ASReml軟件講義ASRemlworkshop課件

ASRemlWorkshopHarryWuUPSC,SwedishUniversityofAgricultureScience,SwedenCSIROPlantIndustry,Canberra,AustraliaWorkshopOutlineLinearmodelMixedlinearmodelBreedingvaluesASRemlandConTEXTPrimerExampleoffull-sibmatingExampleofdiallelmatingRow-ColumndesignLongitudinaldataSpatialanalysisARMSFusion20071.WhatIsaLinearModel?Y=b1X1+b2X2+b3X3+…..e?Alinearcombinationofthings(X)multipliedbysomecoefficients(b)thatexplainthedata(Y),withsomeerror(e)?Xcanbe –Themean –Acovariate –Afactor?WanttoestimatethecoefficientsusingsomedataARMSFusion2007PuttheLinearModelintoMatrixYoucangettheOLSsolutionbyassumingresidualsareiid(independentlyandidenticallydistributed)ARMSFusion2007UsefulMatrixOperationsTransposeMultiplicationTraceDeterminantInverseDirectsum()Directproduct()ARMSFusion20072.WhatIsMixedLinearModelAcombinationoffixedeffectsandrandomeffects.–Fixed:wheretherearedifferentpopulations(levels),eachwithitsownmean.Wearemostlyinterestedinestimatingthemeans.–Random:thelevelsarerandomsamplesfromonepopulation.Weareinterestedinthevariances(althoughwemightwantpredictionforthelevels).VerypowerfulatdealingwithunbalanceddataWhataresomefixedandrandomeffects?ARMSFusion2007MixedLinearModelPutthescalarmodelintomatrixformandTheBLUEofβisestimatedasandBLUPofuisARMSFusion2007SolutionofMixedLinearModelActualsolutionisthroughthestandardMixedModelEquation(MME)ThisMixedModelcanbeappliedinvariousgenetictrialsinforestspecies.ARMSFusion2007TraditionalMixedLinearModelinTreeBreedingIntraditionalanalysisofgenetictrial,suchashalf-sib,full-sibfamiliesSuchsimplemixedmodelcanbeanalyzedbymostcommercialsoftware:SASGLMARMSFusion2007SolutionofMixedLinearModelForsolutionsneedRandG,useand?Thesearethevarianceofeacherrorandeachrandomeffect?Forsimplesituationssothevariancesareneeded.?Theyareunknown,butcanbeestimated?Variousmethods–REMLispopular?ASReml–Estimates(co-)variances–SolvesmixedmodelequationsARMSFusion2007REML?Restricted(orResidual)MaximumLikelihood?Likelihoodofthefixedeffects(b)andthedatavariance(V),giventhedata(y).

Atransformationofthedatasothatfixedeffectsareexcluded?LogLikelihoodismaximisedbyiterativemethodsARMSFusion2007ASRemlASRemlisastatisticalpackagethatfitslinearmixedmodelsusingResidualMaximumLikelihood(REML).UsesaverageinformationalgorithmtoclimbthelikelihoodmountainARMSFusion2007OtherModelComparatorsNon-hierarchicalmodelsAkaikeInformationCriterion–MinimiseAIC=-2*LogL+2p(p=no.vc’s)BayesInformationCriterion–MinimiseBIC=-2*LogL+p*log(dfe)ARMSFusion20073.BasicConceptofBreedingValueConsideringasimplestcasewithindividualtreeswithoutanyreplication,withlinearmodelasyi=+αi+eiwhere

αiistheadditivegeneticvalueofindividual.AistheadditivegeneticrelationshipmatrixwithAij=2*ΘandtheΘisthecoefficientofcoancestrybetweentreeiandj.ThevarianceandcovarianceofuisARMSFusion2007BasicConceptofBreedingValuewhereλ=σE2/σA2=(1-h2)/h2,andsinceR-1=σE-2

I,andG-1=σA-2

A-1SubstituteX,Z,thisreducestoIfweassumeresidualerrorsareunrelatedbetweenindividuals,R=σE2

I,theMMEreducedtoARMSFusion2007BasicConceptofBreedingValueAnumericalexampleoffiveindividualsintwogenerations12534ARMSFusion2007BasicConceptofBreedingValueAnumericalexampleoffiveindividualsintwogenerations12534λ=σE2/σA2=(1-h2)/h2ARMSFusion20074.ASRemlprimerPreparethedata(usingaspreadsheetordatabaseprogram)

