R语言vegan包使用教程(8)

R语言中的外在软件包“Vegan”是专门用于群落生态学分析的工具。Vegan能够提供所有基本的排序方法,同时具有生成精美排序图的功能,版本更新很快。我们认为Vegan包完全可以取代CANOCO,成为今后排序分析的首选统计工具。

2.3Comparingordinations:Procrustesrotation2ORDINATION:BASICMETHOD

2.3Comparingordinations:Procrustesrotation

Procrustes errors

q

Twoordinationscanbeverysimilar,butthismaybedi culttosee,becauseaxeshaveslightlydi erentorientationandscaling.Actually,innmdsthesign,orientation,scaleandlocationoftheaxesarenotde- ned,althoughmetaMDSusessimplemethodto xthelastthreecompo-nents.ThebestwaytocompareordinationsistouseProcrustesrotation.Procrustesrotationusesuniformscaling(expansionorcontraction)androtationtominimizethesquareddi erencesbetweentwoordinations.PackageveganhasfunctionprocrustestoperformProcrustesanalysis.

HowmuchdidwegainwithusingmetaMDSinsteadofdefaultisoMDS?

q

0.4

q

q

Dimension 2

0.0

q

q

q

q

q

q

>>>>>tmp<-wisconsin(sqrt(varespec))dis<-vegdist(tmp)

vare.mds0<-isoMDS(dis,trace=0)pro<-procrustes(vare.mds,vare.mds0)pro

0.2

q

q

q

q

Call:

procrustes(X=vare.mds,Y=vare.mds0)Procrustessumofsquares:0.156>plot(pro)

0.4 0.2

q

0.4 0.20.00.20.40.6

Dimension 1

Procrustes errors

0.30

Inthiscasethedi erenceswerefairlysmall,andmainlyconcernedtwopoints.Youcanuseidentifyfunctiontoidentifythosepointsinaninteractivesession,oryoucanaskaplotofresidualdi erencesonly:

>plot(pro,kind=

2)

0.250.000.05

Thedescriptivestatisticis“Procrustessumofsquares”orthesumofsquaredarrowsintheProcrustesplot.Procrustesrotationisnonsym-metric,andthestatisticwouldchangewithreversingtheorderofordina-tionsinthecall.Withargumentsymmetric=TRUE,bothsolutionsare rstscaledtounitvariance,andamorescale-independentandsymmetricstatisticisfound(oftenknownasProcrustesm2).

Procrustes residual

0.100.150.20

2.4

5

10

Index

15

20

Eigenvectormethods

methodnmdsmdspcaca

metricanyanyEuclideanChi-square

mappingnonlinearlinearlinear

weightedlinear

djk

N

= (xij xik)2

i=1

Non-metricmultidimensionalscalingwasahardtask,becauseanykindofdissimilaritymeasurecouldbeusedanddissimilaritieswerenonlinearlymappedintoordination.Ifweacceptonlycertaintypesofdissimilaritiesandmakealinearmapping,theordinationbecomesasimpletaskofrotationandprojection.Inthatcasewecanuseeigenvectormethods.Principalcomponentsanalysis(pca)andcorrespondenceanalysis(ca)arethemostimportanteigenvectormethodsincommunityordination.Inaddition,principalcoordinatesanalysisa.k.a.metricscaling(mds)isusedoccasionally.PcaisbasedonEuclideandistances,caisbasedonChi-squaredistances,andprincipalcoordinatescanuseanydissimilarities(butwithEuclideandistancesitisequaltopca).

Pcaisastandardstatisticalmethod,andcanbeperformedwithbaseRfunctionsprcomporprincomp.Correspondenceanalysisisnotasubiq-uitous,butthereareseveralalternativeimplementationsforthatalso.In

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