预计仓储害虫分布的两种模型

TWOMODELSOFGRAINTEMPERATURESANDINSECTPOPULATIONSINSTOREDWHEATS.Mani,P.W.Flinn,W.E.Muir,D.S.Jayas,N.D.G.WhiteABSTRACT.Storedgraintemperaturesandpopulationdynamicsofrustygrainbeetles,Cryptolestesferrugineus(Stephens),predictedbyahotspotmodel,whichincludedfeedbackfromtheinsectmodeltothetemperaturemodel,andaspatialmodel,whichdidnotincludethatfeedback,werecompared.Foraninitialgraintemperatureof30³Candaninitialpopulationof10,000adultinsectsinstoredgrainatWinnipeg,Canada,thehotspotmodelpredictedamaximumof120adults/kgofwheatatthecenterofthegrainbulktowardtheendoffallandamaximumtemperatureof39³C.Thespatialmodelpredictedanadultpopulationof500adults/kgofwheatandnoincreasesintemperatures.ForthesamesimulationconditionsbutusingweatherdataforTopeka,Kansas,thehotspotmodelpredictedamaximumof150adults/kgofwheatatthecenterofthebulkinfall,whilethespatialmodelpredictedamaximumof800adults/kg.Thehotspotmodelisclosertorealitythanthespatialmodelbecauseitsimulatestheeffectsofvariableheatingaroundthebinwall,insectheatproduction,andinsectmovement.Keywords.Hotspotmodel,Spatialmodel,Cryptolestesferrugineus,Insectpopulationdynamics,Insectmigration,Storedgrain.tored–grainecosystemsarecomplexduetothelargeandaffectthepopulationdynamicsanddistributionsofnumberofabioticandbioticfactorsandtheirinsectsinstoredgrainbulks.Onlyafewattemptshavebeeninterrelationships.ComputermodelshavebeenusedmadetosimulatethefeedbackfromheattransfermodelstoStosimulateabioticfactors,suchastemperatures,insectmodels(Longstaffetal.,1981;Flinnetal.,1992;Mani,moisturecontents,andgasconcentrations,andbioticfactors,1999).Longstaffetal.(1981)incorporatedamodelofthesuchaspopulationdynamicsofinsectsandmites,andfungalpopulationdynamicsofSitophilusoryzae(Cuffandgrowth(Jayas,1995).Mostoftheheattransfermodels,whichHardman,1980)inamodelofheatandmoisturetransferinsimulatetemperaturedistributionsinstoredgrainbulks,aeratedgrain(Sutherlandetal.,1971).assumethattheeffectofinternalheatgenerationongrainFlinnetal.(1992,1997)developedaspatialmodelthattemperaturesisnegligible(Jayas,1995).MostoftheinsectandpestmanagementmodelssimulatetheeffectsofsimulatesthepopulationofCryptolestesferrugineushomogenousgraintemperaturesoninsectpopulationsand(Stephens)basedonnon–homogeneoustemperaturesinassumenomovementoftheinsectswithinthegrainbulkstoredgrainbulks.Mani(1999)simulatedinsect–inducedhot(Throne,1995).spotsinstoredwheat.ThehotspotmodelincludestheeffectsUnderCanadianstorageconditions,thecentersoflargeofinternalheatgenerationongraintemperaturesandthebinsremainwarmandfavorableforthemultiplicationofapopulationdynamicsofC.ferrugineus,aswellasthemajorstoredproductpest,rustygrainbeetles,Cryptolestesmovementofinsectsbasedontemperaturegradientsintheferrugineus(Stephens).Insectstendtomovetothewarmstoredgrain(Mani,1999).Themainobjectiveofthisregionsfromthecoldregionsofgrainbulksandaggregateatresearchwastocomparegraintemperaturesandinsectthecentersofthebulks(Mani,1999;Flinnetal.,1992).populationspredictedbythehotspotmodel(Mani,1999;TemperaturesinstoredgrainbulksvarywithtimeandspaceManietal.,2001)withthosepredictedbythespatialmodel(Flinnetal.,1992)fortwoclimaticregions.ArticlewassubmittedforreviewinMay2000;approvedforpublicationbyFood&ProcessEngineeringInstituteofASAEinFebruary2001DIFFERENCESBETWEENTHEHOTSPOTTheauthorsareSeshadríMani,GraduateStudent,WilliamE.Muir,