Comparison of biometrical methods to describe yield stability in field pea ( Pisum sativum L . ) under south eastern Ethiopian conditions

Sixteen field pea (Pisum sativum L.) genotypes were evaluated using Randomized Complete Block Design (RCBD) with four replications for evaluating genotype x environment interaction (GEI) and yield stability across 12 environments during 2004 to 2006 at south eastern Ethiopia. The objectives were to compare various statistical methods of analyzing yield stability and to determine the most suitable parametric procedure to evaluate and describe yield stability of field pea (Pisum sativum L.) genotypes performance under south eastern Ethiopian conditions. Several statistical analyses were conducted:


INTRODUCTION
In the past, plant breeding programs mostly focused on developing high yielding cultivars.Recently, stable and sustainable yields under various environmental conditions have consistently gained importance over only increased yield.The development of cultivars, which are adapted to a wide range of diversified environments, is the ultimate aim of plant breeders in a crop improvement program (Muhammad et al., 2003).Genotype x Environment (GxE) interactions is an important issue for agriculturalists, who transfer a new variety from another environment.The adaptability of a variety over diverse environments is commonly evaluated by the degree of its interaction with different environments in which it is grown.A variety is considered to be more stable if it has a high mean yield but a low degree of fluctuation in yielding ability when planted over diverse environments (Purchase, 1997).
The basic cause for differences between genotypes in their yield stability is a wide occurrence of GxE interaction.The ranking of the variety depends on the particular environmental conditions in which it is grown.The environment is usually indicated as all non-genetic factors that influence expression of characteristics.It should include water, nutrition, temperature, and diseases that influence the growth of plants and therefore influence the expression of characteristics (Basford and Cooper, 1998).GxE interactions are important facts in cultivar evaluations.GxE interaction is considered quantitative effect (Romagosa and Fox, 1993;Baker, 1988), which is composed of genotype (G) x location (L), genotype (G) x year (Y), and genotype (G) x location (L) x year (Y) constituents.
The concept of stability has been defined in several ways and several biometrical methods including univariate and multivariate ones, have been developed to assess stability (Lin and Binns, 1988).The joint regression analysis of either phenotypic values or interactions on environment indices was discussed by Finlay and Wilkinson (1963) and Eberhart and Russell (1966).Part of the genotype stability is expressed in terms of three empirical parameters: the mean performance, the slope of regression line (b i ), and the sum of squares deviation from regression (S 2 di ) (Crossa, 1990).A two-stability parameter method similar to that of Eberhart and Russell (1966) was also proposed by Tai (1971).In this method, the linear response ( i  ) can be regarded as special form of the regression parameters (bi) and (S 2 di ), when the environmental index is assumed to be random (Lin et al., 1986).Wricke (1962) suggested using genotype environment interactions (GEI) for each genotype as a stability measure, which he termed as ecovalance (W i 2 ).Shukla (1972) developed an unbiased estimate using stability variance ( i 2  ) of genotypes and a method to test the significance of σ 2 i for determining stability of a genotype.Francis and Kannenberg (1978) used the environmental variance (S i 2 ), the coefficient of variation (CV i ), Lin and Binns's (1988) cultivar superiority measure (Pi) and Pinthus (1973) used coefficients of Fikere et al. 2575 determination (Ri 2 ) of each genotype as stability parameter.However, recent development comprises a multiplicative interaction model, which was first introduced in social science (Crossa, 1990), that was later adapted to the agricultural context as additive main effect and multiplicative interaction (AMMI) (Piepho, 1996).This model was considered appropriate if one is interested in predicting genotypic yields in specific environments (Annicchiarico, 1997).It combines the analysis for the genotype and environment main effect with several graphically represented interactions for principal component analysis (IPCAs) (Crossa, 1990).Thus, it helps in summarizing the pattern and relationship of genotypes, environment and their interaction (Gauch and Zobel, 1996).Field pea (Pisum sativum L.) is one of the major pulses grown in the highlands (1800-3000 m a.s.l.) of Ethiopia, where the need for chilling temperature is satisfied.This crop is very much important in the south eastern Ethiopia; since it fetches cash for the farming community and also serves as rotational crop which plays great role in controlling disease epidemics in areas where cereal monocropping is abundant.It also plays a significant role in soil fertility restoration as a suitable rotation crop that fixes atmospheric nitrogen.Generally, it is a crop of manifold merits in the economic lives of the farming communities of highlands of Ethiopia.However, to date, little information is available on this crop and its adaptation pattern, especially under southeastern Ethiopian conditions.The present study were carried out (1) To compare various statistical methods of analyzing yield stability and to determine the most suitable procedure to evaluate and describe yield stability of field pea (P.sativum L.) genotypes performance under South eastern Ethiopian conditions (2) to measure the genotype-environment interaction in field pea genotypes, giving emphasis to grain yield and (3) To estimate rank correlations between stability statistics.Sinja and Agarfa with an altitude of 2400-2440 m.a.s.l., respectively.These locations represent the Highlands of Bale,south eastern Ethiopia.
The experiment was laid down in a complete randomized block design with four replications.Based on seed size of genotypes (small to medium seed size) the seeding rate was 75 to100 kg ha -1 and fertilizer rate was 18/46 N/P 2 O 5 Kg ha -1 .Each genotype was sown in 3.2 m 2 plot size with 4 rows of 4 m length and 20 cm interrow spacing.Harvesting was done by hand.Grain yield was obtained by converting plot grain yields to a hectare basis (kg ha -1 ).

