生物测定的统计基础及试验设计.ppt

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1、生物测定的统计基础及试验设计 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。概率分布 反应-剂量对数的概率分布曲线G=1/(2)e*(-(x-)2/22):为中数或均数为中数或均数,是分布的中心是分布的中心,决定了曲线在横坐标上的位置，决定了曲线在横坐标上的位置，在概率分布曲线中在概率分布曲线中,它表示有效中量它表示有效中量(median effective dose,(med

2、ian effective dose,ED50)ED50)的对数值的对数值 2 2:方差方差,它代表了分布的离散度它代表了分布的离散度,2 2大大,分布曲线低而宽分布曲线低而宽,2 2小小,分布曲线高而窄。低而宽的反应分布曲线高而窄。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。体中个体之间对药剂的忍受能力差异小。试验的精密度试验误差试验误差试验误差试验误差experimental error experimental error

3、 experimental error experimental error 一个试验的试验误差大小说明了该试验的精密一个试验的试验误差大小说明了该试验的精密一个试验的试验误差大小说明了该试验的精密一个试验的试验误差大小说明了该试验的精密程度如何。试验的精密度程度如何。试验的精密度程度如何。试验的精密度程度如何。试验的精密度(precision)(precision)(precision)(precision)是表示试是表示试是表示试是表示试验结果的可重复性。验结果的可重复性。验结果的可重复性。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试验误差可能由供试生物个体间的差异试验误差可能由

4、供试生物个体间的差异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操作上的不一致造成的操作上的不一致造成的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由一些未被试验人员所察觉的随机误差所引起由一些未被试验人员所察觉的随机误差所引起由一些未被试验人员所察觉的随机误差所引起的。的。的。的。除了选用一致的生物个体作试验材料、保持试除了选用一致的生物个体作试验材料、保持试除了选用一致的生物个体作试验材料、保持试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验条件的稳定、规范试验操作可减少试验误差验条件的稳定、规范试验操作可减少试验误差验条件的

5、稳定、规范试验操作可减少试验误差外外外外,选择适当的试验设计也可减少试验误差。选择适当的试验设计也可减少试验误差。选择适当的试验设计也可减少试验误差。选择适当的试验设计也可减少试验误差。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选择适合的试验设计差异较小的试验材料差异较小的试验材料增加n，即是增加试验单元(experimental unit)大小和数量试验单元(experimental unit)某

6、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一株植物一盆种十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十粒种子一个培养皿中装一百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试验设计 无重复的试验 扩展试验设计(augmented design)单因子试验多因子试验剂量反应曲线及其模型 分为质反应(quantal response)量反应(quantitative response)质反应曲线 When=1,=0 zip=1/(22)exp(-1/2 Z2)dz -xip=1

7、/(22)exp(-1/2(x-)2/2)dx -直线化变换直线化变换 Probit tranformation Z=1/Z=1/(x-(x-)Y=Z+5 =1/Y=Z+5 =1/(x-(x-)+5=-1/)+5=-1/+5+1/+5+1/x x 在标准正态偏离上加在标准正态偏离上加5 5是为了使所有的机率值为正数。因为是为了使所有的机率值为正数。因为,在反应率在反应率p p等于等于50%,Z50%,Z为为0,0,反应率小于反应率小于50%50%时时,Z,Z为负值。为负值。如当反应率等于如当反应率等于25.87%,Z25.87%,Z为为-1;-1;反应率等于反应率等于2.28%2.28%时时,

8、Z,Z为为-2.-2.将将Z Z加上加上5 5后后,在任何反应率下在任何反应率下,机率值均为正数机率值均为正数 Dose response curveDose-response model模型的检验直线化变换变换移项得(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)Herbicide BioassayRelative potencyThe relative potency(RP)of Herbicide A with respect to Herbi

9、cide B is defined as:RP(A/B)=ED50(compound)/ED50(compoud B)ParallelQuantal response Y1=a1+b1X1 Y2=a1+b2X2 doseresponset test whether the two line are parallel or not If not significant,then b1=b2 and two lines are parallel Pooled residual mean square(S2p)=(n1-2)S2b1+(n2-2)S2b2/(n1+n2-4)Where:S2b1is

10、residual mean square for the 1st set of data;S2b2 is residual mean square for the 2nd set of data.Combined slope(bc):Quantitative response(four-parameter model)F test First,suppose b1=b2,ED501=ED502,and run the First,suppose b1=b2,ED501=ED502,and run the model Imodel IThen suppose b1 Then suppose b1

11、 b2,ED501=ED502,and run the model b2,ED501=ED502,and run the model II II (SS (SSII II-SS-SSI I)/(df)/(dfII II-df-dfI I)F=F=SS SSI I/df/dfI I where SS where SSII II is error sum of square of Model II;is error sum of square of Model II;SS SSI I is error sum of square of Model I is error sum of square

