Simultaneous selection for yield, adaptability, and genotypic stability in immature cowpea using REML/BLUP

Abstract: The objective of this work was to select cowpea genotypes simultaneously for high yield of immature grains, adaptability, and genotypic stability, taking into account genotype x environment interactions. The mixed models restricted maximum likelihood (REML)/best linear unbiased prediction (BLUP) were used. Sixteen cowpea genotypes were evaluated in nine environments, consisting of a combination of location (Pentecoste in the state of Ceará, Acaraú in Ceará, Teresina in Piauí, and Mossoró in Rio Grande do Norte, Brazil) and year (2012, 2013, 2014, 2015, and 2017). In all trials, a randomized complete block design with four replicates was used. Significant differences were observed for effects of genotypes and the genotype x environment interaction. Environmental variance was the largest component of phenotypic variance, followed by the genotype x environment interaction and genotypic variances. The immature grain yield of the evaluated cowpea genotypes interacts strongly with the studied environments, resulting in a low genotypic correlation between environments. The MNC00-595F-27, MNC05-847B-123, and BRS Tumucumaque cowpea genotypes present high yield of immature grains, adaptability, and genotypic stability, being the most suitable for cultivation in the states of Ceará, Piauí, and Rio Grande do Norte or in other environments with similar soil and climatic conditions.

In Brazil, the three main market segments for cowpea are dry beans, green beans (pods to obtain the immature grain or the immature grain already threshed), and seeds. Other segments include: bean pods (yardlong bean) of the Sesquipedalis cultivation group, which are currently more concentrated in some states of the Northern region, but with great possibilities of expansion; and industrially processed beans, in an initial phase, but with good prospects (Freire Filho et al., 2017).
The production of cowpea is mainly focused on the consumption of dry grains. However, the market for immature grains is growing every day, mainly in the Northeastern region of Brazil, where it is highly appreciated, being used as the main component of several typical dishes, especially "baião-de-dois", a flavorful combination of rice and beans (Rocha et al., 2012).
The market for immature cowpea is highly promising, as it represents an important source of employment and income around the producing region (Freire Filho, 2011;Rocha et al., 2017a). However, it is currently characterized by the inexistence of improved cultivars and by the cultivation of landraces, generally with a low grain yield, late maturation cycle, and low disease resistance (Sousa et al., 2015). In addition, the pod is usually harvested at a stage with about 60 to 70% moisture (Sousa et al., 2015).
Although there are no official statistics on the area or on the cultivation of cowpea for the production of immature pods and grains in Brazil, both are quite significant for the agribusiness of the crop. The reason is that immature cowpea grains are traditionally grown and consumed in practically all states of the Northeastern region of the country.
However, the traditional cultivars used do not present completely favorable characteristics for cultivation and commerce, representing losses for the producers. Therefore, there is a great demand for more productive and better post-harvest cowpea cultivars, requiring the selection and development of materials with these specific characteristics according to Souza et al. (2019); this will add more value to the product and contribute to a greater sustainability of the cowpea agribusiness for immature pods and grains in Brazil.
In the breeding process, which includes the selection and recommendation of cultivars for a particular region, it is necessary to evaluate how genotypes behave in several environments due to environmental variations or to the genotype x environment (GxE) interaction. These variations affect the performance of genotypes in different environments, and the best strategy to manage the GxE interaction is to select genotypes with high adaptability and stability (Rocha et al., 2012).
The procedure based on mixed models has been applied in different research lines in the plant breeding area, such as in the analysis of the GxE interaction. It allows the estimation of the components of variance by the restricted maximum likelihood (REML) and of the genotypic value by the best linear unbiased prediction (BLUP), being called REML/BLUP. One of the advantages of this approach is that it allows simultaneous genotypic selection for yield, adaptability, and stability in the context of mixed models, through the use of the harmonic mean of the relative performance of genotypic values (HMRPGV) (Resende, 2007).
The REML/BLUP procedure has been widely used in studies of the adaptability and stability of dry grain yield in cowpea (Torres et al., 2015(Torres et al., , 2016Santos et al., 2016;Carvalho et al., 2017;Torres Filho et al., 2017;Rocha et al., 2017bRocha et al., , 2017c. However, works using this approach to assess the adaptability and stability of immature grain yield are still rare (Torres Filho et al., 2017).
The objective of this work was to select cowpea genotypes simultaneously for high yield of immature grains, adaptability, and genotypic stability, taking into account genotype x environment interactions.
