Selection of black bean pre-cultivars based on adaptability and stability for the State of Rio de Janeiro

Seleção de pré-cultivares de feijão preto baseada na adaptabilidade e estabilidade para o Estado do Rio de Janeiro

Abstract

The development of new cultivars is a strategy used in breeding programs to increase food production with environmental sustainability. The genotype × environment interaction is a great challenge in the identification and selection of superior genotypes for different edaphoclimatic conditions. Due to this interaction, it is essential to select and develop materials that can provide not only high productivity but also wide adaptability and production stability. Given the above, this work aims to select bean pre-cultivars regarding grain productivity, adaptability and stability for the State of Rio de Janeiro. In the 2018 harvest, two inbred lines competition trials were carried out and three in the 2019 harvest. Eleven black bean genotypes were evaluated in five environments, and the experiments were set up in a randomized block design with three replications. The adaptability and genotypic stability were assessed via the GGE Biplot, Eberhart and Russell and Lin and Binns methodologies, with the aid of the GENES and R software systems. The methodologies based on simple linear regression and non-parametric statistical analysis were concordant in the identification of genotypes with production stability (BRS Esteio, BRS FP 403 and CNFP 16459), responsive to environmental improvement (BRS Esteio) and adapted to unfavorable environments (BRS Esteio). Furthermore, BRS Esteio was classified as the ideotype and presented the best adaptability, high stability and performance above the general average. Thus, the adaptability and stability analysis methodologies proved to be effective and consistent in identifying superior genotypes.

Keywords:
Phaseolus vulgaris L.; non-parametric analysis; genotype × environment interaction; GGE Biplot; linear regression

Resumo

O desenvolvimento de novas cultivares é uma estratégia utilizada em programas de melhoramento genético para aumentar a produção de alimentos com sustentabilidade ambiental. A interação genótipos × ambientes é um grande desafio na identificação e seleção de genótipos superiores para diferentes condições edafoclimáticas. Devido a esta interação, é essencial selecionar e desenvolver materiais que possam proporcionar não apenas alta produtividade, mas também ampla adaptabilidade e estabilidade de produção. Diante do exposto, este trabalho tem como objetivo selecionar pré-cultivares de feijão quanto a produtividade de grãos, adaptabilidade e estabilidade para o Estado do Rio de Janeiro. Na safra de 2018 foram realizados dois ensaios de competição de linhagens e três na safra de 2019. Foram avaliados onze genótipos de feijão preto em cinco ambientes, sendo os experimentos instalados em delineamento de blocos casualizados com três repetições. A adaptabilidade e estabilidade fenotípica foram avaliadas através das metodologias GGE Biplot, Eberhart and Russell e Lin and Binns, com auxílio dos softwares GENES e R. As metodologias baseadas em regressão linear simples e análise estatística não paramétrica foram concordantes na identificação de genótipos com estabilidade produtiva (BRS Esteio, BRS FP 403 e CNFP 16459), responsivos à melhoria ambiental (BRS Esteio) e adaptados a ambientes desfavoráveis (BRS Esteio). Além disso, o BRS Esteio foi classificado como ideótipo e apresentou melhor adaptabilidade, alta estabilidade e desempenho acima da média geral. Assim, as metodologias de análise de adaptabilidade e estabilidade mostraram-se eficientes e concordantes na identificação de genótipos superiores.

Palavras-chave:
Phaseolus vulgaris L.; análise não paramétrica; interação genótipos × ambientes; GGE Biplot; regressão linear

1. Introduction

Common bean (Phaseolus vulgaris L.) is one of the most produced and consumed legumes in the world and stands out as the third most important species, after soybean (Glycine max L.) and peanut (Arachis hypogaea L.). Its importance goes beyond the economic aspect, given its relevance as a food and nutritional security factor, due to its significant levels of proteins, carbohydrates, vitamins, minerals and fibers (Carneiro et al., 2015) and cultural relevance in the cuisine of different countries and cultures.

