Introduction

The harnessing the variability and genetic diversity of native materials in bean (Vicia faba L.) is important for higheryielding varieties and stability, with larger seeds, resistant and/or tolerant to pests and diseases, among others, among others. The significant IGA may limit the identification of superior genotypes (^{Crossa et al., 1990}; ^{Yan and Kang, 2003}; ^{Annicchiarico and Iannucci, 2008}; ^{Gauch et al., 2008}; ^{Yahia et al., 2012}; ^{Pérez et al., 2015}), mega-environments favorable or optimal technological packages that contribute to increasing the income of farmers (^{Annicchiarico, 1997}; ^{Flores et al., 2013}; ^{Temesgen et al., 2015}).

The models of ^{Eberhart and Russell (1966)} and main additive and multiplicative interaction (AMMI Model) effects have been widely used in maize (Zea mays L.; ^{González et al., 2010}), bean (^{Mulusew et al., 2008}; ^{Karadavut et al., 2010}; ^{Al- Aysh, 2013}; ^{Abebe et al., 2015}) and potato (Solanum tuberosum L.; ^{Pérez et al., 2007}; ^{Pérez et al., 2009}), among others. The AMMI model is superior to other multivariate techniques to enable the graphical interpretation of the responses of varieties of environments and the IGA and is still efficient with few repetitions (^{Zobel et al., 1988}; ^{Rodríguez et al., 2005}; ^{Gauch, 2006}).

The bean is well suited to the Center of Mexico, tolerates low temperatures, fixes atmospheric nitrogen, has a high protein content and is advantageously associated with other species such as bean (Phaseoulus vulgaris L.) or maize (Zea mays L.). In the central region of Mexico there is little information on their agronomic performance, yield potential and stability. The main objective of this study was to identify collections of higher production and lower grain genotype*environment interaction using two methodologies.

Materials and methods

Results and discussion

The highly significant differences (p= 0.01) than were detected in Table 3, 4 and 5 indicate that at least two locations or between two cultivars there are real differences in grain yield and the behavior of beans varied depending on the environments; They also suggest that the five towns in the Central Estado de Mexico are very heterogeneous, that there is sufficient genetic variability among 36 cultivars of bean and the IGA difficult to identify cultivars greater performance and stability, making it possible that some of the cultivars have better adaptation to a specific environment (^{Annicchiarico and Iannucci, 2008}; ^{Yahia et al., 2012}; ^{Flores et al., 2013}; ^{Temesgen et al., 2015}), very common situation for the Valles Altos the Mexico, where there is great environmental heterogeneity (^{González et al., 2010}; ^{Pérez et al., 2014}).

In the Valle de Toluca-Atlacomulco, Estado de Mexico and other locations in Central Mexico has been concluded that the environmental variability that prevails in this region is mainly attributed to the differences in altitude, soil types, temperatures and rainfall (^{Rodríguez et al., 2005}; ^{González et al., 2008}; ^{Reynoso et al., 2014}; ^{Rodríguez et al., 2015}; ^{Franco et al., 2015}), as those that can be seen in Table 1.

The heterogeneity between localities (Figure 1) is explained by the significant differences were mainly observed among the best environments (SNG and BG) with the other three sites (SL, SD and LB). The average grain yields for LB, SD, SL, BG and SNG were 0.93, 1.05, 1.34, 2 and 2.85 t ha^-1, with an arithmetic mean of 1.63 t ha^-1 (Table 4). This value is similar to the state of Mexico (1.48 t ha^-1; ^{Orozco et al., 2013}) and higher than the national (0.66 t ha^-1; ^{Pérez et al., 2014}). In considering the phenotypic variability within localities it noted that SNG and the BG highest grain yields were recorded (6 and 4.16 t ha^-1, respectively). Both values are higher than those obtained commercially in other Mexican states like Morelos, Sonora, Durango, Guanajuato and Veracruz (between 1.48 and 3.42 t ha^-1; ^{Pérez et al., 2014}). ^{Karadavut et al. (2010)} recorded grain yields between 2.52 and 3.21 t ha^-1. The above results are similar to those observed by ^{Orozco et al. (2013)} and ^{Pérez et al. (2014)}.

Figure 1 Grain yield for cultivars and environments and their interaction with the principal component 1 of AMMI model (the codes were defined in Table 1, 3 and 4). 

^{Rodríguez et al. (2015)} and ^{Franco et al. (2015)} commented that the places that make the Valle de Toluca, in the Estado de Mexico, are very heterogeneous and that an average of 20 km distance between two of them is sufficient to cause statistically significant environmental variability. In this study the greatest distance corresponded to the towns of SNG and SL, and is greater than 100 km.