The trials were conducted in Brazil, in different municipalities and years: Teresina A randomized block design was used, with four replicates. The experimental plot had the dimensions of 2.0x5.0 m and consisted of four rows; the two central rows were considered as the useful area. The spacing between rows was 0.50 m and between holes within the row, 0.25 m, resulting in 20 holes per row. Four seeds were sown per hole, and, 15 days after sowing, thinning was performed, maintaining two plants per hole, totalizing 160 plants in the plot and 80 plants per useful area of the plot.
Crop management was carried out whenever necessary to ensure that there was no competition between cowpea plants and weeds and that the crop was not over attacked by pests and diseases. Immature cowpea grains were harvested and threshed manually. The immature grain yield of the plot area was measured in grams per useful plot area, extrapolated to kilograms per hectare.
The yield data of the immature grains obtained in the different environments were subjected to the statistical analysis. Statistical model 54 (stability, adaptability, and yield: blocks, genotypes, several environments, and one observation per plot) of the Selegen-REML/BLUP software was used (Resende, 2007). The following model was adopted: y = Xb + Zg + Wc + e, where y, b, g, c, and e correspond, respectively, to the vectors of observed values, fixed effects of blocks within different environments, random effects of genotypes, random effects of the GxE interaction, and random errors; and X, Z, and W correspond, respectively, to the incidence matrices for b, g, and c.
The following parameters were estimated: phenotypic variance ( σ f 2 ); genotypic variance ( σ g 2 ); residual variance ( σ e 2 ); variance of the genotype x environment interaction ( σ ge 2 ); genotypic correlation ( r ge g g e gloc = + σ σ σ , where e is the number of environments; accuracy in the selection of genotypes (   r h gg mg = 2 ); and relative coefficient of variation, obtained by CV g /CV e , where CV g and CV e are the coefficients of genetic and environmental variations, respectively.
The significance of the effects of the model was estimated by the deviance analysis (Resende, 2002). The deviances were obtained through analyzes with and without the effects of g, b, and ge. The deviation without these effects was then subtracted from each complete model deviation and compared with the chi-square value, with 1 degree of freedom, at 1% probability.
Based on the used model, the empirical BLUP predictors (eBLUP or REML/BLUP) of the genotypic values free Pesq. agropec. bras., Brasília, v.54, e01234, 2019 DOI: 10.1590/S1678-3921.pab2019.v54.01234 of the GxE interaction were given by   µ + g i , where μ is the average of all environments and  g i is the genotypic effect free of the GxE interaction. For each environment j, genotypic values (GV ij ) were predicted by where μ j is the average of environment j,  g i is the genotypic effect of genotype i in environment j, and (gê) ij is the effect of the G×E interaction relative to genotype i. The prediction of genotypic values by capitalizing on the average GxE interaction (ge a ) in the different environments was given by , where μ is the general average of all environments, e is the number of environments, and  g i is the genotypic effect of i (Resende, 2007).
The harmonic mean of genotypic values (HMGV) was obtained by the equation: where e is the number of environments in which genotype i was evaluated; and GV ij is the genotypic value of genotype i in environment j, expressed as the proportion of the mean of that environment (Resende, 2007). The relative performance of genotypic values (RPGV) was obtained according to the expression: whose terms have already been explained. The lower the standard deviation of the behavior of the genotypes in the environments, the higher the HMGV; therefore, selection by higher HMGV implies selection for yield and stability, simultaneously. The mean genotypic value, capitalizing on adaptability, is obtained by the relative performance of genotypic values multiplied by the general mean of all environments (RPGVμ). The average genotypic value penalized by instability and capitalized by stability is determined by the HMRPGV multiplied by the general average of all environments (HMRPGVμ) (Resende, 2007).

Results and Discussion
Genotypes and the GxE interaction were significant (p≤0.01) by the deviance analysis (Table 1), indicating the presence of genetic variability for immature grain yield in the group of evaluated genotypes, as well as of a differentiated behavior of genotypes in the different environments. The existence of the GxE interaction causes an inconsistency in yield, meaning that one genotype may stand out in a given environment and another may not, which makes it necessary to evaluate the adaptability and stability of different genotypes. According to Rocha et al. (2012), the identification and selection of genotypes that are highly productive and stable in various environments is one of the main objectives of cowpea breeding programs. Aquino et al. (2016) evaluated the adaptability and stability of the immature grain yield of 30 cowpea genotypes in the region of Juazeiro, in state of Bahia, and in the municipality of Petrolina, in the state of Pernambuco, both in Brazil, and also found significant differences for the genotype and GxE interaction effects.