Genotypic performance is affected by each environment in which the bean genotypes are cultivated, due to the genotype × environment interaction (G × E). Such interaction poises a great challenge for selection, since genotypes may present distinct performances, according to the environment, which means that a certain genotype may be the best in one environment, but not in another (Oliveira et al., 2018). To alleviate the effect of the G × E interaction and its impact on the selection and recommendation of superior genotypes, the experiments should be implemented in as many locations and/or agricultural years as possible. In order to obtain more precise information about genotypic performance according to environmental variations and understand the effects of the G × E interaction, studies focused on adaptability and stability are needed, so as to provide the necessary support for selection, considering that adaptability is related to the genotype capacity to benefit from environmental changes, while stability refers to the predictability of genotypes as a result of environmental variations (Cruz et al., 2014).

Several methodologies capable of accurately explaining the effects of this interaction are currently available, including those based on simple linear regression analysis (Eberhart and Russell, 1966), non-parametric statistical analysis (Lin and Binns, 1988), mixed models (mixed models) and principal components, such as GGE Biplot (Yan, 2011). In the GGE Biplot analysis, the graphs are constructed based on the main components. The first and second components represent the proportion of grain yield as a result of the characteristics of the genotype and the G × E interaction, respectively (Miranda et al. 2009; Yan and Holland, 2010). Therefore, this analysis increases knowledge about the G × E interaction and allows us to predict the average performance of genotypes in different environments, in addition to identifying which genotypes are more stable (Santos et al., 2019; Yan and Kang, 2019; Souza et al., 2023). Thus, the present work aimed to select the best black bean genotypes based, simultaneously, on productivity, adaptability and stability through the GGE Biplot, Eberhart & Russell and Lin & Binns methodologies.

2. Material and Methods

The assessments were conducted in the 2018 and 2019 agricultural years, at the State Center for Research in Agroenergy and Waste Use (CEPAAR) of the Agricultural Research Corporation of the State of Rio de Janeiro (Pesagro-Rio), located in Campos dos Goytacazes and on private properties located in the municipalitys of Italva and Macaé.

Eleven black bean genotypes, from experiments of Value for Cultivation and Use (VCU), were evaluated, namely, seven inbred lines (identified by the prefix ‘CNFP’) developed by Embrapa Arroz e Feijão and four cultivars designated as controls (BRS Esteio, BRS FP 403, IPR Tuiuiu and IPR Uirapuru) (Table 1). The experiment was arranged in a randomized block design with three replications. Each experimental unit consisted of 4 lines of 4 m, 0.5 m spacing and a total population of 240 thousand plants ha^-1.

Table 1
Black bean genotypes and their origins, evaluated in five environments, in the state of Rio de Janeiro, in 2018 and 2019.

No.	Genotype	Origin	Type
1	BRS Esteio	Embrapa	Cultivar
2	BRS FP403	Embrapa	Cultivar
3	IPR Tuiuiu	IAPAR	Cultivar
4	IPR Uirapuru	IAPAR	Cultivar
5	CNFP 16379	Embrapa	Inbred line
6	CNFP 16380	Embrapa	Inbred line
7	CNFP 16383	Embrapa	Inbred line
8	CNFP 16384	Embrapa	Inbred line
9	CNFP 16404	Embrapa	Inbred line
10	CNFP 16416	Embrapa	Inbred line
11	CNFP 16459	Embrapa	Inbred line

Planting was carried out in April, and the harvest, in July 2018, for the environments of Campos dos Goytacazes and Macaé. In the following year, sowing was carried out in April, May and June and the harvest, in July, August and September, for the environments of Campos dos Goytacazes, Italva and Macaé, respectively. The harvest was carried out in phase R9, and started 90 days after sowing. Data collection was carried out in the two central rows, without considering the border lines. The data were collected by weighing in grams, humidity was adjusted to 13%, and the results were expressed in kg ha^-1.

The individual analysis of variance was initially carried out for each environment, for the statistical analysis of the data, in order to verify the genetic variability and homogeneity of the variances, according to the following model (Equation 1):

$Y_{ijk}=\mu +G_i+B_j+{\epsilon }_{ij}$ (1)

where: $Y_{ij}$: observed value of the i-th genotype in the j-th block; µ: overall mean; $G_i$: fixed effect of the i-th genotype; $B_i$: random effect of the j-th block; and ${\epsilon }_{ij}$: experimental error.