Statistical analysis
Combined analysis of variance was performed across test environments of location and years.Stability analysis was performed using Mstat-c (Michigan state University, 1991) and IRRI stat computer program (IRRI Stat, 2003).AMMI's stability value (ASV) was calculated as suggested by Purchase (1997).The stability parameters were performed in accordance with Eberthart and Russell's (1996) (the slope value (b i ) and deviation from regression (S 2 di ), Wricke's (1962) ecovalance (W i 2 ), Shukla's (1972) stability variance (σ 2 i), (Tai, 1971) deviation from linear response (λ i ), Lin and Binns's (1988) cultivar superiority measure (Pi) and Pinthus (1973) coefficients of determination (Ri 2 ), Francis and Kannenberg's (1978) coefficient of variability (CV i ) and environmental stability variance (S 2 i ) were calculated for each genotypes using spread sheet programs.Spearman's coefficient of rank correlation was computed for each pair of the possible pairwise comparison of the stability parameters by Minitab computer software (Minitab, 1996) and the significance of the rank correlation coefficient was tested according to Steel and Torrie (1980).

)
Environmental variance (S i 2) is one of the major stability measures for static stability concept, Type-1 stability (Lins et al., 1986) that is, the variance of genotype yields recorded across test or selection environments (that is, individual trials).For the genotype i. greatest stability is S i Where: S i 2 = Environmental variance, R ij = Observed genotype yield response in the environment j, mi= genotype mean yield across environments; e = number of environments.
A drawback with this method is that, in general, genotypes with high phenotypic stability measure through the environmental variance show low yield.In consequences, plant breeders do not use this method to evaluate the phenotypic stability of the genotype yields, or other related random variables.However, it is useful to evaluate the phenotypic stability of traits that should maintain their levels.Among these are qualitative traits such as resistance to disease or tolerance to environmental stresses.

Regression coefficient (b i ) and deviation mean square (S 2
di )

Joint regression analysis (b i )
According to Finlay and Wilkinson (1963), regression coefficients approximating to 1.0 indicate average stability, but must always be associated and interpreted with the genotype mean yield to determine adaptability.When the regression coefficients are approximating to 1.0 and are associated with high yield mean, genotypes are adapted to all environments.b i = ∑ y i j I j / ∑ I j 2 Where: b i = the regression coefficient, Y i j = the performance of the i th genotype in the j th environment, I j = the environmental index which is the mean of all the genotypes at the j th environments.When associated with low mean yields, genotypes are poorly adapted to all environments.Regression coefficients above 1.0 indicate genotypes with increasing sensitivity to environmental change, showing below average stability and great specific adaptability to high yielding environments.Regression coefficients decreasing below 1.0 provide a measure of greater resistance to environmental change, having above average stability but showing more specific adapted to low yielding environments.

