生物測定的統(tǒng)計基礎及試驗設計

1、生物測定的統(tǒng)計基礎及試驗設計,對試驗數(shù)據(jù)進行分析, 指導試驗的設計。只有在生物統(tǒng)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(shù)據(jù)。 在應用生物統(tǒng)計工具對試驗結果分析時, 我們必須結合專業(yè)知識, 選用適當?shù)哪Ｐ蛠矸治? 在不了解生物現(xiàn)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(shù)的概率分布曲線,G = 1/(2) e*(-(x-)2/22),:為中數(shù)或均數(shù), 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(median effective dose, ED50)的對數(shù)值 2: 方差, 它代表了分布的離散度

2、, 2大, 分布曲線低而寬, 2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。,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(wěn)定、規(guī)范試驗操作可減少試驗誤差外, 選擇適當?shù)脑囼炘O計也可減少試驗誤差。,精密度S

3、2(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 試驗設計和試驗材料差異 N 試驗單元的大小和數(shù)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(experimental unit)大小和數(shù)量,試驗單元(experimental unit),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(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

4、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(augmented design) 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(quantal response) 量反應(quantitative response),質反應曲線,When =1, =0,zi p = 1/(22)exp( -1/2 Z2 )dz -,xi p = 1/(22)exp( -1/2 (x - )2 /2)dx -,直線化變換,Probit tranformation Z = 1/ (x - ) Y = Z + 5 = 1/ (x - ) + 5 = - 1/ + 5 + 1/

5、x 在標準正態(tài)偏離上加5是為了使所有的機率值為正數(shù)。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(shù),Dose response curve,Dose-response model,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(shù)得 log(D - y)/(y-C) = b(logx - logx0) 令v = log(D - y)/(y-C), 則 v = b(logx - log

6、x0) (2.12),Herbicide Bioassay,Relative potency,The relative potency (RP) of Herbicide A with respect to Herbicide B is defined as: RP (A/B) = ED50(compound )/ED50(compoud B),Parallel,Quantal response Y1 = a1 + b1X1 Y2 = a1 + b2X2,dose,response,t test,whether the two line are parallel or not If not s

7、ignificant, then b1 = b2 and two lines are parallel,Pooled 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 set of data.,Combined slope (bc):,Quantitative response (four-param

8、eter model),F test,First, suppose b1 = b2, ED501 = ED502, and run the model I Then suppose b1 b2, ED501= ED502, and run the model II (SSII - 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 cur

9、ves are parallel.,Parallel curves:,Two compounds having the same action mode; Different formulations of a compound; One compound with different adjuvants,Non-parallel,Slope (b) - not constant for tested compounds. Compare relative potency of two compounds effectively only under a certain equivalent

10、effective dose.,Vertical vs horizontal assessments,Vertical assessment Compare plant responses at preset doses. Horizontal assessment Compare the doses of two or more compounds that produce a similar plant response.,Cautions with the parallel-line dose-response theory,a. Not parallel in field condit

11、ions b. 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 procedures,a. Primary screen b. Secondary screen c. Field screen and physiological and biochemical sel

12、ectivity studies d. Advanced selectivity screen e. Field evaluation,Expressing selectivity,a. Vertical assessment b. Selectivity indices (SI) SI = ED50 (species A) / ED50 (species B) SI = ED10 (crop) / ED90 (weed) SI 2 Good selectivity SI 1- 2 Marginal selectivity SI 1 Non Selectivity,Be careful whe

13、n using the criteria,1. ED10 may significantly reduce crop yields. 2. The limitations of bioassay in the prediction of field response a. Temperature b. Day length, light quality, irradiance c. Wind effects d. Plant growth stage e. Soil conditions 3. Overlap of sprayed areas 4. Apply higher dose than

14、 recommended dose,No-observable-effect level (NOEL) and No-effect level (NEL),Determination of NOEL a. Multiple comparison test Effect of expt. design More replications, more precision. Disadvantage: Different responses Different slopes b. Dose-response relationshi,Problems in determining the NOEL,a

15、. Stimulation b. Effect of expt. design and response variable c. Duration of exposure,Parameters used in herbicide bioassay,Biomass including fresh weight and dry weight Mortality Plant height Physiological parameters,INTERACTION BETWEEN HERBICIDES,Response Factor A at level 1 Factor A at level 1 Fa

16、ctor B,INTERACTION BETWEEN HERBICIDES,Response Factor A at level 1 Factor A at level 1 Factor B,Herbicide mixtures,Reasons for using herbicide mixtures: Widen the spectrum of weeds controlled Reduce costs of weed control Reduce herbicide use Reduce number of sprayings Prevent/overcome resistance,Her

17、bicide mixtures,Additivity The performance of a mixture is as predicted by a reference model Antagonism The performance of a mixture is poorer than predicted by a reference model Synergism The performance of a mixture is better than predicted by a reference model,Antagonism,Reduced uptake and/or tra

