生物測定的統計基礎

及試驗設計對試驗數據進行分析,指導試驗的設計。只有在生物統計理論指導下制定的試驗方案,才能消耗最少的人力、物力和時間,獲得最多有用的數據。在應用生物統計工具對試驗結果分析時,我們必須結合專業知識,選用適當的模型來分析,在不了解生物現象的情況下,機械地套用有可能得出錯誤的結論。概率分布反應-劑量對數的概率分布曲線G=1/√(2)e**(-(x-)2/2σ2)

:為中數或均數,是分布的中心,決定了曲線在橫坐標上的位置，在概率分布曲線中,它表示有效中量(medianeffectivedose,ED50)的對數值

σ2:方差,它代表了分布的離散度,σ2大,分布曲線低而寬,σ2小,分布曲線高而窄。低而寬的反應-劑量分布曲線表明生物群體中個體之間對藥劑的忍受能力差異大,高而窄的曲線則表明生物群體中個體之間對藥劑的忍受能力差異小。μμ試驗的精密度試驗誤差experimentalerror一個試驗的試驗誤差大小說明了該試驗的精密程度如何。試驗的精密度(precision)是表示試驗結果的可重復性。試驗誤差可能由供試生物個體間的差異操作上的不一致造成的,由一些未被試驗人員所察覺的隨機誤差所引起的。除了選用一致的生物個體作試驗材料、保持試驗條件的穩定、規范試驗操作可減少試驗誤差外,選擇適當的試驗設計也可減少試驗誤差。精密度[S2(y)]的表示方法S2(y)=S2/n其中，S2(y)表示處理平均數的方差，S2表示樣本方差，n表示觀察值的個數。S2

－試驗設計和試驗材料差異N－試驗單元的大小和數量提高試驗的精密度途徑減小S2

，即是降低樣本的方差選擇適合的試驗設計差異較小的試驗材料增加n，即是增加試驗單元(experimentalunit)大小和數量試驗單元(experimentalunit)某一處理在某一重復中的試驗材料的總和一盆種一株植物一盆種十株植物一個培養皿中裝十粒種子一個培養皿中裝一百粒種子在不同的試驗單元間存在著固有的差異在同一試驗單元中的不同個體的表現趨于一致不能把試驗單元中的不同個體當成重復試驗設計無重復的試驗擴展試驗設計(augmenteddesign)單因子試驗多因子試驗劑量－反應曲線及其模型分為質反應(quantalresponse)量反應(quantitativeresponse)質反應曲線When=1,=0

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

)dz -

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

直線化變換

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

+5+1/x

在標準正態偏離上加5是為了使所有的機率值為正數。因為,在反應率p等于50%,Z為0,反應率小于50%時,Z為負值。如當反應率等于25.87%,Z為-1;反應率等于2.28%時,Z為-2.將Z加上5后,在任何反應率下,機率值均為正數DoseresponsecurveDose-responsemodel模型的檢驗直線化變換移項得

(D-C)/(y-C)-1=(x/x0)b兩邊同時取對數得

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

v=b(logx-logx0)……(2.12)HerbicideBioassayRelativepotencyTherelativepotency(RP)ofHerbicideAwithrespecttoHerbicideBisdefinedas:

RP(A/B)=ED50(compound)/ED50(compoudB)Parallel

Quantalresponse

Y1=a1+b1X1 Y2=a1+b2X2

doseresponsettest

whetherthetwolineareparallelornot

Ifnotsignificant,thenb1=b2andtwolinesareparallel

Pooledresidualmeansquare(S2p)

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

Where:S2b1isresidualmeansquareforthe1stsetofdata;S2b2isresidualmeansquareforthe2ndsetofdata.

Combinedslope(bc):

Quantitativeresponse(four-parametermodel)

Ftest

First,supposeb1=b2,ED501=ED502,andrunthemodelIThensupposeb1b2,ED501=ED502,andrunthemodelII(SSII-SSI)/(dfII-dfI) F= SSI/dfIwhereSSIIiserrorsumofsquareofModelII;SSIiserrorsumofsquareofModelIIfnotsignificant,thenb1=b2andtwocurvesareparallel.Parallelcurves:Twocompoundshavingthesameactionmode;Differentformulationsofacompound;OnecompoundwithdifferentadjuvantsNon-parallelSlope(b)-notconstantfortestedcompounds.Comparerelativepotencyoftwocompoundseffectively onlyunderacertainequivalenteffectivedose.VerticalvshorizontalassessmentsVerticalassessment– Compareplantresponsesatpresetdoses.Horizontalassessment–Comparethedosesoftwoormorecompoundsthatproduceasimilarplantresponse.Cautionswiththeparallel-linedose-responsetheory a. Notparallelinfieldconditions b. Worklesswellwithherbicideshavingcomplexormultiplemodesofaction. c. Maybeworklesswellwithdifferentplantspecies. d. Maybedoesn’tworkwithdifferentgrowthstages.Screeningprocedures a.Primaryscreen b.Secondaryscreen c.Fieldscreenandphysiologicalandbiochemicalselectivitystudies d.Advancedselectivityscreen e.FieldevaluationExpressingselectivity

a.Verticalassessment

b.Selectivityindices(SI)

