ADAPTABILITY AND PRODUCTIVE STABILITY OF SOYBEAN GENOTYPES UNDER NATURAL RUST INFECTION WITHOUT FUNGICIDE ADAPTABILIDADE E ESTABILIDADE PRODUTIVA DE GENÓTIPOS DE SOJA SOB INFECÇÃO NATURAL POR FERRUGEM, SEM FUNGICIDA

The genetic breeding of soybean aims to obtain productive genotypes, so it is necessary that the genetic components, environment and the interaction between them be understood. The G x E interaction is the differential behavior of the genotypes against environmental. The objective was to study the G x E interaction and analyze the adaptability and stability of soybean genotypes under natural rust infection without fungicide. The experiment was conducted in the Genetic Breeding Program of the Federal University of Uberlândia. Fourteen soybean genotypes were evaluated, with 10 lines developed by the UFU Program (UFUS1117: 01, 02, 03, 05, 06, 07, 08, 09, 10 and 11) and 4 cultivars: UFUS 7415, UFUS Riqueza, TMG 801 and BRSGO 7560 in four seasons: 2013/14, 2014/15, 2015/16 and 2016/17, in a randomized complete block design. The G x E interaction was complex and the H was 85.97% indicating superiority of genetic variation in relation to the environment. The average grain yield was 2284.13kg ha. The genotype UFUS 1117-01 was identified by Eberhart and Russel, Wricke, AMMI 2 and Centroid as being a highly productive stability genotype. The UFUS 1117-07 showed high stability by Eberhart and Russel, Wricke, Lin and Binns modified by Carneiro methods and wide adaptability by Eberhart and Russel and Centroid. The genotype UFUS 1117-09 was identified as being adaptable to unfavorable environments by the Lin and Binns modified by Carneiro and Centroid methods, and UFUS 1117-10 presented favorable environmental adaptability by the Centroid method and high stability by Eberhart and Russel.


INTRODUCTION
Variations in soybean yield grain occur not only as a function of cultivar and environmental conditions but also of genotype interaction by environments (SEDIYAMA; SILVA; BORÉM, 2015). The genotype interaction by environments ( G x E) is characterized as the differential behavior of genotypes due to environmental variations (CRUZ; CARNEIRO; REGAZZI, 2014), hinders the evaluation of productive potential and the selection of superior materials, inflates estimates of genetic variance resulting in overestimation of the expected gains with selection and in less successful breeding programs VENCOVSKY, 1999). A interaction has fundamental importance in the phenotypic manifestation, because it reflects the sensitivity differences of the genotypes towards environmental variations, resulting in changes in the behavior of the materials (RAMALHO et al., 2012), and should, therefore, be estimated and considered in the genetic improvement and indication of cultivars.
Due to the inconsistency of genotype superiority in environments, the use of specific cultivars for each environment or with high adaptability and high stability has been recommended (GARBUGLIO; FERREIRA, 2015). Adaptability is comprehended as the ability of the genotype to benefit from environmental variations, while stability reflects is the ability of genotypes to show a highly predictable behavior in data environmental stimuli (CRUZ; CARNEIRO;REGAZZI, 2014).
From the studies of adaptability and stability, it is possible to infer about the productive characteristics of the genotypes to recommend the appropriate cultivars to different regions of cultivation, allowing to the farmer a greater profitability. In this way, it is possible to obtain more productive cultivars with desirable agronomic characteristics, consistently superior and responsive to environmental variations, which are the main objectives of a breeding program of any economic species.
The objective was to evaluate the productive performance of soybean lines and cultivars in four seasons in the city of Uberlândia, MG and to determine the adaptability and productive stability by parametric, non-parametric and multivariate methods of soybean genotypes under natural rust infection without fungicide.
The experiments were conducted in a randomized complete block design with three replicates. Each plot consisted of four rows of soybean plants, 5.0 m in length with spacing between rows of 0.5 m, totaling 10.0 m 2 . The useful area was the two central lines of each plot, being eliminated 0.50 m from each end, referring to the border, totaling 4.0 m 2 .
The soil was prepared conventionally, with a plowing and two harrowing. Before sowing, the area was furrowed and fertilized with the formulation 02-28-18 at the dose of 400 kg ha -1 . The seeds were treated with the fungicide composed of Carbendazim and Tiram and then inoculated with Bradyrhizobium japonicum.
