生物测定的统计基础及试验设计课件

1、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 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。对试验数据进行分析, 概率分布 概率分布 反应-剂量对数的概率分布曲线G = 1/(2) e*(-(x-)2/22) 反应-剂量对数的概率分布曲线G = 1/(2) e*(: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

2、有效中量(median effective dose, ED50)的对数值 2: 方差, 它代表了分布的离散度, 2大, 分布曲线低而宽, 2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。:为中数或均数, 是分布的中心, 决定了曲线在横坐标上的位试验的精密度试验误差experimental error 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

3、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。 试验的精密度试验误差experimental error 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精密度S2(y)的表示方法S2(y) = S2/n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(experimental unit)大小和数量

4、提高试验的精密度途径试验单元(experimental unit)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试验单元(experimental unit)某一处理在某一试验设计 无重复的试验 扩展试验设计(augmented design)单因子试验多因子试验试验设计 无重复的试验 剂量反应曲线及其模型 分为质反应(quantal response)量反应(quantitative response) 剂量反应曲线及

5、其模型 分为质反应(quantal resp质反应曲线 When =1, =0 zip = 1/(22)exp( -1/2 Z2 )dz - xip = 1/(22)exp( -1/2 (x - )2 /2)dx - 质反应曲线 直线化变换 Probit tranformation Z = 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.

6、 将Z加上5后, 在任何反应率下, 机率值均为正数 直线化变换 Probit tranformationDose response curveDose response curveDose-response modelDose-response model模型的检验模型的检验直线化变换移项得(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)直线化变换移项得Herbicide BioassayHerbi

7、cide BioassayRelative potencyThe relative potency (RP) of Herbicide A with respect to Herbicide B is defined as: RP (A/B) = ED50(compound )/ED50(compoud B)Relative potencyThe relative pParallelQuantal response Y1 = a1 + b1X1 Y2 = a1 + b2X2doseresponseParallelQuantal response dost test whether the tw

8、o line are parallel or not If not significant, then b1 = b2 and two lines are parallel t test whether the two line arPooled residual mean square (S2p) = (n1 - 2)S2b1 + (n2 - 2) S2b2/(n1 + n2 - 4) Where: S2b1is residual mean square for the 1st set of data ; S2b2 is residual mean square for the 2nd se

9、t of data.Pooled residual mean square (S Combined slope (bc): Combined slope (bc): Quantitative response (four-parameter model) Quantitative response (four-pa生物测定的统计基础及试验设计课件F test First, suppose b1 = b2, ED501 = ED502, and run the model IThen suppose b1 b2, ED501= ED502, and run the model II (SSII

10、- SSI)/(dfII - dfI)F = SSI/dfI where SSII is error sum of square of Model II; SSI is error sum of square of Model I If not significant, then b1 = b2 and two curves are parallel. F test First, suppose b1 = b2,Parallel curves:Two compounds having the same action mode;Different formulations of a compou

11、nd;One compound with different adjuvants Parallel curves:Non-parallelSlope (b) - not constant for tested compounds.Compare relative potency of two compounds effectively only under a certain equivalent effective dose.Non-parallelVertical vs horizontal assessmentsVertical assessment Compare plant resp

12、onses at preset doses.Horizontal assessment Compare the doses of two or more compounds that produce a similar plant response.Vertical vs horizontal assessmCautions with the parallel-line dose-response theorya. Not parallel in field conditionsb. Work less well with herbicides having complex or multip

13、le modes of action.c. Maybe work less well with different plant species.d. Maybe doesnt work with different growth stages.Cautions with the parallel-linScreening proceduresa. Primary screenb. Secondary screenc. Field screen and physiological and biochemical selectivity studiesd. Advanced selectivity

14、 screene. Field evaluationScreening proceduresa. PrimarExpressing selectivitya. Vertical assessmentb. Selectivity indices (SI) SI = ED50 (species A) / ED50 (species B) SI = ED10 (crop) / ED90 (weed) SI 2 Good selectivitySI 1- 2 Marginal selectivity SI 1 Non SelectivityExpressing selectivitya. VertBe