12、of Model I If not significant,then b1=b2 and two curves are parallel.If not significant,then b1=b2 and two curves are parallel.Parallel curves:Two compounds having the same action mode;Different formulations of a compound;One compound with different adjuvants Non-parallelSlope(b)-not constant for te

13、sted compounds.Compare relative potency of two compounds effectively only under a certain equivalent effective dose.Vertical vs horizontal assessmentsVertical assessment Compare plant responses at preset doses.Horizontal assessment Compare the doses of two or more compounds that produce a similar pl

14、ant response.Cautions with the parallel-line dose-response theorya.Not parallel in field conditionsb.Work less well with herbicides having complex or multiple modes of action.c.Maybe work less well with different plant species.d.Maybe doesnt work with different growth stages.Screening proceduresa.Pr

15、imary screenb.Secondary screenc.Field screen and physiological and biochemical selectivity studiesd.Advanced selectivity screene.Field evaluationExpressing selectivitya.Vertical assessmenta.Vertical assessment b.Selectivity indices(SI)b.Selectivity indices(SI)SI=SI=ED50(species A)ED50(species A)/ED5

16、0 /ED50(species B)(species B)SI=ED10(crop)/ED90(weed)SI=ED10(crop)/ED90(weed)SI SI 2 Good selectivity 2 Good selectivitySI 1-2 Marginal selectivity SI 1-2 Marginal selectivity SI 1 Non SelectivitySI 1 Non SelectivityBe careful when using the criteria 1.ED10 may significantly reduce crop yields.1.ED1

17、0 may significantly reduce crop yields.2.The limitations of bioassay in the prediction 2.The limitations of bioassay in the prediction of field responseof field responsea.Temperaturea.Temperatureb.Day length,light quality,irradianceb.Day length,light quality,irradiancec.Wind effectsc.Wind effectsd.P

18、lant growth staged.Plant growth stagee.Soil conditionse.Soil conditions3.Overlap of sprayed areas 3.Overlap of sprayed areas 4.Apply higher dose than recommended dose 4.Apply higher dose than recommended dose No-observable-effect level(NOEL)and No-effect level(NEL)Determination of NOELDetermination

19、of NOEL a.Multiple comparison test a.Multiple comparison testEffect of expt.designEffect of expt.designMore replications,more precision.More replications,more precision.Disadvantage:Disadvantage:Different responses Different responses Different slopesDifferent slopes b.Dose-response relationshi b.Do

20、se-response relationshi Problems in determining the NOELa.Stimulationb.Effect of expt.design and response variablec.Duration of exposureParameters used in herbicide bioassayBiomass including fresh weight and dry weightMortalityPlant heightPhysiological parametersINTERACTION BETWEEN HERBICIDESRespons

21、e Response Factor A at level 1Factor A at level 1 Factor A at level 1 Factor A at level 1 Factor B Factor B INTERACTION BETWEEN HERBICIDESResponse Response Factor A at level 1Factor A at level 1 Factor A at level 1 Factor A at level 1 Factor B Factor B Herbicide mixturesReasons for using herbicide m

22、ixtures:Reasons for using herbicide mixtures:Widen the spectrum of weeds controlledWiden the spectrum of weeds controlled Reduce costs of weed controlReduce costs of weed control Reduce herbicide useReduce herbicide use Reduce number of sprayingsReduce number of sprayings Prevent/overcome resistance

23、Prevent/overcome resistanceHerbicide mixturesAdditivityAdditivityThe performance of a mixture is as predicted The performance of a mixture is as predicted by a reference modelby a reference modelAntagonismAntagonismThe performance of a mixture is poorer than The performance of a mixture is poorer th

24、an predicted by a reference modelpredicted by a reference modelSynergismSynergismThe performance of a mixture is better than The performance of a mixture is better than predicted by a reference model predicted by a reference model AntagonismReduced uptake and/or translocation of a Reduced uptake and

25、/or translocation of a herbicide or an increased metabolism of a herbicide or an increased metabolism of a herbicide(biochemical antagonism)herbicide(biochemical antagonism)PS II inhibitors+glyphosatePS II inhibitors+glyphosatedinitroanilines+PS II inhibitorsdinitroanilines+PS II inhibitors”fops”+au

26、xin herbicides”fops”+auxin herbicides difenzoquat/flamprop-M-isopropyl+auxin difenzoquat/flamprop-M-isopropyl+auxin herbicidesherbicidesPreventing binding of active ingredient at the site Preventing binding of active ingredient at the site of action(competitive antagonism)of action(competitive antag

