生物测定的统计基础及试验设计

生物测定的统计基础及试验设计第1页/共80页对试验数据进行分析,指导试验的设计。只有在生物统计理论指导下制定的试验方案,才能消耗最少的人力、物力和时间,获得最多有用的数据。在应用生物统计工具对试验结果分析时,我们必须结合专业知识,选用适当的模型来分析,在不了解生物现象的情况下,机械地套用有可能得出错误的结论。第2页/共80页概率分布第3页/共80页反应-剂量对数的概率分布曲线G=1/√(2)e**(-(x-)2/2σ2)

第4页/共80页:为中数或均数,是分布的中心,决定了曲线在横坐标上的位置，在概率分布曲线中,它表示有效中量(medianeffectivedose,ED50)的对数值

σ2:方差,它代表了分布的离散度,σ2大,分布曲线低而宽,σ2小,分布曲线高而窄。低而宽的反应-剂量分布曲线表明生物群体中个体之间对药剂的忍受能力差异大,高而窄的曲线则表明生物群体中个体之间对药剂的忍受能力差异小。μμ第5页/共80页试验的精密度试验误差experimentalerror一个试验的试验误差大小说明了该试验的精密程度如何。试验的精密度(precision)是表示试验结果的可重复性。试验误差可能由供试生物个体间的差异操作上的不一致造成的,由一些未被试验人员所察觉的随机误差所引起的。除了选用一致的生物个体作试验材料、保持试验条件的稳定、规范试验操作可减少试验误差外,选择适当的试验设计也可减少试验误差。第6页/共80页精密度[S2(y)]的表示方法S2(y)=S2/n其中，S2(y)表示处理平均数的方差，S2表示样本方差，n表示观察值的个数。S2

－试验设计和试验材料差异N－试验单元的大小和数量第7页/共80页提高试验的精密度途径减小S2

，即是降低样本的方差选择适合的试验设计差异较小的试验材料增加n，即是增加试验单元(experimentalunit)大小和数量第8页/共80页试验单元(experimentalunit)某一处理在某一重复中的试验材料的总和一盆种一株植物一盆种十株植物一个培养皿中装十粒种子一个培养皿中装一百粒种子在不同的试验单元间存在着固有的差异在同一试验单元中的不同个体的表现趋于一致不能把试验单元中的不同个体当成重复第9页/共80页试验设计无重复的试验扩展试验设计(augmenteddesign)单因子试验多因子试验第10页/共80页剂量－反应曲线及其模型分为质反应(quantalresponse)量反应(quantitativeresponse)第11页/共80页质反应曲线When=1,=0

zip=1/(22)exp(-1/2Z2

)dz -

xip=1/(22)exp(-1/2(x-)2/2)dx -

第12页/共80页直线化变换

ProbittranformationZ=1/(x-)Y=Z+5=1/(x-)+5=-1/

+5+1/x

在标准正态偏离上加5是为了使所有的机率值为正数。因为,在反应率p等于50%,Z为0,反应率小于50%时,Z为负值。如当反应率等于25.87%,Z为-1;反应率等于2.28%时,Z为-2.将Z加上5后,在任何反应率下,机率值均为正数第13页/共80页Doseresponsecurve第14页/共80页Dose-responsemodel第15页/共80页模型的检验第16页/共80页直线化变换移项得

(D-C)/(y-C)-1=(x/x0)b两边同时取对数得

log{(D-y)/(y-C)}=b(logx-logx0)令v=log{(D-y)/(y-C)},则

v=b(logx-logx0)……(2.12)第17页/共80页HerbicideBioassay第18页/共80页RelativepotencyTherelativepotency(RP)ofHerbicideAwithrespecttoHerbicideBisdefinedas:

RP(A/B)=ED50(compound)/ED50(compoudB)第19页/共80页Parallel

Quantalresponse

Y1=a1+b1X1 Y2=a1+b2X2

doseresponse第20页/共80页ttest

whetherthetwolineareparallelornot

Ifnotsignificant,thenb1=b2andtwolinesareparallel

第21页/共80页Pooledresidualmeansquare(S2p)

=[(n1-2)S2b1+(n2-2)S2b2]/(n1+n2-4)

Where:S2b1isresidualmeansquareforthe1stsetofdata;S2b2isresidualmeansquareforthe2ndsetofdata.第22页/共80页

Combinedslope(bc):

第23页/共80页Quantitativeresponse(four-parametermodel)

第24页/共80页第25页/共80页Ftest

First,supposeb1=b2,ED501=ED502,andrunthemodelIThensupposeb1b2,ED501=ED502,andrunthemodelII(SSII-SSI)/(dfII-dfI) F= SSI/dfIwhereSSIIiserrorsumofsquareofModelII;SSIiserrorsumofsquareofModelIIfnotsignificant,thenb1=b2andtwocurvesareparallel.第26页/共80页Parallelcurves:Twocompoundshavingthesameactionmode;Differentformulationsofacompound;Onecompoundwithdifferentadjuvants第27页/共80页Non-parallelSlope(b)-notconstantfortestedcompounds.Comparerelativepotencyoftwocompoundseffectively onlyunderacertainequivalenteffectivedose.第28页/共80页VerticalvshorizontalassessmentsVerticalassessment– Compareplantresponsesatpresetdoses.Horizontalassessment–Comparethedosesoftwoormorecompoundsthatproduceasimilarplantresponse.第29页/共80页Cautionswiththeparallel-linedose-responsetheory a. Notparallelinfieldconditions b. Worklesswellwithherbicideshavingcomplexormultiplemodesofaction. c. Maybeworklesswellwithdifferentplantspecies. d. Maybedoesn’tworkwithdifferentgrowthstages.第30页/共80页Screeningprocedures a.Primaryscreen b.Secondaryscreen c.Fieldscreenandphysiologicalandbiochemicalselectivitystudies d.Advancedselectivityscreen e.Fieldevaluation第31页/共80页Expressingselectivity

a.Verticalassessment

b.Selectivityindices(SI)

SI=ED50(speciesA)/ED50(speciesB)

SI=ED10(crop)/ED90(weed)

SI2Goodselectivity SI1-2Marginalselectivity SI<1NonSelectivity第32页/共80页Becarefulwhenusingthecriteria

1.ED10maysignificantlyreducecropyields.2.Thelimitationsofbioassayinthepredictionoffieldresponse a.Temperature b.Daylength,lightquality,irradiance c.Windeffects d.Plantgrowthstage e.Soilconditions3.Overlapofsprayedareas4.Applyhigherdosethanrecommendeddose第33页/共80页No-observable-effectlevel(NOEL)andNo-effect

level(NEL)

DeterminationofNOEL

a.Multiplecomparisontest

Effectofexpt.design Morereplications,moreprecision. Disadvantage: Differentresponses Differentslopesb.Dose-responserelationshi

第34页/共80页ProblemsindeterminingtheNOEL a.Stimulation b.Effectofexpt.designandresponsevariable c.Durationofexposure第35页/共80页ParametersusedinherbicidebioassayBiomassincludingfreshweightanddryweightMortalityPlantheightPhysiologicalparameters第36页/共80页INTERACTIONBETWEENHERBICIDESResponseFactorAatlevel1

FactorAatlevel1FactorB

第37页/共80页INTERACTIONBETWEENHERBICIDESResponseFactorAatlevel1

FactorAatlevel1FactorB

第38页/共80页HerbicidemixturesReasonsforusingherbicidemixtures:WidenthespectrumofweedscontrolledReducecostsofweedcontrolReduceherbicideuseReducenumberofsprayingsPrevent/overcomeresistance第39页/共80页HerbicidemixturesAdditivity TheperformanceofamixtureisaspredictedbyareferencemodelAntagonism TheperformanceofamixtureispoorerthanpredictedbyareferencemodelSynergism Theperformanceofamixtureisbetterthanpredictedbyareferencemodel第40页/共80页AntagonismReduceduptakeand/ortranslocationofaherbicideoranincreasedmetabolismofaherbicide(biochemicalantagonism) PSIIinhibitors+glyphosate dinitroanilines+PSIIinhibitors ”fops”+auxinherbicides difenzoquat/flamprop-M-isopropyl+auxinherbicidesPreventingbindingofactiveingredientatthesiteofaction(competitiveantagonism) Safeners Activeandinactiveisomersoftheherbicide第41页/共80页AntagonismOppositephysiologicaleffects(physiologicalantagonism) difenzoquat/flamprop-M-isopropyl+phenoxyherbicidesChemicalreactioninthespraysolution(chemicalantagonism) glyphosate+cations paraquat+MCPA第42页/共80页SynergismIncreaseduptakeand/ortranslocationofaherbicide adjuvants desmedipham+ethofumesate growthregulators+glyphosate/dicambaReducedmetabolismofaherbicide insekticides+herbicides 第43页/共80页HerbicidemixturesThreepossiblescenariosNoneofthecompoundsareactiveappliedalonebutappliedinmixturetheyexertactivity(coalitiveaction)第44页/共80页HerbicidemixturesThreepossiblescenariosNoneofthecompoundsareactiveappliedalonebutappliedinmixturetheyexertactivity(coalitiveaction)Onecompoundisactivewhiletheotherisinactive(herbicide+adjuvant,herbicide+fungicide/insecticide/growthregulator)Twocompoundareactive(herbicide+herbicide)第45页/共80页Adjuvants第46页/共80页Adjuvants第47页/共80页Doseresponsecurves第48页/共80页AdjuvantsFluazifop-bytyl+variousadjuvantsSunSprayPlus: R=1.000.1%Sandovit: R=1.410.3%Sandovit R=1.791%Atplus221 R=1.843%Atplus R=2.34第49页/共80页Herbicidemixtures第50页/共80页Herbicidemixtures第51页/共80页ReferencemodelsEffectmultiplicationalsocalledMultiplikativeSurvivalModel(MSM)ConcentrationadditionalsocalledAdditiveDoseModel(ADM)第52页/共80页MultiplicativeSurvivalModelQA,B=QAxQBQisaproportionoftheuntreatedcontrol,i.e.O=100%controland1=nocontrolIfPis%effect(from0to1)then(1-PA,B)=(1-PA)x(1-PB)orPA,B=PA+PB-PAxPB