15、 careful when using the criteria 1. ED10 may significantly reduce crop yields.2. The limitations of bioassay in the prediction of field responsea. Temperatureb. Day length, light quality, irradiancec. Wind effectsd. Plant growth stagee. Soil conditions3. Overlap of sprayed areas 4. Apply higher dose

16、 than recommended dose Be careful when using the critNo-observable-effect level (NOEL) and No-effect level (NEL) Determination of NOEL a. Multiple comparison testEffect of expt. designMore replications, more precision.Disadvantage: Different responses Different slopes b. Dose-response relationshi No

17、-observable-effect level (NOProblems in determining the NOELa. Stimulationb. Effect of expt. design and response variablec. Duration of exposureProblems in determining the NOParameters used in herbicide bioassayBiomass including fresh weight and dry weightMortalityPlant heightPhysiological parameter

18、sParameters used in herbicide bINTERACTION BETWEEN HERBICIDESResponse Factor A at level 1 Factor A at level 1 Factor B INTERACTION BETWEEN HERBICIDESINTERACTION BETWEEN HERBICIDESResponse Factor A at level 1 Factor A at level 1 Factor B INTERACTION BETWEEN HERBICIDESHerbicide mixturesReasons for usi

19、ng herbicide mixtures:Widen the spectrum of weeds controlledReduce costs of weed controlReduce herbicide useReduce number of sprayingsPrevent/overcome resistanceHerbicide mixturesReasons for Herbicide mixturesAdditivityThe performance of a mixture is as predicted by a reference modelAntagonismThe pe

20、rformance of a mixture is poorer than predicted by a reference modelSynergismThe performance of a mixture is better than predicted by a reference model Herbicide mixturesAdditivityAntagonismReduced uptake and/or translocation of a herbicide or an increased metabolism of a herbicide (biochemical anta

21、gonism)PS II inhibitors + glyphosatedinitroanilines + PS II inhibitors”fops” + auxin herbicides difenzoquat/flamprop-M-isopropyl + auxin herbicidesPreventing binding of active ingredient at the site of action (competitive antagonism)SafenersActive and inactive isomers of the herbicideAntagonismReduc

22、ed uptake and/oAntagonismOpposite physiological effects (physiological antagonism)difenzoquat/flamprop-M-isopropyl + phenoxy herbicidesChemical reaction in the spray solution (chemical antagonism)glyphosate + cationsparaquat + MCPAAntagonismOpposite physiologicSynergismIncreased uptake and/or transl

23、ocation of a herbicideadjuvantsdesmedipham + ethofumesategrowth regulators + glyphosate/dicambaReduced metabolism of a herbicideinsekticides + herbicidesSynergismIncreased uptake and/Herbicide mixturesThree possible scenariosNone of the compounds are active applied alone but applied in mixture they

24、exert activity (coalitive action)Herbicide mixturesThree possibHerbicide mixturesThree possible scenariosNone of the compounds are active applied alone but applied in mixture they exert activity (coalitive action)One compound is active while the other is inactive (herbicide+adjuvant, herbicide+fungi

25、cide/insecticide/ growth regulator)Two compound are active (herbicide+herbicide)Herbicide mixturesThree possibAdjuvantsAdjuvantsAdjuvantsAdjuvantsDose response curvesDose response curvesAdjuvantsFluazifop-bytyl + various adjuvantsSun Spray Plus:R=1.000.1% Sandovit:R=1.410.3% SandovitR=1.791% Atplus

26、221R=1.843% AtplusR=2.34AdjuvantsFluazifop-bytyl + varHerbicide mixtures Herbicide mixtures Herbicide mixturesHerbicide mixturesReference modelsEffect multiplication also called Multiplikative Survival Model (MSM)Concentration addition also called Additive Dose Model (ADM)Reference modelsEffect mult