ASAEMember,Professor,andDigvirS.Jayas,ASAEMember,AssociateANDSPATIALMODELSVice–President(Research),DepartmentofBiosystemsEngineering,Thedifferencesbetweenthehotspot(Mani,1999;UniversityofManitoba,Winnipeg,Canada;PaulW.Flinn,ResearchManietal.,2001)andspatialmodels(Flinnetal.,1992)Biologist,USDAAgriculturalResearchService,GrainMarketingandProductionResearchCenter,Manhattan,Kansas;andNoelD.G.White,were:ResearchScientist,CerealResearchCentre,AgricultureandAgri–Food(1)Thehotspotmodelusesathree–dimensional,finite–Canada,Winnipeg,Canada.Correspondingauthor:WilliamE.Muir,elementmodelofheattransfer,whichsimulatesvari-DepartmentofBiosystemsEngineering,UniversityofManitoba,Winnipegableheatingaroundthebinwall(Alagusundarametal.,MBCanadaR3T5V6;phone:204–474–9660;fax:204–474–7512;e–mail:william_muir@umanitoba.ca.1990).Thespatialmodelusesatwo–dimensional,fi-TransactionsoftheASAEVol.44(3):655–660E2001AmericanSocietyofAgriculturalEngineers655nitedifferencemodeltosimulatethegraintempera-Tocomparethetwomodels,foursetsofconditionswereturesinasouth–facingsectorofacylindricalbinsimulatedwithbothmodels:(Flinnetal.,1992).(1)Adultinsectpopulationsweresimulatedforwheat(2)Acohort–structuredmodelofthepopulationdynamicsmaintainedatconstanttemperaturesof25³,30³,35³,ofC.ferrugineus(Kawamotoetal.,1989)isusedintheand40³Cforoneyear.Thiscomparisoneliminatedthehotspotmodel.Ontheotherhand,adistributed–delayeffectsofthedifferentheattransferandheatproductionmodelofthepopulationdynamicsofC.ferrugineuscomponentsofthetwomodelsandcomparedthedif-(Flinnetal.,1992)isusedinthespatialmodel.IntheferentsubmodelsforthepopulationdynamicsofC.fer-cohort–structuredmodel,dailycohortsoftheinsectsrugineus.Theinitialinsectdensitywassetatmovethroughthelife–stages,andacontinuousagedis-0.01newlyemergedadultfemales/kgofwheat.tributionissimulated.Inthedistributed–delaymodel,a(2)InsectpopulationsandcentralgraintemperaturesweredelayprocessisusedtomovetheimmatureinsectssimulatedforWinnipegweatherwheninitialcondi-throughtheirlife–stagesandtosimulatevariationsintionswerefavorable(10,000adultsand30³C)anddevelopmentalrates.werenotfavorable(20adultsand25³C)forthedevel-(3)Inthehotspotmodel,adultageisdesignatedasphysio-opmentofahotspotinthebin.logicalage,whichismeasuredindegree–days(Kawa-(3)Insectpopulationsandcentralgraintemperaturesweremotoetal.,1989)afteremergenceofadults.InthesimulatedforTopekaweatherwheninitialconditionsspatialmodel,adultageisstoredina70–elementarray,werethesameasthosesimulatedforWinnipegwhichlimitsthemaximumageofadultsto70d.Inthe(10,000adultsand30³C;20adultsand25³C).hotspotmodel,adultageisdependentongraintemper-(4)Insectpopulationsandcentralgraintemperatureswereatures,whileinthespatialmodeladultageistempera-simulatedforTopekaweatherwhendailyimmigrationture–independent.ofinsectsintothebinwasincluded.Adailyimmigra-(4)ThespatialmodeldoesnotincludefeedbackfromthetionrateforC.ferrugineushasnotbeenmeasuredun-insectmodeltotheheattransfermodel.ThehotspotderWinnipegstorageconditions.Becauseofthelowmodel,however,simulatestheeffectsofinsectheatambienttemperaturesduringfall,dailyimmigrationofproductionongraintemperaturesandtheeffectsofC.ferrugineusisprobablyquitelowornegligible.graintemperaturesoninsectheatproduction(Cofie–Hence,thiscomparisonwasdoneonlyforTopekastor-Agbloretal.,1996a,1996b).ageconditions.Dailyimmigrationratesof0.0014adult