Deviation mean square (S 2 di )
Joint linear regression (JLR) is a model used for analyzing and interpreting the non-additive structure (interaction) of two-way classification data.The GEI is partitioned into a component due to linear regression (bi) of the i th genotype on the environment mean, and a deviation.
This model uses the marginal means of the environments as independent variables in the regression analysis and restricts the interaction to a multiplicative form.Eberhart and Russell (1966) proposed pooling the sum of squares for environments and GEI and subdividing it into a linear effect between environments (with 1 df), a linear effect for genotype x environment (with E-2 df).In effect the residual mean squares from the regression model across environments is used as an index of stability, and a stable genotype is one in which the deviation from regression mean squares (S 2 di ) is small.Pinthus (1973) proposed to use the coefficient of determination (R 2 i) instead of deviation mean squares to estimate stability of genotypes, because R 2 i is strongly related to (S 2 di ) deviation mean square (Becker, 1981).

Coefficient of determination (R
The application of R 2 i and b i has the advantage that both statistics are dependent of units of measurement.

AMMI model and ammi stability value (ASV)
The AMMI model does not make provision for a quantitative stability measure, such a measure is essential in order to quantify and rank genotypes according their yield stability, The principal component analysis (PCA) scores of a genotype in the AMMI analysis are an indicator of the stability of a genotype over environments.The greater the PCA scores, either negative or positive, the more specifically adapted a genotype is to certain environments.The more the PCA scores approximate zero (0), the more stable the genotype is over all environments sampled (Schoeman, 2003).The following measure was proposed by Purchase (1997): Where: SS IPCA 1/ SS IPCA 2= is the weight given to the PCA 1 by value dividing the PCA 1 sum of square by the PCA 2 sum of square.Wricke's (1962) ecovalence (W i 2 ): evaluates stability on the basis of the contribution of each genotype to the total GEI sum of Fikere et al. 2577 squares.For this reason, genotypes with a low W i value have smaller deviations from the mean across environments and are thus more stable.According to Becker and Leon (1988) ecovalence measures the contribution of a genotype to the GEI; a genotype with zero ecovalence is regarded as stable and is given by the following formula: Shukla (1972): defined the stability variance of genotype i as its variance across environments after the main effects of environmental means have been removed.Since the genotype main effect is constant, the stability variance is thus based on the residual (GE ij + e ij ) matrix in a two-way classification.The stability statistic is termed stability variance (  2 i ) and is estimated as follows:


Where: QMGE= is the genotype x environment interaction mean square, p=number of genotypes, q= number of environments A genotype is called stable if its stability variance (  2 i ) is equal to the environmental variance (  2 i ) which means that  2 i =0.A relatively large value of (  2 i ) will thus indicate greater instability of genotype i.As the stability variance is the difference between two sums of squares, it can be negative, but negative estimates of variances are not uncommon in variance component problems.

Negative estimates of  2
i may be taken as equal to zero as usual (Shukla, 1972).Homogeneity of estimates can be tested using Shukla's (1972) approximate test (Lin et al., 1986).The stability variance is a linear combination of the ecovalence, and therefore both W i and  2 i are equivalent for ranking purposes (Wricke and Weber, 1980).
Cultivar superiority measure (Pi) Lin and Binns (1988) suggested the use of the cultivar performance measure (Pi) and stated Pi of genotype i as the mean squares of distance between genotype i and the genotype with the maximum response.This method is similar to the one used by Plaisted and Peterson (1959), except that, (a) the stability statistics are based on both the average genotypic effects and GEI effects and (b) each genotype is compared only with the one maximum response at each environment (Crossa, 1990).The genotypes with the lowest (Pi) values are considered the most stable.The stability statistic is measured as follows: Tai (λ i ) (1971): partitioned the GE (ge ij ) interaction term into the components: linear response to environmental effects and deviation from linear response (λ i ).Measures the deviation from the linear response in terms of the magnitude of error variance and is given by: Where: MSD i -mean square deviation from regression, m -Number of genotypes, MSE -mean square error, r -Number of replications.Francis and Kannenberg (1978) presented a simple, descriptive method for grouping genotypes on the bases of their yields and consistency of performance (measured by the coefficient of variation).Thus the two statistics necessary in this model are the genotype mean and the coefficient of variation (CV).Linear correlations were then calculated between various stability parameters to investigate their relationships.