According to Pimentel-Gomes and Garcia (2002), if the relationship between the largest and smallest residual mean square is less than seven, the joint analysis can be performed, but when this relationship is higher than seven, it is advisable to consider, separately, the subgroups of experiments with residual mean squares that are not very heterogeneous.

The factorial scheme was considered for the joint analysis of variance, according to Steel et al. (1997), as described below (Equation 2):

$Y_{ij}=\mu +G_i+A_j+G{A}_{ij}+\frac{B}{A_{kj}}+{\epsilon }_{ijk}$ (2)

where: $Y_{ij}$: observed value for the i-th genotype in the j-th environment and in the k-th block; µ: overall mean of the tests; $G_i$: fixed effect of the i-th genotype; $A_j$: random effect of the j-th environment; $G{A}_{ij}$: fixed effect of the i-th genotype × j-th environment interaction; $\frac{B}{A_{kj}}$: effect of the k-th block within the j-th environment; ${\epsilon }_{ijk}$: error associated with the i-th genotype, in the j-th environment and in the k-th block.

When the G × E interaction was observed (significant F test), the analyses of the adaptability and productivity stability of black bean genotypes were carried out using the following methodologies, based on simple linear regression, in non-parametric statistical analysis and principal component analysis – GGE Biplot (Genotype and Genotype-Environment Interaction).

The Eberhart and Russell (1966) methodology, proposes that the regression coefficient parameters (${\beta }_{1i}$) and the average productivity (${\beta }_{0i}$) estimate the adaptability of the genotype, while the variance of the regression deviations (${\sigma }_{di}^2$) and/or the coefficient of determination (R²) measure its stability. This method adopts the following linear regression model (Equation 3):

$$Y_{ij}={\beta }_{0i}+{\beta }_{1i}{I}_j+{\delta }_{ij}+{\overline{\epsilon }}_{ij}$$ (3)

where: $Y_{ij}$: observed value for the i-th genotype in the j-th environment; ${\beta }_{0i}$: overall mean of the i-th genotype; ${\beta }_{1i}$: linear regression coefficient, which measures the response of the i-th genotype to environmental variation; $I_j$: encoded environmental index (${\displaystyle \sum }_j{I}_j=0$); ${\delta }_{ij}$: regression deviation of the i-th genotype with the j-th environment; ${\overline{\epsilon }}_{ij}$: error associated with the i-th genotype in the j-th environment.

The parameter ${\widehat{\beta }}_{1i}$, used as the genotype response pattern to different environments, was estimated according to the following expression (Equation 4):

${\widehat{\beta }}_{1i}=\frac{{{\displaystyle \sum }}_j{Y}_{ij}{I}_j}{{{\displaystyle \sum }}_i{I}_j^2}$ (4)

where: $Y_{ij}$: mean of the i-th genotype in the j-th environment; $I_j$: environmental index, where: $I_j=\left[\left(\frac{Y_j}{p}\right)-\left(\frac{Y\mathrm{..}}{pn}\right)\right]$

where: $Y_j$: average of all genotypes in the jth environment; $Y_{\mathrm{..}}$: overall average; $n$: number of genotypes; $p$: number of environments.

Hypotheses H₀: ${\beta }_{1i}=1$ and H₁: ${\beta }_{1i}\ne 1$ were evaluated by the t statistics, given by (Equation 5):

$t=\frac{{\widehat{\beta }}_{1i}-1}{\sqrt{\widehat{V}}\left({\widehat{\beta }}_{1i}\right)}$ (5)

The genotypes were classified into three groups according to their adaptability: I) general or broad adaptability with ${\beta }_{1i}=1$, whose average is above the general average. This type is desirable for environments with many unpredictable variations; II) Specific adaptability to favorable environments with ${\beta }_{1i}>1$, which groups genotypes with high performance in favorable environments; III) adaptability specific to unfavorable environments ${\beta }_{1i}<1$, which joins the genotypes that stand out in unfavorable environments.

The parameter ${\sigma }_{di}^2$ was determined according to the expression below (Equation 6):

${\sigma }_{di}^2=\frac{\sum {\delta }_{ij}^2}{\left(a-2\right)}=QMDi-QMR/r$ (6)

where: $QMDi$is the mean square of the regression deviations of the i-th genotype; $QMR$: is the mean square of the residue; and $r$ is the number of replications.