(5)Inthehotspotmodel,themovementofadultsisdeter-females/kgofwheatinthetoplayer(0.0to1.2mdepth)minedbythetemperaturegradientsandinsectdensitiesand0.00074adultfemales/kgofwheatintheotherlay-inthegrainbulk(Mani,1999;Manietal.,2001).Theers(1.2to6.0mdepth)wereassumedforthestoragespatialmodeldoesnotincludeinsectmovement.periodfrom15Julyto01October(Flinnetal.,1997).Aninitialgraintemperatureof32³Candmoisturecon-tentof12%(wetbasis)wereassumedforthiscompari-SIMULATIONPROCEDUREsonatTopeka.Todeterminetheeffectofimmigration,Temperaturedistributionsandinsectdensitiesinanthesamestorageconditionsweresimulatedforanini-unaerated,8.5–mdiameterbinfilledwithwheattoadepthoftialintroductionof10,000adultsatthecenterofthe6mweresimulatedbyboththehotspotandspatialmodels.bulkandnodailyimmigration.Inthehotspotmodel,thebinwasdiscretizedinto440linear,three–dimensionalelements.Themassofwheatineachelementwasapproximately600kg.The6–mtallbulkwasRESULTSANDDISCUSSIONdividedinto5layers,1.2–mthick.TemperatureswerePREDICTEDINSECTPOPULATIONSATCONSTANTpredictedat109nodesineachhorizontalplane,foratotalofTEMPERATURES654nodesforthegrainbulk(Mani,1999;Manietal.,2001).ThesubmodelsofthepopulationdynamicsofInthespatialmodel,asectorofan8.5–mdiameterbinwasCryptolestesferrugineus(Stephens)inthehotspotanddividedinto16compartmentswith77nodes(Flinnetal.,spatialmodelswerecomparedbysimulatingtheeffectsof1992).Inthespatialmodel,thetemperaturemodelfeedstheconstantgraintemperaturesoninsectpopulationdensitiesinsectmodelwithcompartmentgraintemperaturesand(fig.1).Ataconstantgraintemperatureof25³C,thehotspotmoisturecontents.modelpredictedaninsectpopulationof2,200adults/kgafterInthehotspotmodel,insectswereintroducedintofour360dofstorage,whilethespatialmodelpredictedelementsatthe3–mdepthandfourelementsatthe1.8–m170adults/kg(fig.1).Thehotspotmodelpredictedanearlierdepth(Mani,1999).Thelocationandvolumeofthesedevelopmentoftheinsectpopulationwhenthegrainelementswereequivalenttothecenter–middlecompartmenttemperaturewasat30³C.Theinsectpopulationreachedawheretheinsectswereintroducedinthespatialmodel.Thepeakof3,800adults/kg,andduetothesimulatedmortalitymoisturecontentofthewheatwasassumedtobe14.5%(wetatthehighinsectdensity(Mani,1999;Manietal.,2001),thebasis).Becauseofthedifferentharvestingseasons,theinsectpopulationthendecreased(fig.1).At30³C,theinsectstartingdatesofsimulationswere15July1986forTopeka,populationpredictedbythespatialmodelincreasedtoKansas,and01September1986forWinnipeg,Canada.5,300adults/kg.656TRANSACTIONSOFTHEASAEFigure2.AveragetemperaturesandadultC.ferrugineuspopulationspredictedbythehotspotandspatialmodelsatthecenterofan8.5–mFigure1.AdultC.ferrugineuspopulationsinwheatmaintainedatdiameterbinfilledwithwheattoadepthof6matWinnipeg,Canada,constanttemperaturespredictedbythehotspotandspatialmodels(initialwhen20adults(IIP=initialinsectpopulation)wereintroducedattheinsectdensitywas0.01newlyemergedadultfemales/kgofwheat).centerofthewheatbulkon01Sept1986(initialgraintemperature=25³C,totalmassofwheatatthecenterofthebulk=5,000kg).TheAt35³C,thehotspotmodelpredictedamaximumoftemperatureswithIIPequalto0and20werenearlyidentical.4,000adults/kg,andthespatialmodelpredictedamaximumof6,600adults/kg.At40³C,whichwasthemaximumtwo–dimensionalmodelofheattransferinthespatialmodeltemperaturepredictedinaninsect–inducedhotspot(Mani,calculatedradiationonthesouthern55%ofthebinwall.1999),thehotspotmodelpredictednodevelopmentofBecausethespatialmodeldoesnotincludethevariationsininsects,andthespatialmodelpredictedslowdevelopment.solarheatingaroundthebinandpredictsthetemperaturesonForconstanttemperaturesfrom30³to40³C,theinsectonlythesouthsideofthebin,thetemperaturespredictedbypopulationspredictedbythehotspotmodelwerelowerthanthespatialmodelwerehigherthanthosepredictedbythehotthosepredictedbythespatialmodel,butat25³C,thehotspotspotmodel.modelpredictedhigherinsectpopulationsthanthoseTheinsectpopulationdensitiespredictedbythespatialpredictedbythespatialmodel.ThesevariationswereduetomodelincreaseduntilMarchandthendecreasedtozeroasthethedifferentwaysthemodelssimulateinsectages.temperatureatthecenterofthebincontinuedtodecreaseduetothermallag.ThespatialmodelisbasedonadevelopmentSIMULATIONSUNDERWINNIPEGSTORAGECONDITIONSperiodthatrapidlylengthenswithdecreasingtemperatures.³Foralowinitialpopulationof20adultinsectsandanBecausegraintemperaturesatthebincenterfellbelow20C,initialgraintemperatureof25³CunderWinnipegstoragereproductionanddevelopmentoftheinsectswerereducedtoconditions,thetemperaturessimulatedbythehotspotmodelnearzero.Cryptolestesferrugineusdonotdevelopand³withandwithoutinsectswerethesame(fig.2).Eventhoughmultiplyattemperaturesbelow17C,buttheysurvivetheinsectpopulationincreasedoverthetimeperiod,theheat(FieldsandWhite,1997).ThemodelofC.ferrugineusintheproducedbytheinsectswasnotsufficienttoincreasethehotspotmodelsimulatescontinuedslowdevelopmentandgraintemperatures.Themaximumdifferencebetweenthereproductionatlowtemperatures.Hence,theinsectdensitiescentertemperaturepredictedbythespatialmodelandthehotpredictedbythehotspotmodel(1.6adults/kg)werehigherspotmodelwas5³Cattheendofthesimulationperiod.Thethanthosepredictedbythespatialmodel(0.1adults/kg),Vol.44(3):655–660657eventhoughthepredictedcentertemperatureswerelowerfollowingsummer,duetoinsectmultiplicationandwarm(fig.2).Insummer,becausethetemperaturesofthegrainambientconditions,thetemperaturesofthesurroundingsurroundingthecenterofthebulkincreased,theadultsgrainbulkincreasedandtheaveragetemperaturesatthemigratedfromthecenterofthebulktothesurroundinggrain,centerofthebulkalsoincreased.therebycausingtheadultpopulationatthecenterofthebulkThetemperaturespredictedbythespatialmodelweretodecrease(fig.2).Thetotaladultpopulationinthebin,10³Cbelowthosepredictedbythehotspotmodel(fig.3).however,didnotdecrease.Thepopulationdensitypredictedbythespatialmodel,Foraninitialinsectpopulationof10,000adultsandanhowever,reachedahighermaximumof500adults/kg.Thisinitialgraintemperatureof30³C,thehotspotmodelwasbecausethespatialmodelpredictsrapidmultiplication³simulatedahotspotatthecenterofthebulktowardthestartofinsectsattemperaturesgreaterthan25C(fig.1)andnooffall(fig.3).Apeaktemperatureof39³Cwaspredictedatinsectmovementawayfromhightemperaturesandinsectthecenterofthebulkattheendoffallwhenthespatialmodeldensitiesatthecenterofthebin.predicted27³C.Thehotspotmodelpredictedamaximuminsectpopulationof120adults/kgatthecenterofthebulk.SIMULATIONSUNDERTOPEKASTORAGECONDITIONSBecauseofthedetrimentallyhightemperatureofthehotForaninitialinsectpopulationof20adultsandaninitialspot,themodelsimulatedinsectmigrationfromthehotspotgraintemperatureof25³C,temperaturespredictedbythehottothesurroundingbulkanddecreasedtheinsectpopulationspotmodelwerelowerthanthosepredictedbythespatialtonearzeroatthecenterofthebulk.ThetotaladultmodelforTopeka,Kansas(fig.4).Temperaturespredictedbypopulationinthebin,however,didnotdecrease.InthethehotspotmodelunderTopekaweatherconditions(fig.4)Figure3.AveragetemperaturesandadultC.ferrugineuspopulationsFigure4.AveragetemperaturesandadultC.ferrugineuspopulationspredictedbythehotspotandspatialmodelsatthecenterofan8.5–mpredictedbythehotspotandspatialmodelsatthecenterofan8.5–mdiameterbinfilledwithwheattoadepthof6matWinnipeg,Canada,diameterbinfilledwithwheattoadepthof6matTopeka,Kansas,whenwhen10,000adults(IIP=initialinsectpopulation,adults)were20adults(IIP=initialinsectpopulation,adults)wereintroducedattheintroducedatthecenterofthewheatbulkon01Sept1986(initialgraincenterofthewheatbulkon15July1986.ThetemperatureswithIIPequaltemperature=30³C,totalmassofwheatatthecenterofthewheatbulk=to0and20werenearlyidentical.5,000kg).658TRANSACTIONSOFTHEASAEwerehigherthanthosepredictedunderWinnipegweatherpopulationof150adults/kgwaspredictedbythehotspotconditions(fig.2).ThiswasbecausethegrainunderTopekamodel,whichwasonlyslightlyhigherthan120adults/kgforstorageconditionswasharvestedandstored45dearlierWinnipeg(fig.3).UnderTopekastorageconditions,the(15July)thanunderWinnipegstorageconditions(01Sep-spatialmodelalsopredictedahigherinsectpopulationtember),andtheambienttemperaturesinTopekawere(amaximumof800adults/kg)thanunderWinnipegstoragewarmerthanthoseinWinnipeg.Hence,initialinsectconditions(amaximumof500adults/kg).Duringthemultiplicationwashighandthepopulationreachedapeakoffollowingsummer,duetopredictedcentertemperatures34adults/kgunderTopekastorageconditions,whereasunderbelow25³C,theinsectpopulationdecreasedto400adults/kgWinnipegstorageconditionsitreachedapeakvalueof(fig.5).1.6adults/kg.Eventhoughtheinsectpopulationincreasedrapidly,theheatproducedbytheinsectswasinsufficienttoSIMULATIONSBASEDONDAILYIMMIGRATIONOFINSECTScauseahotspotinthegrainbulk(fig.4).AmaximumWhendailyimmigrationofinsectsintothegrainbinwaspopulationof1.8adults/kgwaspredictedbythespatialassumedunderTopekastorageconditions(Flinnetal.,1992),modelunderTopekastorageconditions(fig.4).Bothmodelshotspotsdevelopedinlatefall,andthehotspotmodelpredictedmaximumpopulationsatTopeka(fig.4)aboutpredictedwarmgraintemperaturesthroughoutthe20timeshigherthanatWinnipeg(fig.2).simulationperiod(fig.6).Attheendofthesimulationperiod,Foraninitialinsectdensityof10,000adultsandaninitial³themaximumdifferencebetweenthetemperaturespredictedgraintemperatureof30C,thehotspotmodelpredictedahotbythehotspotandspatialmodelswas10³C.Thehotspotspotinearlyfallandtemperaturesremainedwarmmodelpredictedamaximumof100adults/kgbytheendofthroughoutthesimulationperiod(fig.5).AmaximumFigure5.AveragetemperaturesandadultC.ferrugineuspopulationsFigure6.AveragetemperaturesandadultC.ferrugineuspopulationspredictedbythehotspotandspatialmodelsatthecenterofan8.5–mpredictedbythehotspotandspatialmodelsatthecenterofan8.5–mdiameterbinfilledwithwheattoadepthof6matTopeka,Kansas,whendiameterbinfilledwithwheattoadepthof6matTopeka,Kansas,and10,000adults(IIP=initialinsectpopulation,adults)wereintroducedatdailyimmigrationratesof0.0014adultfemales/kgofwheatinthetopthecenterofthewheatbulkon15July1986.layer(0.0to1.2mdepth)and0.00074adultfemales/kgofwheatintheotherlayers(1.2to6.0mdepth)from15Julyto01October.Vol.44(3):655