Global endemics-area relationships of vascular plants

SupportedbyBotic´arioGroupFoundationforNatureProtection

www.perspectecolconserv.com

Essays and perspectives

Global endemics-area relationships of vascular plants

Carsten Hobohm

, Monika Janiˇsová

, Manuel Steinbauer

, Sara Landi

, Richard Field

, Sula Vanderplank

, Carl Beierkuhnlein

, John-Arvid Grytnes

, Ole Reidar Vetaas

,

Alessandra Fidelis

, Lea de Nascimento

, Vincent Ralph Clark

, José María Fernández-Palacios

, Scott Franklin

, Riccardo Guarino

, Jihong Huang

, Pavel Krestov

, Keping Ma

,

Vladimir Onipchenko

, Mike W. Palmer

, Marcelo Fragomeni Simon

, Christian Stolz

, Alessandro Chiarucci

aUniversityofFlensburg(EUF),24943Flensburg,Flensburg,Germany

bInstituteofBotany,PlantScienceandBiodiversityCentre,SlovakAcademyofSciences, ˇDumbierska1,97411BanskáBystrica,SlovakRepublic

cGeoZentrumNordbayern,DepartmentofGeographyandGeosciences,Friedrich-AlexanderUniversityofErlangen-Nürnberg(FAU),Erlangen,Germany

dSectionEcoinformaticsandBiodiversity,DepartmentofBioscience,AarhusUniversity,Aarhus,Denmark

eDepartmentofScienceforNatureandResources,UniversityofSassari,Sassari,Italy

fSchoolofGeography,UniversityofNottingham,NG72RDNottingham,Nottingham,UnitedKingdom

gCentrodeInvestigaciónCientíficaydeEducaciónSuperiordeEnsenada,B.C.,DepartamentodeBiologíadelaConservación,22860Ensenada,BC,Mexico

hUniversityofBayreuth,BayCEER,DepartmentofBiogeography,95447Bayreuth,Germany

iUniversityofBergen,DepartmentofBiology,5021Bergen,Norway

jUniversityofBergen,DepartmentofGeography,5021Bergen,Norway

kUniversidadeEstadualPaulista,(UNESP),InstitutodeBiociências,RioClaro,Brazil

lIslandEcologyandBiogeographyGroup.InstitutoUniversitariodeEnfermedadesTropicalesySaludPública(IUETSPC),UniversidaddeLaLaguna,Tenerife,CanaryIslands,Spain

mGreatEscarpmentBiodiversityResearchProgramme,DepartmentofBotany,RhodesUniversity,Grahamstown,SouthAfrica

nAfromontaneResearchUnit,UniversityoftheFreeState,QwaqwaCampus,Phuthaditjhaba,9866,SouthAfrica

oUniversityofNorthernColorado,Greeley,CO80639,UnitedStates

pUniversityofPalermo,DepartmentSTEBICEF-BotanicalUnit,90123Palermo,Italy

qInstituteofForestEcology,EnvironmentandProtection,ChineseAcademyofForestry,Beijing100091,China

rBotanicalGarden-InstituteFEBRAS,Vladivostok,Russia

sInstituteofBotany,ChineseAcademyofSciences,Beijing100093,China

tLomonosovMoscowStateUniversity,FacultyofBiology1-12LeninskieGory,119234,Moscow,Russia

uOklahomaStateUniversity,DepartmentofPlantBiology,EcologyandEvolution,Stillwater,OK74078-3013,UnitedStates

vEmbrapaRecursosGenéticoseBiotecnologia,Brasılia,DF70770-901,Brazil

wDepartmentofBiological,GeologicalandEnvironmentalSciences,AlmaMaterStudiorum-UniversityofBologna,Bologna,Italy

a r t i c l e i n f o

Articlehistory:

Received3February2019 Accepted19April2019 Availableonline30April2019

Keywords:

Expertknowledge

Minimumandmaximumestimates Zero-endemicplots

Distributionoflandandsea Globalreference

a b s t r a c t

Endemics–AreaRelationships(EARs)arefundamentalintheoreticalandappliedbiogeographyforunder- standingdistributionpatternsandpromotingbiodiversityconservation.However,calculatingEARsfor vascularplantspeciesfromexistingdataisproblematicbecauseofbiasedknowledgeofendemicspecies distributionsanddifferencesbetweentaxonomies.Weaimedtoovercomethesechallengesbydevelop- inganewstandardizedglobaldatasetbasedonexpertknowledgetoproduceasetofglobalEARs.

Wedevelopedanestedcircledesign,withgrainsizesof10⁴,10⁵,10⁶,10⁷,and10⁸km²,respectively, andaglobaldistributionofplotsbasedonastratifiedrandomscheme.Thenumberofvascularplant speciesendemictoeachcirclewasthenestimatedindependentlybyfiveexpertsrandomlychosenfrom apoolof23,asbothaminimumandamaximumvalue(lowerandupperboundsoftheestimation),taking intoaccountthelimitationsofcurrentknowledgeandvariedspeciesconceptsinexistingtaxonomies.

Thisprocedureresultedinadatasetof3000expertestimates.