Exportthatdataasa.csvExcel

Prepareajobextension.as

RunthejobASReml

Reviewthevariousoutputfiles

Revisethejobandre-runit,or

ExtractresultsforyourreportExamples:ARMSFusion2007CaseAnalysisFull-sib(2-waytreatmentinaRCB)DiallelmatingstructureRow-columndesignLongitudinaldatastructureSpatialdataanalysisARMSFusion20075.Full-sib(2-waytreatmentinRCB)Thephenotypicvaluecanbederivedfrom:Non-additiveSCAMD(i.e.dominanceandepistasis)effectscanbecalculatedas:ARMSFusion2007Full-sib(FactorialtreatmentinRCB)Single-pairmatingsARMSFusion2007Full-sib(FactorialtreatmentinRCB)Full-factorialmatingsARMSFusion2007Full-sib(FactorialtreatmentinRCB)Tester(male)design:ARMSFusion2007Full-sib(FactorialtreatmentinRCB)Example2:RAD200pfull-factorialdesignanalyses:TrialID–TrialNameFSHS(Ch.)TreesLatLongAltPlanted200–Dandongadale,Blades4x4Factorial16-480-36?49’146?39’3206/1986ARMSFusion2007Full-sib(FactorialtreatmentinRCB)ARMSFusion20076.DiallelMatingStructureSameparentcanbemale♂

andfemale♀FourtypesofdiallelmatingmethodMethod1-fulldiallelincludingselfandreciprocalMethod2-halfdiallelwithselfMethod3–fulldiallelwithoutselfMethod4–halfdiallelSex

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ARMSFusion2007DiallelMatingStructureUniquenessofdiallel–sameindividualusedformaleandfemaleIntheZsub-matrixforadditiveeffect,notadiagonalsub-matrixThemodelwithoutdesignstructureisy=+gi+gj+sij+eijkwheregiandgjaretheithandjthgeneralcombiningability(GCA),andsijistheijkthSCAeffect.

ARMSFusion2007DiallelMatingStructureUniquenessofdiallel–sameindividualusedformaleandfemaleIntheZsub-matrixfornon-additiveeffect,adiagonalsub-matrixThemodelwithoutdesignstructureisy=+gi+gj+sij+eijkwheregiandgjaretheithandjthgeneralcombiningability(GCA),andsijistheijkthSCAeffect.

ARMSFusion2007DiallelMatingStructureExampleusingSASMixedandASRemlWithoutmissingcrosses,Diallel-SASandDiallel-SAS05Withmissingcrosses,DIAFIXEDandDIARAND(WuandMatheson)ASRemlExample:DiallelHaymanM4.asDiallelanalyses-HaymandiallelMethed4data(1954)rep2mother!Ifather!ASmotheryS5E_DiallelHaymanM4.txt!skip1y~murep!rmotherand(father)mother.fatherARMSFusion2007DiallelMatingStructurey~murep!rmotherand(father)mother.fatherARMSFusion2007DiallelMatingStructureBLUPforGCAandfirst8SCAlistedARMSFusion2007DiallelMatingStructureAlsocanbeanalysedbyindividualtreemodelDiallelanalyses-HaymandiallelMethed4data(1954)genotype!Prep2mother7father8yS5E_DiallelHaymanM4p.txt!skip1S5E_DiallelHaymanM4.txt!skip1!AISING#Diallelindividualtreemodely~murep!rgenotypeARMSFusion2007DiallelMatingStructureBLUPforGCAcomparedusingdiallelmodelandindividualtreemodelARMSFusion20077.Row-columnDesignTreatmentStructureDesignStructureRandomizationExperimentalDesignHalf-sibFactorialfull-sibDiallelmatingProv/familyRCBSplit-plotIncompleteblockLatticedesignLatinsquareRow-columnOverallAim:reducingresidualerrorARMSFusion2007Row-columnDesignWeusearow-columndesigntodemonstrateincompleteblockdesign.TheexampleisbasedonaCSIROCasuarinatrial.Thedesign(seefollowingfigureforlayout)Therewere60seedlots,Alatinizedrow-columndesignfor4replicatesgenerated,eachwithsixrowsand10columns.Only59seedlotswereplanted.Eachplotconsistedof5x5trees.ARMSFusion20075Row-columnDesignARMSFusion2007Row-columnDesignLinearmodelforRCB

yijm=+γi+αj+eijm

Linearmodelforrowandcolumnyijklm=+γi+αj+ck+γcik+γril+eijklm

AnalysesweredonebyRCB,androw-columntodemonstratetheextraefficiencyusingincompleteblocks.ASRemlExample:RCCasuarina.asARMSFusion2007Row-columnDesignCasuarinaRow-ColumnDesignModelRepl4Row6Column10Inoc2Prov59!ICountry18DBH