By applying the method of ^{Eberhart and Russell (1966)}, with the modification ^{Carballo and Márquez (1970)} found that only T27, collected in Almoloya del Río, had good response in all environments but this was inconsistent; production of grain (1.70 t ha^-1) was slightly higher than the average for the state of Mexico (^{Pérez et al., 2014}) and ranged in five locations from 0.63 to 2.68 t ha^-1 (Table 4, 5 and 6). This method has been widely used but has also been widely criticized because of the dependence of the environmental effects of the varieties chosen and the nonlinearity of these responses to the environment (^{Shukla, 1972}). However, ^{Márquez (1991)} noted that this methodology is useful to determine adaptability and, therefore, association genotype x environment, allowing identification and recommendation of genotypes with the best response to favorable environments and unfavorable (^{González et al., 2010}).

Cultivars identified as T20, T31, T33 and T35 showed better response and were consistent in unfavorable environments (bi <1; S²di= 0); sites with negative environmental indices were LB, SD and SL. The average of this group was 1.17 t ha-1 but T31 only produced 0.63 t ha^-1; this group value is higher than the national average (0.66 t ha^-1) and lower than the averages of the state of Mexico and global (1.48 and 2.06 t ha^-1, respectively; ^{Pérez et al., 2014}).

The cultivars T1, T3, T8, T9, T10, T11, T14, T15, T16, T17, T18, T19, T21, T22, T25, T29, T32, and T34 had better response in unfavorable environments but were inconsistent; their grain yields ranged from 1.12 to 1.87 t ha^-1. According to ^{Pérez et al. (2014)} the arithmetic mean is higher than the national (0.66 t ha^-1), slightly larger than the state of Mexico (1.46 t ha^-1) and lower than the world (2.06 t ha^-1). Of these, the most outstanding were T1, T14, T8 and T22 (1.87, 1.83, 1.77 and 1.75 t ha^-1, respectively; Table 4, 5 and 6).

The group formed by T4, T13, and T24 had a better response in good environments and were consistent (bi >1; S²di = 0). T4 (2.13 t ha^-1) was the best but the group average was 1.79 t ha^-1, higher than the national and the state of Mexico and lower than the world (Table 4, 5 and 6; ^{Pérez et al., 2014}).

The above results suggest that the exploitation of specific adaptation should receive more attention as a proposal to increase diversity and bean grain yields because the instability of the genetic material reliable identification difficult in the Central region of the Estado de Mexico. ^{Rodríguez et al. (2005)}, ^{Crossa et al. (1990)}; ^{Pérez et al. (2009)}; ^{Annicchiarico and Iannucci (2008)}; ^{Pérez et al. (2014)} have highlighted the previous situation.

In Figure 2 it was found that the main components 1 (48.68%) and 2 (40.61%) accounted 89.29% of the variation related environments (E), cultivars (C) and their interaction (E x C). In this context the graphical interpretation of the interrelationships in the biplot are reliable (^{Annicchiarico and Iannucci, 2008}, ^{Tadesse and Abay, 2011}; ^{Abebe et al., 2015}). In the combined variance analysis it can be seen that the contribution of A, C and A x C was 44.37, 14.36 and 41.27%, respectively. These results confirm the fact that genetic variability between beans that are grown in the central region of the state of Mexico is masked by the effects originating locations and interaction A x C. As other researchers have noted, genotype x environment interaction causes confusion in the estimation of genetic parameters, reduces the response to selection, and difficult to identify superior genotypes; however, analysis and proper interpretation identifies mega-environments, detect genotypes with specific or broad adaptation, propose strategies appropriate or generate, validate, apply and/or transfer technology (^{Márquez, 1992}; ^{Crossa, 1990}; ^{Rodríguez et al., 2002}; ^{González et al., 2010}; ^{Pérez et al., 2014}).

Figure 2 Biplot for 1 and 2 main components of AMMI model. 

In other multivariate techniques have been recommended values greater than 50% for the interrelationships that can be detected in the CP1 and CP2 are reliable (^{Sánchez, 1995}; ^{González et al., 2010}; ^{Reynoso et al., 2014}). ^{González et al. (2010)} concluded that the contribution of AMMI model variability caused by environments, genotypes and their interaction was 45.11, 48.40 and 6.48%, respectively, when they evaluated the stability of the performance of corns recommended for commercial planting in Valle de TolucaAtlacomulco, Mexico.

Conclusions

The highly significant differences were observed among cultivars, between localities and their interaction (IGA) suggest that there is enough genetic variability to start a new program of plant breeding, the center environments state of Mexico are heterogeneous and significant IGA difficult to identify stable cultivars. These results were confirmed by applying the AMMI model and Eberhart and Russell with the modifications proposed by Carballo and Marquez. The best environment were San Nicolas Guadalupe and Barrio de Guadalupe, located in the State of Mexico municipalities of San Felipe del Progreso and Metepec. Grain yield in five locations ranged from 0.24 to 6 t ha^-1. Although there was no stable cultivars, the most outstanding were identified as T2, T4, T5, T6, T7, T26 and T30 (between 2.05 and 2.61 t ha^-1), collected in the municipalities of Acambay, Jocotitlan, Zinacantepec and Metepec; except T4, which showed better response in good environments and was consistent, T12, T23, T28 and T36 responded better to good environments but were inconsistent.