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

- Cowpea is grown in different environmental 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-prostrate plant simultaneously for high yield, adaptability, and genotypic stability in the Northeast region of Brazil by the REML/BLUP procedure. Twenty semi-prostrate genotypes—16 lines and four cultivars—were evaluated in 36 environments of the Northeast region from 2013-2015. The experiments were carried out under rainfed conditions in a completely randomized block design with four replications. The adaptability and genotypic stability were evaluated by the REML/BLUP procedure. The genotype × environment interaction was complex-type, with the grain yield ranging from 260 kg ha -1 (Campo Grande do Piauí PI, 2015) to 2,764 kg ha -1 (Araripina PE, 2015), with overall mean of 1,304 kg ha -1 . According to the Harmonic Mean of Relative Performance of Genetic Values (HMRPGV) estimates, the cultivars BRS Marataoã and BRS Pajeú and the line MNC04-792F-129 had simultaneously high yield, adaptability, and genotypic stability, and can be recommended and grown with greater probability of success in all the environments of the Northeast region of Brazil.


INTRODUCTION
Cowpea (Vigna unguiculata (L.) Walp.) is an important crop species in the Northeast region of Brazil. It generates employment and income for the population of this region and is a source of energy and protein.
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 (130.600 Mg), Ceará (56.700 Mg), and Maranhão (39.300 Mg).
Considering the area (1,247,100 ha) and total production (362,500 Mg) of cowpea in Brazil in 2016, and assuming that one hectare with this crop generates 0.8 jobs, the average annual consumption per capita is 18.21 kg (FEIJÃO..., 2009), the minimum price for a 60-kg bag is R$ 80.00 (HETZEL, 2009), and the crop generated 997,680 jobs in 2016, produced a food supply for 19,906,645 people, and its production generated an income of R$ 483,333,333.
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). 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 production stability, which subsidize the recommendation of cultivars.
In the last 60 years, several methodologies to study the adaptability and stability of genotypes in multiple environments were developed to help the breeder to select the most stable and suitable genotypes for crops in different environments (CARVALHO et al., 2016). The most commonly methodologies used in cowpea are the AMMI (BARROS et al., 2013;DDAMULIRA et al., 2015;SANTOS et al., 2015), GGE Biplot (OKORONKWO;NWOFIA, 2016;OLAYIWOLA;SOREMI;OKELEYE, 2015;SANTOS et al., 2016), and the Bayesian approach (BARROSO et al., 2016;TEODORO et al., 2015).
The REML/BLUP procedure has been one of the most used techniques in studies on adaptability and genotypic stability in Brazil; 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), and wheat (SILVA et al., 2011).
The number of adaptability and stability studies in cowpea using the REML/BLUP procedure have increased (SANTOS et al., 2016;TORRES et al., 2015;TORRES 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 semiprostrate 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-prostrate plant-16 lines and four cultivars-from the Embrapa Meio-Norte Cowpea Breeding Program (Table 1) were evaluated. 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 3.20 m x 5.0 m with four 5 m rows spaced 0.80 m apart, with 0.25 m between plants; the evaluation area consisted of the two central rows. Four seeds were sown per hole, and 20 days after sowing the plants were thinned, leaving two plants per Yield adaptability and stability of semi-prostrate cowpea genotypes in the Northeast region of Brazil by REML/BLUP BRS Pujante TE90-180-26F × Epace 10 ML G20 BRS Xiquexique TE87-108-6G × TE87-98-8G BL 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: wherein 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 h(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 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: wherein: 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) wherein: 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) has the advantages of providing adaptability and genotypicrather than phenotypic-stability; allowing the managing of heterogeneity of variances. 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.
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 relation (Table 1) and underwent several selection cycles, they differed significantly (p<0.01), denoting the existence of selectable variability. Barros et al. (2013) and Santos et al. (2015), evaluated the grain yield of 20 cowpea genotypes for adaptability and productive stability in the Mid-North region and in Mato Grosso do Sul, Brazil, respectively, and also found differences between genotypes with a high inbreeding level.
The environments also differed for grain yield (p<0.01), denoting that the characteristics of the testing environments (Table 2), combined with climatic variations affected this trait. Barroso et al. (2016) evaluate the grain yield of 20 cowpea genotypes in six environments of Mato Grosso do Sul and also found differences between the testing environments, and affirmed that the edaphoclimatic factors had the greatest effect on the adaptability and stability of the genotypes.
Contrasts between environments for grain yield were also observed by Ddamulira et al. (2015) who evaluated the adaptability and stability of 25 cowpea genotypes in three environments in Uganda, and Carvalho et al. (2015) who evaluated 20 cowpea genotypes in several environments of the Agreste and Tabuleiros Costeiros regions in the states of Alagoas and Sergipe, Brazil.
The G×E interaction for grain yield was significant (p<0.01) ( 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 (TEODORO et al., 2015). Olayiwola, Soremi and Okeleye (2015) evaluated the adaptability and stability of the grain yield of seven cowpea genotypes in four environments in Nigeria, and Santos et al. (2015) evaluated the grain yield of 25 cowpea genotypes in three environments in Uganda; both studies found different behavior of genotypes depending on the growing environments.