Analysis of variance (ANOVA)
The result of combined analysis of variance for grain yield of 16 field pea genotypes tested across 12 environments showed that 79.68% of the total sum of squares was attributed to environmental effects, whereas genotypic and GEI effects explained 4.53 and 5.70%, respectively.The large environmental sum of squares indicated that environments were diverse, with large differences among environmental means causing most of the variation in grain yield.The magnitude of the GEI sum of squares was 1.26 times larger than of genotypes, indicating that there were differences in genotypic response across environments (Table 3).This variability was mainly due to the distribution of rainfall, which differed greatly across locations and seasons during the experimental years.

Comparison of yield stability parameters
The AMMI analysis of variance for grain yield (ton ha -1 ) of 16 field pea genotypes tested in 12 environments showed that 88.62% of the total sum of squares was attributable to environment effects, while only 5.04 and 6.34% of the sum of square were contributed to genotypic effect and to GEI respectively (Table 3).A large sum of squares of environments indicates that the environments were diverse, with large differences among environmental means causing most of the variation in grain yield.The IPCA scores of a genotype in the AMMI analysis were reported by Gauch and Zobel (1996) and Purchase (1997) as indication of the stability of genotypes are across their testing environments.Therefore, the postdictive evaluation using an F-test at P<0.01 suggested that two principal component axes of the interaction were significant for the model with 48 degrees of freedom.However, the prediction assessment indicated that AMMI with only two interaction principal component axes was the best predictive model (Zobel et al., 1988).Further interaction principal component axes captured mostly noise and therefore did not help to predict validation observations.Thus, the interaction of the 16 field pea genotypes with twelve environments was best predicted by the first two principal components of genotypes and environments.The most accurate model for AMMI can be predicted by using the first two PCAs (Mulusew et al., 2008;Yan and Rajcan 2002).Conversely, Sivapalan et al. (2000) recommended a predictive AMMI model with the first four PCAs.These results indicate that the number of the terms to be included in an AMMI model cannot be specified a priori without first trying AMMI predictive assessment.In general, factors like type of crop, diversity of the genotypes, and range of environmental conditions will affect the degree of complexity of the best predictive model (Crossa, 1990).
Wricke's ecovalence analysis (W i ) defined the concept of ecovalence, to describe the stability of a genotype, as the contribution of each genotype to the genotype x environment interaction sum of squares.Genotypes with low ecovalence have smaller fluctuations across environments and therefore are stable.Accordingly, the most stable hybrids according to the ecovalence method of Wricke were IFPI-3803, I-163, and IFPI -2711.These hybrids were not the best ranked for mean yield, being 10 th , 9 th and 8 th respectively.The most unstable genotypes according to the ecovalence method were IFPI -3933, IFPI-4132, and Helina these genotypes were ranked 16 th ,15 th and 1 st for mean yield respectively (Table 4).Lin and Binns's (1988) cultivar superiority measure (Pi) procedure showed the greatest deviation from all the other procedures, having negative rank correlation coefficients compared to the other procedures.It was significantly correlated CV.Lin and Binns define stability as the deviation of a specific genotype's performance from the performance of the best cultivar in a trial.This implies that a stable cultivar is one that performs in tandem with the environment.This procedure appears to be considerably more of a genotype performance measure, rather than a stability measure over sites.The genotype mean yield could then rather be used to identify a superior yield performing cultivar.Genotype Dadimos, ranked second on mean yield, was ranked 14 th for this procedure as the most unstable cultivar; which is above average stable genotype according to the other procedures, Dadimos and local cultivar were unstable according to Lin and Binn's procedure.
The coefficient of determination (R 2 i), which is the predictability of response estimates response (R 2 i = 1), ranged from 0.88 to 0.97, in which a variation of mean grain yield was explained by genotype response across environments.None of values of coefficient of determinations was significantly different from 1.0.In regard to this parameter, all of genotypes could be considered stable for grain yield (Table 4).
The average grain yield and their ranks for 16 field pea genotypes tested across four locations over the three years are presented in Table 2.The highest yield 6.22 t/ha were obtained from genotype IFPI-1523 at Sinana, while the lowest was 1.27 t/ha from variety 'weyitu' at Selka with a coefficient of variation of 15.88%.The mean yield across locations over 3 years (Table 2) showed substantial changes in ranks among the genotypes, reflecting the presence of high GXE interactions.
Similarly, the majority of the tested genotypes (Table 4) were non-significantly different from a unit regression coefficient (b i =1) and had small deviation from regression (S 2 di ), and thus possessed average stability.Finlay and Wilkinson (1963) and Eberhart and Russell (1966) stated that genotypes with high mean yield, regression coefficient equal to unity (b i =1) and deviation from regression as small as possible (S 2 di =0) are considered stable.Tai (1971) partitioned the GE (ge ij ) interaction Table 4. Summary of overall mean yield (t/ha), joint regression, Additive Main effects and Multiplicative Interaction (AMMI), other stability parameters and their rank (R) orders for 16 field pea genotypes tested in 12 environments in the South eastern Ethiopia, 2004Ethiopia, -2006.