Basedonthedata,weproducedthreeglobalEARsforendemicspeciesrichnessusingminimum,maxi- mumandaverageestimates.Asavalidation,weusedallthreemodelstoextrapolatetotheentireworld, producingestimatesof284,493(minimum),398,364(maximum)and312,243(average)vascularplant species.Thesefiguresconformtotherangeoftaxonomists’estimates.Fromthemodels,wecalculated theaverageareaneededtoharbourasingleendemicspeciesas12,875km²(range9675–20,529).

∗ Correspondingauthor.

E-mailaddress:[email protected](A.Chiarucci).

https://doi.org/10.1016/j.pecon.2019.04.002

2530-0644/CrownCopyright©2019PublishedbyElsevierEditoraLtda.onbehalfofAssociac¸˜aoBrasileiradeCiˆenciaEcol ´ogicaeConservac¸˜ao.Thisisanopenaccessarticle undertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

CrownCopyright©2019PublishedbyElsevierEditoraLtda.onbehalfofAssociac¸˜aoBrasileiradeCiˆencia Ecol ´ogicaeConservac¸˜ao.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://

creativecommons.org/licenses/by-nc-nd/4.0/).

Introduction

Taxa withrestricted geographical distribution (here termed endemicswhenfullycontainedwithinagivensamplingunit)are fundamentaltobiogeographyandbiodiversityconservation.They areusedfordelineatingbiodiversityhotspotsandshapinginter- nationaland national conservationpolicies(Myersetal., 2000;

Mittermeieret al., 2005; Beierkuhnlein, 2006; Hobohm, 2014).

Understanding the distribution patterns of endemic species is increasinglyimportantforbiodiversityconservationanditsplan- ning.However,baselinedataonendemisminvascularplantsare scarce, and very uneven in theirquality and geographical dis- tribution(Kierand Barthlott,2001; Stohlgren,2007; Kier etal., 2009;Storchetal.,2012;Guerinetal.,2015).Despiteeffortsto improveknowledgeofplantbiodiversity(e.g.,GlobalStrategyfor PlantConservationhttps://www.cbd.int/gspc/strategy.shtml)and approximately2000newplantspeciesdescribedeachyear(RBG Kew,2016),ourknowledgeoftheworld’splantspecieslistisfar fromcomplete(the‘LinnaeanShortfall’,BrownandLomolino,1998;

Oliveiraetal.,2016).Anothermajorproblemforunderstanding distributionpatternsofendemicsisthatourknowledgeofthose plants’geographicalrangesisfarfromcomplete(the‘Wallacean Shortfall’,LomolinoandHeaney,2004;Meyeretal.,2016;Oliveira etal.,2016).

Endemics-AreaRelationships(EARs)arefundamentaltoolsfor understandingbiodiversityandendemismpatterns.Theycanpro- videreferencevaluesagainstwhichtocompareobservednumbers ofendemicsinanyspecifiedarea,servingasabasisforanalysing andinterpretingpatternsofplantendemismatdifferentspatial scales.However, fitting suchmodels requires comparable data acrosslargeareas,and is therefore hinderedbya range of key problems,including:(1)insufficientdataavailability,(2)geograph- icalvariation in taxonomies and species concepts,(3) different shapesoftheareassampledinproducingexistingdata,(4)different shapesoftheregionsintowhichdatahavebeenaggregated(often definedbypoliticalborders),and(5)inconsistencybetweenwhat isincludedinsuchaggregationunits.Anexampleof(5)isthatdata forcertaincountriesmayincludeonlymainland(e.g.,Switzerland, Paraguay),setsofislands(e.g.,CaboVerde,Seychelles,Mauritius) ormainlandplusislands(e.g.,Spain,Greece,USA)(Barnoskyetal., 2005;Pyˇseketal.,2008;TrimbleandvanAarde,2012;Güleretal., 2016).Biasesrelatedtotaxonomyandbiogeographyreducethe abilitytomakesoundcomparisonsofdiversitypatterns,except whenreliablegriddataareavailableand thespecies conceptis consistent(Storchetal.,2012;Hobohm,2014).

Giventheselimitationsandshortfalls,weaimedtomodelthe globalrelationshipbetweenthenumberofendemicvascularplant speciesandareausingaradicallydifferentapproachtoanything ofwhichweareaware,startingbygeneratinganewsetofcompa- rabledata,basedonstandardized,spatiallynestedsamplingunits (Stohlgren,2007;Storch,2016).Sinceavailabledataonvascular plantspecies’distributionscurrentlydonotfitthispurpose, we usedexpert knowledge tointegrateinformation fromavailable florasanddistributionmaps toestimatethenumberof species endemictoeachsamplingunit.Expertknowledgeplaysanimpor- tantroleintheanalysesofecologicalandevolutionaryprocesses

inspaceandtimewheneverempiricaldataarescarceorweak,or relatingmodelsaremissing(McBrideandBurgman,2012).This is becausethestandardizationand conceptualdata harmoniza- tionisachievedbyutilizingtheknowledgeandunderstandingof endemismpatternsbuiltupovertheircareersbyexperts.