–660659fallandthen,duetothesimulatedmigrationofinsectsfromexperimentaldata,theoverallmodelhasnotbeentested.Thethehightemperaturesandinsectdensities,insectpopulationspatialmodelwasvalidatedwithdatafroma350m3bininatthecenterdecreasedtonearzero(fig.6).ThespatialmodelKansas(Flinnetal.,1992).predictedamaximumof250adults/kgatthecenterofthebulkinthefollowingspring.ThesevariationsintheACKNOWLEDGEMENTSmaximumpopulationwereduetotheinherentdifferencesTheauthorsthanktheNaturalSciencesandEngineeringbetweenthehotspotandspatialmodels.DuetothelowgrainResearchCouncilofCanadaforfundingthisstudyandDr.P.temperaturesandnoimmigrationofinsects,insectG.Fieldsforhiscommentsonthemanuscript.populationsdecreasedduringthefollowingsummer.Forthespatialmodel,themaximumpopulationpredictedbasedondailyimmigrationofinsects(fig.6)was3.2timeslowerthanthemaximumpopulationpredicted,forthesameREFERENCESsimulationconditions,when10,000adultswereintroducedAlagusundaram,K.,D.S.Jayas,N.D.G.White,andW.E.Muir.initiallyatthecenterofthebulkwithnodailyimmigration1990.Threedimensional,finiteelement,heattransfermodeloftemperaturedistributioningrainstoragebins.Trans.ASAE(datanotshown).Dailyimmigrationcausesslowinitial33(2):577–584.developmentoftheinsectsinthecenter–middleCofie–Agblor,R.,W.E.Muir,R.N.Sinha,andP.G.Fields.1996a.compartmentandnomovementofinsectsbetweenHeatproductionbyadultCryptolestesferrugineus(Stephens)ofcompartments.Forthehotspotmodel,themaximumdifferentagesanddensities.PostharvestBiologyandTechnol.7:populationpredictedbasedonadailyimmigrationofinsects371–380.(fig.6)wasthesameasthemaximumpopulationpredicted,Cofie–Agblor,R.,W.E.Muir,Q.Zhang,andR.N.Sinha.1996b.HeatofrespirationofCryptolestesferrugineus(Stephens)adultsforthesamesimulationconditions,when10,000adultswereandlarvaeinstoredwheat.Can.Agric.Eng.38(1):37–44.introducedinitiallyatthecenterofthebulkwithnodailyCuff,W.R.,andJ.M.Hardman.1980.AdevelopmentoftheLeslieimmigration(datanotshown).Themaximumpopulationmatrixformulationforrestructuringandextendinganecosystembasedondailyimmigrationofinsects,however,wasattainedmodel:TheinfestationofstoredwheatbySitophilusoryzae.75dlaterthanwheninsectswereintroducedinitially.ThisEcologicalModelling9:281–305.wasbecauseofthetimetakenbytheimmigrantinsectstoFields,P.G.,andN.D.G.White.1997.Survivalandmultiplicationofstored–productbeetlesatsimulatedandactualwintermovetoandaggregateatthecenterofthegrainbulk.temperatures.Can.Entomol.129(5):887–898.Flinn,P.W.,D.W.Hagstrum,W.E.Muir,andK.Sudayappa.1992.SpatialmodelforsimulatingchangesintemperatureandinsectCONCLUSIONSpopulationdynamicsinstoredgrain.Environ.Entomol.21(6):1351–1356.UnderWinnipegstorageconditions,withaninitialgrainFlinn,P.W.,D.W.Hagstrum,andW.E.Muir.1997.Effectsoftimetemperatureof30³Candaninitialinsectpopulationofofaeration,binsize,andlatitudeoninsectpopulationsinstored10,000adults(2adults/kg),theinsectdensityatthecenterwheat:Asimulationstudy.J.EconomicEntomol.90(2):predictedbythehotspotmodelreachedamaximumof646–651.120adults/kgneartheendoffallandcentertemperaturesJayas,D.S.1995.Mathematicalmodellingofheat,moisture,andreachedapeakof39³C.Thespatialmodel,however,gastransferinstored–grainecosystems.InStored–GrainEcosystems,527–567.D.S.Jayas,N.D.G.White,andW.E.predictedamaximumadultpopulationof500adults/kgandMuir,eds.NewYork,N.Y.:MarcelDekker,Inc.noincreaseingraintemperatures.F