27、onism)SafenersSafenersActive and inactive isomers of the herbicideActive and inactive isomers of the herbicideAntagonismOpposite physiological effects(physiological Opposite physiological effects(physiological antagonism)antagonism)difenzoquat/flamprop-M-isopropyl+phenoxy difenzoquat/flamprop-M-isop

28、ropyl+phenoxy herbicidesherbicidesChemical reaction in the spray solution Chemical reaction in the spray solution(chemical antagonism)(chemical antagonism)glyphosate+cationsglyphosate+cationsparaquat+MCPAparaquat+MCPASynergismIncreased uptake and/or translocation of a Increased uptake and/or translo

29、cation of a herbicideherbicideadjuvantsadjuvantsdesmedipham+ethofumesatedesmedipham+ethofumesategrowth regulators+glyphosate/dicambagrowth regulators+glyphosate/dicambaReduced metabolism of a herbicideReduced metabolism of a herbicideinsekticides+herbicidesinsekticides+herbicidesHerbicide mixturesTh

30、ree possible scenariosThree possible scenariosNone of the compounds are active applied None of the compounds are active applied alone but applied in mixture they exert activity alone but applied in mixture they exert activity(coalitive action)(coalitive action)Herbicide mixturesThree possible scenar

31、iosThree possible scenariosNone of the compounds are active applied None of the compounds are active applied alone but applied in mixture they exert alone but applied in mixture they exert activity(coalitive action)activity(coalitive action)One compound is active while the other is One compound is a

32、ctive while the other is inactive(herbicide+adjuvant,inactive(herbicide+adjuvant,herbicide+fungicide/insecticide/growth herbicide+fungicide/insecticide/growth regulator)regulator)Two compound are active Two compound are active(herbicide+herbicide)(herbicide+herbicide)AdjuvantsAdjuvantsDose response

33、curvesAdjuvantsFluazifop-bytyl+various adjuvantsHerbicide mixtures Herbicide mixturesReference modelsEffect multiplication also called Multiplikative Effect multiplication also called Multiplikative Survival Model(MSM)Survival Model(MSM)Concentration addition also called Additive Concentration addit

34、ion also called Additive Dose Model(ADM)Dose Model(ADM)Multiplicative Survival ModelQQA,BA,B=Q=QA A x Q x QB BQ is a proportion of the untreated control,Q is a proportion of the untreated control,i.e.O=100%control and 1=no controli.e.O=100%control and 1=no controlIf P is%effect(from 0 to 1)thenIf P

35、is%effect(from 0 to 1)then(1-P(1-PA,BA,B)=(1-P)=(1-PA A)x(1-P)x(1-PB B)or)orP PA,BA,B=P=PA A+P+PB B-P-PA A x P x PB B Multiplicative Survival ModelExample:Example:1 kg/ha Herbicide A:75%effect1 kg/ha Herbicide A:75%effect1 kg/ha Herbicide B:80%effect1 kg/ha Herbicide B:80%effectExpected effect of a

36、mixture containing 1 Expected effect of a mixture containing 1 kg/ha of each herbicide according to MSM:kg/ha of each herbicide according to MSM:P=0.95 i.e.95%effect P=0.95 i.e.95%effect Multiplicative Survival ModelMSM assumes independent action of the MSM assumes independent action of the herbicid

37、es,i.e.the herbicides exert their herbicides,i.e.the herbicides exert their action independently of each other action independently of each other(=sequential)which seems to be an(=sequential)which seems to be an unrealistic assumption for most herbicide unrealistic assumption for most herbicide mixt

38、ures.mixtures.MSM has traditionally been considered to be MSM has traditionally been considered to be the correct reference model for mixtures of the correct reference model for mixtures of herbicides with different modes of action.herbicides with different modes of action.Additive Dose ModelAt a gi

39、ven response level ADM can be expressed as:At a given response level ADM can be expressed as:z zA A/Z/ZA A+z+zB B/Z/ZB B=1=1where Zwhere ZA A and Z and ZB B are the doses of herbicides A and B are the doses of herbicides A and Bapplied separately and zapplied separately and zA A and z and zB B are t

40、he doses of the are the doses of theherbicides in a mixture consisting of zherbicides in a mixture consisting of zA A+z+zB B.The relative potency between herbicides A and B is:The relative potency between herbicides A and B is:R=ZR=ZA A/Z/ZB B The relative potency corresponds to the exchange rateThe

41、 relative potency corresponds to the exchange ratebetween currencies.between currencies.Additive Dose ModelExample:Example:EDED5050 of Herbicide A:4 kg/ha of Herbicide A:4 kg/ha EDED5050 of Herbicide B:2 kg/ha of Herbicide B:2 kg/ha R=4/2=2 i.e.Herbicide B is twice as active as R=4/2=2 i.e.Herbicide

