Measuring β‐diversity by remote sensing: A challenge for ...€¦ · ment of remote sensing...

Methods Ecol Evol 201891787ndash1798 wileyonlinelibrarycomjournalmee3 emsp|emsp1787copy 2018 The Authors Methods in Ecology and Evolution copy 2018 British Ecological Society

Received22September2017emsp |emsp Accepted11November2017DOI 1011112041-210X12941

I M P R O V I N G B I O D I V E R S I T Y M O N I T O R I N G U S I N G S A T E L L I T E R E M O T E S E N S I N G

Measuring β-diversity by remote sensing A challenge for biodiversity monitoring

1CenterAgricultureFoodEnvironmentUniversityofTrentoSMicheleallrsquoAdige(TN)Italy2CentreforIntegrativeBiologyUniversityofTrentoPovo(TN)Italy 3DepartmentofBiodiversityandMolecularEcologyFondazioneEdmundMachResearchandInnovationCentreSMicheleallrsquoAdige(TN)Italy4UMR-TETISIRSTEAMontpellierMaisondelaTeacuteleacutedeacutetectionMontpellierCedex5France5InstituteofZoologyTheZoologicalSocietyofLondonLondonUK6SchoolofComputerScienceAstonUniversityBirminghamUK7DepartmentComputationalLandscapeEcologyHelmholtzCentreforEnvironmentalResearchndashUFZLeipzigGermany8DepartmentofComputerScienceandEngineeringUniversityofBolognaBolognaItaly9InstitutfuumlrGeographieFriedrich-AlexanderUniversitaumltErlangen-NuumlrnbergErlangenGermany10SchoolofGeographyUniversityofNottinghamNottinghamUK11SchoolofBiologyFacultyofbiologicalScienceUniversityofLeedsLeedsUK12InstituteofMediterraneanAgriculturalandEnvironmentalSciences(ICAAM)UniversidadedeEvoraEvoraPortugal13SchoolofBiologyUniversityofLeedsLeedsUK14DepartmentLandscapeEcologyandEnvironmentalSystemAnalysisTechnischeUniversitaumltBraunschweigBraunschweigGermany15GeographyDepartmentHumboldt-UniversitaumltzuBerlinBerlinGermany16DepartmentofPathologyMicrobiologyandImmunologySchoolofVeterinaryMedicineUniversityofCaliforniaDavisCAUSA17MundialisGmbHampCoKGBonnGermany18DepartmentofEnvironmentalBiologyUniversityofRomeldquoLaSapienzardquoRomeItaly19KarlsruherInstitutfuumlrTechnologie(KIT)InstitutfuumlrGeographieundGeooumlkologieKarlsruheGermany20NaturalEnvironmentCentreFinnishEnvironmentInstitute(SYKE)HelsinkiFinland21DepartmentofRemoteSensingRemoteSensingandBiodiversityResearchGroupUniversityofWuerzburgWuerzburgGermanyand22AzimPremjiUniversityBangaloreIndia

Correspondence DuccioRocchini Emailsducciorocchinigmailcom ducciorocchinifmachit

Present addressLucyBastinKnowledgeManagementUnitJointResearchCentreoftheEuropeanCommissionIspraItaly

HandlingEditorFrancescaParrini

Abstract1 BiodiversityincludesmultiscalarandmultitemporalstructuresandprocesseswithdifferentlevelsoffunctionalorganizationfromgenetictoecosystemiclevelsOneofthemostlyusedmethodstoinferbiodiversityisbasedontaxonomicapproachesandcommunityecologytheoriesHowevergatheringextensivedatainthefieldisdifficultduetologisticproblemsespeciallywhenaimingatmodellingbiodiversitychangesinspaceandtimewhichassumesstatisticallysoundsamplingschemesInthiscontextairborneorsatelliteremotesensingallowsinformationtobegatheredoverwideareasinareasonabletime

2 MostofthebiodiversitymapsobtainedfromremotesensinghavebeenbasedontheinferenceofspeciesrichnessbyregressionanalysisOnthecontraryestimatingcompositionalturnover(β-diversity)mightaddcrucial informationrelatedtorela-tiveabundanceofdifferentspeciesinsteadofjustrichnessPresentlyfewstudieshaveaddressedthemeasurementofspeciescompositionalturnoverfromspace

3 Extendingonpreviouswork inthismanuscriptweproposenoveltechniquestomeasure β-diversity from airborne or satellite remote sensingmainly based on (1)multivariatestatisticalanalysis(2)thespectralspeciesconcept(3)self-organizing

1788emsp |emsp emspenspMethods in Ecology and Evolu13on ROCCHINI et al

1emsp |emspINTRODUCTION

Biodiversitycannotbefullyinvestigatedwithoutconsideringthespa-tialcomponentofitsvariationInfactitisknownthatthedispersalofspeciesoverwideareasisdrivenbyspatialconstraintsdirectlyrelatedtothedistanceamongsitesAnegativeexponentialdispersalkernelisusuallyadoptedtomathematicallydescribetheoccupancyofnewsitesbyspeciesasfollows

wheredik=distancebetweentwolocationsi and k and aisaparam-eterregulatingthedispersalfromlocalizedareas(lowvaluesofa)towidespreadones (highvaluesofaMeentemeyerAnackerMarkampRizzo2008)