Regarding stability, the genotypes were classified into: high (${\sigma }_{di}^2=0$) and low stability materials (${\sigma }_{di}^2\ne 0$). Estimates for the variance of the regression deviations were tested according to the hypothesis H₀: ${\sigma }_{di}^2=0$ and H₁: ${\sigma }_{di}^2\ne 0$, using the F test according to the following expression (Equation 7):

$F=QMDi⁄QMR$ (7)

The stability parameters were estimated using the methodology proposed by Lin and Binns (1988) and modified by Carneiro (1998). Lin and Binns (1988) defined the mean square of the distance between the mean of the genotype and the maximum response for all environments as a measure to estimate genotypic performance ($P_i$), according to the following expression (Equation 8):

$P_i=\frac{{{\displaystyle \sum }}_{j=i}^n\left(Y_{ij}-M_i\right)²}{2a}$ (8)

where: $P_i$, is the estimate of the stability parameter of genotype i; $Y_{ij}$ is the productivity of the i-th genotype in the j-th environment; $M_i$: is the maximum response observed among all genotypes in the environment j; a is the number of environments.

In order recommend the black bean genotypes for different types of environments (favorable and unfavorable), the estimator ($P_i$) was decomposed into the parts corresponding to favorable ($P_{if}$) and unfavorable ($P_{id}$) environments, according to Carneiro (1998).

For favorable environments, with indexes higher than or equal to zero, the estimates were based on (Equation 9):

$P_i=\frac{{{\displaystyle \sum }}_{j=i}^n\left(Y_{ij}-M_i\right)²}{2f}$ (9)

where $f$ is the number of favorable environments and $Y_{ij}$ and $M_i$, as defined above.

For unfavorable environments, whose indices are negative, the previous formula was used, and $d$ is the number of unfavorable environments, according to the expression below (Equation 10):

$P_i=\frac{{{\displaystyle \sum }}_{j=i}^n\left(Y_{ij}-M_i\right)²}{2d}$ (10)

Therefore, it is possible to identify genotypes with greater stability (< $P_i$), more responsive to favorable environments (< $P_{if}$) and more adapted to unfavorable environments (< $P_{id}$).

The GGE Biplot multivariate analysis was performed with the aid of the GGE BiplotGui package of the R statistical software system (R Development Core Team, 2021), considering the following model (Equation 11):

$Y_{ij}-\mu -E_j=G_i+G{E}_{ij}$ (11)

where: $Y_{ij}$is the average productivity of the i-th genotype in the j-th environment; µ is the overall mean; $G_i$ is the main effect of the i-th genotype for the j-th environment; $E_i$; $G{E}_{ij}$ is the specific interaction between the i-th genotype and the j-th environment (Yan, 2011).

The GGE Biplot methodology considers the main genotype effect plus the G × E interaction, that is, this model does not separate the genotype effect (G) from the genotype × environment (G × E) effect. They are maintained together in two multiplicative terms (Yan and Kang, 2019), as shown in the following Equation 12:

$Y_{ij}-\mu -{\beta }_j=g_{1i}{e}_{1j}+g_{2i}{e}_{2j}+{\epsilon }_{ij}$ (12)

where: $Y_{ij}$ is the expected performance of the i-th genotype in the j-th environment; µ is the overall mean of observations; ${\beta }_j$ is the main effect of the j-th environment; $g_{1i}$ and $e_{1j}$ are the main scores of the i-th genotype in the j-th environment, respectively; ${\epsilon }_{ij}$ is the unexplained residue of both effects.

The Biplot analysis is based on the principal components technique, and the first two components are represented by the axes of the multivariate analysis graph (Miranda et al., 2009).

The GGE Biplot graph was performed by the simple dispersion of $g_{i1}$ and $g_{i2}$ for genotypes $e_{j1}$ and $e_{j2}$ for environments, through Singular Value Decomposition (DVS), using the following Equation 13:

$Y_{ij}-\mu -{\beta }_j={\lambda }_1{\xi }_{i1}{\eta }_{1j}+{\lambda }_2{\xi }_{i2}{\eta }_{2j}+{\epsilon }_{ij}$ (13)

where:${\lambda }_1$ and ${\lambda }_2$ are the highest singular values of the first and second principal components: PC1 and PC2, respectively; ${\xi }_{i1}$ and ${\xi }_{i2}$ are coordinates of the eigenvectors of the i-th genotype of PC1 and PC2, respectively; ${\eta }_{1j}$ and ${\eta }_{2j}$ are coordinates of the eigenvectors of the j-th environment of PC1 and PC2, respectively (Yan and Kang, 2019).