27、iplMultiplicative Survival ModelQA,B = QA x QBQ is a proportion of the untreated control,i.e. O = 100% control and 1 = no controlIf P is % effect (from 0 to 1) then(1 - PA,B) = (1 - PA) x (1 - PB) orPA,B = PA + PB - PA x PB Multiplicative Survival ModelQMultiplicative Survival ModelExample:1 kg/ha H

28、erbicide A: 75% effect1 kg/ha Herbicide B: 80% effectExpected effect of a mixture containing 1 kg/ha of each herbicide according to MSM:P =0.75 + 0.80 - 0.75 x 0.80P =0.95 i.e. 95% effect Multiplicative Survival ModelEMultiplicative Survival ModelMSM assumes independent action of the herbicides, i.e

29、. the herbicides exert their action independently of each other (=sequential) which seems to be an unrealistic assumption for most herbicide mixtures. MSM has traditionally been considered to be the correct reference model for mixtures of herbicides with different modes of action.Multiplicative Surv

30、ival ModelMAdditive Dose ModelAt a given response level ADM can be expressed as:zA/ZA + zB/ZB = 1where ZA and ZB are the doses of herbicides A and Bapplied separately and zA and zB are the doses of theherbicides in a mixture consisting of zA + zB. The relative potency between herbicides A and B is:R

31、 = ZA/ZB The relative potency corresponds to the exchange ratebetween currencies. Additive Dose ModelAt a given Additive Dose ModelExample:ED50 of Herbicide A: 4 kg/haED50 of Herbicide B: 2 kg/haR = 4/2 = 2 i.e. Herbicide B is twice as active as Herbicide AAdditive Dose ModelExample:Additive Dose Mo

32、delAdditive Dose ModelAdditive Dose ModelED50 or EDxED50 or EDxAdditive Dose ModelED50 or EDxAdditive Dose ModelAdditive Dose ModelAdditive Dose ModelExample:Herbicide A: 4 kg/haHerbicide B: 2 kg/haMixture 1 (75% A : 25% B): 3.2 kg/ha2.4 kg/ha Herbicide A + 0.8 kg/ha Herbicide B0.6 Herbicide A + 0.4

33、 Herbicide BMixture 2 (50% A : 50% B): 2.7 kg/ha1.35 kg/ha Herbicide A + 1.35 kg/ha Herbicide B0.33 Herbicide A + 0.67 Herbicide BMixture 3 (25% A : 75% B): 2.3 kg/ha0.58 kg/ha Herbicide A + 1.72 kg/ha Herbicide B0.14 Herbicide A + 0.86 Herbicide BAdditive Dose ModelExample:Additive Dose ModelAdditi

34、ve Dose ModelAdditive Dose ModelExample:Herbicide A: 4 kg/haHerbicide B: 2 kg/haMixture 1 (75% A : 25% B): 4.4 kg/ha3.3 kg/ha Herbicide A + 1.1 kg/ha Herbicide B0.83 Herbicide A + 0.55 Herbicide BMixture 2 (50% A : 50% B): 3.8 kg/ha1.9 kg/ha Herbicide A + 1.9 kg/ha Herbicide B0.48 Herbicide A + 0.95

35、 Herbicide BMixture 3 (25% A : 75% B): 3.6 kg/ha0.9 kg/ha Herbicide A + 2.7 kg/ha Herbicide B0.23 Herbicide A + 1.35 Herbicide BAdditive Dose ModelExample:Additive Dose ModelAdditive Dose ModelAdditive Dose ModelExample:Herbicide A: 4 kg/haHerbicide B: 2 kg/haMixture 1 (75% A : 25% B): 2.4 kg/ha1.8

36、kg/ha Herbicide A + 0.6 kg/ha Herbicide B0.45 Herbicide A + 0.3 Herbicide BMixture 2 (50% A : 50% B): 2.0 kg/ha1.0 kg/ha Herbicide A + 1.0 kg/ha Herbicide B0.25 Herbicide A + 0.50 Herbicide BMixture 3 (25% A : 75% B): 1.6 kg/ha0.4 kg/ha Herbicide A + 1.2 kg/ha Herbicide B0.1 Herbicide A + 0.6 Herbicide BAdditive Dose Mo