Inthissensedistanceacquiresasignificantroleinecologytoesti-matebiodiversitychangeHencespatiallyexplicitmethodshavebeenacknowledged inecologyforprovidingrobustestimatesofdiversityatdifferenthierarchical levelsfromindividuals (TyrePossinghamampLindenmayer2001)topopulations(Vernesietal2012)tocommu-nities(RocchiniAndreiniButiniampChiarucci2005)

Whendealingwithspatialexplicitmethodsremotesensingimagesrepresent a powerful tool (Rocchini et al 2017) particularlywhencoupling information on compositional properties of the landscapewithitsstructure(Figure1)Remotesensinghaswidelybeenusedforconservationpracticesincludingverydifferenttypesofdatasuchasnightlightsdata(Mazoretal2013)LandSurfaceTemperatureesti-matedfromMODISdata (MetzRocchiniampNeteler2014)spectralindices(Gillespie2005)

Mostoftheremotesensingapplicationsforbiodiversityestima-tionhave reliedon theestimateof localdiversityhotspots consid-eringlandusediversity(Wegmannetal2017)orcontinuousspatialvariabilityofthespectralsignal(Rocchinietal2010)Thisismainlygrounded in the assumption that a higher landscape heterogeneityis strictly related to a higher amount of species occupying differ-ent niches (Scmheller et al in press) However given two sites s1 and s2 the finaldiversity isnotonly relatedto thespeciesspectralrichnessof s1 and s2 but overall to the amountof shared speciesspectralvaluesInotherwordsthelowerthetheirintersections1caps2the higherwill be the total diversity while the lowest total diver-sitywill be reachedwhen s1caps2 = s1cups2 Such intersectionhasbeen

widelystudiedinecologyafterthedevelopmentofβ-diversitytheory(Whittaker1960)

Tuomisto etal (2003) demonstrated the power of substitutingdistance in Equation 1 by spectral distance to directly account forthe distance between sites in an environmental space instead of amerelyspatialoneHoweverwhile spectraldistanceexamplesexistwhenmeasuring theβ-diversity amongpairs of sites (eg RocchiniHernaacutendezStefanoniampHe2015)fewstudieshavetestedthepossi-bilityofmeasuringβ-diversityoverwideareasconsideringseveralsitesatthesametime(howeverseeAlahuhtaetal2017HarrisCharnockampLucas2015)Thisisespeciallytruewhenconsideringthedevelop-mentofremotesensingtools(RocchiniampNeteler2012)fordiversityestimateinwhichtheconceptofβ-diversityisstillpioneering

The aim of this paper is to present themost novelmethods tomeasureβ-diversityfromremotelysensedimagerybasedonthemostrecentlypublishedecologicalmodelsInparticularwewilldealwith(1)multivariatestatisticaltechniques(2)theapplicabilityofthespec-tralspeciesconcept(3)multidimensionaldistancematrices(4)met-ricscouplingabundanceanddistance-basedmeasures

Thismanuscriptisthefirstmethodologicalexampleencompassing(and enhancing)most of the availablemethods for estimating β-di-versityfromremotelysensedimageryandpotentiallyrelatethemtospeciesdiversityinthefield

2emsp |emspMULTIVARIATE STATISTICAL ANALYSIS FOR SPECIES DIVERSITY ESTIMATE FROM REMOTE SENSING

UnivariatestatisticshavebeenusedtodirectlyfindrelationsbetweenspectralandspeciesdiversityHowevertheamountofvariabilityex-plainedbysinglebandsvegetationindicesversusspeciesdiversityisgenerallyrelativelylowduetothefactthatdifferentaspectsrelatedtothecomplexityofhabitatsmightactinshapingdiversityfromdis-turbanceandlanduseatlocalscalestoclimateandelementfluxesatglobalscales

Ordination techniques are designed to quantitatively describemultivariategradualtransitionsinthespeciescompositionofsampledsitesMeasuringthedistancebetweentwosamplingsitesinthemulti-dimensionalordinationspaceisagoodproxyofthechangeinspeciescompositionWhenthismeasureisrelatedtothegeographicaldistance

NsumK=1

eminusdik

featuremaps(4)multidimensionaldistancematricesandthe(5)RaosQdiversityEachofthesemeasuresaddressesoneorseveralissuesrelatedtoturnovermeas-urementThismanuscript is thefirstmethodologicalexampleencompassing (andenhancing)mostoftheavailablemethodsforestimatingβ-diversityfromremotelysensedimageryandpotentiallyrelatingthemtospeciesdiversityinthefield

K E Y W O R D S

β-diversityKohonenself-organizingfeaturemapsRaosQdiversityindexremotesensingsatelliteimagerysparsegeneralizeddissimilaritymodelspectralspeciesconcept

emspensp emsp | emsp1789Methods in Ecology and Evolu13onROCCHINI et al

betweentheconsideredsitesthebetadiversityatthisparticularscalecanbeassessed

Of thevariousavailableordination techniquesdetrendedcorre-spondenceanalysis(DCAHillampGauch1980)isparticularlysuitablefor such analyses The axes (ie gradients) of the DCA ordinationspacearescaledinSDunitswhereadistanceof4SDisrelatedtoafullspecies turnoverThisenablesaversatileanalysis thateasily revealswhethertwosampledsitesstillhavespeciesincommon