Ourmaingoalwastodevelopasetofmodelsfortherelationship betweenthenumberofendemicvascularplantspeciesandarea, usinganapproachtoavoidorbypassthebiasesand difficulties resulting fromdifferent taxonomiesand species concepts, geo- graphicaldistributionofsea,mainlandandislands,differentshapes orsizesofsamplingunitsandregions,andinsufficientandbiased existingdata.WesetouttoproduceaglobalEARthatisasaccurate aspossible,butalsoparallelEARstogiveminimumandmaximum valuesforeachgivensamplingunitsize,takingintoaccountthe rangeof speciesconceptsusedin differenttaxonomiesandthe deficienciesinourknowledgeofspeciesandtheirdistributions.

Methods

Nestedcircledesign(NCD)

Oursamplingdesignwasbasedon60geographicalpoints,ran- domlylocatedontheEarth’ssurfaceusingthefollowingprotocol.

WedividedtheEarth’ssurfaceinto12sectors,6intheNorthern and6intheSouthernhemisphere(seeAppendixS1inSupporting Information,forgeographicaldetails).Eachsectorwasasliceofthe Earthof60^◦oflongitude,stretchingfromtheequatortotheNorth orSouthPole.Wegenerated5randompointsineachsector,such thatallpartsofthesurface,whetherlandorsea(henceradically differenttoexistingapproaches),hadanequalchanceofselection.

Then,weconstructed5nestedcircularplots,centredoneachpoint, withareas(grainsizes)of10⁴,10⁵,10⁶,10⁷,and10⁸km²,respec- tively.Thisprocedurecorrespondstoastratifiedrandomsampling ofnestedplotswiththesamecentre(Stohlgren,2007).Forreasons ofcomparison,weimplementedthesamenumberofplotsforeach grainsize(n=60).Asthelargestplotsizecoversalmostafifthofthe Earth(e.g.,Fig.1e),manyoftheseplotsoverlap(Fig.1e).Thecircular shapewaschosenbecauseallpointsontheedgehavethesamedis- tancetothecentre,minimizingtheperimeter/arearatio.Wecon- sideredthisimportantgiventhataspecies’rangemustbeentirely containedwithinthesamplingunitforthatspeciestobeendemic.

TheNCDprovidessimple unitsforestimatingthenumberof endemicplantspecies,unaffectedbythedistributionoflandand sea,differentshapesofsamplingunits,orbiaseddistributionsof plots.Conceptually,ifarelativelysmallsamplingunitiscentred ontheCanaryIslands,orthetropicalAndes,weconcludethatthe areahasmoreendemicvascularplantspeciesthanisaverageacross thewholeplanet’ssurfaceforasamplingunitofthatsize.Bythe sametoken,iftheunitisinthemiddleoftheAntarcticicecap, orapartoftheseawithfewornoislands,andthereforecontains noendemicvascularplantspecies,weconcludethatthisareahas fewerendemicspeciesthanisaverageacrossthewholeplanet’s surface.Inbothcases,thereasonsarewellknownfrombiogeogra- phy.Whiletheseexamplesmaybetrivial,theyillustratethatour conceptofaglobalendemismreference,providedbytheresulting EARs,appliesanywhereonEarth.

Fig.1.Exampleofthenestedcircledesign(NCD).Grainsizes(a)10⁴km²,(b)10⁵km²,(c)10⁶km²,(d)10⁷km²,and(e)10⁸km².Allthecirclesarecentredonthepoint43N, 18E,whichisnearDubrovnik.ThesmallestgrainsizescoverpartsofBosniaandHerzegovinaandtheCroatiancoast;thelargestincludespartsofNEAmerica,Eurasiaand Africa(seeAppendixS1inSupportingInformation).Notethatthisillustrationisschematiconly,showinghowtheNCDwasorganized;highresolutionmapswereutilized fortheestimates.

Databasecompilation

Sincepublisheddistributionaldataofendemicvascularplants forarandomsamplingatglobalscalesarenotavailable,andin ordertoachievethestandardizationandconceptualharmonization requiredofthedata,wecreatedadatabaseusingexpert-estimation ofthenumbersofendemicplantspeciesforeachcircularplot.Over- all,23expertsparticipated.Foreachrandomlyselectedpoint,five oftheseexpertsindependentlyestimatedtheminimumandmax- imumnumberofendemicspeciesineachofthefiveplotscentred onthatpoint.Eachexpertwasprovidedwiththesamesetofinfor- mationfromexistingflorasanddata,asareference,butwasasked toexercisehis/herownjudgementfromexperienceofresearchin thisfield.Thefirstexpertstoproduceestimateswerethreeofthe authors(CH,ACandMJ),whoalsocoordinatedtheprocess.Then, 20otherexpertswereinvitedtoproduceindependentestimates ofrandomlyallocatedplots,withoutknowingwhattheotheresti- mateswereforthoseplots. Further,eachexpertwasnotaware oftheidentitiesoftheotherexpertsprovidingestimatesforthe sameorotherplots,ensuringthattheydidnotcommunicateamong themselvesabouttheirestimatesorabouttheirapproachtocalcu- latingthoseestimates.Subsequently,allexpertswereinvitedto jointheteamforproceedingwithanalysesand writing,andall accepted(becoming co-authors).Part of thegroupthen metin Flensburg,Germany,2nd–6thFebruary2018,toplantherestof theresearch.Theoverallprocedurewasdesignedtoharnessthe advantagesofusingexpertknowledge,whilebeingawareoftypi- caldisadvantages(AraújoandNew,2007;McBrideandBurgman, 2012),whichwesoughttominimizebydeterminingtheconsensus ofexpertestimatesforeachplot.