The genetic-statistical analyses were performed using the GENES software system (Cruz, 2016) and the GGE BiplotGui package, with the aid of the R statistical software system (R Development Core Team, 2021).

3. Results and Discussion

The results of the individual analysis of variance (Table 2) reveal significant differences between genotypes for grain yield in all environments evaluated by the F test, at 1% and 5% probability level. Such significance indicates variability for the selection of superior genotypes.

Table 2
Summary of individual analysis of variance for the trait yield, in kg.ha-1, in five environments with eleven black bean genotypes evaluated in the state of Rio de Janeiro, in 2018 and 2019.

Source of variation	DF	Mean square
		2018		2019
		Campos	Macaé	Campos	Italva	Macaé
Blocks	2	194.145.64	197,729.55	105,004.73	240,978.03	26,354.73
Genotypes	10	103,813.03*	178,558.03*	110,312.51*	164,745.45**	170,418.37*
Residues	20	41,159.39	53,764.34	44,947.44	41,773.86	66,783.48
Mean		1,409.47	2,946.36	2,354.17	2,991.06	2,611.06
CV (%)		14.39	7.87	9.01	6.83	9.90

• ^*
  and ** significant at 5% and 1% probability, by the F test, respectively. CV: coefficient of variation; DF: Degree of freedom.

The average productivity ranged from 1,409.47 to 2,991.06 kg.ha^-1 in Campos dos Goytacazes in the 2018 crop year and Italva, in the 2019 crop year, respectively (Table 2).

According to Nascimento et al. (2023), the G × E interaction indicates heterogeneity of environmental conditions, which is explained by the non-coincident behavior of genotypes in different environments. This is explained by the edaphoclimatic conditions of each environment where the genotypes were evaluated.

Analyses of variance, according to Cruz et al. (2012), are important for allowing the assessment of the magnitude of the genetic variability between the genotypes evaluated, the relative precision of the experiment and the discrepancies between the estimated residual variances.

The coefficient of variation estimated in the analysis of variance indicates the degree of precision of an experimental test. According to Pimentel-Gomes (2009), the experimental precision represented by the coefficient of variation must be considered high when it presents an index lower than 10%; medium, from 10 to 20%; low, when it is higher than 20 and less than or equal to 30% and; very low, superior to 30%. Therefore, in Table 2, it is observed that the experimental precision for the trait grain yield was classified as high for all environments, except for Campos dos Goytacazes, in 2018, which was ranked as medium. Regarding the data from the joint analysis, the coefficient of variation found was 9.05%, which indicates high experimental precision, lower experimental error and reliability in the selection of the best genotypes.

A low coefficient of experimental variation indicates greater participation of genetic variation in phenotypic variation, which is a favorable factor for the selection of superior genotypes, since selection will be based on the heritable proportion of phenotypic variance. However, such classification must take other factors into account, such as the edaphoclimatic conditions of the location, the reproductive cycle and particularities of the studied culture, besides the nature of the evaluated trait (Nascimento et al., 2024).

The data from the joint analysis of variance (Table 3) reveal that the effects of genotypes, environments and G × E interaction were significant at 1% probability, by the F test. Thus, the significant effect of the G × E interaction indicates inconsistent performance of the genotypes, due to environmental variations, that is, different response of the genotypes to the environments. Therefore, studies focused on adaptability and phenotypic stability are justifiable, for the identification of the most stable and productive genotypes.

Table 3
Summary of the joint analysis of variance for the trait yield, in kg.ha^-1, in five environments with eleven black bean genotypes evaluated in the state of Rio de Janeiro, in 2018 and 2019.