The sowing occurred on 12/12/2013, 11/29/2014, 02/12/2015 and 11/5/2016, in a depth of 3 to 5 cm. Soon after sowing, the herbicides of active principles S-Metolachlor and Haloxyfop-P-Methyl were applied. The thinning was performed maintaining 15 seeds per linear meter. Manual weeding was performed during the cycle to maintain the culture clean.
Thirty days after emerging, foliar fertilizer composed of Cobalt and Molybdenum at a dose of 100 mL ha -1 was applied and pest control was performed with Acefate at the dose of 0.4 kg ha -1 and insecticide composed of Tiametoxam and Lambda-Cyhalothrin at a dose of 200 mL ha -1 .
Grain yield was determined by harvesting the useful area of each plot followed by grain weighing. We proceeded with the analysis of joint variance with 14 genotypes in 4 environments, in which the effects of genotypes and environment were considered fixed. The statistical analyzes were performed in the Genes Program (CRUZ, 2016).
A study of the G x E interaction was carried out from the decomposition in a complex part between environment pairs, as described by Cruz and Castoldi (1991). Thus, the complex part was obtained by the expression: where: Q1 and Q2: correspond to the average squares of genotypes in environments 1 and 2 respectively; r: correlation between the means of the genotypes in the two environments.
The experimental precision was evaluated by the coefficient of variation (CV %) and then the genotype determination coefficient was determined (H 2 ). Once the significant G x E interaction was detected, adaptability and productive stability were analyzed by the methods of Eberhart and Russel (1966)

RESULTS AND DISCUSSION
The analysis of variance was performed as it was found homogeneity of the variances from the ratio between the largest and the smallest mean square, 4.81 (Table 1), a value lower than seven which is the limit (RAMALHO et al., 2012 ). The coefficient of variation (CV %) was estimated at 21.26% (Table 1), which is acceptable since productivity is quantitative and highly influenced by the environment (LEITE et al., 2015).
Significance was verified by the F test (P <0.01), for the effects of genotypes, environments and G x E interaction ( Table 1). The interaction G x E reflects on significant changes in the behavior of the genotypes when submitted to environmental differences and are frequently reported in different autogamous cultures (RAMALHO et al., 2012) as soybean, and it appears due to the different responses of the same set in different environments (COCKERHAM, 1963).
The heritability (H 2 ) is a genetic parameter of great importance for the breeding, however, in advanced generations, in which the genotypes present high homozygosity, it is called the genotypic determination coefficient (VASCONCELOS et al., 2012;YOKOMIZO;VELLO, 2000).
The parameter H 2 provides information of the proportion of phenotypic variability that is attributed to genetic causes (RAMALHO et al., 2012), thereby measuring the reliability of phenotypic value as an indicator of genotypic value. The estimate of H 2 for the productivity trait was 85.97% (Table 1), being of high magnitude (CRUZ; CARNEIRO; REGAZZI, 2014) and indicating that the genetic variation was superior to environmental. Table 1. Summary of the joint variance analysis for grain yield (kg ha -1 ) evaluated in 14 soybean genotypes grown in 4 seasons, in Uberlândia-MG.
The nature of the G x E interaction was estimated by the method of Cruz and Castoldi (1991), in which it was possible to identify complex type interaction in all pairs of environments. The interaction of the complex type denotes an inconsistency in the superiority of the genotype with the environmental variation, which hinders the process of improvement in the indication of the materials (BORÉM; MIRANDA, 2013), in addition, the interaction between the two species is associated with a lack of genetic correlation between the genotypes.
Through the environmental index of Finlay and Wilkinson (1963), it was possible to identify favorable environments (2013/14 and 2015/16) and unfavorable ones (2014/15 and 2016/17). Favorable environments are those where the influence of abiotic and biotic factors was not able to drastically reduce productivity when compared to unfavorable environments.
In Table 2 it was possible to observe that in relation to the 2014/15 crop, the averages ranged from 1126.42 kg ha -1 for UFUS Riqueza, to 2088.943 kg ha -1 for UFUS 1117-08. Among the most productive genotypes, the UFUS 7415 cultivar was also identified, coinciding with the previous harvest.
Due to the complex classification of G x E interaction, the identification of superior genotypes is difficult, and for this reason, the analysis of adaptability and phenotypic stability are justified in order to attenuate the effects of the interaction on the recommendation of cultivars (CRUZ; CARNEIRO; REGAZZI, 2014). The Eberhart and Russel (1966) methodology, which is one of the most used methods to study the adaptability and stability in soybean, is based on a linear regression obtained between the productivity variable and the environmental index. A suitable interpretation is obtained when the regression coefficient (R 2 ) is greater than 70% (EBERHART; RUSSEL 1966;CAVALCANTE et al., 2014).
