Plant breeders inevitably face GEI once testing varieties across a number of environments. Reckoning on the magnitude of the interactions or the differential genotypic responses to environment, the varietal rankings can dissent greatly across environment (Dehghani et al., 2008; Crossa, 1990). Bartlett's homogeneity test evidenced that the mean squares of individual environments were unvarying and so the combine analysis of variance was performed. The combined analysis of variance (ANOVA) for TPH is shown in Table 2. Genotypes and environment showed high significant difference (P<0.01) while GEI was significant (P<0.05) indicating rank difference in genotypes response at different environments and the need for extension of stability analysis.

Table 2

The mean TPH across environments over three years (Table 3) showed considerable changes in ranks among the genotypes, reflective the presence of high GE interactions (Rea et al., 2015). These results show that the heterogeneousness of the environments and genetic variability of the genotypes becomes manifest. The environment mean yield ranged from 13.12 TPH in Santa Lucia to 17.56 TPH in Montaña Verde indicating differences among test environments. The highest yield 23.27 TPH was obtained from genotype V98-120 at Montaña Verde, while the lowest was 8.26 TPH from genotype V91-6 at Santa Lucia. The results of the non-parametric and parametric statistics and their ranks are presented in Table 4 and 5, respectively.

Table 3

Table 4

Table 5

Univariate stability. In Table 4 is presented the mean yield values (TPH) and stability parameters. Finlay and Wilkinson (1963) and Eberhart and Russell (1966) considered genotypes with high mean yield, coefficients of regression equivalent to unity (bi= 1) and deviation from regression proximate zero (S²di=0) to be stable. According to these parameters only V99-236 and V00-50 genotypes meet these conditions. Francis and Kannenberg (1978) defined a stable genotype as one that provides high yield and constant performance across locations. In conformity with this definition, V99-236, V99-190, V99-213, V98-62 and V98-120 are considered stable since that presented low CV and high TPH. Rea and De Sousa-Vieira (2002) used this method and concluded that the CV could be used to identify genotypes on a group basis rather than individually; however, the method can also be used in a plant-breeding context. In the method of Lin and Binns (1988) the best genotype is considered to be the one with the greatest performance and the lowest value of Pi. Here, we found that genotypes V99-236, V00-50, V98-120, V98-62, and V99-208 showed lower Pi values, indicating greater adaptability to these environments. Wricke (1962) recommended using ecovalance (W) as a stability parameter. Genotypes with the smallest ecovalance (W) values are contemplated stable. The W was lowest for genotypes CP74-2005, V00-50 and V99-236. Shukla (1972) defined a stability variance value, which considered a genotype with relatively large variance to have low stability. By Shukla's definition, genotypes CP74-2005, V00-50 and V99-236 ranked the most highly stables. Considering all methods of univariate stability can conclude that genotypes V99-236 and V00-50 were the most stable and high yields.

Multivariate stability. The AMMI model does not make specification for a quantitative stability measure, and as such a measure is important in order to quantify and sort genotypes in terms of yield stability. Hence, AMMI stability value (ASV) suggested by Purchase et al (2000) was applied to quantify and rank genotypes according to their yield stability. The genotype with the lowest ASV value is taken as most stable. Consequently, genotypes V99-236, CP74-2005 and B80-408 were the most stable (Table 4).

Non parametric stability. The results of 10 nonparametric stability measures and genotypes mean yield are resumed in Table 4. The Si⁽¹⁾ and Si⁽²⁾ statistics are based on ranks of genotypes across locations and they give proportional weight to each environment. Genotypes with less modification in rank are considered to be more stable. According to both Si ⁽¹⁾ and Si ⁽²⁾ V99-236 and V00-50 had the smallest changes in ranks and are thus considered as the most stable genotypes. Two other non-parametric statistics, Si ⁽³⁾ and Si ⁽⁶⁾, integrate yield and stability based on yield orders of genotypes in each environment (Nassar and Huehn, 1987). The lowest value for each of these statistics reveals maximal stability for a certain genotype. Genotypes V99-236, V00-50, V98-120, V99-208, V99-213 had the lowest Si ⁽³⁾ and Si ⁽⁶⁾ values hence, these genotypes were identified as the most stable genotypes.