Theprocedureresultedin3000records,eachbeinganestimate ofthenumberofendemicvascularplantspeciesinacircularplot (i.e.,12sectors×5points×5magnitudes×2min/max×5experts).

Althoughthedatasetproduced isnot perfect,theestimatesare basedonthebestandmostup-to-dateavailabledata,andmaybe consideredtorepresentthecurrentstateofknowledge–includ- ingthevariabilityamongtheestimates.Thenumbersofendemics inmanybiogeographicalanalysesorconservationreportsareoften basedonexpertopinionsthatdependondifferentspeciesconcepts (cf.Myersetal.,2000;Mittermeieretal.,2005).Furthermore,many of thepublishednumbersof endemic species withinparticular regionshaverecentlybeenadjusted,andtheseimprovementsare

ongoing.Therefore,weconsiderthedataobtainedbyourapproach tobecomparable in qualitytodataused forother researchon endemismatcoarsespatialscales(Storchetal.,2012;cf.Tables 5.1–5.5inHobohmetal.,2014),withthemajoradvantageofbeing comparableacrosstheworld.

Descriptiveandinferentialstatistics

Theminimumandmaximumnumberofendemicplantspecies ineachcircleoftheNCDareheremadeavailableforfuturestudies (seeAppendixS1inSupportingInformation).Foreachcircle,we usedmedianvaluesacrosstheexpertstoeliminatetheinfluence ofoutliersandimprovetheestimate(BatesandGranger,1969).

Thevariabilityamongestimatesbyexpertsforthesamecirclewas calculatedbyusingstandardizedAnalysisofVariance(Foxetal., 2015).

Endemics–arearelationships(EARs)andextrapolationofplant speciesrichnesstothewholeEarth

Tomodelthenumberofendemicspeciesasafunctionofarea, wecalculated linear,powerandpolynomialEARs (Storchetal., 2012).TheArrhenius(1921)powerfunction,which isthemost frequentlyusedmodelinthecontextofSARs(species–arearela- tionships)andEARs(Drakareetal.,2006),wasthebestfittingcurve totheseriesofestimatespresentedhere(seeResults).Sincethe numberofendemicsinalargenumberofplotswasestimatedas zero,weusedthenon-logarithmicformoftheArrheniusequation:

E=cA^z (1)

where Eisthe numberof endemicvascular plantspecies, A is thesurface areaof thecircle,in km², cand zare twofitted parametersrepresentingtheintercept(i.e.thenumberofendemic speciesperunitarea)andtheexponent(whichisalsotheslope oftheincreaseofthelog(numberofendemicspecies)perunit increaseinlog(area)),respectively.WefittedEquation(1)using threedifferentdatasetsextractedbythetenestimatesprovided by the experts per each circle (5 experts×2 values): the first composedbythemedianvalues(n=300),thesecondcomposed bytheminimumvalues(n=300)andthethirdcomposedbythe maximum values (n=300). Model fitting was performed using

planet,andcomparingtheresultswiththosederivedfromother waysofestimatingthetotalnumberofvascularplantspecieson Earth,asdonebyStorchetal.(2012)forvertebrates.Fortheentire Earth,thenumberofendemicspecies(E)equalsthetotalnum- berofspecies(S).Weusedourmodelstocalculatethenumber ofendemicvascularplantspeciesfortheEarth,byextrapolating toA=510,000,000km².Wealsousedthemodelstocalculatethe averageareaharbouringonesingleendemicspecies.Wecompared theresultswithpublishedestimatesofthetotalnumberofvascular plantspecies.

Results

Estimatednumberofendemicvascularplantspecies

Ofthe3000estimatesofthenumberofendemicspeciesina circularplotinourdataset,about40%werezero.Mostofthese zeroestimateswereforplotsofthefinergrainsizesandcentred onpointsinthesea(Table1).Overall,about51%oftheestimates inplotscentredintheseaandabout83%ofthoseinplotscen- tredonlandinclude endemics(Table1).As expectedfromthe widerangeofbiogeographicalandecologicalfeaturesofdifferent regionsonEarth,theestimatesofnumbersofendemicplantspecies inplotsofthesamesizedifferconsiderably(Fig.2,Table2;alsosee AppendixS1inSupportingInformation).Thehighestcoefficientof variation,withavalueof2.236(223.6%),resultedwhenfourofthe fiveestimatesforacertainplotandmagnitudewerezeroendemics andtheotherestimatewasoneor moreendemics.Despitethe highcoefficientofvariation,thesefrequentcasesrepresentsmall absolutedifferencesinestimates.Despitethehighvariancewithin each grain size and theuncertainty inherent to the estimates, valuesestimatedbydifferentexpertsareingeneralsurprisingly similar,asshownbythemeanofthecoefficientsofvariationcal- culatedonthevaluesprovidedbythefiveexpertsforeachcircle (Table2).

Endemics–AreaRelationships

Fig.3illustrates thevariation ofendemicspeciesrichness in spaceandacrossgrainsizes.Onenotablefeatureishowthespatial patternsintherichnessofendemicschangewiththegrainsize.