According to the components of variance by the REML, environmental variance contributed the most (51%) to phenotypic variance, followed by the GxE interaction variance (36%), and genotypic variance (13%) ( Table 2). The high influence of environmental variance can be justified by the polygenic nature of the trait in question. In other studies evaluating the dry grain yield of cowpea genotypes in multiple environments (Torres et al., 2015;Rocha et al., 2017bRocha et al., , 2017c, a higher proportion of environmental variance was also observed when the genotypic and G×E interaction variances were taken into account. In spite of a higher effect of environmental factors, shown by the relative coefficient of variation of 0.49, the mean genotype heritability among the various environments had a high magnitude of 0.70 (Table 2), indicating a favorable situation for selection. The heritability obtained in the present study was similar to that found by Torres et al. (2015), who evaluated the dry grain yield of 20 cowpea genotypes in several environments of the state of Mato Grosso do Sul, Brazil, but was higher than that reported by Torres Filho et al. (2017), who observed a low magnitude of 0.4 for the immature grain yield of cowpea genotypes in the climate and soil conditions of Mossoró, in the state of Rio Grande do Norte. According to Chiorato et al. (2008), average heritability is based on the number of replicates and plants assessed per plot in the experiment. The size of the experimental area of the present study may have contributed positively to the reduction of environmental effects, because the genotypes were represented by 80 plants in the useful area of the plot used for the evaluations.
Selective accuracy is an important parameter in the context of genotype evaluation and corresponds to the correlation between the true genotypic value of each genotype, which is estimated or predicted from experimental data, varying from 0 to 1; the appropriate accuracy values are those close to unity (Resende & Duarte, 2007). The accuracy of 0.83 obtained in the present study was considered high (Table 2), indicating experimental quality, as well as safety and reliability in the selection of superior genotypes for immature grain yield. This estimate was higher than that found by Torres Filho et al. (2017), who observed a low precision of 0.20 while also evaluating the immature grain yield of cowpea genotypes under the edaphoclimatic conditions of Mossoró, in the state of Rio Grande do Norte.
The second component that most influenced phenotypic variance was the GxE interaction variance, which resulted in a low genotype correlation of 0.26 among environments (Table 2). These results show that the GxE interaction is probably of the complex type, causing a significant inversion in genotype classification throughout environments (Resende, 2007). This could lead to difficulties in the selection of genotypes with a broader adaptation, showing the importance of analyzing adaptability and stability in order to provide more accurate information for the selection of cowpea genotypes with more predictable immature grain yield. Rocha et al. (2017bRocha et al. ( , 2017c) evaluated the dry grain yield of 20 cowpea genotypes in the Northeastern region of Brazil and also found that the GxE interaction was the second component to influence phenotypic variance. However, Torres et al. (2016) reported similar percentages for the GxE interaction and the environmental variances, when studying cowpea genotypes in environments in the state of Mato Grosso do Sul.
The average immature grain yield was 1,599 kg ha -1 (Table 3), which was considered low, probably because most of the trials were conducted under irrigation and there was overgrowth during the production period in some of them. This average was lower than those of 1,957 and 2,390 kg ha -1 found by Sousa et al. (2015) for rainfed and irrigated cultivation, respectively, when evaluating 16 cowpea genotypes in the municipality of Teresina, in the state of Piauí, Brazil, and than that of 2,827 kg ha -1 reported by Freitas et al. (2016) for irrigated cultivation, when studying 12 cowpea genotypes under the soil and climate conditions of the municipality of Mossoró, in the state of Rio Grande do Norte. However, the average immature grain yield obtained in the present study was superior to that of 1,353 kg ha -1 observed by Silva et al. (2013) for rainfed cultivation, when evaluating 8 cowpea cultivars under the edaphoclimatic conditions of the municipality of Serra Talhada, in the state of Pernambuco, Brazil. According to the estimates of mean components by the BLUP and to the confidence intervals associated with genotypic values (μ + g), BRS Tumucumaque, MNC00-595F-27, and MNC05-847B-123 showed higher values than most of the evaluated genotypes, as well the highest genetic gains of 292.58 kg or 18.29%, 288.52 kg or 18.04%, and 248.35 kg or 15.53%, respectively, compared with the general average ( Table 3). The gains obtained in the present study were higher than those observed by Rocha et al. (2017c), who assessed the dry grain yield of 20 cowpea genotypes in the Northeastern region of Brazil and obtained a gain of 10.56, 8.52, and 7.76% for the three best genotypes.