Source of variation		DF	Mean square
Blocks/Environments		10	152.842,54
Genotypes		10	293.729,19*
Environments		4	13.663.480,78**
G × A		40	108.529,55**
Residue		100	49.685,71
Total		164	-
Mean			2462,42
CV (%)			9.05
QMr+/QMr-			1.62

• ^*
  and ** significant at 5% and 1% probability by the F test, respectively. QMr+/QMr-: ratio between the largest and smallest mean square residual. CV: coefficient of variation; DF: Degree of freedom.

The ratio between the largest and smallest mean square of the residue was 1.62 (Table 3), which indicates relative homogeneity of variances and allows using all environments evaluated in the joint analysis of variance (Pimentel-Gomes and Garcia, 2002).

Estimates of adaptability and stability parameters carried out using the simple linear regression method (Eberhart and Russell, 1966) and non-parametric statistical analyzes (Lin and Binns, 1988) are presented in Table 4.

Table 4
Estimates of regression coefficients, regression deviations and coefficient of determination (R²) according to the Eberhart and Russell (1966) method and general indices (Pi), favorable (Pif) and unfavorable environments (Pid), according to the Lin and Binns (1988) method, modified by Carneiro (1998), for the trait yield, in kg.ha^-1, evaluated in five environments with eleven black bean genotypes in the state of Rio de Janeiro, in 2018 and 2019.

Genotypes	${\beta }_{0i}$	Eberhart and Russell				Lin and Binns
		$\widehat{{\beta }_{1i}}$	$\widehat{{\sigma }_{di}^2}$	R2(%)		Pi	Pif	Pid
BRS Esteio	2,820.0 a	1.17ns	-5,269.1ns		98.53	2,078.4	0.0	5,196.0
BRS FP403	2,616.0 a	1.12ns	-9,447.8ns		98.98	34,022.3	39,240.7	26,194.6
IPR Tuiuiu	2,367.3 b	0.99ns	5,439.8ns		96.11	128,050.9	147,573.1	98,767.5
IPR Uirapuru	2,320.2 b	1.09ns	-5,02.9ns		98.37	140,481.0	133,596.9	150,807.1
CNFP 16379	2,395.7 b	0.87ns	35,170.5*		89.09	140,447.6	220,030.2	21,073.6
CNFP 16380	2,401.7 b	1.05ns	8,563.5ns		96.04	110,418.4	138,370.8	68,489.8
CNFP 16383	2,420.8 b	0.77*	81,615.8**		76.72	135,596.3	175,401.0	75,889.1
CNFP 16384	2,419.5 b	1.21*	1,432.2ns		97.81	107,243.8	98,200.1	120,809.2
CNFP 16404	2,409.5 b	0.61**	-5,269.6ns		94.81	136,987.9	221,079.4	10,850.7
CNFP 16416	2,441.7 b	1.09ns	22,064.1ns		94.42	90,814.0	101,445.0	74,867.4
CNFP 16459	2,474.3 b	1.03ns	-9,240.3ns		98.76	79,082.7	98,860.0	49,416.8

• ^**
  ,*, ^nssignificant (P<0.01), significant (P<0.05) and non-significant, respectively. Means followed by the same letters do not differ by the Scott and Knott test, at 1% probability.

Genotype grain yield averages were compared by Scott and Knott test, at 1% probability. It is observed the formation of two classes, and the cultivars BRS Esteio and BRS FP 403 stood out for presenting the highest averages (Table 4). The imbred line CNFP 16459 presented productivity higher than the general average (2,462.4 kg.ha^-1), but different from the cultivars already mentioned.

Grain yield (${\beta }_0$) ranged from 2.320,2 to 2.820,0 kg.ha^-1, in the genotypes IPR Uirapuru and BRS Esteio, respectively (Table 4), which denotes the high potential for productivity of the evaluated set when compared to the national (982 kg.ha^-1) and state (1.222 kg.ha^-1) means of the 2022/2023 harvest (Brasil, 2024). It is observed that three of the eleven genotypes evaluated presented yield above the general average, namely, the cultivars BRS Esteio and BRS FP 403 and the lineage CNFP 16459 (Table 4). According to Vencovsky and Barriga (1992), genotypes with grain yield averages above the general average present better adaptation.

Note that the three genotypes selected as the best fit (${\beta }_{0i}$ > overall mean) also exhibited regression coefficients statistically equal to one (${\widehat{\beta }}_{1i}$=1), which indicates their broad or general adaptability under the different environmental conditions found, that is, the genotypes maintained their yield close to the general average, under both favorable and unfavorable environmental conditions.

