Adaptability and yield stability of cowpea elite lines of semi-prostrate growth habit in the cerrado biome 1

- The effects of the genotype × environment interaction can be reduced by using cultivars with high adaptability and good yield stability. Studies on this subject allow identification of genotypes of predictable behavior, and responsive to environmental variations in specific and general conditions, in favorable or unfavorable environments. The objective of this work was to evaluate the adaptability and phenotypic stability of cowpea elite lines of semi-prostrate growth habit in the Cerrado biome in Brazil. Twenty cowpea genotypes of semi-prostrate growth habit were evaluated in nine VCU (value for cultivation and use) tests from 2010 to 2012. Grain yield data were subjected to analysis of variance, and stability and adaptability analyses were carried out by the methods of Eberhart and Russell (1966), Lin and Binns (1988) (modified), Wricke (1965), and Annicchiarico (1992). The method of Wricke (1965) was not very descriptive, since it indicates only the contribution of each genotype to the genotype × environment interaction. The results obtained by the methods of Lin and Binns (1988) (modified), Annicchiarico (1992) and Eberhart and Russell (1966) were more descriptive, and similar in indicating the most promising cultivar (BRS-Xiquexique) and lines (Pingo-de-Ouro-1-2, MNC02-676F-1, MNC01-649F-2-1 and MNC02-677F-2). These lines have potential for the development of new cultivars because they present adaptability and yield stability in the Cerrado biome of Brazil.


INTRODUCTION
Walp] is cultivated in the Northeast, North and Center-West regions of Brazil. However, the average productivity of cowpea crops varies greatly among different regions, mainly due to environmental variations and the use of genetic materials that are not very productive or with undesirable characteristics (FREIRE FILHO et al., 2011).
One of the main challenges in genetic improvement of species is to understand genotype × environments interaction (G×E), which is assessed by the evaluation of the genotypes in different environments (CRUZ; REGAZZI, 2014). The evaluation of G×E is very important because of the possibilities of genotypes behave differently in different environments due to G×E (RESENDE;DUARTE, 2007). This behavior affects the selection gain and makes it difficult to recommend cultivars with wide adaptability.
Studies on adaptability and stability of plant species provide tools to identify genotypes that present high productivity in different environmental conditions (FIGUEIREDO et al., 2015, PEREIRA et al., 2012. The adaptability and stability of cowpea genotypes have been the goal of several studies (BARROS et al., 2013;NUNES et al., 2014;ROCHA et al., 2007;SANTOS et al., 2016;VALADARES et al., 2010). These studies have subsidized the improvement and release of cultivars in several states of the North, Northeast and Center-West regions of Brazil (FREIRE FILHO et al., 2011).
There are several methods to evaluate the G×E and to determine the adaptability and yield stability of the cultivars. According to the Eberhart and Russell (1966) method, based on simple linear regression, an ideal cultivar presents overall adaptability and stability while maintaining a good performance when the environmental conditions are unfavorable. However, when the data do not fulfill the assumptions of the regression analysis, an alternative would be the use of non-parametric analyzes such as the method of Lin and Binns (1988) (modified) described by Cruz, Carneiro and Regazzi (2014). This method allows the identification of the most stable genotypes by a single parameter of stability and adaptability, and includes the deviations in relation to the maximum yield obtained in each environment; making it possible to detail this information for favorable and unfavorable environments. Other examples are the method of Annicchiarico (1992), which presents an easy application and is based on the estimation of a risk index for the recommendation of a given cultivar; and the method of Wricke (1965), called ecovalence, which is estimated by the distribution of the sum of squares of the G×E into parts due to single genotypes. This method has an easy interpretation; however, the data need to be balanced to meet the assumptions of a regression analysis (CARVALHO et al., 2016).
Choosing the method to characterize genotypes regarding adaptability and stability depends on the available experimental data, the required precision, and the type of information desired by the breeder (CRUZ; REGAZZI, 2014). Each one of these methods has peculiarities that can contribute to improve the analysis; and in some cases, these methods may be complementary to each other, therefore, it is important to use more than one method (PEREIRA et al., 2009). In this context, the objective of this study was to evaluate the adaptability and phenotypic stability of cowpea elite lines of semi-prostrate growth habit in the Cerrado biome in Brazil.

