Stability parameters for comparing varieties (eberhart and russell 1966)

Phenotype is a result of genotype, environment and GE interaction. GENOTYPE- environment interactions are of major
importance to the plant breeder in developing
improved varieties. The performance of a single variety is not the same in all the environments. To identify a genotype whose performance is stable across environments various models were proposed. One such model was proposed by EBERHART and RUSSELL in 1966. Even after decades, this model is still preferred over others and used till date for stability analysis.

1. STABILITY PARAMETERS FOR COMPARING VARIETIES (EBERHART AND RUSSELL 1966) -DHANUJA N 2019508005

2. STABILITY ANALYSIS The phenotype of an individual is determined by the effects of its genotype and environment surrounding it. The interplay in the effect of genetic and non-genetic on development is termed as 'genotype-environment interaction'. P=G+E+GE

3. GE INTRACTION GENOTYPE- environment interactions are of major importance to the plant breeder in developing improved varieties. When varieties are compared over a series of environments, the relative rankings usually differ. This causes difficulty in demonstrating the significant superiority of any variety. Large genotype-environment interactions reduce the progress from selection (Comstock and Moll )

4. STRATIFICATION Stratification of environments has been used effectively to reduce the genotype-environment interaction. This stratification usually is based on macro-environment Even with this, the interaction of genotypes in a subregion , and with environments at the same location in different years, remains too large. Allard and Bradshaw classify as unpredictable the environmental variation, for which stratification is not effective.

5. STRATIFICATION Select stable genotypes that interact less with the environments in which they are to be grown. If stability of performance, (minimum of interaction with the environment), is a genetic characteristic, then preliminary evaluation could be planned to identify the stable genotypes. With only the more stable genotypes remaining for the final stages of testing, the breeder would be greatly aided in his selection of superior genotypes. However, selection for stability is not possible until a model with suitable parameters is available to provide the criteria necessary to rank varieties for stability.

6. SUGGESTIONS TO REDUCE GEI The use of genetic mixtures rather than homogeneous or pure-lines Multiline variety (Jensen) Heterozygous and Heterogeneous populations (Allard and Bradshaw) They used the term " individual buffering " (each member of the population is well adapted to a range of environments), and " population buffering " (variety consists of a number of genotypes each adapted to a different range of environments). Heterozygous or homozygous genotype may possess individual buffering Heterogeneous population will possess population buffering.

7. Double crosses interact with environments less than single crosses. Double crosses are superior to single crosses for stability (Sprague and Federer ) Hybrid x Year interactions were significantly greater for single crosses than for three-way crosses (Eberhart, Russell, and Penny) Some single crosses may show more, phenotypic stability than the most stable three-way or double cross. Because the variance of a mean is less than the variance of an individual, the average genotype-environment interaction of a mixture may be expected to be less than the interaction for a single genotype.

8. STEPS IN STABILITY ANALYSIS Done from replicated data over several environments 1. Environment wise analysis of variance Following usual method of analysis of variance , the data are analyzed for a quantitative trait in all the environments separately. The data of environments, where significant difference for genotypes are observed, are used for pooled analysis.

9. Before proceeding to pooled analysis, the test of homogenity of variances ( Bartlets ‘ chi square test) is to be done for the environments. If the X 2 value is non-significant , there is homogeneity of variance among the environments. Hence, pooled analysis can be carried out. In case, the X 2 value is significant , it can be concluded that there is heterogenity of variances among the environments If the error variances are heterogeneous, divide each value by square root of corresponding mean square of error variance and use for the combined analysis.

