生物測定的統(tǒng)計基礎(chǔ)及試驗設(shè)計課件

1、生物測定的統(tǒng)計基礎(chǔ)及試驗設(shè)計 生物測定的統(tǒng)計基礎(chǔ)及試驗設(shè)計 對試驗數(shù)據(jù)進(jìn)行分析, 指導(dǎo)試驗的設(shè)計。只有在生物統(tǒng)計理論指導(dǎo)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(shù)據(jù)。在應(yīng)用生物統(tǒng)計工具對試驗結(jié)果分析時, 我們必須結(jié)合專業(yè)知識, 選用適當(dāng)?shù)哪Ｐ蛠矸治? 在不了解生物現(xiàn)象的情況下, 機(jī)械地套用有可能得出錯誤的結(jié)論。對試驗數(shù)據(jù)進(jìn)行分析, 概率分布 概率分布 反應(yīng)-劑量對數(shù)的概率分布曲線G = 1/(2) e*(-(x-)2/22) 反應(yīng)-劑量對數(shù)的概率分布曲線G = 1/(2) e*(:為中數(shù)或均數(shù), 是分布的中心, 決定了曲線在橫坐標(biāo)上的位置，在概率分布曲線中, 它表示

2、有效中量(median effective dose, ED50)的對數(shù)值 2: 方差, 它代表了分布的離散度, 2大, 分布曲線低而寬, 2小, 分布曲線高而窄。低而寬的反應(yīng)-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。:為中數(shù)或均數(shù), 是分布的中心, 決定了曲線在橫坐標(biāo)上的位試驗的精密度試驗誤差experimental error 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(jié)果的可重復(fù)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

3、員所察覺的隨機(jī)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(wěn)定、規(guī)范試驗操作可減少試驗誤差外, 選擇適當(dāng)?shù)脑囼炘O(shè)計也可減少試驗誤差。 試驗的精密度試驗誤差experimental error 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(shù)的方差，S2表示樣本方差，n表示觀察值的個數(shù)。S2 試驗設(shè)計和試驗材料差異N 試驗單元的大小和數(shù)量精密度S2(y)的表示方法S2(y) = S2/n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(shè)計差異較小的試驗材料增加n，即是增加試驗單元(experimental unit)大小和數(shù)量

4、提高試驗的精密度途徑試驗單元(experimental unit)某一處理在某一重復(fù)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(yǎng)皿中裝十粒種子一個培養(yǎng)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(xiàn)趨于一致不能把試驗單元中的不同個體當(dāng)成重復(fù)試驗單元(experimental unit)某一處理在某一試驗設(shè)計 無重復(fù)的試驗 擴(kuò)展試驗設(shè)計(augmented design)單因子試驗多因子試驗試驗設(shè)計 無重復(fù)的試驗 劑量反應(yīng)曲線及其模型 分為質(zhì)反應(yīng)(quantal response)量反應(yīng)(quantitative response) 劑量反應(yīng)曲線及

5、其模型 分為質(zhì)反應(yīng)(quantal resp質(zhì)反應(yīng)曲線 When =1, =0 zip = 1/(22)exp( -1/2 Z2 )dz - xip = 1/(22)exp( -1/2 (x - )2 /2)dx - 質(zhì)反應(yīng)曲線 直線化變換 Probit tranformation Z = 1/ (x - ) Y = Z + 5 = 1/ (x - ) + 5 = - 1/ + 5 + 1/ x 在標(biāo)準(zhǔn)正態(tài)偏離上加5是為了使所有的機(jī)率值為正數(shù)。因為, 在反應(yīng)率p等于50%, Z為0, 反應(yīng)率小于50%時, Z為負(fù)值。如當(dāng)反應(yīng)率等于25.87%, Z為-1; 反應(yīng)率等于2.28%時, Z為-2.

6、 將Z加上5后, 在任何反應(yīng)率下, 機(jī)率值均為正數(shù) 直線化變換 Probit tranformationDose response curveDose response curveDose-response modelDose-response model模型的檢驗?zāi)Ｐ偷臋z驗直線化變換移項得(D - C)/(y - C) - 1 = (x/x0) b兩邊同時取對數(shù)得log(D - y)/(y-C) = b(logx - logx0) 令v = log(D - y)/(y-C), 則v = b(logx - logx0) (2.12)直線化變換移項得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生物測定的統(tǒng)計基礎(chǔ)及試驗設(shè)計課件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