematical Distributions (1993).

MacArthur R. H., On the relative abundance of bird species. Proc. Natl. Acad. Sci. U.S.A. 43, 293–295 (1957). PubMed PMC

Motomura I., A statistical treatment of associations. Jap. J. Zool. 44, 379–383 (1932).

Preston F. W., The canonical distribution of commonness and rarity: Part II. Ecology 43, 410–432 (1962).

B. Mandelbrot, Information theory and psycholinguistics: A theory of word frequencies, in Readings in Mathematical Social Sciences, P. F. Lazarsfeld, N. W. Henry, Eds. (Science Research Associates Inc., 1966).

Kerkhoff A. J., Enquist B. J., Multiplicative by nature: Why logarithmic transformation is necessary in allometry. J. Theor. Biol. 257, 519–521 (2009).

Galton F., The geometric mean, in vital and social statistics. Proc. R. Soc. London 29, 365–367 (1879).

Gingerich P. D., Arithmetic or geometric normality of biological variation: An empirical test of theory. J. Theor. Biol. 204, 201–221 (2000). PubMed

McAlister D., XIII. The law of the geometric mean. Proc. R. Soc. London 29, 367–376 (1879).

Halloy S. R., A theoretical framework for abundance distributions in complex systems. Complex. Int. 6, 1–16 (1998).

He F., Tang D., Estimating the niche preemption parameter of the geometric series. Acta Oecol. 33, 105–107 (2008).

A. E. Magurran, Ecological Diversity and Its Measurement (Princeton Univ. Press, 1988).

McCarthy B. C., Magurran A. E., Measuring biological diversity. J. Torrey Bot. Soc. 131, 277 (2004).

Izsák J., Some practical aspects of fitting and testing the Zipf-Mandelbrot model: A short essay. Scientometrics 67, 107–120 (2006).

Bulmer M. G., On fitting the Poisson lognormal distribution to species-abundance data. Biometrics 30, 101–110 (1974).

Ziegel E. R., Evans M., Hastings N., Peacock B., Statistical distributions. Technometrics 36, 229 (1994).

McGill B. J., A test of the unified neutral theory of biodiversity. Nature 422, 881–885 (2003). PubMed

R. Margaleff, Temporal succession and spatial heterogeneity in phytoplankton, in Perspectives in Marine Biology, A. A. Buzzati-Traverso, Ed. (University of California, 1958), pp. 323–349.

Menhinick E. F., A comparison of some species-individuals diversity indices applied to samples of field insects. Ecology 45, 859–861 (1964).

Feng G., Ma Z., Sandel B., Mao L., Normand S., Ordonez A., Svenning J.-C., Species and phylogenetic endemism in angiosperm trees across theNorthern Hemisphere are jointly shaped by modern climate and glacial-interglacial climate change. Glob. Ecol. Biogeogr. 28, 1393–1402 (2019).

Feng G., Mao L., Sandel B., Swenson N. G., Svenning J.-C., High plant endemism in China is partially linked to reduced glacial-interglacial climate change. J. Biogeogr. 43, 145–154 (2016).

Kreft H., Jetz W., Global patterns and determinants of vascular plant diversity. Proc. Natl. Acad. Sci. U.S.A. 104, 5925–5930 (2007). PubMed PMC

Park D. S., Razafindratsima O. H., Anthropogenic threats can have cascading homogenizing effects on the phylogenetic and functional diversity of tropical ecosystems. Ecography 42, 148–161 (2019).

Kissling W. D., Carl G., Spatial autocorrelation and the selection of simultaneous autoregressive models. Glob. Ecol. Biogeogr. 17, 59–71 (2008).

R Development Core Team, R: A language and environment for statistical computing (2019); www.r-project.org/.

R. J. Hijmans, J. van Etten, M. Mattiuzzi, M. Sumner, J. A. Greenberg, O. P. Lamigueiro, A. Bevan, E. B. Racine, A. Shortridge, Raster package in R (2013); www.rspatial.org/raster/RasterPackage.pdf.

Calcagno V., de Mazancourt C., glmulti: An R package for easy automated model selection with (generalized) linear models. J. Stat. Softw. 34, 1–29 (2010).

R. Bivand, L. Anselin, O. Berke, A. Bernat, M. Carvalho, Y. Chun, C. F. Dormann, S. Dray, R. Halbersma, N. Lewin-Koh, H. Ono, P. Peres-Neto, M. Tiefelsdorf, D. Yu, spdep: Spatial dependence: Weighting schemes, statistics and models (2011); http://ftp.auckland.ac.nz/software/CRAN/src/contrib/Descriptions/spdep.html.

Evolutionary imbalance, climate and human history jointly shape the global biogeography of alien plants

Climatic stability and geological history shape global centers of neo- and paleoendemism in seed plants

Disentangling the relationships among abundance, invasiveness and invasibility in trait space

The number of tree species on Earth