10. 2. POLLED ANALYSIS OF VARIANCE A two way table is formed for tabulating the data of genotypes in different environments. If GE interaction is non- significant, no need to proceed further If significant, estimate phenotypic stability . Genotypes E1 E2 …….. En 1 2 : : n

11. MODELS FOR STABILITY ANALYSIS A. Conventional models Stability factor model (Lewis 1954) Ecovalence model ( Wricke 1964) Stability variance model ( Shukla 1972) Lin and Binns model (198) B. Regression coefficient model Finlay and Wilkinson model (1963) Eberhart and Russell model (1966) Perkins and Jinks model (1968) Freeman and Perkins model (1971) Genotypic stability model (Tai 1971)

12. C. Principle component analysis Perkins (1972); Freeman and Dowkar (1975); Seif et al (1979) Additive main effect and multiplicative interaction effect Shifted multiplication model Redundancy analysis Factor regression analysis GGE biplot D. Cluster analysis Grouping by cluster analysis ( Westcot 1987) Webber and Wricke (1990) E. Pattern analysis Mungomery et al 1974 Delacy et al (1990) F. Factor analysis Johnson and Wichern (1982) Calinski et al (1987)

13. REGRESSION COEFFICIENT MODEL For phenotypic stability analysis, regression analysis has proved to be valuable for assessing response under changing environments. The regression of each variety in an experiment on an environmental index and a function of the squared deviations from this regression would provide estimates of the desired stability parameters

14. EBERHART AND RUSSELL (1966) In 1966, Eberhart and Russell (1966) made further improvement in stability analysis. Three parameter model 1. Mean yield over locations or seasons 2. Regression coefficient (b) 3. Deviation from regression (s 2 d )

15. PARTITION Total variance 1. Genotypes 2. Environment + interaction (E + G × E) 1. Environment (linear) 2. G × E (Linear) 3. Pooled deviations Sum of square due to pooled deviations is partitioned in to sum of square due to individual genotype

16. The model considered by Eberhart and Russell may be written as y ij = μ i + b i I j + δ ij y ij - Mean of i th variety in j th environment μ i - Mean of all varieties over all environments b i - Regression co-efficient of i th variety on environmental index which measures the response of this variety to varying environments I j - Environmental index i.e. the deviation of the mean of all the varieties at a given environment from the over all mean δ ij - The deviation from regression of i th variety at j th environment

17. MAIN FEATURES • Analysis of stability is simple as compared to other models • Degree of freedom for environment is 1 • Less expensive than Freeman and Perkins model •It does not provide independent estimation for mean performance and environmental index Stable genotype is one with b i = 1, s 2 d = 0 and high mean yield

18. STABILITY PARAMETERS With this approach, the first stability parameter is a regression coefficient , b i which can be estimated by The deviation can be squared and summed to provide an estimate of another stability parameter, mean square deviation

19. THE MODEL PROVIDES A MEANS OF PARTITIONING THE GE INTERACTION OF EACH GENOTYPE INTO TWO PARTS

20. STABLE GENOTYPE A genotype with high/ desirable mean value A genotype with deviation not significantly deviating from 0 is stable A genotype with unit regression coefficient

21. Further, they define that the stable variety will be one with b i = 1.0 and s 2 d = 0 ; and the null hypothesis H : μ 1 = μ 2 = … = μ m (To test the significance among the genotype means) can be tested by the F-test (approximately) F = M G / M d ( F=MS 1 /MS 3) with homogeneous deviation mean squares, being M d the pooled deviations. The hypothesis that there are no genetic differences among phenotypes for their regression on the environmental index H : β 1 = β 2 = … = β m (To test if the varieties differ for their regression on EI) can be tested by the F-test F = M EI / M d ( F=MS 2 /MS 3)

22. The deviations from regression for each genotype can be further tested by Thus, in this approach one can see that two measures of sensitivity of the genotype to changes on environment are worked out: ( i ) the linear sensitivity measure in terms of the linear regression coefficient, b i of the i th genotype to the environmental change (ii) the non linear sensitivity measure in terms of the deviation from regression mean square

23. APPLICATION OF THE MODEL TO MAIZE YIELD TRIALS Single crosses were grown in the Iowa State University experimental yield trials for 1945-51. Data for a diallel set of single crosses from 11 lines grown in 8 environments in 1945-47 and for a diallel set frown 8 lines in 12 environments in 1948-51 were extracted and analyzed.