Casuarina.csv!SKIP1!DOPART3!PART1#RCBanalysisDBH~muReplProv!PART2#Row-ColumnfixedDBH~muReplColumnRepl.RowRepl.ColumnProv!PART3#Row-ColumnrandomDBH~muReplColumnProv!rRepl.RowRepl.ColumnARMSFusion2007Row-columnDesignThebestprovenancechangedARMSFusion2007Row-columnDesignThepredictionerrorreducedARMSFusion20078.LongitudinalDataStructureRepeatedmeasuresontimeandspaceonthesamesubjectsARMSFusion2007LongitudinalDataStructureARMSFusion2007LongitudinalDataStructureThemixedlinearmodelis:ARMSFusion2007LongitudinalDataStructureUnstructured(US)co-variancematrixbetweennmeasurementsn(n+1)/2parameterstoestimate.i.e.forn=10measurementsthereare55parameterstoestimateARMSFusion2007LongitudinalDataStructureParameterscanbereducedwithastructuredvarianceandcovariances:AR1correlationstructurehasonlyonecorrelationparameter

ρ

ARMSFusion2007LongitudinalDataStructureExamplesusing36radiatafamilies:1.ModellingAR1correlationstructure2.RandomregressionmodelARMSFusion2007LongitudinalDataStructure!PART2D80D85D90D95~Trait!rTrait.BlkTrait.Family!fmv1220!S2==1Trait0DIAG93188283421Trait.Blk2Trait0DIAG151017!GPBlkTrait.Family2Trait0DIAG5203050!GPFamilyFirst,regardeachmeasurementasindependenttraitandestimatevarianceforresidual,blockandfamilyARMSFusion2007LongitudinalDataStructure!PART2D80D85D90D95~Trait!rTrait.BlkTrait.Family!fmv1220!S2==1Trait0DIAG93188283421Trait.Blk2Trait0DIAG151017!GPBlkTrait.Family2Trait0DIAG5203050!GPFamilyFirst,regardeachmeasurementasindependenttraitandestimatevarianceforresidual,blockandfamilyARMSFusion2007LongitudinalDataStructureSourceModeltermsGammaComponentComp/SE%CResidualDIAGonal1108.362108.36216.320UResidualDIAGonal2194.844194.84416.300UResidualDIAGonal3289.454289.45416.270UResidualDIAGonal4428.241428.24116.170UTrait.BlkDIAGonal10.7032810.7032810.450PTrait.BlkDIAGonal24.144384.144381.040PTrait.BlkDIAGonal39.324649.324641.310PTrait.BlkDIAGonal415.649515.64951.390PTrait.FamilyDIAGonal14.648904.648901.670PTrait.FamilyDIAGonal217.504917.50492.400PTrait.FamilyDIAGonal333.192633.19262.630PTrait.FamilyDIAGonal455.770355.77032.740P

MostBlkeffectsarenotsignificantARMSFusion2007LongitudinalDataStructureSowefocusedoncorrelatedresidualandfamilyeffect!PART5D80D85D90D95~TraitRep!rTrait.Family!fmv#1210!S2==1Trait0US!+10113.5142.4215.6158.6259.3330.3173.1299.9397.6499.4Trait.Family2Trait0AR1H0.95183355FamilyARMSFusion2007LongitudinalDataStructureSowefocusedoncorrelatedresidualandfamilyeffectρ=0.999σ12=5.04,σ22=21.06,σ32=40.25,σ42=65.72Covariance/Variance/CorrelationMatrixUnStructuredResidual 1 2 3 41 97.560.92210.83470.74192 128.7199.60.97050.91033 142.6237.2299.30.97754 155.3272.5358.3449.0ARMSFusion2007LongitudinalDataStructure!PART2Diam~muRepMeas!rpol(Meas,2).FamilypredictMeasFamilyFittingrandomregressionforatwo-degreepolynomialARMSFusion2007LongitudinalDataStructureFittingrandomregressionforatwo-degreepolynomial3parametersforeachfamily? pol(Meas,2).Family1.311-0.13571.904pol(Meas,2).Family1.5111.1031.828.pol(Meas,2).Family2.311-0.13682.261pol(Meas,2).Family2.5111.0122.163.pol(Meas,2).Family3.311-0.30022.338pol(Meas,2).Family3.5110.15682.249ARMSFusion20079.SpatialDataAnalysis“Thingsclosertogetheraremorelikelytobemoresimilar”SaintRonaldA.Fisher,