Several studieshavemapped theordinationspaceusing remotesensing data (eg Feilhauer amp Schmidtlein 2009 Feilhauer FaudeampSchmidtlein2011Feilhaueretal2014GuSinghampTownsend2015Harris etal 2015 Leitatildeoetal 2015Neumannetal 2015SchmidtleinampSassin2004SchmidtleinZimmermannSchuumlpferlingampWeiss2007)Forthispurposetheaxesscoresofthesampledsitesare regressed against the corresponding canopy reflectance values

extractedfromair-orspaceborneimagedataTheresultingmultivar-iateregressionmodelsoneperordinationaxisandmostoftengener-atedwithmachine learning regression techniques are subsequentlyappliedontheimagedataforaspatialpredictionofordinationscoresEachpixeloftheimagedataisassignedtoaspecificpositionintheordinationspacethatindicatesitsspeciescompositionTheresultinggradientmapsareapowerfultoolforanalysesofbetadiversityacrossdifferent spatial scales (Feilhauer amp Schmidtlein 2009 Hernandez-Stefanonietal2012)

AsimpleanalysisofthevariabilityoftheDCAscoresinadefinedpixelneighbourhood(ieamovingwindow)resultsinaefficientbetadiversityassessmentThespatialscaleofthisassessmentcanbevariedeitherbyresamplingthegradientmaptoacoarserspatialresolution(iepixelsize)orbychangingthekernelsizeoftheconsideredpixelneighbourhood Such techniques have been further developed egfor spatial conservationprioritizationprogrammes such asZonation(Moilanenetal2005MoilanenKujalaampLeathwick2009)

Figure2showsanexampleofaDCA-basedassessmentofbetadiversityonaverylocalscale(10m)followingtheapproachdescribedinFeilhauerandSchmidtlein(2009)Theanalysedlandscapeisamo-saicofraisedbogsfenstransitionmiresandMoliniameadowsForadetaileddescriptionofthedataandsitepleaserefertoFeilhaueretal(2014)andFeilhauerDoktorSchmidtleinandSkidmore(2016)

Analyses like this require two different datasets (1) a sampleoffielddatathatisrepresentativeforthevegetationinthestudiedarea and is used to generate theordination space (2) imagedatawithasufficientspectral resolutiontodiscriminatethevegetationtypeswithintheordinationspaceandwithaspatialresolutionthatisinlinewiththesamplingdesignofthefielddata(Feilhaueretal2013)

F I G U R E 1 emsp Anexampleofhowtocoupleinformationoncompositionalpropertiesofthelandscapebyopticaldatatogetherwithstructural(3D)propertiesbylaserscanningLiDARdata

F I G U R E 2 emsp β-diversityassessmentwithacombinationofordinationtechniquesandremotesensing(a)Three-dimensionaldetrendedcorrespondenceanalysis(DCA)ordinationspaceofn=100vegetationplotssampledinraisedbogsfenstransitionmiresandMoliniameadowsinthealpinefoothillsofSouthernGermanyAninter-plotdistanceof4SDcorrespondstoafullspeciesturnover(b)MapsoftheordinationaxesresultingfromaspatialpredictionbasedoncanopyreflectanceEachpixelhasapredictedpositionintheordinationspacethatisindicatedbyitscolourThecolourschemecorrespondsto(a)Themaphasaspatialresolutionof2times2m2whichisinlinewiththesampledplotsize (c)CumulativechangeratesalongthethreeDCAaxesina5times5pixelneighbourhoodAhighchangerateindicatesahighbetadiversity

Using these data the continuous spatial variability of the spec-tralsignalintheimagepixelsistranslatedintoaspatiallycontinuousmeasureofspeciescompositionTheadvantagesofthisapproachareobvioussincethediversityanalysesareconductedinthefloristicgra-dientspacetheresultingmeasuresresemblefieldstudiesandarethuseasiertointerpretthanspectralproxiesandclosertothepointofviewofmanyend-usersFurthermoretheanalysisofordinationscoresindefinedpixelneighbourhoodsisnotrestrictedtoasinglespatialscalebutofferstheopportunitytoimplementassessmentsofbetadiversityonmultiplescales

3emsp |emspTHE SPECTRAL SPECIES CONCEPT

ThespectralspeciesconcepthasbeenproposedbyFeacuteretandAsner(2014a) tomap bothα and β component of the biodiversity usinga unique framework It is rooted in the convergence between twootherconceptsthespectralvariationhypothesis(SVH)proposedbyPalmer Earls Hoagland White andWohlgemuth (2002) and theplantopticaltypesproposedbyUstinandGamon(2010)sustainedbythetechnologicaladvances in thedomainofhighspatial resolu-tionimagingspectroscopyTheSVHstatesthatthespatialvariabilityin the remotely sensed signal that is the spectral heterogeneity isrelatedtoenvironmentalheterogeneityandcouldthereforebeusedasapowerfulproxyofspeciesdiversitySVHhasbeentestedindif-ferentsituations(Rocchinietal2010)andconclusionsshowthattheperformanceofthisapproach isverydependentonseveralfactorsincludingtheinstrumentcharacteristics(spectralspatialandtempo-ral resolution) the typeofvegetation investigatedand themetricsderivedfromremotelysensedinformationtoestimatespectralheter-ogeneityPlantopticaltypesrefertothecapacityofsensorstomeas-ure signals that aggregate information about vegetation structurephenology biochemistry andphysiology Therefore this concept isalsotightly linkedtotheperformancesofthesensorandfindspar-ticularechowiththeincreasinguseofhighspatialresolutionimagingspectroscopyfortheestimationandidentificationofmultiplevegeta-tionproperties