FittingtheArrheniuspowerfunction(Table3)tothedataset comprisingthemedianvaluesofallestimatesproduceanR²values of0.68.Fittingthefunctiontotheminimumandmaximumexpert estimatesgaveR²valuesof0.65and0.67,respectively.Thecvalue, i.e.thenumberofendemicspeciesperunitofarea(here1km²), isextremelysmall,asexpected.Alsoasexpected,thezvaluesare alwaysalittlelargerthan1.Thebest-fittingEAR(forallmedian values)isdescribedbytheformulaE=0.00001227·A^1.195.

ExtrapolatingtothesurfaceareaoftheEarth,themodelesti- mates312,243 vascular plant species. Using the model for the mediansoftheminimumestimatesgivesatotalof284,493species, whileusingthemodel forthemediansofthemaximatheesti- mategivesatotalof398,364species.Theassociatedaverageareato findasingleendemicspecies(Table3)isestimatedas12,875km², rangingfrom9675to20,529km²(medianvaluesformaximaand minima,respectively).

At biogeographical scales, numbers of species are typically counted,estimatedandassembledbymanyresearchersusinghet- erogeneoussources, and asa resulttheycanbeheterogeneous andvariableinquality(Chiaruccietal.,2011).Formanyregions onEarth,itis stillimpossibletogetaccuratedataonthenum- berofendemicvascularplantspecies,andevenwherereasonable dataexist,differencesinmethodologyandspeciesconceptscause largevariationinestimatesorcountsforthesameregion(Hobohm, 2014).

Mostofthepublisheddataonthenumberofendemicspecies arerelatedtopoliticalunits,suchascountriesorprovinces.Very often,whennumbersdorefertonaturalbiogeographicalunits,they referspecificallytoislands,archipelagosormountainranges(cf.

Hobohm,2014).Manylargecountriesathighlatitudesorinarid regionsarerelativelypoorinendemics,whilemanyislandsintrop- icalandsubtropicalregionsareextraordinarilyrichinendemics (GroombridgeandJenkins,2002;Kieretal.,2009).Usingthesedata, whicharestronglybiasedinspatialrepresentativeness,doesnot guaranteeamodelreflectingtherealandhighlyunevendistribu- tionofendemicplantsonEarth.

The sequences count – estimate– guess and fact – hypothe- sis–speculationareoften consideredtoindicate anorderfrom scientificcertaintytoweakconjecture(Franklin,2009;Burgman etal.,2011).Expertknowledgeissometimesassociatedwiththe weakersideofscience,thoughspecies’rangemapsareoftenbased inlargepartonsuchknowledge.Nobodyknowstheexactnum- berofendemicspeciesinacircularplotconstituting20%ofthe Earth’ssurfaceandincludingpartsofdifferentcontinentsandmany islands.However,intheabsenceofidealdata(exacerbatedbythe recent,widespreadreductioninsupportforsystematics,taxonomy andotherareasofbasicscience),theuseofexpertknowledgeis increasinglyimportant,especiallyinnatureconservationscience andpractice(MaddockandSamways,2000;Drescheretal.,2013;

Grêt-Regameyetal.,2013).Thisisforatleasttworeasons.First, natureconservationpracticecannotwaituntilallindividualsand speciesofalltaxonomicgroupsinaregionarecountedoriden- tified;natureconservationmanagementoftenhastoactonthe basisofimperfectdata,ordespitealackofknowledge.Weused expertknowledgesimplybecauseofthelackofadatasetappro- priateforcalculatingglobalplantEARsforareasofstandardized grainandshape.AsweoutlineintheIntroduction,thecountsthat doexistcannotbecomparedorcombinedandanalysedwithout biasedresults.OurfirstglobalvascularplantEARcancertainlybe improvedinthefuture,butfornowaddressesthelackofsucha toolwithareasonablemodel.Second,measuresofuncertaintycan bebuiltintotheuseofexpertknowledge,asherein.Whenthisis done,expertknowledgedoesnotnecessarilyresultinweakercon- clusionsthanmodelsbasedonincompleteorbiasedoccurrence data(cf.Yamadaetal.,2003;Pereraetal.,2012;Taraetal.,2012;

Resideetal.,2019).

Wethereforeconsiderthatharnessingexpertknowledgeisthe bestapproachtoovercomingthelackofaccurateempiricaldata andbiasedresults.Weaccountedforuncertaintiesassociatedwith datadeficienciesandvaryingspeciesconceptsbyestimatingmini- mumandmaximumvaluesforthenumberofendemicsineachplot.

Further,ourcombinationofestimatesbyfiverandomlyselected expertsperplotreduceserrorsassociatedwiththesubjectivepart ofthisprocess(McBrideandBurgman,2012).Inourdata,thehigh- estvariabilityamongexperts’estimateswasobservedatplotsizes intherange100,000–10,000,000km²,forboththeminimumand maximumvaluesofendemicspeciesrichness.Becausetheplotsof thesmallestsize(10,000km²)oftenrepresentareaswithoutvege-

Table1

Numberofestimateswithorwithoutvascularplantendemicsinthecircularplots,accordingtothelocationoftheircentre(landorsea)andtheplotsize.

