Yield adaptability and stability of semi-erect cowpea genotypes in the Northeast region of Brazil by REML/BLUP 1 Adaptabilidade

- Cowpea is grown in the various soil and climatic conditions of the Northeast region of Brazil. Thus, selecting and developing cultivars with high yield, stability, and adaptability for this region is necessary due to the genotype × environment interaction. The objective of this work was to select cowpea lines of semi-erect plant simultaneously for high yield, adaptability, and genotypic stability in the Northeast region of Brazil by the REML/BLUP procedure. Twenty semi-erect genotypes— 15 lines and five cultivars—were evaluated in 37 environments of the Northeast region from 2013-2015. The experiments were carried out under rainfed conditions in a randomized complete block design with four replications. The adaptability and genotypic stability were evaluated by the REML/BLUP procedure. The environmental variance was the largest factor in the phenotypic variance and the genotype × environment interaction was complex-type, with a grain yield ranging from 277 kg ha -1 (Serra Talhada PE, 2015) to 2,845 kg ha -1 (São Raimundo das Mangabeiras MA, 2013), and an overall mean of 1,342 kg ha -1 . According to the Harmonic Mean of Relative Performance of Genetic Values (HMRPGV) estimates, the lines MNC04-795F-153 and MNC04-795F-159 were those that simultaneously had high yield, adaptability, and genotypic stability, and can be recommended and grown with greater probability of success in the evaluated environments in the Northeast region of Brazil.


INTRODUCTION
Cowpea (Vigna unguiculata (L.) Walp.) is an important legume in the Northeast region of Brazil, and a source of energy and protein.The cultivation of this species generates employment and income for the population of this region.Cowpea is the second most consumed type of bean in Brazil, and its cultivation is concentrated in the North, Northeast, and Center-West regions.There are no official statistics on cowpea production in Brazil; thus, based on the estimates of CONAB (2017), the Northeast region presented in 2016 an area of 1,029,600 ha with a production of 196,100 Mg.This represents 82.56% and 54.00% of the area and production of this legume in Brazil, respectively.The largest national producers are the states of Mato Grosso, Ceará, and Maranhão.The total area for cowpea production in Brazil is 1,247,100 ha and its production is 362,500 Mg, which represents 14.43% of all beans produced in Brazil.
Considering that cowpea is cultivated in a wide range of environments in Brazil, but the occurrence of genotype × environment interaction (G×E) may hinder the selection of superior genotypes and the recommendation of cultivars (CARVALHO et al., 2016;OLIVEIRA;FONTES;ROCHA, 2015;ROCHA et al., 2012).Thus, in the final stages of a breeding program, elite lines are tested in various environments; this allows an investigation of the magnitude of the G×E, adaptability, and yield stability, which subsidize the recommendation of cultivars for broad or specific conditions of adaptation.
The REML/BLUP procedure has been one of the most used techniques in studies on adaptability and genotypic stability; it is based on mixed models.This procedure estimates the components of variance by the Restricted Maximum Likelihood (REML) and the prediction of genetic values by the Best Linear Unbiased Prediction (BLUP) (CARIAS et al., 2014).It was originally recommended for studies on quantitative genetics and selection of perennial plants (RESENDE, 2007a,b); however, it has also been used in annual species such as rice (BORGES et al., 2010), common bean (CHIORATO et al., 2008;PEREIRA et al., 2016), soybean (TESSELE et al., 2016), andwheat (SILVA et al., 2011).
Adaptability and stability studies in cowpea using the REML/BLUP procedure have increased (SANTOS et al., 2016;TORRES et al., 2015TORRES et al., , 2016)).This is because it allows simultaneous selection for yield, adaptability, and stability in the context of mixed models through the use of the Harmonic Mean of Relative Performance of Genetic Values (HMRPGV) method, proposed by Resende (2004).
The objective of this work was to select semi-erect cowpea lines simultaneously for high yield, adaptability, and genotypic stability in the Northeast region of Brazil by the REML/BLUP procedure.