Thedetailsprovidedbyhighspatialresolutionimagingspectros-copyare sufficient toperformanalysesofplantoptical traitsat theindividual treescale inorder todifferentiate treespeciesobtain in-formationaboutleafchemicaltraitsandestimatetheαcomponentofbiodiversity(AsnerampMartin2008AsnerMartinAndersonampKnapp2015ChadwickampAsner2016ClarkampRoberts2012ClarkRobertsampClark2005FeacuteretampAsner2013VaglioLaurinetal2014)TheseresultsillustratethatspectralinformationcanberelatedtotaxonomicorfunctionalinformationofthevegetationwhichsupportstheSVHunderthehypothesisthatthemetricsusedtocomputespectralhet-erogeneityandagivencomponentofvegetationdiversityareprop-erlydefinedHowevertheseapplicationsarecurrentlylimitedbytheimportantamountoffielddatarequiredtotrainregressionorclassi-ficationmodelswhich isalsodirectly linkedtotheir lowgeneraliza-tionabilityintimeandspaceUnsupervisedapproachesthenappearasvaluablealternatives for theanalysisofecosystemheterogeneity

(Baldeck amp Asner 2013 Baldeck etal 2014 Feilhauer Faude ampSchmidtlein2011FeacuteretampAsner2014b)asecologicalindicatorsofα and βdiversityatlandscapescaleusuallyrequireoneorseverallevelsofabstractionbeyondthecorrecttaxonomicidentification(TuomistoampRuokolainen2006)

Clustering(properlypre-processed)spectralinformationshouldre-sultinpixelsfromthesamespeciesnaturallygroupingtogetherratherthandistributing randomlyamongclustersFeacuteretandAsner (2014a)proposedagroupingmethodaimingatassigninglabelstopixelsbasedon multiple clustering of spectroscopic data acquired at landscapescaleThesepixelslabelledwithasetoftheso-calledspectralspeciescan thenbeused straightforwardly in order to computevarious di-versitymetricssuchasShannonindexforαdiversityandBray-Curtisdissimilarity forβ diversityThepre-processing stage is divided intoseveralstagesAftermaskingallnon-vegetatedpixelsanormalizationbased on continuous removal is applied to each pixel and over thefullspectraldomainthenaprincipalcomponentanalysisisperformedonthecontinuouslyremovedspectraldataThenormalizationreduceseffectsduetochangesinilluminationcanopygeometryandotherfac-torsunrelatedtovegetationwhileenhancingthesignalcorrespondingtovegetationThecomponentsincludingindividual-specificinforma-tionarethecomponentsof interestTheycanbe identifiedaftervi-sual inspectionorautomated routines if initialdata showsufficientsignaltonoiseratioOncealimitednumberofcomponentshavebeenselectedk-means clustering is then applied to a certain number ofsubsetsandforeachof thesesubsetscentroidsarecomputedandeachpixelintheimageislabelledbasedontheclosestcentroidTherepetitionofclusteringbasedonvarioussubsetsoftheimagetendstominimizetheriskofassigningcentroidstoirrelevantgroupsofpixelsExperimental results showed that the averaging of diversity indicescomputedfrommultiplecentroidmapscanbeseenasananalogoustosignalaveragingwhichconsists in increasingsignaltonoiseratiobyreplicatingmeasurementsForeachrepetitiontheclosestcentroidcorrespondstothespectralspeciesandforeachspatialunitofagivensizethespectralspeciesdistribution isderivedinordertocomputeanydiversitymetricrequiringeitherinformationatthelocalscaleorcomparisonofinformationacrossspatiallydistantplots

Theconceptsofspectralspeciesandspectralspeciesdistributionhavebeentestedsuccessfullyona limitednumberofsituationsandtypesofecosystems(seeRocchinietal2016forareviewandLauschetal 2016 for an application to similar concepts) As an exampleFeacuteretandAsner(2014a)showedabilitytoproperlyestimatelandscapeheterogeneityatmoderatespatialscaleuptofewdozensquarekilo-metersovertropicalforestsbasedonhighspatialresolutionimagingspectroscopy (Figure 3) A generic parameterization of the methodshowed robust performances for α diversity mapping across spaceandtimebutmappingβdiversityacrosslargespatialscalesusingim-agesacquiredduringdifferentairbornecampaignremainschallengingwhichleadstoanunsolvedproblemwhenconsideringoperationalre-gionalmappingIntheperspectiveofglobalmonitoringofbiodiversityandgiventheunprecedentedremotesensingcapacityallowedbytheCopernicusprogramincludingtheSentinel-2multispectralsatellitesseveralotherchallengesareforeseenandcurrentlyinvestigatedThe

influenceofdecreasedspatialandspectralresolutionontheabilitytoproperlydifferentiateecologicallymeaningfulspectralspeciesacrosslandscapesandoverregionswillneedtobeinvestigatedTheapplica-tionofthisconceptbeyondtropicalforestsandsavannaecosystemsshouldalsobeinvestigatedasitmaynotholdwhenappliedonmoder-atelydiverseecosystemsorsystemswithindividualswhoseindividu-alshavedimensionswellbelowtheresolvingpoweroftheinstrument