24. ANOVA

25. PARTITION The differences among regression coefficients [SC x Env (linear)] can be partitioned into General x Env (linear) and Specific X Env (linear). Since the Specific X Env (linear) squares are not significantly greater than the respective deviation mean squares, there is no evidence that regression coefficients differ because of non additive gene action. However, the General x Env (linear) mean squares were significant (P ~ .05) for both diallels .

26. Differences in stability of 2 single crosses and their performance in relation to average of the test 1. WF9 X M14 is a very desirable hybrid because its performance is uniformly superior b=1.06, s 2 d = 0 2. M14 X B7 is expected to equal or exceed average performance only under very unfavorable conditions b=.76, s 2 d =5

27. The vertical lines are one SD above and below the GM , whereas the horizontal lines are one SD above and below the average slope (b=1.0). The relation of yield stability of 28 single crosses. Estimates of s 2 d were significant only for those hybrids indicated by +

28. The single cross with above-average performance and satisfactory stability in the 1945-47 diallel is WF9 x Oh28 WF9 x M14 had above-average performance over environments, but the estimate of s 2 d was 30. In the 1948-51 diallel , two single crosses gave high yields with stability WF9 x M14 and WF9 x W22 The line Hy performed consistently better in favorable environments (b = l.15 and 1.15), whereas O8420 performance was relatively better in less favorable environments (b = .95 and .55)

29. AVERAGE LINE PERFORMANCE IN DIALLEL CROSSES

30. Three-way crosses involving three single-cross testers and six inbreds The difference in the response of three-way crosses to varying environments was due to the different responses of the lines as indicated by the large Lines X Env (linear) mean square. T hree-way crosses involving W22 performed much below average in unfavorable environments, whereas N22A and B37 did extremely well under less favorable conditions. The performance of B37 in three-way crosses was much more predictable than hybrids involving B54 or B46, as indicated by the estimates, s 2 d

31. Analysis of 18 three way cross and three single cross testers grown at 2 locations

32. AVERAGE PERFORMANCE OF SIX INBRED LINES WITH THREE TESTERS

33. PERFORMANCE OF THE TESTERS (SINGLE CROSSES) COMPARED WITH THEIR AVERAGE TESTCROSS PERFORMANCE (THREE-WAY CROSSES)

34. None of the three-way crosses falling in the center section to the right had a non significant deviation mean square. However, the hybrid (WF9 x M14) N22A (x = 119.8, b = 1.05, s 2 d = 41) is the most nearly acceptable even though s 2 d is larger than desirable. (WF9 X B14) B37 (x = 119.5, b — .74, s 2 d — 0) would be especially good under less favorable environments but not good under favorable conditions. The hybrid with the highest mean yield (WF9 X M14) B37 is unacceptable for both stability parameters

35. Although the inbred lines of maize in this experiment differed in their average responses to varying environments, the Variety X Env (linear) sum of squares was not a very large proportion of the Variety X Environmental interaction. Hence, the second stability parameter (s 2 d ) appears very important. Because the variance of s 2 d is a function of the number of environments, several environments with minimum replication per environment are necessary to obtain reliable estimates of s 2 d . However, a good estimate of the regression coefficients can be obtained from a few environments if they cover the range of expected responses.

36. MERITS AND DEMERITS This model measures three parameters of stability, viz . (1) mean yield over environments (2) regression coefficient and (3) deviation from the regression line. This model provides more reliable information about varietal stability than Finlay and Wilkinson model. The analysis is also simple . In this model, the estimation of mean performance and environmental index is not independent. There is combined estimation of S.S. for environments and interactions , which is not proper.

37. REFERENCES Eberhart, S., and Russell, W.A., 1966, Stability parameters for comparing varieties, Crop Sci., 6: 36–40 Nadarajan N, Manivannan M, Gunasekharan M, Quantitative genetics and biometrical techniques in plant breeding, kalyani publishers , 253-260 .