MATERIAL AND METHODS
Twenty cowpea genotypes of semi-prostrate growth habit from VCU (value for cultivation and use) tests were evaluated, where fifteen lines were from the Embrapa Mid-North Cowpea Breeding Program and five were commercial cultivars (Table 1) Table 2).
All experiments were conducted in a complete randomized block experimental design with four replications. The randomization was performed individually for each environment. The plots of the experiments consisted of four 5.0-meter rows spaced 0.80 m apart, with 0.25 m between plants, and the evaluation area consisted of the two central rows. Weed, pest and disease control was carried out according to the recommendations for cowpea LIMA;RIBEIRO, 2005).
The statistical analysis was carried out assuming that each combination of years with locations represents an environment, making nine environments. The yield data were subjected to analysis of variance, considering the mixed model with effect of treatments as fixed and the others as random. A joint analysis of the environments was performed after evaluating the homogeneity of the residual variances. According to Pimentel-Gomes (2000), if the ratio between the largest and the smallest mean square of the residue is less than seven, the residual variances are homogeneous. However, due to the lack of homogeneity of variance, the degrees of freedom of   Cochran (1954). The Scott-Knott test at 5% probability was used to identify the existence of homogeneous groups, by minimizing the variation within, and maximizing between groups.
In the method of Eberhart and Russell (1966), the adaptability was given by the estimation of the parameter β 1i and by the average yield β 0i ; and the stability by the variance of the regression deviations δ ĳ , according to the following model Y ĳ = β 0i + β 1i I j + δ ĳ + Ʃ ĳ , where: Y ĳ is the average grain yield (kg ha -1 ) of genotype i in environment j; β 0i is the overall mean; β 1 i is the linear regression coefficient; I j is the environmental index; δ ĳ is the variance of the regression deviations; and Ʃ ĳ is the mean experimental error.
According to the method of Lin and Binns (1988) (modified) described by Cruz, Carneiro and Regazzi (2014), the decomposition of P i in the parts related to favorable and unfavorable environments was performed. The estimate of P i was given by the M. B. Sousa et al.

equation:
, where: P i is the estimation of the adaptability and stability of the genotype i; Y ĳ is the yield of the genotype i in the environment j; M j is the maximum observed response among all genotypes in the j environment; and α is the number of environments.
In the Annicchiarico method (1992), the confidence index I i was calculated for the favorable and unfavorable environments according to the equation: wherein Ȳ i is the overall mean of genotype i in percentage; Z is the percentile (1-α) of the cumulative normal distribution function; α is the level of significance; and S i is the standard deviation of the percentage values. The coefficient of confidence was 75%, i.e., α = 0.25.
The stability parameter proposed by Wricke (1965) was estimated using the statistic ω i , through the equation: where: Y ij is the mean of the genotype i in the environment j; Ȳ i. is the mean of genotype i; Ȳ. i is the mean of the environment j; and Ȳ .. is the overall mean.
The individual and joint analysis of variance, and tests of comparison of means, stability and adaptability were performed using the software GENES (CRUZ, 2013).