42、 B is twice as active as Herbicide AHerbicide AAdditive Dose ModelAdditive Dose ModelED50 or EDxED50 or EDxAdditive Dose ModelAdditive Dose ModelExample:Example:Herbicide A:4 kg/haHerbicide A:4 kg/ha Herbicide B:2 kg/haHerbicide B:2 kg/ha Mixture 1(75%A:25%B):3.2 kg/haMixture 1(75%A:25%B):3.2 kg/ha2

43、.4 kg/ha Herbicide A+0.8 kg/ha Herbicide B2.4 kg/ha Herbicide A+0.8 kg/ha Herbicide B0.6 Herbicide A+0.4 Herbicide B0.6 Herbicide A+0.4 Herbicide B Mixture 2(50%A:50%B):2.7 kg/haMixture 2(50%A:50%B):2.7 kg/ha1.35 kg/ha Herbicide A+1.35 kg/ha Herbicide B1.35 kg/ha Herbicide A+1.35 kg/ha Herbicide B0.

44、33 Herbicide A+0.67 Herbicide B0.33 Herbicide A+0.67 Herbicide B Mixture 3(25%A:75%B):2.3 kg/haMixture 3(25%A:75%B):2.3 kg/ha0.58 kg/ha Herbicide A+1.72 kg/ha Herbicide B0.58 kg/ha Herbicide A+1.72 kg/ha Herbicide B0.14 Herbicide A+0.86 Herbicide B0.14 Herbicide A+0.86 Herbicide BAdditive Dose Model

45、Additive Dose ModelExample:Example:Herbicide A:4 kg/haHerbicide A:4 kg/ha Herbicide B:2 kg/haHerbicide B:2 kg/ha Mixture 1(75%A:25%B):4.4 kg/haMixture 1(75%A:25%B):4.4 kg/ha3.3 kg/ha Herbicide A+1.1 kg/ha Herbicide B3.3 kg/ha Herbicide A+1.1 kg/ha Herbicide B0.83 Herbicide A+0.55 Herbicide B0.83 Her

46、bicide A+0.55 Herbicide B Mixture 2(50%A:50%B):3.8 kg/haMixture 2(50%A:50%B):3.8 kg/ha1.9 kg/ha Herbicide A+1.9 kg/ha Herbicide B1.9 kg/ha Herbicide A+1.9 kg/ha Herbicide B0.48 Herbicide A+0.95 Herbicide B0.48 Herbicide A+0.95 Herbicide B Mixture 3(25%A:75%B):3.6 kg/haMixture 3(25%A:75%B):3.6 kg/ha0

47、.9 kg/ha Herbicide A+2.7 kg/ha Herbicide B0.9 kg/ha Herbicide A+2.7 kg/ha Herbicide B0.23 Herbicide A+1.35 Herbicide B0.23 Herbicide A+1.35 Herbicide BAdditive Dose ModelAdditive Dose ModelExample:Example:Herbicide A:4 kg/haHerbicide A:4 kg/ha Herbicide B:2 kg/haHerbicide B:2 kg/ha Mixture 1(75%A:25

48、%B):2.4 kg/haMixture 1(75%A:25%B):2.4 kg/ha1.8 kg/ha Herbicide A+0.6 kg/ha Herbicide B1.8 kg/ha Herbicide A+0.6 kg/ha Herbicide B0.45 Herbicide A+0.3 Herbicide B0.45 Herbicide A+0.3 Herbicide B Mixture 2(50%A:50%B):2.0 kg/haMixture 2(50%A:50%B):2.0 kg/ha1.0 kg/ha Herbicide A+1.0 kg/ha Herbicide B1.0

49、 kg/ha Herbicide A+1.0 kg/ha Herbicide B0.25 Herbicide A+0.50 Herbicide B0.25 Herbicide A+0.50 Herbicide B Mixture 3(25%A:75%B):1.6 kg/haMixture 3(25%A:75%B):1.6 kg/ha0.4 kg/ha Herbicide A+1.2 kg/ha Herbicide B0.4 kg/ha Herbicide A+1.2 kg/ha Herbicide B0.1 Herbicide A+0.6 Herbicide B0.1 Herbicide A+

50、0.6 Herbicide BAdditive Dose ModelParallel dose response curvesAdditive Dose ModelParallel dose response curvesNon parallel dose response curvesAdditive Dose ModelNon-parallel dose response curvesAdditive Dose ModelDesign of ADM experimentsHerbicide mixturesMetsulfuron+MCPA on Stellaria mediaHerbici