Locationofthecentre Presenceofendemics Area(km²) Total

10⁴ 10⁵ 10⁶ 10⁷ 10⁸

Land Yes 98 126 150 163 170 707

No 72 44 20 7 0 143

Sea Yes 40 106 180 342 430 1098

No 390 324 250 88 0 1052

Total 600 600 600 600 600 3000

Fig.2.Minimumandmaximumestimates(medianestimateforeachplot)ofthenumberofendemicvascularplantspeciesforthevariousplotsizesbasedontheestimates providedbytheexperts.ThelargestplotsizerepresentsvaluesforthewholeEarth(seetext).Boxesindicateinter-quartilerangeswhilewhiskersindicatetheranges.Richness valueshavebeenaddedto1toallowplottingonalogscale.

Table2

Estimatedminimaandmaxima(medianestimateforeachplot)andcoefficientsofvariation(meanandrange).Whenallfiveestimatesofthenumberofendemicvascular plantspeciesrelatedtoaspecificcircularplotwerezero,thecoefficientofvariationwasdefinedaszeroaswell.

Area(km²) Minimaofendemics Maximaofendemics

Medianestimate Meancoefficient ofvariation

Rangeofcoefficientsof variation

Medianestimate Meancoefficient ofvariation

Rangeofcoefficientsof variation

10,000 0 0.492 0–2.236 0 0.537 0–2.236

100,000 0 0.755 0–2.236 0 0.598 0–2.186

1,000,000 1 0.759 0–2.236 10 0.742 0–2.236

10,000,000 400 0.924 0–2.236 928 0.741 0–1.705

100,000,000 33,700 0.360 0.075–1.038 50,000 0.358 0.095–1.054

Table3

ModelfittingoftheEndemics–AreaRelationships(EARs)basedontheArrheniuspowerfunction,extrapolationtothetotalnumberofvascularplantspeciesonEarth(that isthetotalspeciesrichnessoftheEarth)andextrapolationoftheaverageareawithoneendemicspecies(basedonmedianvaluesofallestimates,ofminimaandmaxima, respectively).

Medianvalues R² c z Estimatednumberofvascular

plantsonEarth

Areawithoneendemicplant species(km²)

Allestimates(n=300) 0.68 0.00001227 1.195 312,243 12,875

Minima(n=300) 0.65 0.00000445 1.241 284,493 20,529

Maxima(n=300) 0.67 0.00001875 1.186 398,364 9675

tation,orwithminimalvegetation,manyestimateswerezeroat this scale.Atintermediate plotsizes(100,000–10,000,000km²), many of the circles had zero and non-zero estimates, result- ingin relativelyhighproportionalvariation betweenestimates.

For many islands and countries, official estimates of numbers of endemic species have had tobe adjusted in recent decades becauseofbetterknowledgeandchangingtaxonomies(Hobohm, 2014).Thelargestcirclesinouranalysis,ontheotherhand,usu- allycontainentireendemic-richfloristicregions,nozero-endemic estimates,and thus, thevariationbetween themwasrelatively low.

Samplingdesign

Incomparisonto‘strictlynestedquadrat’(SNQ)and‘continen- talshape’(CS)designs(Storchetal.,2012;Storch,2016),theNCD hasnoplotlargeenoughtoincludethewholeoralmostthewhole surfaceoftheEarth.However,thenumberofNCDsamplingunits pergrainsizeiskeptconstant(n=60inthisapplication),whereas thenumberofsamplingunitsdeclineswithincreasinggrainsize bothintheSNQandCSdesigns.Havingthesamenumberofsam- plingunitspergrainsize,NCDallowsmorespatiallyrepresentative estimates.

Fig.3.a-eMapsshowingthepositionofthecircularplotsandestimatesofthediversityofendemicvascularplants(medians,aslog(e+1))incircularplotsof10⁴(a)to 10⁸km²(e).Sizesofsmallcirclesin(a)and(b)areexaggeratedtoaidinterpretationand,ineachpanel,onepointcentreiscoveredbythelegend.Coloursreflecttheamount ofendemism;blueindicatinglowandredhighnumbers.Thedistortionofthecircularplotstowardsellipsesinhighlatitudesisanartefactofthecartographicreferencewe used,hatbasedongeographicco-ordinatesprovidedbyWorldClim(WGS84Datum)..

Thereare currently few published EAR models for vascular plants(CowlingandSamways,1995;Hobohm,2003;Georghiou andDelipetrou,2010;HobohmandTucker,2014).Curvesforthe Greekmainlandandislandregionswererelativelysteep,withz- valuesof1.49and1.15,respectively(GeorghiouandDelipetrou, 2010).Thecurveforacombinationofmainlandandarchipelagos (GeorghiouandDelipetrou,2010),incontrast,wasshallow(z-value of0.42).Thisexampleshowshowthesamplingof geographical unitscanstronglyaffect theresultingEAR,when checklistsare combined.Ourz-valuesareslightlyhigherthan1,asexpectedfor EARsatthisscale(Storchetal.,2012).Ourmethod,coupledwiththe useofensemblesofexpert-derivedestimatestogeneratethedata, isintendedtoprovideastandardizedestimateofendemicspecies richnessperunitareathatisunbiasedanddirectlycomparablein termsofgrainsizeandshape,thusreducingrelatingproblemsof inconsistency.Theresultsofthevarianceanalysis,thecomparison withtheoreticalexpectations(Kieretal.,2009;Storchetal.,2012;

Storch,2016;HobohmandTucker,2014),andtheresultsproduced byextrapolatingtothetotalnumberofvascularplantspecieson Earth,indicatethatourmodelisreasonable,andhaspotentialfor furtherapplications.