MATERIAL AND METHODS
Twenty cowpea genotypes of semi-erect plant were evaluated-15 lines and five cultivars-from the Embrapa Meio-Norte Cowpea Breeding Program (Table 1).These lines are part of the value-of-cultivation and use (VCU) trials, which are required for registering new cultivars by the National Register of Cultivars (RNC) of the Ministry of Agriculture, Livestock, and Food Supply (MAPA).These genotypes were selected in intermediate trials, which precede the VCU trials.
The planting season varied according to the rainy season in the states, which occurred in January to March, except in Alagoas and Sergipe, which occurred in June.All the trials were conducted in a complete randomized block design with 20 treatments and four replications.The treatments were represented by a plot of 2.0 m x 5.0 m with four 5.0 m rows spaced 0.50 m apart, with 0.25 m between plants.The evaluation area was represented by the two central rows.Four seeds were sown per hole, and 20 days after sowing the plants were thinned, leaving two plants per hole.Cultural practices were carried out for the crop as recommended.
Individual analysis of variance for environments and joint analysis of variance for all environments were performed.The joint analysis of variance considered the effect of genotypes as fixed, and the effect of environments as random.The statistical model used followed the equation: where in: Y ijk is the observed value of the genotype i in the environment j and block k; µ is the overall mean of the trait; g i is the effect of the genotype i; e j is the effect of the environment j; ge ij is the effect of the interaction of the genotype i with the environment j; β k(J) is the effect of the block k within the environment j; and ε ijk is the experimental error associated with the plot ijk.
The mixed models approach through Restricted Maximum Likelihood (REML) and Best Linear Unbiased Prediction (BLUP) multivariate, i.e., REML/BLUP procedure, (RESENDE, 2007b) was used for the analysis of adaptability and stability.This procedure is a method for ordering the genotype simultaneously regarding their genetic values (yield) and stability; it represents the BLUP procedure under the harmonic mean of the data.The lower the standard deviation of the genotypic behavior in the environments, the greater the harmonic mean of genotypic values (HMGV) in the environments.Thus, selection by the highest HMGV implies both selection for yield and stability (RESENDE, 2007b).
In the context of the mixed models, a simple and efficient measure is the relative performance of genotypic values (RPGV) in the environments, i.e., the adaptability of genetic values.The quantity RPGV*OM refers to the relative performance genotypic value multiplied by the overall mean of all environments, providing the average genotypic value, capitalizing the adaptability (RESENDE, 2007b).
Simultaneous selection for yield adaptability and stability in the context of mixed models can be performed by the Harmonic Mean of Relative Performance of Genetic Values (HMRPGV), proposed by Resende (2004).The quantity HMRPGV*OM refers to the HMRPGV multiplied by the overall mean of all environments, which M. M. Rocha et al.
provides the mean genotypic value penalized by instability and capitalized by adaptability.
The following statistical model was used for the randomized block designs with one observation per plot and several environments: where in: y, b, g, ga, and e are the data vectors of fixed effects (mean of blocks through environments), of genotypic effects of the genotype (random), of effects of the genotype × environment interaction (G×E) (random), and of random errors, respectively; X, Z and W are the incidence matrices for b, g, and ga, respectively.
The Harmonic Mean of Genotypic Values (HMGV) was used for the evaluation of stability; the RPGV was used for the simultaneous evaluation of yield and adaptability; and the HMRPGV was used for the simultaneous evaluation of yield, adaptability, and stability.These evaluation were carried out using the following expressions: (3) (4) (5) where in: n is the number of evaluation environments of the genotype i; Vg ij is the genotypic value of the genotype i in the environment j, expressed as a proportion of the average of this environment.
The HMRPGV method (RESENDE, 2007a)   The analysis of variance was performed using the SAS software (SAS INSTITUTE, 2002).The analyses of adaptability and genotypic stability were performed by the model 54 of the Selegen-Reml/Blup software (RESENDE, 2007b).