In the interpretation of the results two statistical hypotheses are elaborated: H 0 : e H 1 : , which informs about the adaptability, where refers to genotypes with wide adaptability, and adaptability to favorable and unfavorable environments, respectively. The second hypothesis refers to stability: H 0 : = 0 (high stability) and H 1 : 0 (low stability). For Eberhart and Russel (1966) the ideal genotype is the one with high productivity, R 2 equal to unity, and non-significant. For this aspect, the ideal genotypes were TMG 801, UFUS 1117-01, UFUS 1117-07 and UFUS 1117-08 (Table  3), as they presented above-average productivity, 2284.13 kg ha -1 (Table 4), were able to respond satisfactorily to the improvement of the environment and presented high productive capacity in favorable and unfavorable environments (CARVALHO et al., 2013).
In spite of the cultivar, UFUS Riqueza and the line UFUS 1117-02 were characterized as broad adaptation and high stability, they did not present high yields (Table 3). This information corroborates that obtained by Marques et al. (2010), who also identified the cultivar UFUS Riqueza, by the same method, as being of wide adaptation and high stability. However, the genotypes UFUS 7415, UFUS 1117-5, UFUS 1117-06 and UFUS 1117-11 were identified as having broad adaptation but low stability, while UFUS 1117-09 genotypes were 1291 Adaptability and productive… SILVA, N. S. et al. adapted to unfavorable environments and high stability (Table 3). Table 3. Soybean grain yield and parameters of adaptability and stability by the methods of Eberhart and Russel (1966) and Wricke (1965), in 14 soybean genotypes grown in 4 seasons, in Uberlândia-MG.  Eberhart and Russel (1966); ns: not significant, * and ** significant at 5% and 1% respectively by the F test; + and ++ significant at 5% and 1% respectively by the T-test.
The UFUS 1117-10 line was identified as being adaptable to favorable environmental conditions and high stability (Table 3). In studies with 29 soybean genotypes in the state of Mato Grosso, three lines of adaptation to favorable environments were identified, however, only one had high stability (BARROS et al., 2010).
Still, in Table 3, the methodology of Wricke (1965), based on the analysis of variance, uses the parameter of ecovalence to infer about the stability characteristics. Therefore, the genotype more stable is that with lowest value, indicating a lower contribution to the G x E interaction, in this way they were: UFUS 1117-01, TMG 801, UFUS 1117-02, UFUS Riqueza and UFUS 1117-07, being UFUS 1117-01 the most stable genotype, since its parameter was less than unity. Of the genotypes analyzed, 57% had high values, being the genotype UFUS 1117-09 the largest contribution, with a value of = 14, 53% followed by UFUS 7415, with = 12.26%. The Wricke methodology should be associated with Lin and Binns in order to increase safety in the recommendation of cultivars with high grain yield and that are stable (FRANCESHCI et al., 2010).
The Lin and Binns (1988) modified by Carneiro (1998) analysis provide information about the adaptability and stability of the genotype by the Pi parameter. The general recommendation is based on the original Pi of Lin and Binns, so, according to Table 4, the three genotypes that presented lower values of Pi, and therefore greater stability were: BRSGO 7560, TMG 801, UFUS 1117-07.
The modification by Carneiro (1998) better stratified the genotypes for favorable and unfavorable conditions. Oliveira et al. (2006) recommend the use of the method of Lin and Binns modified by Carneiro. The UFUS 1117-05 line was adapted to favorable conditions, while UFUS 1117-09 for unfavorable conditions (Table 4), which was also identified by the Eberhart and Russel methodology (Table 3) as being adaptable to unfavorable conditions. The genotypes UFUS 1117-09 and UFUS 1117-02 presented the highest favorable Pi. Silva and Duarte (2006), working with soybean, stated that the method of Lin and Binns modified by Carneiro should be used in combination with that of Eberhart and Russel. However, other authors believe that the method of Lin and Bins modified by Carneiro discriminates cultivars better than Wricke and Eberhart and Russel (FRANCESHCI et al., 2010). , analyzing methodologies of adaptability and stability, based on regression analysis, analysis of variance and non-parametric analysis, concluded that the best methodologies were those based on Lin and Binns modified by Carneiro and Annicchiarico (1992) that encompass a single adaptation and stability, facilitating the interpretation of the results. Table 4. Soybean grain yield and parameters of adaptability and stability by Lin and Binns (1988) modified by Carneiro (1998)  The evaluation of the G x E interaction, through the analysis of additive main effects and multiplicative interactions (AMMI), has been successfully applied to several crops (MELO et al., 2007;MARJANOVIĆ JÉROMELA et al. 2011). It has the advantage of discarding the portion of the interaction noise, which is neither attributed to the genotype not to the environment, which improves the predictive capacity of the model, bringing direct benefits to the selection of genotypes (ZOBEL et al., 1988).