AMMI model Joint regression
Other stability parameters , λ i = deviation from the linear response 10 , Pi = cultivar performance measure 6 F = frequency of the number of stability parameters over all of stability parameters for each genotype, if a genotype had eight/ nine values of F, it could be considered stable.
term into the components: linear response to environmental effects and deviation from linear response (λ i ).However, Eberhart and Russell's (1966) model is one of the most widely used stability models that consider both linear and nonlinear components of GE interaction in judging the stability of genotypes.In this model a variety with high mean, regression coefficient b i =1 and deviation from regression not significantly different from zero (S 2 di = 0) is said to be stable.Accordingly, genotypes IFPI-1523 and IFPI -2711 were the most stable genotypes since the regression coefficients almost unity and had one of the lowest deviations from regression and also have above average mean yield.Besides, their W i 2 and S 2 xi were low and they had lower coefficient of variability (CV %) and Shukla stability variance (σi 2 ) confirming their stability.In contrast, varieties such as NDP-77, 'weyitu' and 'dadimos' with regression coefficients greater than one were regarded as sensitive for environmental change.According to the IPCA 1 scores, genotype IFPI -2711 and 'weyitu' was the most stable genotype, followed by IFPI-1523, IFPI-3803 and IFPI-4132.On the other hand, when IPCA 2 is considered, this stability order had a different picture.According to IPCA 2 scores, genotype I-163 and EH 96009-1-1 was the most stable genotype followed by IFPI -6064, IFPI-3803 and 88PO22-6.This means that the two IPCAs have different values and meanings.Therefore, the other better option is, to calculate ASV using a principle of the Pythagoras theorem and to get estimated values between IPCA 1 and IPCA 2 scores.ASV was reported to produce a balanced measurement between the two IPCA scores (Purchase, 1997).Spearman's coefficient of rank correlation was computed among all the stability parameters (Table 5).Highly significant (P<0.01)rank correlation between CV i and S i 2 (r=0.747) was observed.The same held true between W i and ASV (r=0.947).Similarly, Shukla's stability parameters (σ i 2 ) were significantly correlated with ASV (r=0.946),S 2 di (r=0.964), and W i 2 (r=0.99),S 2 di were highly correlated with ASV (r=0.90).On the other hand, deviation from linear response (λ i ) significantly correlated with ASV (r=0.915),W i (r=0.941),σ i 2 (r=0.94) and S 2 di (r=0.985).Similarly, Alberts (2004) reported high rank correlations between S 2 di and σi 2 ; W i , S 2 di and ASV, CV i , b i , ASV, λ i and W i and this implies their strong relationship in detecting the stable genotype.In contrary, No significant rank correlation between Lin and Binns's superiority measure (Pi) and Finlay and Wilkinson's procedure (b i ) with the other procedures were found.Thus, these two procedures are not recommended for use on their own as a measurement of yield stability.In general, AMMI, joint regression, Wricke (W i ), S 2 xi , λ i and Shukla's (σ i 2 ) stability parameters were found to be useful in assessing yield stability of field pea (P.sativum L.) genotypes under the studied environments of south eastern Ethiopian condition.Although, AMMI was found to be more informative in depicting the adaptive response of the genotypes (Purchase, 1997), the joint regression analysis also remains a good option.Hence, AMMI, S 2 di , S 2 i , CV i , σ i 2 , W i 2 , and λ i were useful in determining the relative stability of field pea genotypes under the test environments of the Highlands of Bale, south eastern Ethiopia.Therefore, it is possible to use only one of them as a measure of stability.There were also high correlations between AMMI, S 2 di , S 2 i , CV i , σ i 2 , W i 2 , and λ i (P < 0.01).Hence, it is possible to use only one of them as a measure of stability.Generally, from evaluated field pea (P.sativum L.) genotypes at highlands of Bale, south eastern Ethiopia, IFPI-1523, IFPI -2711, I-163, IFPI-3803 and 88PO22-6 were stable cultivars, which had 8, 8, 7, 7, and 7 out of all 10 stability statistics used, respectively.Among these cultivars, IFPI-1523 and IFPI -2711 were the most stable ones, because both of them had 8 out of all 10 stability statistics used, respectively.In summary, AMMI, S 2 di , W i 2 , i 2  , i  and S 2 i were generally found to be important in determining the comparative stability of the field pea genotypes tested and this fact also reflected by spearman's rank correlation coefficient that displayed significant correlations among these stability parameters; the significant GxE interactions and the changes in the rank of genotypes across environments suggests a breeding strategy of specifically adapted genotypes in homogenously grouped environments and whenever, new varieties are proposed for commercial release, information on GxE interactions and stability, clearly indicating their specific and/or general adaptations needs to be available to the users.

