Grain yield

According to the combined analysis, the performance varied significantly (p≤ 0.01) between environments, genotypes and in the interaction of both factors. Table 2 shows that, in Carranza, Chiapas, autumn-winter cycle of 2016-2017, under residual humidity conditions (A3), the highest average yield was obtained, which was significantly higher than the rest of the environments.

The highest average yield obtained in this locality, was mainly due to the fact that the crop had adequate humidity during its development cycle (568 mm of rainfall in total), without occurrence of periods of terminal drought. In turn, in the environments of New Mexico, Chiapas, summer cycle 2016, under conditions of whitewashed acid soil (A1), CEIXTA, Veracruz (A8) and Rincón Grande, Veracruz (A4), both in autumn-winter of 2016-2017 with residual humidity, as well as in El Rubi, Veracruz, in winter-spring of 2017 under irrigation conditions (A9) and in autumn-winter of 2016-17 with residual humidity (A5), also high average yields were obtained, because in all cases, the humidity conditions for the development of the beans were adequate (more than 320 mm of water during the cycle, of which about 150 mm were provided through the application of irrigation or received for the rains that occurred during the reproductive stage of the crop). For an adequate development and yield of the bean crop, at least 300 mm of rainfall are well distributed during its phenological cycle, 50 to 90 mm being convenient, from flowering to pod filling (^{Acosta et al., 2009}; ^{Ruiz et al., 2013}).

On the contrary, the lowest average yields were obtained at the Agricultural Technology Institute of Juan Rodríguez Clara (ITA-JRC), Veracruz, in autumn-winter 2016-17, in acid soil, with application of dolomite lime (A6) and without application of dolomite (A7) (Table 2). This was mainly due to the water stress suffered by bean plants during their phenological cycle, since in the experimental site where both trials were conducted, there was a rainfall of the sowing until the harvest of 150.4 mm, of which only 24.4 mm precipitated during the reproductive phase of the crop, specifically the stages of pod formation when filling them, which limited the development of genotypes in both soil acid conditions. The lack of moisture during flowering, the formation of pods and their filling, causes a significant decrease in grain yield, due to a reduction in the number of pods per plant and a poor filling of pods (^{Acosta et al., 2009}).

The same table shows that; through the evaluation environments, Jamapa Plus/XRAV-187-3-1-2, was the most productive line, whose average grain yield was statistically similar to that of five other lines and the control varieties, Negro Comapa and Negro Grijalva This same line, together with Negro Citlali/XRAV-187-3-1-8, obtained a significantly outstanding grain yield in five of the 10 test environments. Negro Citlali/XRAV-187-3-1-8, ranked first in performance in the environments of CEIXTA, Veracruz, in autumn-winter 2016-17, as well as in the ITA-JRC, Veracruz, in the same agricultural cycle, in acid soil, with and without application of dolomite lime, where it was the one with the highest productive efficiency (^{Tosquy et al., 2018}). Meanwhile, Jamapa Plus/XRAV-187-3-1-2 was located first in the environments of New Mexico, Chiapas, in summer 2016, in whitewashed acid soil, and in El Rubi, Veracruz, in winter-spring 2017, with irrigation suspension at the beginning of the reproductive stage of the crop, where it showed greater tolerance to terminal drought and productive efficiency (with irrigation and drought), than the Negro Comapa and Negro Grijalva varieties (^{Ibarra et al., 2018}).

AMMI analysis

According to the AMMI analysis, highly significant variability was detected in the first five main components, which accumulated 96.1% in the explanation of the variance, of these five, the first three were the most important in the representation of the IGA, since they explained 81.9% of the sum of squares. According to ^{Pereira et al. (2009)}, the first three main components of this analysis should explain more than 60%, to be considered sufficient and at least 70% satisfactory.

This model allowed us to identify three groups of relatively homogeneous and well-defined environments, based on their average performance and their interaction with genotypes (^{Williams et al., 2010}). The first group included three environments from Veracruz: El CEIXTA (A8), Rincón Grande (A4) and El Rubi (A5), all of them are similar in crop cycle (AW 2016-17) and humidity condition (residual moisture with adequate distribution of rainfall). These environments combined high average grain yield, significantly higher than the general average of 1 312 kg ha^-1 and low interaction with genotypes (CP 1= -6.4547, -7.9732 and -11.2433) (Table 3, Figure 1). These two characteristics, in the process of genetic improvement, make them ideal for identifying opaque black bean germplasm, with high and stable yield, for the northern areas and region of the High Mountains in the center of the state of Veracruz (^{López et al., 2015}).

