第4章 群落相似性和聚類分析

EstimatingCommunityParameters

Communityecologistsfaceaspecialsetofstatisticalproblemsinattemptingtocharacterizeandmeasurethepropertiesofcommunitiesofplantsandanimals.Onecommunityparameterissimilarity.Speciesdiversityisanotheroneofthemostobviousandcharacteristicfeaturesofacommunity.

1.MeasurementofSimilarity2.SpeciesDiversityMeasures第四章群落相似性和聚類分析第一節(jié)相似性測量在群落研究中，生態(tài)學家經(jīng)常會得到某一群落的物種組成和數(shù)量。例如在保護區(qū)研究中，我們經(jīng)常要回答的問題是這幾個保護區(qū)他們在區(qū)系組成上有什么不同？哪些更相似，哪些差異較明顯？要回答群落分類的這樣復雜問題，我們先以測量兩個群落的相似性著手。4.1.1BinaryCoefficients4.1.2DistanceCoefficients4.1.3CorrelationCoefficients4.1.4Morisita’sIndexofSimilarityBinaryCoefficientsThesimplestsimilaritymeasuresdealonlywithpresence/absencedata.Thebasicdataforcalculatingbinary(orassociation)coefficientsisa2×2table.SampleANo.ofspeciespresentNo.ofspeciesabsentabcdSampleBNo.ofspeciespresentNo.ofspeciesabsentWherea=NumberofspeciesinsampleAandsampleB(jointoccurrences)

b=NumberofspeciesinsampleBbutnotinsampleAc=NumberofspeciesinsampleAbutnotinsampleBd=Numberofspeciesabsentinbothsamples(zeromatches)

where=Jaccard’ssimilaritycoefficient=Asdefinedaboveinpresence/absencematrix

BinaryCoefficientsThereisconsiderabledisagreementintheliteratureaboutwhetherdisabiologicallymeaningfulnumber.Therearemorethan20binarysimilaritymeasuresavailableintheliterature(CheethamandHazel1969),andtheyhavebeenreviewedbyCliffordandStephenson(1975)andbyRomesburg(1984).CoefficientofJaccard

ThecoefficientofJaccardisexpressedasfollows:where=Euclideandistancebetweensamplesand=Numberofindividuals(orbiomass)ofspeciesinsample=Numberofindividuals(orbiomass)ofspeciesinsample=TotalnumberofspeciesEuclideanDistance

ThisdistanceisformallycalledEuclidiandistanceandcouldbemeasuredfromFigure11.2witharuler.Moreformally.Euclideandistanceincreaseswiththenumberofspeciesinthesamples,andtocompensateforthis,theaveragedistanceisusuallycalculated:where=AverageEuclideandistancebetweensamplesjandk

=Euclideandistance(calculatedinequation11.5)

n=NumberofspeciesinsamplesBothEuclideandistanceandaverageEuclideandistancevaryfrom0toinfinity;thelargerthedistance,thelesssimilarthetwocommunities.OneofthesimplestmetricfunctionsiscalledtheManhattan,orcity-block,metric:where=Manhattandistancebetweensamplesjandk=Numberofindividualsinspeciesiineachsamplejandkn=NumberofspeciesinsamplesThisfunctionmeasuresdistancesasthelengthofthepathyouhavetowalkinacity—hencethename.TwomeasuresbasedontheManhattanmetrichavebeenusedwidelyinplantecologytomeasuresimilarity.Bray-CurtisMeasure

BrayandCurtis(1957)standardizedtheManhattanmetricsothatithasarangefrom0(similar)to1(dissimilar).whereB=Bray-Curtismeasureofdissimilarity=Numberofindividualsinspeciesiineachsample(j,k)

n=NumberofspeciesinsamplesSomeauthors(e.g.,Wolda1981)prefertodefinethisasameasureofsimilaritybyusingthecomplementoftheBray-Curtismeasure(1.0–B).TheBray-Curtismeasureisdominatedbytheabundantspecies,sothatrarespeciesaddverylittletothevalueofthecoefficient.CanberraMetric

LanceandWilliams(1967)standardizedtheManhattanmetricoverspeciesinsteadofindividualsandinventedtheCanberrametric:whereC=Canberrametriccoefficientofdissimilaritybetweensamplesjandk

n=Numberofspeciesinsamples=NumberofindividualsinspeciesIinthesample(j,k)TheCanberrametricisnotaffectedasmuchbythemoreabundantspeciesinthecommunity,andthusdiffersfromtheBray-Curtismeasure.TheCanberrametrichastwoproblems.Itisundefinedwhentherearespeciesthatareabsentfrombothcommunitysamples,andconsequentlymissingspeciescancontributenoinformationandmustbeignored.Whennoindividualsofaspeciesarepresentinonesample,butarepresentinthesecondsample,theindexisatmaximumvalue(CliffordandStephenson1975).Toavoidthissecondproblem,manyecologistsreplaceallzerovaluesbyasmallnumber(like0.1)whendoingthesummations.TheCanberrametricrangesfrom0to1.0and,liketheBray-Curtismeasure,canbeconvertedintoasimilaritymeasurebyusingthecomplement(1.0–C).BoththeBray-CurtismeasureandtheCanberrametricmeasurearestronglyaffectedbysamplesize(Wolda1981).

