第4章 群落相似性和聚类分析

EstimatingCommunityParameters

Communityecologistsfaceaspecialsetofstatisticalproblemsinattemptingtocharacterizeandmeasurethepropertiesofcommunitiesofplantsandanimals.Onecommunityparameterissimilarity.Speciesdiversityisanotheroneofthemostobviousandcharacteristicfeaturesofacommunity.

1.MeasurementofSimilarity2.SpeciesDiversityMeasures第四章群落相似性和聚类分析第一节相似性测量在群落研究中，生态学家经常会得到某一群落的物种组成和数量。例如在保护区研究中，我们经常要回答的问题是这几个保护区他们在区系组成上有什么不同？哪些更相似，哪些差异较明显？要回答群落分类的这样复杂问题，我们先以测量两个群落的相似性着手。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

相关系数测度有人们希望的特点：当两个群落的样本之间是成比例的，或可加的差异，那么该系数对差异是极不敏感的。而所有距离测度对这些差异却很敏感。而相关系数测度的缺点则是强烈受样本大小的影响。特别是在高多样性的群落中更是这样。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第二节聚类分析聚类分析是研究分类问题的一种多元统计方法。4.2.1类与类之间的距离4.2.1.1最短距离法设类与类中两个最近元素之间的距离为与类之间的最短距离。4.2.1.2最长距离法4.2.1.3类平均法[unweigtedpair-groupmethodusingarithmeticaverages,UPGMA(SneathandSokal1973;Raneslurg1984)]设类与类中任意两个元素之间距离的平均值为两类之间的类平均距离。为与中任意两个元素之间距离。为中元素个数。为中元素个数。4.2.2聚类过程（1）从距离最短的一对样本开始，聚成第一类。（2）寻找第二对距离最短的样本，或者是于已形成的类最短的样本，形成新的一类。（3）重复步骤（2），直到所有的样本形成一大类。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