近朱者赤,近墨者黑ARMSFusion2007SpatialDataAnalysisAccountformacro(trend)ormicro-environmentvariabilitywithinsiteandincreasepowerfordetectingdifferencesamonggenotypesARMSFusion2007SpatialDataAnalysisTypesofspatialvariationEnvironmentoffieldtrialsinforestryisusuallyhighlyvariableGlobalpattern–agradientorlargescaletrend(slope,soildepth,oldroad…)Localvariation–patchypattern(variationinsoilormicroclimate)Extraneousvariation–non-spatialvariation(plantingprocedure,labellingmistakesormeasurementerrors)ARMSFusion2007SpatialDataAnalysisMethodsforspatialanalysesAdjustmentsofdataforglobalandlocalvariation:Nearestneighbouranalyses[rij=0.5(ri-1,j+ri+1,j)andcij=0.5(ci,j-1+ri,j+1)]

Row-column

latiniseddesignfittedwithinreplicationsasrandomeffectspermittingdifferentpaternswithinblocks(erblockinformationrecovery)

KriginginterpolationmethodsmoothsurfacesofBLUPsonaspatialgrid: 1)variogram-optimalinterpolationweights 2)interpolationARMSFusion2007SpatialDataAnalysisSemivarianceandVariogramThesemi-varianceγ(h)wascalculatedas:Semivarianceincreaseswithdistanceifthereisaspatialassociation:VariogramARMSFusion2007SpatialDataAnalysisThefocusofspatialanalysesistomodelthebigRARMSFusion2007SpatialDataAnalysisModellingoftheautoregressiveprocessOrdinaryleastsquareserrorsAR1-One-dimensionalauto-correlatedcomponentinfieldorderρ=0.9ρ=0.6ρ=0.3ARMSFusion2007SpatialDataAnalysisModellingoftheautoregressiveprocessAR1-One-dimensionalauto-correlatedcomponentinfieldorderARMSFusion2007SpatialDataAnalysisModellingoftheautoregressiveprocessTwo-dimensionalseparablespatiallyauto-correlatedcomponentisafirst-orderautoregressivecorrelationmatrixwithanautocorrelationρ:

ARMSFusion2007SpatialDataAnalysisTwo-dimensionalseparablespatiallyauto-correlatedcomponentEndingupaverybigmatrixofnr*ncrowsandnr*nccolumnsARMSFusion2007SpatialDataAnalysisModellingoftheautoregressiveprocess“Nugget”effectunstructuredenvironmentalcorrelation:ARMSFusion2007SpatialDataAnalysisModellingoftheautoregressiveprocessRAD195trialDothistromainfectiondata(0-10scores)surfaceplotARMSFusion2007SpatialDataAnalysis!PART1Dothitr_0400~mu!rRepPlotGenotype_id!fmv120ProwProwIDENPposPposIDEN!PART2Dothitr_0400~mu!rRepPlotGenotype_id!fmv120ProwProwAR10.8PposPposAR10.8!PART3Dothitr_0400~mu!rRepPlotGenotype_idunits!fmv120ProwProwAR10.8PposPposAR10.8ARMSFusion2007SpatialDataAnalysisARMSFusion2007SpatialDataAnalysisModel1givesavariogramthatisflatwhichindicatesthattheresidualshavelittlespatialstructureARMSFusion2007SpatialDataAnalysisMakingtheRmatrixhaveanauto-regressivestructure(model2)givesaconsiderablemodelimprovement,withtheauto-correlationsarelow(0.42-0.65)ARMSFusion2007SpatialData