The five best genotypes based on the HMGV and RPGV criteria (Table 4) do not necessarily correspond to the five best by the criterion of the average genotypic value (μ + g). The coincidence was 80% for both HMGV and RPGV, with a reverse order among the matched genotypes. The coincidence among the five best genotypes by the mean genotypic value and HMRPGV was 100%; however, there was also an inversion in genotype order. This shows that it is possible to make reliable predictions about genetic values with a single selection criterion, covering yield, stability and adaptability, which allows a more refined selection.
These results differed from those of Torres et al. (2016), who reported a coincidence in the order of the five best genotypes of approximately 80%, considering the mean genotypic values by the HMGV and HMRPGV, and of 40% by the RPGV, while evaluating the dry grain yield of 20 cowpea genotypes in the state of Mato Grosso do Sul, Brazil. Rocha et al. (2017b) assessed the dry grain yield of 20 cowpea genotypes in Northeastern Brazil and found a percentage of 80% coincidence between the HMGV and RPGV ordering, similar to that observed in the present study.
The three best genotypes (MNC00-595F-27, MNC05-847B-123, and BRS Tumucumaque) showed immature grain yields of 1,973, 1,844, and 1,797 kg ha -1 , i.e., an average superiority of 23, 15, and 12%, respectively, in relation to the general average of the nine studied environments (Table 4). These values were obtained through a process that penalizes the instability of genotypes and capitalizes their response capacity (adaptability) to improve the environment (Resende, 2007). These properties are specific of the HMRPGV statistic. Table 3. Averages by the individual best linear unbiased prediction of genotypic effects and predicted genotypic values (u + g) free of the interaction with environments, as well as lower and higher limits of the confidence interval (LL and HL, respectively), and genetic gain of 16 cowpea (Vigna unguiculata) genotypes evaluated in nine environments, consisting of a combination of locations in the states of Ceará, Piauí, and Rio Grande do Norte, Brazil, and of years from 2012 to 2017.

Genotype
Genotypic effects u + g (LL-HL) (1) Genetic gain (kg) The values of RPGV and HMRPGV showed the average superiority of the genotype in relation to the average of a given environment. Therefore, MNC00-595F-27, MNC05-847B-123, and BRS Tumucumaque were, respectively, 1.24, 1.16, and 1.13 time superior to the average of any environment where they were grown.
In general, genotypes MNC00-595F-27, MNC05-847B-123, and BRS Tumucumaque were superior regarding immature grain yield, adaptability, and stability and, therefore, could be recommended for the environments evaluated in the present study, with a lower loss of immature grain yield due to unpredictable environmental factors. According to Torres et al. (2016), genotypes that present the attributes yield, adaptability and stability, simultaneously, can be used as a selection criterion in cowpea breeding programs.
Grain color is an important visual aspect of the market of immature cowpea grains. Genotypes MNC00-595F-27 and MNC05-847B-123 stood out because they belong to the "Verde" commercial subclass, characterized by green tegument and cotyledons. According to Freire Filho et al. (2007), genotypes of this commercial subclass have high potential in this regard due to their greater capacity of preserving their green color postharvest, compared with the other commercial subclasses of cowpea.

Conclusions
1. The immature grain yield of the evaluated cowpea (Vigna unguiculata) genotypes interacts highly with the assessed environments, which results in a low genotypic correlation between environments.
2. The MNC00-595F-27, MNC05-847B-123, and BRS Tumucumaque genotypes present high immature grain yield, adaptability, and genotypic stability, being the most suitable for cultivation in the states of Ceará, Piauí, and Rio Grande do Norte, Brazil, or in other areas with similar soil and climatic conditions. Table 4. Stability of genotypic values by the harmonic mean of genotypic values (HMGV), adaptability of genotypic values by the relative performance of genotypic values (RPGV), adaptability and stability of genotypic values by the harmonic mean of the relative performance of genotypic values (HMRPGV), genotypic value capitalizing adaptability by the RPGV multiplied by the general mean of all environments (RPGVµ), and genotypic value penalized by instability and capitalized by adaptability by the HMRPGV multiplied by the general average of all environments (HMRPGVµ) of 16 cowpea (Vigna unguiculata) genotypes evaluated in nine environments, consisting of a combination of locations in the states of Ceará, Piauí and Rio Grande do Norte, Brazil, and of years from 2012 to 2017 (1) .