4.1.3CorrelationCoefficients

Onefrequentlyusedapproachtothemeasurementofsimilarityistousecorrelationcoefficientsofthestandardkinddescribedineverystatisticsbook(e.g.,SokalandRohlf1995)Armstrong(1977)trappedninespeciesofsmallmammalsintheRockyMountainsofColoradoandobtainedrelativeabundance(percentageoftotalcatch)estimatesfortwohabitattypes(“communities”)asfollows:例:SmallmammalspeciesHabitattypeScSvEmPmCgPiMlMmZpWillowoverstory7058504031535Nooverstory1011202098114644EuclideanDistanceFromequation(11.5),AverageEuclideandistanceBray-CurtisMeasureTouseasameasureofsimilaritycalculatethecomplementofB:CanberrametricTousetheCanberrametricasameasureofsimilaritycalculateitscomplement:例

EFFECTSOFADDITIVEANDPROPORTIONALCHANGESINSPECIESABUNDANCESONDISTANCEMEASURESANDCORRELATIONCOEFFICIENTS.HypotheticalComparisonofNumberofIndividualsinTwoCommunitieswithFourSpecies

Species1234CommunityA5025105CommunityB40302010CommunityB1(proportionalchange,2×)80604020CommunityB2(additivechange,+30)70605040

相關(guān)系數(shù)測度有人們希望的特點：當兩個群落的樣本之間是成比例的，或可加的差異，那么該系數(shù)對差異是極不敏感的。而所有距離測度對這些差異卻很敏感。而相關(guān)系數(shù)測度的缺點則是強烈受樣本大小的影響。特別是在高多樣性的群落中更是這樣。SamplescomparedA–BA–B1A–B2AverageEuclideandistance7.9028.5033.35Bray-Curtismeasure0.160.380.42Canberrametric0.220.460.51Pearsoncorrelationcoefficient0.960.960.96Spearmanrankcorrelationcoefficient1.001.001.00Conclusion:Ifyouwishyourmeasureofsimilaritytobeindependentofproportionaloradditivechangesinspeciesabundances,youshouldnotuseadistancecoefficienttomeasuresimilarity.Morisita’sIndexofSimilarity

ThismeasurewasfirstproposedbyMorisita(1959)tomeasuresimilaritybetweentwocommunities.ItshouldnotbeconfusedwithMorisita’sindexofdispersion(Section6.4.4).ItiscalculatedasProbabilitythatanindividualdrawnfromsamplejandonedrawnfromsamplekwillbelongtothesamespeciesProbabilitythattwoindividualdrawnfromeitherjorkwillbelongtothesamespeciesXij=numberofindividualsofspeciesiinsamplejNj=TotelnumberofindividualsinsamplejTheMorisitaindexvariesfrom0(nosimilarity)toabout1.0(completesimilarity).TheMorisitaindexwasfromulatedforcountsofindividualsandnotforotherabundanceestimatesbasedonbiomass,productivity,orcover.Horn(1966)proposedasimplifiedMorisitaindexinwhichallthe(－1)termsinequations(11.13)and(11.14)areignored:whereSimplifiedMorisitaindexofsimilarity(Horn1966)Thisformulaisappropriatewhentheoriginaldataareexpressedasproportionsratherthannumbersofindividualsandshouldbeusedwhentheoriginaldataarenotnumbersbutbiomass,cover,orproductivity.TheMorisitaindexofsimilarityisnearlyindependentofsamplesize,exceptforsamplesofverysmallsize.Morisita(1959)didextensivesimulationexperimentstoshowthis,andtheseresultswereconfirmedbyWolda(1981),whorecommendedMorisita’sindexasthebestoverallmeasureofsimilarityforecologicaluse.H.Wolda1981SimilarityIndices,SampleSizeandDiversityOecologia50:296-302第二節(jié)聚類分析聚類分析是研究分類問題的一種多元統(tǒng)計方法。4.2.1類與類之間的距離4.2.1.1最短距離法設(shè)類與類中兩個最近元素之間的距離為與類之間的最短距離。4.2.1.2最長距離法4.2.1.3類平均法[unweigtedpair-groupmethodusingarithmeticaverages,UPGMA(SneathandSokal1973;Raneslurg1984)]設(shè)類與類中任意兩個元素之間距離的平均值為兩類之間的類平均距離。為與中任意兩個元素之間距離。為中元素個數(shù)。為中元素個數(shù)。4.2.2聚類過程（1）從距離最短的一對樣本開始，聚成第一類。（2）尋找第二對距離最短的樣本，或者是于已形成的類最短的樣本，形成新的一類。（3）重復步驟（2），直到所有的樣本形成一大類。例

MATRIXOFSIMILARITYCOEFFICIENTSFORTHESEABIRDDATAINTABLE11.5.ISLANDSAREPRESENTEDINSAMEORDERASINTABLE11.5a

CHPLICINSCLCTSISPISGICH1.00.880.990.660.770.750.360.510.49PLI1.00.880.620.700.710.360.510.49CI1.00.660.780.750.360.500.48NS1.00.730.640.280.530.50CL1.00.760.290.510.49CT1.00.340.460.45SI1.00.190.20SPI1.00.80SGI1.0

aThecomplementoftheCanberrametric(1.0–C)isusedastheindexofsimilarity.Notethatthematrixissymmetricalaboutthediagonal.4.2.3ClassificationClassificationisoftenthefinalgoalofcommunityanalyses,sothatecologistscanassignnamestoclassesorgroups.Classificationisespeciallyimportantinappliedecologyandconservation.Ecologistshaveclassifiedplantcommunitiesonthebasisofmanydifferentcharacteristics,andsincetheadventofcomputers,therehasbeenagrowingliteratureonobjective,quantitativemethodsof