Becauseofthenewsamplingdesign,theresultsofthemodels wepresentarenotdirectlycomparabletoformerlypublishedmod- els.Recentlypublishedcurves(Storchetal.,2012;Storch,2016) showa slightlyascendingEARtotherighthandsideinlog–log spaceatglobal.Thiscanbeexplained bythelesserrepresenta- tionofregionsattheedgesofcontinents,whichareoftenmore richinendemicsthanthemoreinlandregions(DavidStorch,pers.

comm.,2016).TheNCDdoesnotshowsuchaneffectbecausethe

numberofunitsforeveryplotsizeisthesame(n=60),andproba- blyalsobecausethecircledesignincorporatesthesegeographical gradients,asdiscussedinthenextsection.

Distributionoflandandsea,andrepresentationofsampleswith zeroendemics

Itmightnotseemusefulorappropriatetoincludeareaswithout terrestrialvegetationinouranalysis.However,shouldplotswithno endemicplantspecies,suchasregionsoftheoceanwithoutislands, beexcludedfromsamplingoranalyses?Ifyes,thenwhatabout otherwaterbodieswithincountries,someofwhichdonotcontain endemicvascularplants,thatarenotusuallyexcludedfromcalcula- tionsorestimates?Orwhatabouticecaps,barerockorunvegetated desert?Further,seagrassesshowthatvascularplantscanlivein theoceans.However, almostallseagrass-beds arespecies-poor anddominatedbywidespreadspecies,givingverylownumbers ofendemicsinanylocalmarinearea.Thisispartoftheglobalpat- ternofvascularplantendemism.Ourapproachthereforehighlights thattheareascoveredbyseasarenotqualitativelyverydifferent fromareascoveredbylakes,icecaps,orsandydeserts,fromthe pointofviewofplantspeciesdiversityandendemism.

Whileitmayseemtrivialthatmostplotscontainingnohabit- ablelandhavenoendemicvascularplants,theisolationcreated bytheseregionsthatareinhospitabletovascularplantsiskeyto whymanyislandsintheoceanhavesomanyendemics.Thesame applies,toalesserextent,aroundcoastlines.Ourapproachdoes notexcludethoseinfluences,thusbringingthephysicalgeography oftheEarthintoourmodellingandintotheresultingreference

valuesforthenumbersofendemics.Thedistributionofendemics isa patternthat developsover longtime-periods,of whichthe present-dayisasnapshot,andisaffectedbyevolutionaryprocesses relatedtocontinentaldriftandchangingecologicalconditions,by isolationanddispersal,and thus,bythedistributionpatternsof landandsea(e.g.Huston,1994;Gaston,1996).Toproduceaglobal referenceandtohelpinunderstandingthepatterns,itisappropri- atetoincludealltheseareasinthemodels.Ourapproachtherefore hasstrengthsnotsharedbyothers,includingovercomingsomeof thebiasesaffectingotherapproaches,suchasthecontinental-edge biasidentifiedbyDavidStorch(pers.comm.,2016).

Eliminatingzero-endemicplots,especiallyatthesmallestsize, wouldincreasetheaveragenumberofendemicsofthesmallersizes andflattenthecurve(cf.CowlingandSamways,1995;Williams, 1996).Weconsideritinappropriatebecausethesamplingdesign musthavepriorityandshouldbeindependentoftheresult;the distributionofplotswithandwithoutendemicsistheresult.More- over,previousSARsandEARshaveusedsampleswithzerovascular plantspeciesorzeroendemicplantspecies,respectively(Green andOstling,2003;WernerandBuszko,2005;DenglerandBoch, 2008;Duarteetal.,2008;GeorghiouandDelipetrou,2010;Storch etal.,2012;Polyakovaetal.,2016).Sinceweweredevelopinga globalEAR,wewantedtorepresenttheoverallglobalpatternof endemics,includingregionswithmanyorfewendemics,aswellas aridorcoldregions,glaciersorocean,wherewedidnotexpectto findanyendemicplants.

Forallthesereasons,weconsiderthatthereisnobiogeograph- icalargumenttoexcludezero-endemicplotsfromoursamplingor analyses.Further,wesuggestthattheresultingmodelsreflectthe totalnumberofvascularplantspecieswell(seenextsection)inpart becausewedidnotexcludezero-endemicplotsfromsampling.

Modelextrapolationsandtotalnumberofvascularplantspecies onEarth

Atpresent,thetotalnumberofvascularplantspeciesestimated onEarthvariesalotbetweenpublishedestimates,dependingon thedatasourcesandtheassociatedtaxonomicorotherbiases.The numberofseedplantshasbeenestimatedas223,300(Govaerts, 2001),352,000(ScotlandandWortley,2003)and422,127(Paton etal.,2008),forexample.Estimatesof308,312(Christenhuszand Byng,2016),315,903(Kieretal.,2009)and383,671(NicLughadha etal.,2016)werecalculatedforthetotalnumberofvascularplant species,and298,000(Moraetal.,2011)and320,000(Groombridge andJenkins,2002)forallplants.Clearly,presentknowledgeisvery incompleteandneedsfurtherdatagatheringandintegration.Fur- thermore,itisdifficulttocalculatepotentialoverestimationand underestimationresultingfromtaxonomicornomenclaturalarte- facts,and potentialunderestimationreflecting thelikelihood of ongoingexplorationanddiscovery(Ungricht,2004).Bearingthese limitationsinmind,andassumingthatpteridophytescomprisec.

