Stability-parameters-for-comparing-varieties-Eberh

StabilityParametersforComparingVarieties1S.A.EberhartandW.A.Russell2ABSTRACTThemodel,Y,,=/t,-f/?,Ij-f5ij,definesstabil-ityparametersthatmaybeusedtodescribetheper-formanceofavarietyoveraseriesofenvironments.Yuisthevarietymeanoftheilhvarietyatthejthenviron-ment,fiiisthej'hvarietymeanoverallenvironments,/?[istheregressioncoefficientthatmeasurestheresponseofthejthvarietytovaryingenvironments,Stjisthedevia-tionfromregressionofthei'hvarietyatthejthenviron-ment,andIjistheenvironmentalindex.Thedatafromtwosingle-crossdiallelsandasetof3-waycrosseswereexaminedtoseewhethergeneticdif-ferencescouldbedetected.Geneticdifferencesamonglineswereindicatedfortheregressionofthelinesontheenvironmentalindexwithnoevidenceofnonadditivegeneaction.Theestimatesofthesquareddeviationsfromregressionformanyhybridswerenearzero,whereasextremelylargeestimateswereobtainedforotherhybrids.GENOTYPE-environmentinteractionsareofmajorimportancetotheplantbreederindevelopingimprovedvarieties.Whenvarietiesarecomparedoveraseriesofenvironments,therelativerankingsusuallydiffer.Thiscausesdifficultyindemonstratingthesignificantsuperiorityofanyvariety.Thisinteractionisusuallypresentwhetherthevarietiesarepurelines,single-crossordouble-crosshybrids,topcrosses,Silines,oranyothermaterialwithwhichthebreedermaybeworking.ComstockandMoll(2)haveshownstatisticallytheeffectoflargegenotype-environmentinteractionsinreducingprogressfromselection.Stratificationofenvironmentshasbeenusedeffec-tivelytoreducethegenotype-environmentinteraction.Theregionforwhichabreederisdevelopingimprovedvarietiescanoftenbesosubdividedthatallenviron-mentsinthesubregionaresomewhatsimilar.Thisstratificationusuallyisbasedonsuchmacro-environ-mentaldifferencesastemperaturegradients,rainfalldistribution,aridsoiltypes.However,evenwiththisrefinementoftechnique,theinteractionofgenotypeswithlocationsinasubregion,andwithenvironmentsencounteredatthesamelocationindifferentyears,frequentlyremainstoolarge.AllardandBradshaw(1)classifyasunpredictabletheenvironmentalvaria-tionforwhichstratificationisnoteffective.Sincelittleadditionalprogresscanbeexpectedin1ContributionfromtheIowaAgriculturalandHomeEco-nomicsExperimentStation,Ames,andtheCropsResearchDivi-sion,ARS,USDA,cooperating.JournalPaperNo.J-5144oftheIowaAgr.andHomeEcon.Exp.Sta.Project1335.ReceivedforpublicationJuly16,1965.2ResearchGeneticist,USDA,andProfessor,IowaStateUni-versity,Ames,Iowa,respectively.reducinggenotype-environmentinteractionsbythestratificationofenvironments,othermethodsneedtobeinvestigated.Onesuchmethodwouldbetoselectstablegenotypesthatinteractlesswiththeenviron-mentsinwhichtheyaretobegrown.Ifstabilityofperformance,ortheabilitytoshowaminimumofinteractionwiththeenvironment,isageneticchar-acteristic,thenpreliminaryevaluationcouldbeplan-nedtoidentifythestablegenotypes.Withonlythemorestablegenotypesremainingforthefinalstagesoftesting,thebreederwouldbegreatlyaidedinhisselectionofsuperiorgenotypes.However,selectionforstabilityisnotpossibleuntilamodelwithsuitableparametersisavailabletoprovidethecriterianeces-sarytorankvarietiesforstabilily.Thepurposeofthispaperistoproposesuchamodelandtoillustrateitsusefulness.REVIEWOFLITERATURETheuseofgeneticmixturesratherthanhomogene-ous,orpure-line,varietieshasbeensuggestedasameanstoreducegenotype-environmentinteractions.Jensen(5)suggestedthatamult::linevarietyofoatsascomparedtopure-linevarietieswouldpossessgreaterstabilityofproduction,broaderadaptationtoenviron-ment,andgreaterprotectionagainstdisease.AllardandBradshaw(1)suggestedthatheterozygousandheterogeneouspopulationsofferthebestopportunitytoproducevarietieswhichshowsmallgenotype-en-vironmentinteractions.Theyusedthetermindivid-ualbufferingforindividualswheretheindividualmembersofapopulationarewellbufferedsuchthateachmemberofthepopulationiswelladaptedtoarangeofenvironments,andpopulationbufferingifthevarietyconsistsofanumberofgenotypeseachadaptedtoasomewhatdifferentrangeofenviron-ments.Thusaheterozygousorhomozygousgenotypemaypossessindividualbufferingandalieterogeneouspopulationwillpossesspopulationbuffering.SpragueandFederer(8),inareanalysisofmaizedataobtainedovermanyenvironments,presentedevi-dencethatdoublecrossesinteractwithenvironmentslessthansinglecrosses.Thedatasuggestthatdoublecrossesaresuperiortosinglecrossesforstabilityofperformance.Also,Eberhart,Russell,andPenny(3)reportedthatwhenthetwotypesofcrosseswerecom-paredinthesameexperimentHybridXYearinter-actionsweresignificantlygreaterforsinglecrossesthanforthree-waycrosses.Itispossible,however,thatsomesinglecrossesmayshowasmuch,ormore,EBERHARTg:RUSSELL:STABILITYPARAMETERSFORCOMPARINGVARIETIES37phenotypicstabilitythanthemoststablethree-wayordoublecross.Becausethevarianceofameanislessthanthevarianceofanindividual,theaveragegenotype-environmentinteractionofamixturemaybeexpectedtobelessthantheinteractionforasinglegenotype.LetT12.abethepredictedperformanceofthethree-waycross(1X2)3,andSlaandS2abetheobservedperformanceofthesinglecrosses(1)3)(2~K3).Then,^1T12.a=--(Sla+S2a).21Thevarianceof--(S~aq-S2a)=Var--(S~aq