4emsp |emspSELF-ORGANIZING FEATURE MAPS

TheKohonenself-organizingfeaturemap(SOFMKohonen1982)isaneuralnetworkthatmaybeusedtoundertakeunsupervisedcluster-ingofdataCriticallytheinputtoaSOFMcanbealargemulti-variatedatasetsuchasmaybeacquiredonspeciesfromquadrat-basedfieldsurveysTheSOFMsummarizesthedata ina lowtypicallytwodi-mensionaloutput(Figure4)Inthisoutputspacethedataforindivid-ualquadratsaretopologicallyorderedmdashwithsitesthataresimilarclosetogetherwhilethoseofhighlydifferentspeciescompositionaremoredistantBecause thedatasites in theoutputspacearearrangedby

F I G U R E 3 emsp Spectralspeciescanbeidentifiedinahyper-ormultispectralimagebyspatialclusteringmethodandtheirdistributioncanbemappedSuchmapscanfurtherbeusedtoapplylocal-basedheterogeneitymeasurements(α-diversity)aswellasiterativedistance-basedmethodstobuildβ-diversitymapsReproducedfromFeacuteretandAsner(2014a)

F I G U R E 4 emsp Aself-organizingfeaturemapcanbebuiltstartingfromaninputlayeregthepresenceorabsenceofatreespeciesorofapeculiarspectralvalue)whichisconnectedtoeveryunitintheoutputlayerbyaweightedconnectionTheself-organizingfeaturemapusesunsupervisedlearningtomapthelocationoffieldsiteswithintheoutputspaceonthebasisoftheirrelativesimilarityinspeciesorspectralcompositionRedrawnfromFoodyandCutler(2003)

Output layer

Input units

relativesimilaritytheoutputspacemayalsobeusedtoaggregateorclassifyadatasetAssuchtheSOFMisattractiveasanon-parametricclusteringanalysisandasameanstoundertakeanordination(ChonParkMoonampCha1996)

ASOFMisunlikesomeoftheapproachesusedcommonlyincom-munityecologynotconstrainedbyassumptionsrelatingthestatisticaldistributionofthedatausedTheSOFMusesunsupervisedlearningtoproduceatopologicallyorderedoutputspaceinwhichthesamplesarearrangedspatiallyinrelationtotheirrelativesimilarityinspeciescompositionTheSOFMthusperformsanon-parametricordinationanalysis(Foody1999)TheproductionofaclassificationbyaSOFMcomprisestwomainstages(GiraudelampLek2001)Aniterativeanaly-sisinwhichtime-decayingparametersthatcontrolnetworklearningandthesizeoflocalneighbourhoodslocatedaroundoutputunitsisusedForthistheusermustspecifyanumberofkeyparameterssuchasthesizeandshapeofthenetworknumberofiterationsoftheal-gorithmthelearningrateanditsrateofdeclineandaneighbourhoodparameterTheneedforsuchparameterscanaddsomeuncertaintytotheanalysisWhile therearenoformal rules to follow in thede-signofaSOFMtherearerecommendationsforthedeterminationofSOFMparametersettings (GiraudelampLek2001)Afurtherconcernis thatasanunsupervisedclassifier theclassesdefinedmaynotal-waysbethemostusefulforaninvestigationInadditionthenatureof theanalysismeans thedirectionof thegradientscannotbecon-trolled(Fritzke1995)buttheanalysisperformswellincomparisontopopularordinationtechniquessuchasPCAandDCA(FoodyampCutler2003)TheSOFMmayalsouseavarietyofdifferentdatatypessuchaspresenceabsenceabundanceorimportancevaluesandcansolvecomplexnonlinearproblems(GiraudelampLek2001)

5emsp |emspMULTIDIMENSIONAL DISTANCE MATRICES GDMS AND SGDMS

Oneofthemostwidespreadmethodsforassessingdiversityisusingdistancematrices (LegendreBorcardampPeres-Neto2005) IndeedearlyworkbyWhittaker (1960)suggested thatβ-diversitycouldbequantifiedbydissimilaritymatricesamong(pairsof)sitesFurthermoretheManteltest(MantelampValand1970)designedtoestimatetheas-sociationbetweentwo independentdissimilaritymatriceshasbeenwidelyusedtocorrelateacommunitycompositiondissimilaritymatrixwithanenvironmentdissimilarityonethusprovidingusefulinsightsinto community composition and turnover (Legendre etal 2005Tahvanainen2011)

Generalized dissimilarity modelling (GDM Ferrier Manion Elith ampRichardson2007)canbeconsideredasanextensionoftheManteltestwhichisabletoaccommodatemultidimensionalenvironmentaldatatobecomparedwiththecompositionaldataGDMsalsoallowforthepredictionofcompositionalturnoveraswellasforegenvironmentalclassificationconstrainedtothecompositionaldissimilarity(Ferrieretal2007Leathwicketal2011)InGDMthecompositionaldissimilaritiesbetweenallpairsofsamplesaremodelledasafunctionoftheirrespectiveenvironmentaldis-tancesThisisdonethroughalinearcombinationofmonotonicI-splinebasis

functionsundertheassumptionthatincreasingenvironmentaldissimilarity (egalongagradient)canonlyresultinincreasingcompositionaldissimilar-ityThismethodisthuswellsuitedformeasuringandmappingβ-diversityandisthusbecomingwidelyusedinconservationscienceandmacroecol-ogyandrecentlybeensubject toseveraldevelopmentsaswedescribebelow