RESULTS AND DISCUSSION
The joint analysis of variance for grain yield is presented in Table 3.Although all genotypes have shown a high inbreeding level and some parentage (Table 1) and underwent several selection cycles, they differed significantly (p<0.0001),denoting the existence of selectable variability.Barros et al. (2013), Santos et al. (2015) and Barroso et al. (2016), evaluated 20 cowpea genotypes for yield adaptability and stability in the Mid-North region and in Mato Grosso do Sul, Brazil, respectively, and also found differences between homozygous genotypes.
The environments also differed for grain yield (p<0.0001), denoting that their eco-physiographic differences (Table 2) combined with the climatic variations affected this trait.Barroso et al. (2016) evaluated the grain yield of 20 cowpea genotypes in six environments of Mato Grosso do Sul and also found differences between the testing environments; affirming that the edaphoclimatic factors had the greatest effect on the adaptability and stability of the genotypes.Ddamulira et al. (2015), Table 3 -Joint analysis of variance for grain yield of 20 semi-erect cowpea genotypes evaluated in 37 environments of the Northeast region of Brazil, from 2013 to 2015 who evaluated the yield adaptability and stability of 25 cowpea genotypes in three environments in Uganda, and Oliveira, Fontes and Rocha (2015), who evaluated cowpea genotypes in several environments in the state of Amazonas in Brazil, also found different grain yields depending on the environment.
The overall mean grain yield was 1,342 kg ha -1 .This mean is well above the national (369 kg ha -1 ) and world (461.30kg ha -1 ) mean for yield of cowpea (FREIRE FILHO, 2011) and is also above the means obtained in other studies on cowpea genotypes in Brazil (BARROS et al., 2013;BARROSO et al., 2016;SANTOS et al., 2015;TORRES et al., 2015TORRES et al., , 2016)).This shows the great potential of this line group in regard to grain yield and the possibility of selecting lines with higher means than the commercial cultivars.
The G×E for grain yield was highly significant (p<0.0001)(Table 3); it showed the different behavior of the genotypes depending on the testing environments.This lead to difficulties in the selection of superior genotypes and recommending cultivars (CARVALHO et al., 2016;ROCHA et al., 2012), since the cultivars adapted to a particular condition may not perform well in other environmental conditions (OLAYIWOLA, SOREMI;OKELEYE, 2015;TEODORO et al., 2015).
According to estimates of components of variance (REML), the environmental variance contributed most to the phenotypic variance (Table 4).It represented 64% of this variance, followed by the G×E (30%), and genotypic (6%) variances.analysis of variance (Table 3), the information of the test environments (Table 2), and the environment means (Figure 1), which showed marked contrasts between testing environments for grain yield.
Studies evaluating genotypes of common bean (CHIORATO et al., 2008;PEREIRA et al., 2016) and cowpea (TORRES et al., 2015;OLIVEIRA;FONTES;ROCHA, 2015) in multi-environments also found a higher proportion of environmental variance than genotypic and environmental variances for grain yield.
The low genotype variance found in the group of genotypes evaluated (Table 4) was expected considering that some lines showed relation to each other (Table Table 4 -Estimates of components of variance (individual REML) and genetic parameters obtained from the evaluation of 20 semierect cowpea genotypes in 37 environments in the Northeast region of Brazil, from 2013 to 2015 1) and all are highly inbred, i.e., they have already undergone several selection cycles for high grain yield.Torres et al. (2015Torres et al. ( , 2016) ) evaluated the grain yield of 20 cowpea genotypes in multi-environments of Mato Grosso do Sul and also found lower estimates for the genotypic variance than environmental and G×E variances.
The trait yield is controlled by several genes and, therefore, is heavily affected by the environment.In spite of the great effect of the environmental factors, denoted by the relative coefficient of variation (0.32), the heritability at an average genotypic level among the various environments was high (0.84) since the environmental Parameter Estimate Genotypic variance (σ 2 g ) 7162.05 Residual variance (σ 2 a ) 70027.28 Genotype × environment interaction variance (σ 2 ga ) 32780.83 Phenotypic variance (σ 2 f ) 109970.17Heritability genotype mean (h 2 a ) 0.84 Genotype selection Accuracy (Acgen) 0.92 Genotypic correlation between environments (rgloc) 0.18 Relative coefficient of variation (Cvg%/Cve%) 0.32 Yield adaptability and stability of semi-erect cowpea genotypes in the Northeast region of Brazil by REML/BLUP effects were minimized.This allowed a high accuracy (0.92) in the selection of lines based on the average of the environments (Table 4).The heritability obtained in the present study was higher than those estimated by Torres et al. (2015Torres et al. ( , 2016)), who evaluated the grain yield of 20 cowpea genotypes in multi-environment of Mato Grosso do Sul and found estimates of 0.68 and 0.54.
According to Chiorato et al. (2008), heritability at average level is determined based on the number of replicates and evaluated plants.In the case of the present study, the size of the evaluation area in the experimental unit may have contributed positively to minimize the environmental effects, since the genotypes were represented by 80 plants in the evaluation area of the plot.
The G×E variance was the second most important (30%) (Table 4), which resulted from the low genotypic correlation between environments (0.18).These results showed the existence of G×E of complex-type, and that the best lines in one environment will not necessarily be the best in others (RESENDE, 2007a).This represents a certain difficulty in the selection of genotypes with wider adaptation, which justifies considering in the selection of the lines, their stabilities and adaptabilities.Barros et al. (2013) evaluated the grain yield of 20 cowpea genotypes in the Mid-North region of Brazil and also found the G×E as the second factor affecting the phenotypic variance.On the other hand, Torres et al. (2016) observed similar percentages for the G×E and environmental variances.
According to the mean component estimates (BLUP) and the confidence intervals associated with genotypic values (u+g), the lines G31 (MNC04-795F-153), G34 (MNC04-795F-159), and G26 (MNC04-769F-62) were superior than most of the genotypes evaluated and presented the highest genetic gains compared to the overall mean, with 12.45%; 11.22%; and 9.51%, respectively (Table 5).These gains were lower than those Table 5 -Estimates of mean components (individual BLUP) of the effects (g) predicted genotypic values (u+g) free from interaction with environments, confidence interval lower limit (CILL), confidence interval higher limit (CIHL) and genetic gain (Gg) of 20 semierect cowpea genotypes evaluated in 37 environments of the Northeast region of Brazil, from 2013 to 2015 observed by Torres et al. (2016), who evaluated the grain yield of 20 cowpea genotypes in four environments of Mato Grosso do Sul and found gain estimates for the two best genotypes of 18.79% and 18.04%.
The genetic gain depends on the differential of the selection and heritability of the trait.Although the heritability of grain yield was high, a factor that may have led to lower gains than those observed by Torres et al. (2015Torres et al. ( , 2016) ) was the differences between the overall mean and the means of the superior genotypes, which in the present study were small, relatively to the selection differentials founded by the authors above.
The results of stability (HMGV), adaptability (RPGV), and simultaneous stability and adaptability (HMRPGV) of the genotypes evaluated are presented in Table 6.The five best genotypes, based on the criteria HMGV, RPGV, and HMRPGV were not necessarily the best based on the criterion of the mean genotypic value (Table 5).The coincidence was 80% among the five best genotypes and there was an inversion of order among the coincident ones between HMGV and RPGV.According to Resende (2007a), the use of these attributes or selection criteria can provide further refinement in selection.
Similar results were obtained by Torres et al. (2016), who evaluated the yield of 20 cowpea genotypes in the state of Mato Grosso do Sul, and also observed the same percentage of coincidence between the ordering provided by HMGV and RPGV.