Figure 1 Main effects and interaction observed for 10 test environments. A1= New Mexico, Villaflores, Chiapas, with dolomite; A2= New Mexico, Villaflores, Chiapas, without dolomite; A3= Carranza, Ocozocoautla, Chiapas; A4= Rincón Grande, Orizaba, Veracruz; A5 = El Rubi, Medellín, Veracruz; A6= Rodríguez Clara, Veracruz, with dolomite; A7= Rodríguez Clara, Veracruz, without dolomite; A8= CEIXTA, Tlapacoyan, Veracruz; A9= El Rubi, Medellín, Veracruz, irrigation; A10= El Rubi, Medellín, Veracruz, drought. 

The second group included two environments in the ITA-JRC, Veracruz, similar in crop cycle (AW 2016-17) and humidity condition (residual moisture with terminal drought) and different in soil management: one under soil conditions acid, without application of lime dolomite (A7) and another with application of lime dolomite (A6); both environments also showed reduced interaction with genotypes (CP 1= -6.8706 and -7.0106, respectively), but low average yield, much lower than the general average (Table 3, Figure 1). This behavior observed in both environments, is mainly attributed to the severity of water stress suffered by genotypes, which commonly occurs in that beans producing area (^{Morales et al., 2015}), which did not allow them to express their potential for performance and that the differences between the vast majority of them were minimal.

The third group included three environments with adequate humidity during the crop cycle: Carranza, Chiapas, 2016-2017 AW cycle, with residual humidity (A3), El Rubi, Veracruz, 2017 WS cycle, with irrigation during the crop cycle (A9) and New Mexico, Chiapas, in the summer of 2016, under conditions of temporary and acid soil whitewashed with dolomite (A1), in which high average yield was observed and the highest interaction between the environment and genotypes (CP 1= -21.685, 19.6864 and 16.5182, respectively) (Table 3, Figure 1), this is mainly due to differences in the potential for performance and adaptation of genotypes in those evaluation environments, in which it was arranged of adequate humidity during crop development.

It should be noted that these three environments of high average performance, which are far from the axis of the ordinates (Figure 1) and that contributed more to the genotype-environment interaction, in certain cases, are suitable for bean production, if it has a genotype with specific adaptation to these environments (^{Acosta et al., 2012}).

In relation to genotypes, two groups stood out: one formed with materials that showed very low interaction (close to zero) and therefore, a stable behavior (^{López et al., 2011}), which includes the Jamapa line Plus/XRAV-187-3-1-8 (G10), which in addition to having obtained high average performance, showed the least interaction with the environment with a CP 1= 0.2246 (Table 3 and Figure 2), as well as at lines Negro Citlali/XRAV-187-3-1-6 (G5) and Papaloapan/SEN 46-7-7 (G3), which also showed reduced interaction with the environment (CP 1= -0.4576 and 1.0064, respectively), but their average yield was lower (Figure 2), these genotypes can be used in genetic improvement programs, for the generation of opaque black bean lines and varieties with wide adaptation. In the classification of genotypes for their stability, using the AMMI model, preferably those that are close to the axis of the ordinates should be selected, with CP 1 values equal to or close to zero (which are those that interact in a lesser degree with the environment) and show high grain yield (^{Vargas and Crossa 2000}; ^{Pereira et al., 2009}).

Figure 2 Main effects and interaction observed for the yield of 14 black bean genotypes. 

The other group consisted of three genotypes that presented high average yield but high interaction with the environment; This group includes the Jamapa Plus/XRAV-187-3-1-2 (G11) line, which was the most productive and the one that interacted most with the environment (CP 1= 22.33616) (Table 3, Figure 2). This line showed specific adaptation in environments, with and without abiotic stresses: due to acid soil, in New Mexico, Chiapas, And terminal drought, in El Rubi, Veracruz, conditions in which it obtained significantly outstanding grain yields, so in the future, it may represent an option for planting in this type of soil in the center of the state of Chiapas and in autumn-winter, under conditions of residual humidity, in the state of Veracruz, where the occurrence of drought during the reproductive stage of the crop (^{Tosquy et al., 2014}). The other two genotypes were: Negro Grijalva (G14) with CP 1= 15.4341 and Negro Comapa (G13) with CP 1= 9.7237 (Table 3, Figure 2), these two varieties showed specific adaptation to irrigation conditions and terminal drought in El Rubi, Veracruz, and edaphic acidity in New Mexico, Chiapas; Negro Comapa also showed a significant response in grain yield, to the application of dolomite lime, in the latter environment. Specific adaptation in a given area is also desirable, if the genotype shows stability over years in that area and high grain yield (^{Acosta et al., 2012}).

These results indicate that, the stability of the performance of the genotypes evaluated is not a function of the genetic heritage from which they come, since in general, materials that were derived from the same cross, showed differences in their performance potential and adaptation to the environments test.