第53页/共80页MultiplicativeSurvivalModelExample:1kg/haHerbicideA:75%effect1kg/haHerbicideB:80%effectExpectedeffectofamixturecontaining1kg/haofeachherbicideaccordingtoMSM:P=0.75+0.80-0.75x0.80P=0.95i.e.95%effect第54页/共80页MultiplicativeSurvivalModelMSMassumesindependentactionoftheherbicides,i.e.theherbicidesexerttheiractionindependentlyofeachother(=sequential)whichseemstobeanunrealisticassumptionformostherbicidemixtures.MSMhastraditionallybeenconsideredtobethecorrectreferencemodelformixturesofherbicideswithdifferentmodesofaction.第55页/共80页AdditiveDoseModelAtagivenresponselevelADMcanbeexpressedas:zA/ZA+zB/ZB=1whereZAandZBarethedosesofherbicidesAandBappliedseparatelyandzAandzBarethedosesoftheherbicidesinamixtureconsistingofzA+zB.TherelativepotencybetweenherbicidesAandBis:R=ZA/ZB

Therelativepotencycorrespondstotheexchangeratebetweencurrencies.第56页/共80页AdditiveDoseModelExample:ED50ofHerbicideA:4kg/haED50ofHerbicideB:2kg/haR=4/2=2i.e.HerbicideBistwiceasactiveasHerbicideA第57页/共80页AdditiveDoseModel第58页/共80页AdditiveDoseModelED50orEDxED50orEDx第59页/共80页AdditiveDoseModel第60页/共80页AdditiveDoseModelExample:HerbicideA:4kg/haHerbicideB:2kg/haMixture1(75%A:25%B):3.2kg/ha2.4kg/haHerbicideA+0.8kg/haHerbicideB0.6HerbicideA+0.4HerbicideBMixture2(50%A:50%B):2.7kg/ha1.35kg/haHerbicideA+1.35kg/haHerbicideB0.33HerbicideA+0.67HerbicideBMixture3(25%A:75%B):2.3kg/ha0.58kg/haHerbicideA+1.72kg/haHerbicideB0.14HerbicideA+0.86HerbicideB第61页/共80页AdditiveDoseModel第62页/共80页AdditiveDoseModelExample:HerbicideA:4kg/haHerbicideB:2kg/haMixture1(75%A:25%B):4.4kg/ha3.3kg/haHerbicideA+1.1kg/haHerbicideB0.83HerbicideA+0.55HerbicideBMixture2(50%A:50%B):3.8kg/ha1.9kg/haHerbicideA+1.9kg/haHerbicideB0.48HerbicideA+0.95HerbicideBMixture3(25%A:75%B):3.6kg/ha0.9kg/haHerbicideA+2.7kg/haHerbicideB0.23HerbicideA+1.35HerbicideB第63页/共80页AdditiveDoseModel第64页/共80页AdditiveDoseModelExample:HerbicideA:4kg/haHerbicideB:2kg/haMixture1(75%A:25%B):2.4kg/ha1.8kg/haHerbicideA+0.6kg/haHerbicideB0.45HerbicideA+0.3HerbicideBMixture2(50%A:50%B):2.0kg/ha1.0kg/haHerbicideA+1.0kg/haHerbicideB0.25HerbicideA+0.50HerbicideBMixture3(25%A:75%B):1.6kg/ha0.4kg/haHerbicideA+1.2kg/haHerbici