Figure 1 -
Figure 1 -Behavior of the grain yield of 37 testing environments obtained from evaluation of 20 semi-erect cowpea genotypes in the Northeast region of Brazil from 2013 to 2015

Table 1 -
Semi-erect cowpea genotypes evaluated in the Northeast region of Brazil, from 2013 to 2015, their genealogy and commercial subclass (CS)

Table 2 -
Altitude, geographic coordinate, biome, ecosystem, and climate of the locations where the value-of-cultivation and use trials of semi-erect cowpea were conducted in the Northeast region of Brazil, from 2013 to 2015 Tropical dry of heterogeneity of variances; and providing alreadypenalized genetic values of instability.Moreover, this method can be applied to any number of environments, eliminate noises of the genotype × environment interaction (G×E), while considering the heritability of these effects; and allows the computation of genetic gain with selection by the three attributes simultaneously.
TSu = Tropical sub-humid; TQSu = Tropical hot sub-humid; BSh = Semi-arid mild; TAs = Tropical with dry summer season; Taw = Tropical with dry winter season; Ts = The preponderance of the environmental variance in relation to the other components of the phenotypic variance are in agreement with the results found in the M. M. Rocha et al.

1
Confidence interval associated to the genotypic value estimates, at 95% probability M. M. Rocha et al.

Table 6 -
Genetic value stability (HMGV), genetic values adaptability (RPGV), simultaneous genetic value adaptability and stability (HMRPGV), genotypic value capitalizing the adaptability (RPGV*OM) and genotypic value penalized by instability and capitalized by adaptability (HMRPGV*OM) of 20 semi-erect cowpea genotypes evaluated in 37 environments of Northeast region of Brazil, from 2013 to 2015 , these values are obtained through a process that already penalizes the lines for the instability in the environments and capitalizes the capacity of response (adaptability) to