One such development is the phylogenetic GDM (phylo-GDMRosauer etal 2014) which incorporates phylogenetic dissimilari-ties intoGDMandallows foranalysingandpredictingphylogeneticβ-diversity thus linking ecological and evolutionary processes Thismethod can provide novel insights into themechanisms underlyingcurrentpatternsofbiologicaldiversity(GrahamampFine2008)Anotherrecent development of GDM is the multi-site GDM (MS-GDMLatombeHuiampMcGeoch2017)whichextendsGDMsfrompairwisetomulti-sitedissimilaritymodellingInsuchapapertheauthorstestedMS-GDMbymeansofbothconstrained(monotonical)additivemod-elsand I-splinesalthoughwithnoconclusive results relating to thebestmethod overallThey concluded however thatwhen applyingMS-GDMtoahighnumberofsamplestheycouldbetterexplainthedriversofspeciesturnoverAlsoanimportantdevelopmentofGDMis the Bayesian bootstrapGDM (BBGDMWoolley Foster OrsquoHaraWintleampDunstan2017)designedtocharacterizeuncertaintyingen-eralizeddissimilaritymodelsThisapproachallowsbetterrepresentingtheunderlyinguncertainty inthedatabyestimatingthevarianceinparametersbasedontheavailabledata

FinallyanimplementationofGDMwhichwascreatedparticularlyfordealingwithhigh-dimensional (andpotentiallyhigh-collinear) re-motesensingdataasinputinGDMisthesparsegeneralizeddissim-ilaritymodel (SGDMFigure5Leitatildeoetal2015)Thismethod isatwo-stageapproachthatconsistsofinitiallyreducingtheenvironmen-talspace(egreflectancedata)bymeansofasparsecanonicalcorrela-tionanalysis(SCCAFigure5WittenTibshiraniGrossampNarasimhan2013)andthenfittingtheresultingcomponentswithaGDMmodelTheSCCAisaformofpenalizedcanonicalcorrelationanalysisbasedontheL1(lasso)penaltyfunctionandisthusdesignedtodealwithhigh-dimensionaldataThetwoalgorithmsarecoupledinawaythattheSCCApenalizationisselectedthroughaheuristicgridsearchman-ner in order tominimize the cross-validate rootmean square errorin the dissimilarities predicted by the GDM In this procedure thehigh-dimensionalenvironmentaldata (suchascoming fromtimese-riesofmultispectralorhyperspectraldata)aresubjecttoasupervisedordinationapproachthatreducestheirdimensionwhilecapturingtheaxesofvariationthatmostcorrelatetothoseofthecommunitycom-positionalmatrixSGDMhasbeensuccessfullyusedformodellingandmappingthecompositionalturnoverofbothanimalandplantspeciesusingseveraldifferentsourcesofremotesensing(andauxiliary)data(Leitatildeoetal2015LeitatildeoSchwiederampSenf2017)

6emsp |emspRAOrsquoS Q DIVERSITY

Most of the previously shown metrics are based on the distanceamong pixel values in a multidimensional spectral space None

of them considers the relative abundance of such pixel values in aneighbourhood

Bycontrastabundance-basedmetricssuchastheShannonentropycouldoutputsimilarresultsdespiteavariabledistanceamongpixelval-uesAsanexampleconsidera3times3matrixofremotelysenseddata

composedbythefollowingvalues

thenconsideradifferentmatrix

FromaShannonsentropyperspectivesuchmatricesareequalintermsofheterogeneityTheShannonsentropyisindeedbasedontherelativeabundance(andrichness)ofasampleanditsvalueis2197forboth thematricesThisvalue equalling thenatural logarithmofthenumberofclasses(pixelvalues)isalsoShannonsmaximumtheo-reticalvaluegivena3times3matrixduetothelackofidenticalnumbersinthematricesThisexampleexplicitlyshowsthataccountingforthedistanceamongvaluesandtheirrelativeabundanceiscrucialtodis-criminateamongareasintermsofmeasured(modelled)heterogeneity

Oneof themetrics accounting for both the abundance and thepairwisespectraldistanceamongpixelsistheRaosQdiversityindexasfollows

wheredij=spectraldistanceamongpixels i and j and p = proportion ofoccupiedarea

Hence RaosQ is capable of discriminating among the ecologi-caldiversityofmatrices(3)and(4)turningouttobe459and9070respectivelyAppendix S1provides an example spreadsheet to per-formthecalculationwhilethecompleteRcodeisstoredintheGitHubrepositoryhttpsgithubcommattmarspectralrao