The overall mean grain yield was 1,304 kg ha -1 . This mean is well above the national (369 kg ha -1 ) and world (461.30 kg ha -1 ) mean for cowpea grain yield (FREIRE FILHO, 2011) and is also above the means obtained in other studies on cowpea genotypes in Brazil (BARROS et al., 2013;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. According to estimates of components of variance (REML), the environmental variance was contributed most to the phenotypic variance (Table 4), representing 83% this variance, followed by the G×E (14%) and genotypic (3%) variances.
Evaluations of genotypes in multi-environments conducted by Chiorato et al. (2008) and Pereira et al. (2016) in common bean, and by Torres et al. (2015) and Oliveira, Fontes and Rocha (2015) in cowpea also found 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  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 (Figure 1). In spite of the great effect of the environmental factors, denoted by the relative coefficient of variation (0.18), the heritability at an average genotypic level among the various environments was high (0.73) since the environmental effects were minimized. This allowed a high accuracy (0.85) 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 Yield adaptability and stability of semi-prostrate cowpea genotypes in the Northeast region of Brazil by REML/BLUP 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 (14%) (Table 4), which resulted from the low genotypic correlation between environments (0.15). 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 broader adaptation, which justifies the use of the genotypes' stability and adaptability in the selection of lines. 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) found similar percentages for the G×E and environmental variances evaluating the grain yield of cowpea genotypes in environments of Mato Grosso do Sul. Moreover, Barroso et al. (2016) found the genotypic variance as the second component influencing the phenotypic variance in Mato Grosso do Sul. The magnitudes of the components of variance may be different from one study to another, since they depend on the genetic variability of the genotypes, on the characteristics of the environments, and on the magnitude of the G×E interaction.
According to the mean component estimates (BLUP) and the confidence intervals associated with genotypic values (u+g), the genotypes G17 (BRS Marataoã), G15 (MNC04-792F-129) and G18 (BRS Pajeú) were superior than most of the genotypes evaluated and presented the highest genetic gains compared to the overall mean, with 137.82 kg or 10.56%; 111.09 kg or 8.52% and 101.27 kg or 7.76%, respectively (Table 5). These gains were lower than those observed by Torres et al. (2016), who evaluated Table 5 -Estimates of mean components (individual BLUP) of the effects (g) and 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 semiprostrate cowpea genotypes evaluated in 36 environments of the Northeast region of Brazil, from 2013 to 2015 1 Confidence interval associated to the genotypic value estimates, at 95% probability The genetic gain depends on the differential of the selection and heritability of the trait. Although the heritability of grain yield was high, a factors 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 compared to the differences found by those authors. 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 the best based on the criterion of the mean genotypic value ( Table 5). The coincidence was 100%, with inversion of order among the coincident ones between the genotypic value and the other parameters. According to Resende (2007a), the use of these attributes or selection criteria can provide further refinement in selection. Torres et al. (2016) state that this is an indication that these genotypes have high adaptive synergism in the 36 environments tested and exhibit good predictability, i.e., maintenance of grains yield in the different environments. Similar results were obtained by Torres et al. (2015) who evaluated the grain yield of 20 cowpea genotypes in the State of Mato Grosso do Sul and found a percentage of coincidence in the ordering of the five best genotypes by the genotypic value, HMGV, RPGV and HMRPGV  Torres et al. (2016), with a percentage of coincidence in the ordering of the five best genotypes by the genotypic value, with HMGV and HMRPGV of 80%, and with PRGV of 40%, evaluating grain yield of 20 cowpea genotypes in environments of Mato Grosso do Sul.
The three best genotypes (G17 -BRS Marataoã, G15 -MNC04-792F-129 and G18 -BRS Pajeú) by the criterion MHPRVG*MG had grain yield of 1,458, 1,423 and 1,409 kg ha -1 (Table 6), i.e., an average superiority of 12. 9 and 8%, respectively, over the overall mean of the 36 environments. According to Resende (2007a), 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 the improvement of the environment. These properties are intrinsic to the HMRPGV method.
The values of RPGV and HMRPGV (Table 6) indicate exactly the average superiority of the genotype in relation to the average of a given environment. Thus, the cultivar BRS Marataoã (G17) and the line MNC04-792F-129 (G15) respond on average with 1.12 and 1.09 times, respectively, the mean of any environment in which they are grown.
In general, the cultivars BRS Marataoã and BRS Pajeú, and the line MNC04-792F-129 were superior, simultaneously, for grain yield, adaptability and stability, and can be recommended for the environments of the Northeast region of Brazil with a lower risk of losses in grain yield due mainly to unpredictable environmental factors. According to Torres et al. (2016), genotypes that Yield adaptability and stability of semi-prostrate cowpea genotypes in the Northeast region of Brazil by REML/BLUP simultaneously have these three attributes can be used as selection criteria in breeding programs.

CONCLUSION
The cultivars BRS Marataoã and BRS Pajeú and the line MNC04-792F-129 combine simultaneously high yield, adaptability, and genotypic stability, and can be recommended and grown with greater probability of success in all evaluated environments of the Northeast region of Brazil. Overall mean 1,304 Continued Table 6