It was observed that genotype CNFP 16384 exhibited ${\widehat{\beta }}_{1i}$ statistically higher than the unit (${\widehat{\beta }}_{1i}$ > 1), that is, adaptability specific to favorable environments, which suggests that this genotype has great capacity to advantageously benefit from the improvement of the environment, thereby increasing its average productivity. Therefore, this genotype must be used with caution, since its yields may decrease in unfavorable environments, that is, in regions with low technological level and/or subject to edaphoclimatic variations. In contrast, the genotypes CNFP 16383 and CNFP 16404 presented a ${\widehat{\beta }}_{1i}$ value significantly below one (${\widehat{\beta }}_{1i}$ < 1), which indicates adaptability specific to unfavorable environments. Therefore, they can be considered genotypes with adaptation to unfavorable environments, due to their low capacity to respond to improved environmental conditions. (Table 4).

It has been defined that the selected genotypes will be explored under both favorable and unfavorable environmental conditions and that there is no interest in recommending genotypes that presented ${\widehat{\beta }}_{1i}$i > 1 or ${\widehat{\beta }}_{1i}$i < 1. Thus, taking into account the variables ${\beta }_{0i}$ and ${\beta }_{1i}$, genotypes BRS Esteio, BRS FP 403 and CNFP 16459 presented yield above the general average and index equal to 1. In other words, they have broad adaptability and can be classified as responsive to favorable and unfavorable conditions (general adaptability).

According to the parameter that classifies stability in the method of Eberhart and Russell (1966), the regression deviation (${\sigma }_{di2}^2$), it was observed that circa 82% of all genotypes evaluated presented non-significant deviations (${\sigma }_{di2}^2=0$, which demonstrates that most of them have high performance stability. In other words, their average productivity did not vary in the evaluated environments and were little affected by environmental conditions. However, genotypes CNFP 16379 and CNFP 16383 presented significant regression deviation (${\sigma }_{di2}^2\ne 0$) and, thus, unpredictable performance in the evaluated environments.

As for the estimates of the coefficients of determination (R²), this measure helps to compare genotypes and reflects the degree of fit of the model to the yields found for each genotype evaluated. It was observed that 91% of the genotypes evaluated presented R² > 80%, a percentage considered by Cruz et al. (2014) as a reference for the regression to satisfactorily explain the performance of a genotype depending on the environment.

The ideal genotype, according to Eberhart and Russell (1966), presents high productivity (${\beta }_{0i}$ > overall mean), regression coefficient equal to the unit (${\widehat{\beta }}_{1i}$ = 1) (general adaptability) and regression deviation equal to zero (${\sigma }_{di2}^2=0$) (high stability). In this sense, it is possible to observe that the genotypes BRS Esteio, BRS FP 403 and CNFP 16459 presented these three conditions simultaneously and are recommended for cultivation in the North and Northwest regions of Rio de Janeiro.

By the Lin and Binns (1988) method, the genotypes BRS Esteio, BRS FP 403 and CNFP 16459 presented the lowest Pi value, which evidences greater production stability, and grain yield above the general average (Table 4). Thus, genotypes with lower Pi are desirable, since they presented less deviation from the maximum productivity in each environment. In other words, their performance was close to the maximum rate in most environments.

Considering the decomposition proposed by Carneiro (1998), the genotypes BRS Esteio, BRS FP 403 and CNFP 16384 were identified with adaptation to favorable environments ($P_{if}$), while genotypes BRS Esteio, CNFP 16404 and CNFP 16379 adapted to unfavorable environments ($P_{id}$).

The methodologies of Eberhart and Russell (1966) and Lin and Binns (1988), modified by Carneiro (1998), were consistent in the identification of genotypes with production stability (BRS Esteio, BRS FP 403 and CNFP 16459), with adaptation to favorable environments (BRS Esteio, BRS FP 403 and CNFP 16384) and unfavorable environments (BRS Esteio and CNFP 16404).