Wedecidedtomakeuseofacasestudytohighlightthe impor-tanceofconsideringthedistanceamongpixelvaluesinremotesenseecologicalapplicationTheperformanceofRaosQindexindescrib-ing landscape diversitywas tested in a complex agro-forestry land-scapelocatedinsouthernPortugalAtestsitewithanareaofabout10times10km2(centroidlocatedat38∘39prime1074primeprimeN8∘12prime5230primeprimeW)wasselectedtoconducttheanalysisInthisareaasavanna-likeecosystemcalledmontadooccupiesabout40ofthetestsitefollowedbytra-ditionalolivegrovespasturesvineyardsandirrigatedmonocultures(egcornfields)Montadoisspatiallycharacterizedbythevariabilityofitstreedensity(egGodinhoGilGuiomarNevesampPinto-Correia2016)andthegradientbetweenlowandhightreedensityoverspacecanleadtodifferentstructuralheterogeneityandhabitatdiversity

Within the test site polyculture under the small farming con-text (eg vegetable gardens orchards and cereal crops) is an im-portantfeatureofthislandscapebygeneratingahighcompositionalandconfigurational spatialheterogeneity (Figure6)Themaingoalinusingthiscasestudy is todemonstrate thepotentialandeffec-tivenessoftheRaosQindexinproducingaccuratelyremotesens-ing-based maps of spatial diversity over such complex landscapeFor this study a cloud-free Sentinel-2A (S2A) image acquired onAugust 8 2016wasused to compute theNDVI at a 10m spatialresolutionTheS2Aimagedownloadaswellastheatmosphericcor-rection (DOSmethod)were performed using the Semi-automaticClassificationplugin(SCP)implementedintheQGISsoftware(QGISDevelopmentTeam2016)

TheNDVIwasusedasinputdataforRaosQindexcomputationusingawindowsizeof3times3pixelsTheperformanceoftheRaosQwascomparedtotheShannonEntropyindex(ShannonsH)whichisoneofthesimplestandwidelyusedremotesensing-baseddiversitymeasures for landscape heterogeneity assessment (Rocchini etal2016)To investigatewhetherbothdiversity indicesdifferbetween

⎛⎜⎜⎜⎝

x11 x12 x13

x21 x22 x23

xd1 xd2 xd3

⎞⎟⎟⎟⎠

⎛⎜⎜⎜⎝

10 13 15

18 20 23

19 21 22

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⎛⎜⎜⎜⎝

10 121 227

1 40 251

7 100 149

⎞⎟⎟⎟⎠

(5)Q =

sumsumdij times pi times pj

F I G U R E 5 emsp AnexampleofthesparsegeneralizeddissimilaritymodelapproachRemotesensingdataandbiodiversitydatainthefieldcanbecoupledbysparsecanonicalcorrelationanalysis(SCCA)toproducecanonicalcomponentsandacommunitydissimilaritymatrixwhicharethenusedtobuildageneralizeddissimilaritymodel(GDM)tofinallyderiveaβ-diversitymap

Remote sensing data Biodiversity data

Canonical components Community dissimilarity

Beta-diversity map

land cover types one-wayANOVA testswere performedThis ap-proachwas used for analysing the degree of dissimilarity betweenRaosQandShannonH indexacross twohighcomplex landcovertypes (1) montado and (2) polyculture To do so a sample of 60squareswith 250times250m2 sizewas randomly selected over thesetwolandcovertypesEachsquarerepresentsasampleof625S2ANDVI pixels thus corresponding to a total of 37500pixels overthe60 squares For the comparisonbetweenboth indices the co-efficient of variation (CV) was calculated for each 250times250m2 Regarding the RaosQ performance Figure 6 clearly points to thesignificant improvementsshownbyRaosQ indexcomparedtotheShannonH index indescribing the spatialdiversity Inparticular itcanbeseenthroughtheFigure6 thatRaosQ indexcanhighlightdifferentgradientsofspatialdiversityofmontadoareaswhichpres-enthightreedensityvariability(Figure6)andthushighspatialhet-erogeneityOne-wayANOVAtestsrevealedthatbothindicesvaluesweresignificantlydifferentbetweenthetwolandcovertypes(mon-tado F=5033p lt 001 polyculture F=8898plt001)Overall

theobtainedresultsdemonstratethecapabilityofRaosQindex inproducingaccuratelandscapediversitymapsinacomplexlandscapesuchastheMediterraneanagro-forestrysystems

7emsp |emspCONCLUSION

In this paper we showed several methods based on ecologicalβ-diversitywhichcanbeinvestigatedbyremotesensingthroughthecalculationofecosystemheterogeneitytoestimatethespatialvariabil-ityofbiodiversityWhenthereisawiderangeofheterogeneityforex-amplewhenthedataincludehomogeneousandheterogeneouszonesnosinglemeasuremightcaptureallthedifferentaspectsofβ-diversity(egBaselga2013)Thatiswhywesuggestedinthismanuscriptmul-tivariateandmultidimensionalmethods(egmultivariatestatisticsandmultidimensionaldistancematrices)basedonthespectralsignalanditsvariabilityoverspacetoaccountfordifferentaspectsofdiversityalsoincludingdistance-andabundance-basedmethods(egtheRaosQ)

F I G U R E 6 emsp UpperpanelsSentinel-2Ascene(August82016)andderivedNDVIfortheagro-forestrysystemstestsitelocatedinsouthernPortugalLowerpanelsresultsfromShannonsHandRaosQindicescomputationShannonindextendstooverestimatethelandscapediversitywhencomparedtotheRaosQindex