13,000–14,000species(NicLughadhaetal.,2016),estimatesfor allvascularplantspeciesonEarththusrangebetweenc.236,000 andc.436,000.Thevaluesweestimatedherefitsquarelywithin thatrangeofpublishednumbers,givingussomeconfidenceinthe qualityofourassembleddataandmodels.

Extrapolating in theotherdirection, ourmodelsgive values rangingfrom9675(mediansofmaxima)to20,529km²(medians ofminima) for thereferenceareatoinclude onlyone endemic species(Table3).Thesevaluesrepresenttheaverageexpectations ofourmodelsforthewholesurfaceoftheEarth,includingmarine andterrestrialregions.AccordingtotheformulainGeorghiouand Delipetrou(2010)formainland Greece(aMediterraneanregion knownfor being rich in endemics), one endemic plant species cantypicallybeexpectedinanareaof1374km².Appropriately, accordingtoourmodels,thatareaisendemic-rich.Fromtheoretical

assumptions,HobohmandTucker(2014)foundthattheterres- trialregions(islandormainland)harbouringasingleendemicplant speciesshouldbelargerthan493km².Again,theseestimatescan beimprovedwithfurtherresearch.

Ingeneral,SARsandEARs,suchasthoseweproduced,canbe used toidentifyareas that are significantly richeror poorer in speciesorendemicspeciesthanaverage.AsLomolino(1982)has shown,theregressionresidualsgivethepossibilitytoquantifythe diversityofendemicsinaregionaslog-distancetotheregression lineforeverysizeofarea(seealsoHobohm,2003;Duarteetal., 2008).Thus,themodelspresentedherecanbeconsideredasaver- agetheoreticalexpectations,orreferencevalues,forcomparingand analysingthedistributionpatternsofvascularplantendemismon Earthinareasofstandardizedcirculararea.Asanexample,thearea ofHawaii(BigIsland)isslightlylargerthan10,000km²andhosts82 endemicplantspecies(Price,2004),thushavingc.81moreendemic speciesthanexpectedforacircularareaof10,000km²andbetween 65and74endemicspeciesmorethanexpectedforacirculararea of100,000km².Fromthis,weinferthatthereisastrongconcentra- tionofendemisminthisisland–inlinewithreceivedwisdom,and demonstratingourapproach.Ontheotherhand,manyregionson Earth,suchaspartsoftheoceans,coldoreventemperateregions suchasmanylowlandregionsinEurope(Hendrych,1982),have veryfeworevennoendemicvascularplantspeciesinrelatively largeareas.

Conclusions

Our models providethefirst global referenceagainst which observednumbersofendemicvascularplantscanbecompared, foreachregion(>10,000km²)onEarth,eitheronterrestriallandor inmarineecosystems.Theultimateaimistoenhanceourcurrent understandingofspatialpatternsofplantendemismwithrespect to evolution, environment and ecology (Ferriere and Legendre, 2013).Bydevelopinganovelstandardizeddesign(thenestedcir- cledesign,NCD)andharnessingexpertknowledge,wehavestarted theprocessofderivingreferencevaluesthatovercomeorbypass thecurrentgeographical,taxonomicandmethodologicalproblems.

TheEndemics–AreaRelationships(EARs)herecalculatedresulted ininterceptandslopevaluesthatareconsistentwiththeoretical considerations,andshowaremarkablygoodextrapolationofthe totalnumberofvascularplantspeciesonEarth,givingconfidence inthemethodologyweadopted(cf.CowlingandSamways,1995;

Hobohm,2003;HobohmandTucker,2014).Asasignificantresult, weestimated thetotalvascular plantspeciesrichness onEarth between284,493and398,364species,withanexpectedvalueof 312,243species,andweprovidedreferencevaluesofendemicsfor circulararearangingingrainfrom10⁴km²to10⁸km².

Finally,wewishtostressthatbasicsciencestillisvitaltounder- standing Earth’s biodiversity, and deserves considerably more credit andinvestment thanit iscurrently afforded.Despite the veryincompletebasicknowledgeforvascularplants,weproduced biodiversitymodelsofendemismthatappeartoberealistic,but thesehadtobebasedonexpert estimates.Formanytaxa with greatdiversityandlimitedtaxonomicknowledge,theknowledge gapissolargethatitwouldnotbepossibletomodelendemism, evenusingexpertestimates.Traditionaldescriptivescientificdisci- plines,suchastaxonomy,systematicsandbiogeography,improve ourknowledgeofspatialpatternsofplantdiversityatglobalscales (e.g.,Barthlottetal.,2007),andallowresearchonregionalplant diversitychangesatcentennialtimescales(e.g.,Chiarucci etal., 2017).However,acompleteunderstandingofglobalpatternsand processesisstillalmostimpossiblebecauseofthelackofavailable referencedata.Inthispaper,weprovideamethodologicalframe forestimatingplantdiversityinareasofstandardizedshapeand