Conclusion
Compression of biometrical methods to describe stability analysis for grain yield of field pea genotypes revealed that genotypes IFPI-1523 and IFPI -2711 were stable in yield and such stable performance is a desirable attribute of cultivars, particularly for countries such as Ethiopia, where environmental variations are very high and unpredictable.Breeding efforts for such environments should give more emphasis to develop widely adapted genotypes such as genotypes IFPI-1523 and IFPI -2711.Similarly, breeding for specific localities need to be encouraged using the existing sub-centers and, of course, with in the available resources since the latter is more expensive than the former.Moreover, a genotype with low phenotypic stability is predestined to be eliminated from the market.The use of appropriate biometrics techniques is necessary for identifying the most adapted, responsive and stable genotypes in the final phases of the plant breeding program, where the high cost and the time spent in assays are powerful justifications to search for improved methods.In general, the following major findings can be summarized from this study: (i) AMMI, S 2 di , W i 2 , i 2  , i  and S 2 xi were generally found to be important in determining the comparative stability of the field pea genotypes tested and this fact also reflected by spearman's rank correlation coefficient that displayed significant correlations among these stability parameters; (ii) The increased probability of identifying the next royalty-paying genotype.The interaction of the 16 field pea genotypes with 12 environments was best predicted by the first 2 principal components of genotypes and environments; (iii) The significant GxE interactions and the changes in the rank of genotypes across environments suggests a breeding strategy of specifically adapted genotypes in homogenously grouped environments; (iv) Finally, whenever, new varieties are proposed for commercial release, information on GxE interactions and stability, clearly indicating their specific and/or general adaptations needs to be available to the users.

Table 1 .
List of studied entries, and Origin / Source of entries.
*ICARDA=International Center for Agricultural Research in the Dry Areas, HARC= Holeta Agricultural Research Center and SARC=Sinana Agricultural Research Center.

Table 2 .
Mean grain yield (t/ha) and rank (R) of 16 field pea genotypes tested for 3 years per location inSoutheastern Ethiopia  2004 -2006.

Table 3 .
Combined analysis of variance and Additive Main effect and Multiplicative Interaction (AMMI) analysis of variance for grain yield (t/ha) of field pea genotypes grown in South easternEthiopia during 2004Ethiopia during  -2006.   .
in bold are not significantly different from unity at P < 0.05; cultivars with values in bold are considered stable; c printed values in bold are lower than the mean; cultivars with lower values than the mean for more than eight stability parameters are regarded as stable; G.C= genotype code, b i = regression coefficient, S b printed values