Biodiversitymeasuredasspeciesrichnessisoftenusedforconser-vationpurposeshencetheimportanceofavoidinganunder-orover-estimate has been highlighted (Chiarucci etal 2009) Furthermorepairwisedistance-basedmethodsmightbeprofitablyusedtodetectnotonlydiversityhotspotsinanareabutalsothevariationofbiodi-versityoverspaceandpotentiallyovertimeoncemultitemporalsetsofimagesareused

In this paperwe focused on optimizingmeasures of β-diversitybasedonremotesensingdataSuchmeasuresmightbeusedtoregressspeciesdiversityagainstremotelysensedheterogeneitybasedonnewregressiontechniqueswhichmaximizethepossibilityofpredictingthezones in a study area or at larger spatial scales of peculiar conser-vationvalueAsanexampleshrinkageregressionrecentlyappliedinbiodiversityconservation(AuthierSarauxampPeron2017)couldallowadirectfocusonhabitatmodellingwhichisoneofthemajorstrengthsofremotesensing(GillespieFoodyRocchiniGiorgiampSaatchi2008)MoreoversuchanalysismightbeperformedinaBayesianframeworkallowingto(1)modelmultidimensionalcovariateswithnon-stationaryvariationoverspace(RandellTurnbullEwansampJonathan2016)suchasthebandsofsatelliteimagesand(2)modeltheerrorsintheoutputandtheirvariationoverspace(Rocchinietal2017)

Aspreviouslystatedthesuggestedmethodsforβ-diversityes-timation from remote sensing aremainly based on distances butthey could be effectively translated to relative abundance-basedmethodsAsanexampleRocchinietal(2013)introducedthepos-sibility of applying generalized entropy theory to satellite imageswithonesingleformularepresentingacontinuumofdiversitymea-sures changing one parameter One of the best examples in thisframeworkcouldbe theuseofHill numbers inwhichdiversity isexpressedasfollows

whereS=numberofsamplespixelsandpi=relativeabundanceofaspeciesspectralvaluevaryingtheparameterqqDvariesaccordinglyinseveraldiversity indiceseg forq = 0 qD is thesimplenumberofspeciesforlim(q)=1qDequalsShannonsentropyetc(HsiehMaampChao2016)

Furthermore connectivity analysis might also be taken into ac-count (Moilanen etal 2005 2009) For instance a remote sens-ing-based connectivity network among different sites based onβ-diversitymeasurescouldbeappliedfortheestimateof landscapeconnectivityandconsequentgeneticflowasdemonstratedbyVernesietal(2012)Ithasalsobeenshownthatcommunityrelatedbiodiver-sityindicatorsareoftenmissingfromcurrentmonitoringprogrammes(Vihervaaraetal2017)thusmethodssuchasremotesensing-basedRaosQdiversityappliedforvariousecosystemsmightimproveother-wisechallengingmonitoringofbiologicalcommunities

Withthismanuscriptwehopetostimulatediscussionontheavail-ablemethodsforestimatingβ-diversityfromremotelysensedimagerybyproposinginnovativetechniquesgroundedonecologicaltheory

ACKNOWLEDGEMENTS

WearegratefultothehandlingEditorandtotwoanonymousreview-erswhoimprovedwithskillfulsuggestionsapreviousversionofthepresentmanuscriptDRwaspartiallysupportedby (i) theEU-LIFEproject LIFE14ENVIT000514 FutureForCoppices (ii) the H2020project ECOPOTENTIAL (Grant Agreement no 641762) iii) theH2020TRuStEE-TrainingonRemoteSensingforEcosystemmodEl-ling-project(GrantAgreementno721995)

AUTHORSrsquo CONTRIBUTIONS

All authors contributed to the development and writing of themanuscript

DATA ACCESSIBILITY

Partofthedataandcorrespondingoriginalsourcesareavailableatthefollowinghttpsdoiorg105061dryaddg31k

Duccio Rocchini httporcidorg0000-0003-0087-0594

Sandra Luque httporcidorg0000-0002-4002-3974

Nathalie Pettorelli httporcidorg0000-0002-1594-6208

Lucy Bastin httporcidorg0000-0003-1321-0800

Hannes Feilhauer httporcidorg0000-0001-5758-6303

Jean-Baptiste Feacuteret httporcidorg0000-0002-0151-1334

Giles M Foody httporcidorg0000-0001-6464-3054

Yoni Gavish httporcidorg0000-0002-6025-5668

William E Kunin httporcidorg0000-0002-9812-2326

Angela Lausch httporcidorg0000-0002-4490-7232

Pedro J Leitatildeo httporcidorg0000-0003-3038-9531

Markus Neteler httporcidorg0000-0003-1916-1966

Carlo Ricotta httporcidorg0000-0003-0818-3959 Martin Wegmann httporcidorg0000-0003-0335-9601

Harini Nagendra httporcidorg0000-0002-1585-0724

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Additional Supporting Information may be found online in thesupportinginformationtabforthisarticle

How to cite this articleRocchiniDLuqueSPettorelliNetalMeasuringβ-diversitybyremotesensingAchallengeforbiodiversitymonitoringMethods Ecol Evol 201891787ndash1798 httpsdoiorg1011112041-210X12941