SI=ED50(speciesA)/ED50(speciesB)

SI=ED10(crop)/ED90(weed)

SI2Goodselectivity SI1-2Marginalselectivity SI<1NonSelectivityBecarefulwhenusingthecriteria

1.ED10maysignificantlyreducecropyields.2.Thelimitationsofbioassayinthepredictionoffieldresponse a.Temperature b.Daylength,lightquality,irradiance c.Windeffects d.Plantgrowthstage e.Soilconditions3.Overlapofsprayedareas4.ApplyhigherdosethanrecommendeddoseNo-observable-effectlevel(NOEL)andNo-effect

level(NEL)

DeterminationofNOEL

a.Multiplecomparisontest

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

ProblemsindeterminingtheNOEL a.Stimulation b.Effectofexpt.designandresponsevariable c.DurationofexposureParametersusedinherbicidebioassayBiomassincludingfreshweightanddryweightMortalityPlantheightPhysiologicalparametersINTERACTIONBETWEENHERBICIDESResponseFactorAatlevel1

FactorAatlevel1FactorB

INTERACTIONBETWEENHERBICIDESResponseFactorAatlevel1

FactorAatlevel1FactorB

HerbicidemixturesReasonsforusingherbicidemixtures:WidenthespectrumofweedscontrolledReducecostsofweedcontrolReduceherbicideuseReducenumberofsprayingsPrevent/overcomeresistanceHerbicidemixturesAdditivity TheperformanceofamixtureisaspredictedbyareferencemodelAntagonism TheperformanceofamixtureispoorerthanpredictedbyareferencemodelSynergism TheperformanceofamixtureisbetterthanpredictedbyareferencemodelAntagonismReduceduptakeand/ortranslocationofaherbicideoranincreasedmetabolismofaherbicide(biochemicalantagonism) PSIIinhibitors+glyphosate dinitroanilines+PSIIinhibitors ”fops”+auxinherbicides difenzoquat/flamprop-M-isopropyl+auxinherbicidesPreventingbindingofactiveingredientatthesiteofaction(competitiveantagonism) Safeners ActiveandinactiveisomersoftheherbicideAntagonismOppositephysiologicaleffects(physiologicalantagonism) difenzoquat/flamprop-M-isopropyl+phenoxyherbicidesChemicalreactioninthespraysolution(chemicalantagonism) glyphosate+cations paraquat+MCPASynergismIncreaseduptakeand/ortranslocationofaherbicide adjuvants desmedipham+ethofumesate growthregulators+glyphosate/dicambaReducedmetabolismofaherbicide insekticides+herbicides HerbicidemixturesThreepossiblescenariosNoneofthecompoundsareactiveappliedalonebutappliedinmixturetheyexertactivity(coalitiveaction)HerbicidemixturesThreepossiblescenariosNoneofthecompoundsareactiveappliedalonebutappliedinmixturetheyexertactivity(coalitiveaction)Onecompoundisactivewhiletheotherisinactive(herbicide+adjuvant,herbicide+fungicide/insecticide/growthregulator)Twocompoundareactive(herbicide+herbicide)AdjuvantsAdjuvantsDoseresponsecurvesAdjuvantsFluazifop-bytyl+variousadjuvantsSunSprayPlus: R=1.000.1%Sandovit: R=1.410.3%Sandovit R=1.791%Atplus221 R=1.843%Atplus R=2.34HerbicidemixturesHerbicidemixturesReferencemodelsEffectmultiplicationalsocalledMultiplikativeSurvivalModel(MSM)ConcentrationadditionalsocalledAdditiveDoseModel(ADM)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

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

Therelativepotencycorrespondstotheexchangeratebetweencurrencies.AdditiveDoseModelExample:ED50ofHerbicideA:4kg/haED50ofHerbicideB:2kg/haR=4/2=2i.e.HerbicideBistwiceasactiveasHerbicideAAdditiveDoseModelAdditiveDoseModelED50orEDxED50orEDxAdditiveDoseModelAdditiveDoseModelExample: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+0.86HerbicideBAdditiveDoseModelAdditiveDoseModelExample: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+1.35HerbicideBAdditiveDoseModelAdditiveDoseModelExample: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.