By the AMMI method, the sum of squares of the interaction was decomposed into three main component axes, and it was observed that the first two main components in the AMMI analysis explained 84.96% of the G x E interaction, a value above the limit of 70%, which is suggested to have a good fit of the model and greater accuracy in the predictions (RAMALHO et al., 2012).
For the interpretation of stability by the AMMI 2 (Figure 1), the distance from the representative points of the genotypes and the environment to the zero score of the two main components should be observed (DUARTE; VENCOVSKY, 1999). Thus, the genotypes UFUS 1117-01, UFUS 7415 and UFUS 1117-05 presented greater stability, whereas BRSGO 7560, UFUS 1117-04, UFUS 1117-08 and UFUS 1117-05 smaller, that is, they contributed the most for the G x E interaction (Figure 1) Gonçalves, Mauro and Cargnelutti Filho (2007), studying 29 soybean genotypes for adaptability and stability for grain yield at different sowing times, concluded that the most unstable genotypes were the most productive, however, one of the main objectives of breeding is to select productive genotypes associated with high stability. In this context, all genotypes identified as stable had above-average productivity.
The analysis of adaptability and stability by the Centroid method is distinguished by considering genotypes of maximum specific adaptation as those genotypes with maximum values for certain groups of environments (favorable or unfavorable) and minimum for another group, and not one that shows good performance in the groups of favorable or unfavorable environments (ROCHA et al., 2005).
Predicting the graphical dispersion analysis of the genotypes, the eigenvalues were obtained through the methodology of the main components, in which the first two main components explained 88.13% of the total variation. As two eigenvalues seemed to be sufficient, the evaluation of the position of the genotypes can be done through two-dimensional graphs (CARVALHO et al., 2002). In Figure 3 it was possible to observe the plot of the genotypes according to the Centroid, which allowed verifying the behavior of the genotypes in relation to the ideologies recommended by the method.
The arrow format that assumes the link between the points representing the ideotypes allows a quantitative interpretation of the adaptability of the genotypes. As the genotypes move away from the tail to the arrowhead, productivity increases gradually (HAMAWAKI, 2014). A similar interpretation can be made, those genotypes positioned above the axis of the arrow are more apt to favorable environments and those below are apt to unfavorable environments. The distribution of the genotypes is heterogeneous, due mainly to the study character, grain yield, and allows associating the genotypes with most of the ideotypes (HAMAWAKI, 2014). Therefore, in interpreting Figure 2, the genotypes BRSGO 7560, TMG 801, UFUS 7415, UFUS 1117-01, UFUS 1117-08 and UFUS 1117-07 were the most productive, and 57% of the genotypes were located above the central axis of the arrow, characterizing adaptation to favorable environments. In Table 5, there are the classifications of the genotypes in relation to the Centroid method. The genotypes TMG 801, BRSGO 7560, UFUS 7415 and UFUS 1117-07 were classified as high general adaptability (Table 5), which means less contributed to G x E interaction, and express the concept of stability proposed by Cruz, Regazzi and Carneiro (2004), therefore, they are considered more stable (VASCONCELOS et al., 2011).

CONCLUSIONS
The UFUS 1117-01 lineage was identified by the methodologies of Eberhart and Russel, Wricke, AMMI 2 and Centroid as a genotype of high productive stability.
The UFUS 1117-07 strain showed high stability by the methods Eberhart and Russel, Wricke, Lin and Binns modified by Carneiro and wide adaptability by Eberhart and Russel and Centroid.
As for the UFUS 1117-09 lineage, it was identified as adaptive to unfavorable environments by the methods of Lin and Binns modified by Carneiro and Centroid.
The UFUS 1117-10 genotype presented favorable environmental adaptability by Centroid method and its characterization was complemented by Eberhart and Russel, which identified the genotype as having high stability.
The methods Eberhart and Russel and Centroid have reaffirmed among themselves the information contemplated in their analyzes, showing that they can be used to increase certainty regarding the classification of soybean genotypes.