Results for Thennarasu's (1995) non-parametric stability statistics, estimate from ranks of adjusted yield means, are showed in Table 4. The ranks of genotypes based on these statistics are presented in Table 5. According to NPi⁽¹⁾, genotypes CP74-2005, V00-50, V98-120 were stable in analogy with the other genotypes. Genotypes V00-50, V99-236, V98-120, V99-236 had the lowest value of NPi⁽²⁾ and were judged stable. NPi⁽³⁾ and NPi⁽⁴⁾ also recognized genotypes V00-50, V99-236 and V98-120 how the most stable genotypes and high mean yield.

Kang's (1988) non-parametric stability statistic (RS) applies both yield and stability variance (Shukla, 1972) with the genotype having the lowest rank-sum being the most promising. In this case, the genotypes V00-50, V99-236, V99-213, and CP74-2005 had the lowest values, and were stable genotypes with high yield in comparison with other genotypes. Non-parametric (TOP) superiority measure (Fox et al., 1990) identified genotypes V99-236, V98-62, V00-50 and V99-208 presented mainly in the top third, thus, these genotypes were stable. Similarly, Segherloo et al. (2008) found a highly significant association between mean yield and Fox-rank.

The Spearman’s rank correlations between each combination of stability measures were estimated (Table 6) and demonstrated a high positive significant rank correlation between TPH and PI, TOP, NPi⁽²⁾, NPi⁽³⁾, and NPi⁽⁴⁾. The parameters NPi⁽²⁾, NPi⁽³⁾ and NPi⁽⁴⁾ were associated positive with Si⁽⁶⁾ and Si⁽³⁾ with Si⁽⁶⁾, RS, and NPi⁽²⁾. Therefore, only one of these parameters would be adequate to select stable genotypes in a breeding program (Mohammadi et al., 2007). Complete correlation was found between Wricke’s and Shukla’s statistics. Kang et al. (1987) indicated that Wricke's ecovalance (W) and stability variance (Shukla) were equal; because Shukla's stability variance is a linear combination of the ecovalence so for ranking purposes these methods are equivalent (Bujak et al., 2014). To better comprehend the interrelationships among the parametric and non-parametric statistics, principal component analysis, based on the correlation matrix of rank (Table 5) was used. The first and second principal components of the rank correlation accounted for 48.10% and 18.80% of the variation, respectively, making a total of 66.90% of the original variance among the stability parameters (Figure 1). Similar results have been reported from other studies in faba bean and field pea (Flores et al., 1998), durum wheat (Kilic et al., 2010), barley (Mut et al., 2010) and sugarcane (Rea et al., 2015). Results of the biplot of the first two principal components based on the rank correlation matrix were more or less consistent with the Spearman rank correlation coefficients (Figure 1, Table 6). The stability parameters were separated into two stability concepts: Group 1, parameters that corresponded with the dynamic/agronomic stability concept which were associated to mean yield (TPH) such as PI, TOP, NPi⁽³⁾, Si⁽⁶⁾, NPi⁽²⁾, NPi⁽⁴⁾, Si⁽³⁾, CV and ASV. Group 2, the remaining stability parameters corresponding with the static/ biological stability concept were assigned to RS, Si⁽²⁾, Si⁽¹⁾, (S²di), bi, Shukla, W, NPi⁽¹⁾ (Figure 1). These parameters, which identify genotypes with high phenotypic stability without due consideration of mean yield, may not be appropriate, as both breeders and farmers incline toward to select genotypes of good yield with perform regularity across environments (Mohammadi and Amri, 2008; Farshadfar et al., 2012; Khalili and Pour-Aboughadareh, 2016).

Figure 1

Table 6