18、nslocation of a herbicide or an increased metabolism of a herbicide (biochemical antagonism) PS II inhibitors + glyphosate dinitroanilines + PS II inhibitors ”fops” + auxin herbicides difenzoquat/flamprop-M-isopropyl + auxin herbicides Preventing binding of active ingredient at the site of action (c

19、ompetitive antagonism) Safeners Active and inactive isomers of the herbicide,Antagonism,Opposite physiological effects (physiological antagonism) difenzoquat/flamprop-M-isopropyl + phenoxy herbicides Chemical reaction in the spray solution (chemical antagonism) glyphosate + cations paraquat + MCPA,S

20、ynergism,Increased uptake and/or translocation of a herbicide adjuvants desmedipham + ethofumesate growth regulators + glyphosate/dicamba Reduced metabolism of a herbicide insekticides + herbicides,Herbicide mixtures,Three possible scenarios None of the compounds are active applied alone but applied

21、 in mixture they exert activity (coalitive action),Herbicide mixtures,Three possible scenarios None 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+fungicide/inse

22、cticide/ growth regulator) Two compound are active (herbicide+herbicide),Adjuvants,Adjuvants,Dose response curves,Adjuvants,Fluazifop-bytyl + various adjuvants,Sun Spray Plus:R=1.00 0.1% Sandovit:R=1.41 0.3% SandovitR=1.79 1% Atplus 221R=1.84 3% AtplusR=2.34,Herbicide mixtures,Herbicide mixtures,Ref

23、erence models,Effect multiplication also called Multiplikative Survival Model (MSM) Concentration addition also called Additive Dose Model (ADM),Multiplicative Survival Model,QA,B = QA x QB Q is a proportion of the untreated control, i.e. O = 100% control and 1 = no control If P is % effect (from 0

24、to 1) then (1 - PA,B) = (1 - PA) x (1 - PB) or PA,B = PA + PB - PA x PB,Multiplicative Survival Model,Example: 1 kg/ha Herbicide A: 75% effect 1 kg/ha Herbicide B: 80% effect Expected effect of a mixture containing 1 kg/ha of each herbicide according to MSM: P =0.75 + 0.80 - 0.75 x 0.80 P =0.95 i.e.

25、 95% effect,Multiplicative Survival Model,MSM assumes independent action of the herbicides, i.e. 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 correc

26、t reference model for mixtures of herbicides with different modes of action.,Additive Dose Model,At a given response level ADM can be expressed as: zA/ZA + zB/ZB = 1 where ZA and ZB are the doses of herbicides A and B applied separately and zA and zB are the doses of the herbicides in a mixture cons

27、isting of zA + zB. The relative potency between herbicides A and B is: R = ZA/ZB The relative potency corresponds to the exchange rate between currencies.,Additive Dose Model,Example: ED50 of Herbicide A: 4 kg/ha ED50 of Herbicide B: 2 kg/ha R = 4/2 = 2 i.e. Herbicide B is twice as active as Herbici

28、de A,Additive Dose Model,Additive Dose Model,ED50 or EDx,ED50 or EDx,Additive Dose Model,Additive Dose Model,Example: Herbicide A: 4 kg/ha Herbicide B: 2 kg/ha Mixture 1 (75% A : 25% B): 3.2 kg/ha 2.4 kg/ha Herbicide A + 0.8 kg/ha Herbicide B 0.6 Herbicide A + 0.4 Herbicide B Mixture 2 (50% A : 50%

29、B): 2.7 kg/ha 1.35 kg/ha Herbicide A + 1.35 kg/ha Herbicide B 0.33 Herbicide A + 0.67 Herbicide B Mixture 3 (25% A : 75% B): 2.3 kg/ha 0.58 kg/ha Herbicide A + 1.72 kg/ha Herbicide B 0.14 Herbicide A + 0.86 Herbicide B,Additive Dose Model,Additive Dose Model,Example: Herbicide A: 4 kg/ha Herbicide B

30、: 2 kg/ha Mixture 1 (75% A : 25% B): 4.4 kg/ha 3.3 kg/ha Herbicide A + 1.1 kg/ha Herbicide B 0.83 Herbicide A + 0.55 Herbicide B Mixture 2 (50% A : 50% B): 3.8 kg/ha 1.9 kg/ha Herbicide A + 1.9 kg/ha Herbicide B 0.48 Herbicide A + 0.95 Herbicide B Mixture 3 (25% A : 75% B): 3.6 kg/ha 0.9 kg/ha Herbicide A + 2.7 kg/ha Herbicide B 0.23 Herbicide A + 1.35 Herbicide B,Additive Dose Model,Additive Dose Model,Example: Herbicide A: 4 kg