RESULTS AND DISCUSSION
The genotypes presented significant differences (p<0.05) by the analysis of individual variances, in all Table 3 (Table 3). This result denotes genetic variability among the genotypes evaluated, which is essential to proceed with the genotype selection process.
The coefficient of variation (CV) of the experiments evaluated ranged from 13.85 to 36.10% (Table 3). The means and CV of the tests varied, denoting the different conditions to which the genotypes were subjected. The coefficient of variation (CV) is an estimate of the experimental error of the overall mean of the test, and an indication of the experimental accuracy. According to Pimentel-Gomes (2000), observed CV can be classified as low (lower than 10%), average (10% to 20%), high (20% to 30%), and very high (higher than 30%). The CV values found in this work were within the range found in other studies on cowpea, such as Barros et al. (2013), Benvindo et al. (2010), Bertini, Teófilo and Dias (2009), and Silva and Neves (2011).
The joint analysis of variance showed significant differences (p<0.01) for the sources of variation of environments, genotypes, and G×E (Table 4). The significant effect of the G×E indicates the different response of the genotypes to the environments, thus requiring analyzes of adaptability and phenotypic stability.
The grain yield of the genotypes presented homogeneous groups by the Scott-Knott test (p<0.05) (  Overall Mean 1226.60 28718716 100 ** = significant at 1% probability; * = significant at 5% probability; and ns = not significant by the t test; 1/ Means followed by the same letter belong to the same class (p ≤ 0.05); 2/ H 0 : β 1i = 1; 3/ H 0 : σ 2 di = 0 Table 5 -Estimates of adaptability and phenotypic stability by the methods of Eberhart and Russel (1966) and Wricke (1965) for 20  Regarding the average grain yield, the line MNC02-701F-2 (1451.20 kg ha -1 ) and the cultivar BRS-Xiquexique (1439.60 kg ha -1 )-both from the branco commercial subclass-stood out from the others, presenting promising yields, with good adaptation to the edaphoclimatic conditions of the cerrado biome in Maranhão. However, the overall average yield found in this study (1226.60 kg ha -1 ) is lower than the averages found by Teixeira et al. (2010) (1307.00 kg ha -1 ) and Silva and Neves (2011) (1436.35 kg ha -1 ) in cowpea crops also in the Cerrado biome.
In the evaluation using the method of Wricke (1965), the most stable genotypes, those that contributed least to the interaction, were MNC01-649F-2-1, MNC02-689F-2-8, MNC02-676F-1 and Pingo-de-Ouro-1-2 and BR17-Gurguéia (Table 5). However, the results were not very descriptive in detecting stable and adapted genotypes. The limitation of this methodology is that it indicates only the contribution of each genotype to the G×E; thus, it cannot show the performance of the genotypes, requiring complementation by other methodologies of adaptability analysis.
According to the methodology of Lin and Binns (1988) (modified) (CRUZ; CARNEIRO; REGAZZI, 2014), which classifies genotypes for adaptability and phenotypic stability in favorable and unfavorable environments, the most stable genotype is the one that shows the smallest deviation in maximum yield in each environment, i.e., the smallest P i . Therefore, the lines MNC04-677F-5, MNC02-701F-2 and MNC02-676F-1, and the cultivar BRS-Xiquexique, in addition to presenting the lowest overall P i , also presented the first positions for the parameters P i , favorable and unfavorable ( Table 6).
The cultivar BRS-Xiquexique was the most stable, the second most responsive to the favorable environments, and the most adapted to unfavorable environments. The line MNC02-701F-2 was the most responsive to the favorable environments. The most stable and adapted genotypes are the most productive ones.
According to Pereira et al. (2009), an advantage of the method of Lin and Binns (1988) is the immediate identification of more stable genotypes due to the use of the single parameter P i . Nunes et al. (2014) and Shiringani and Shimelis (2011) evaluated cowpea crops and found similar results regarding the parameter P i , thus confirming that the most adapted and stable genotypes always have the highest yields.
The Eberhart and Russell (1966) methodology was efficient to indicate genotypes of wide adaptability and high stability, especially the genotypes MNC02-676F-1, MNC01-649F-2-1, MNC02-677F-2 and Pingode-Ouro-1-2. This is probably the most appropriate method, since it considers the productivity, adaptability and stability of each cultivar. The genotypes MNC02-676F-1, MNC01-649F-2-1 are among the most stable genotypes, according to methodology of Wricke (1965). This result is similar to that found by Mendes de Paula et al. (2014), where the methods of Wricke (1965) and Eberhart and Russell (1966) tended to select the most stable genotypes.
On the other hand, the method based on nonparametric statistics of Lin and Binns (1988) (modified), and the method of Annicchiarico (1992) indicate the genotypes BRS-Xiquexique and MNC02-701F-2 as those that had the highest yields with high instability and responsiveness to favorable environments. This result is an advantage of this method over methods based on analysis of variance. Conversely, Pereira et al. (2009) reported that the methods of Lin and Binns (1988) (modified) and Annicchiarico (1992) are indicated to be used singly, because they are simple to use and allow the classification of favorable and unfavorable environments, and identification of the most stable and adapted genotypes among the most productive ones. According to the same author, the joint use of methods that presented high correlation is not recommended; in this case, the method of Eberhart and Russell (1966) must be used together with the method of Lin and Binns (1988) (modified) or the method of Annicchiarico (1992), since there was no correlation between these methods. Table 6 -Estimates of adaptability and phenotypic stability by the method of Lin and Binns (1988) (modified), with distribution of P i (parameter of stability and adaptability) in favorable (P if ) and unfavorable (P id ) environments; and by the method of Annicchiarico (1992) (W i -confidence index), with distribution in favorable (W if ) and unfavorable (W id ) environments, of 20 cowpea genotypes of semi-prostrate growth habit evaluated in nine experiments conducted in Balsas MA, São Raimundo das Mangabeiras MA, and Primavera do Leste MT, in the 2010, 2011 and 2012 crop seasons