Figure 1 presents the visual grouping of the tested environments based on the G × E interaction between the best genotypes. It is observed that the analysis based on this interaction presented 70.3% of the total variation found between the genotypes. These results reveal the efficiency of Biplot graphs, which explain the large proportions of the sums of squares of genotypes and G × E interactions, and allow an accurate understanding of the results and reliability for the selection of superior genotypes (Oliveira et al., 2018; Santos et al., 2019).

Figure 1
GGE biplot “which-won-where” for grain yield in black bean genotypes, which indicates the genotypes with the best yield and the environment where it was obtained, Rio de Janeiro, 2018-2019. Genotypes: G1 (BRS Esteio), G2 (BRS FP 403), G3 (IPR Tuiuiu), G4 (IPR Uirapuru), G5 (CNFP 16379), G6 (CNFP 16380), G7 (CNFP 16383), G8 (CNFP 16384), G9 (CNFP 16404), G10 (CNFP 16416) and G11 (CNFP 16459). Environments: A1 (Campos dos Goytacazes 2018), A2 (Campos dos Goytacazes 2019), A3 (Macaé 2018), A4 (Macaé 2019) and A5 (Italva 2019).

In Figure 1, the sectors are originated by perpendicular lines drawn from the origin of the biplot (0,0). The six blue sectioned lines (perpendicular to the PC1 axis) divide the biplot into six sections. In this case, the five evaluation environments were separated into two groups by the lines that came out of the Biplot origin. The first group was formed solely by the A1 environment, while the second group, by the other environments (A2, A3, A4 and A5), which turned it into a mega-environment. Genotypes located within the same sector are the most adapted to that environment, while the performance of the genotypes located within the polygon is poorer.

According to Yan and Kang (2019), a mega-environment can be defined as the condition in which a group of environments is positively correlated, with one or more specifically adapted genotypes. In the GGE Biplot analysis, when mega-environments are studied, the mean in the graph is not linked to the general mean, but to the mean of the mega-environment. This perspective helps in the identification of genotypes with broad or specific adaptation to certain environments or environmental groups (Yan and Kang, 2019).

The vertices of the polygon were defined by the genotypes located farthest from the Biplot origin, that is, those with the best performance and best adaptation within each respective sector, namely, genotypes G1, G10, G6, G4, G9 and G7 (Figure 1). Out of these six, it is observed that genotypes G10, G6 and G4 did not group into any of the five environments evaluated. For this reason, they should be considered unfavorable to the groups of environments tested, and present low productivity.

In the analysis of the performance of genotypes per environment, it is observed that G1 stood out for grain yield in environments A2, A3, A4 and A5 (mega-environment). On the other hand, G7 obtained the best productive performance in the A1 environment (Figure 1).

Selecting genotypes that present high average productivity and high stability is one of the objectives of most breeders and the GGE biplot graph “mean versus stability” (Figure 2) allows to visualize these two characteristics in a simplified way. By this method, the productivity and stability of the genotypes are evaluated from the average environment coordination (AEC) (Yan et al., 2000).

Figure 2
GGE biplot “Average vs Stability” for grain yield of black bean genotypes, Rio de Janeiro, 2018-2019. Genotypes: G1 (BRS Esteio), G2 (BRS FP 403), G3 (IPR Tuiuiu), G4 (IPR Uirapuru), G5 (CNFP 16379), G6 (CNFP 16380), G7 (CNFP 16383), G8 (CNFP 16384), G9 (CNFP 16404), G10 (CNFP 16416) and G11 (CNFP 16459). Environments: A1 (Campos dos Goytacazes 2018), A2 (Campos dos Goytacazes 2019), A3 (Macaé 2018), A4 (Macaé 2019) and A5 (Italva 2019).

Based on Figure 2, an ideal environment is defined from the average of the scores of the two main components (PC1 and PC2) of all environments. The line passing through the biplot origin and the ideal environment is called the ideal environment axis and represents the AEC abscissa. The ordinate AEC is the axis that passes through the origin and is perpendicular to the abscissa AEC. Unlike the abscissa AEC, which has only one direction, with the arrow pointing to the largest genotypic value of main effect, the ordered AEC is represented by two arrows that point in the opposite direction of the origin of the biplot and indicate a greater effect of the genotype and interaction environment and less stability.

Genotype stability is defined by the vector extension over the axis of the ideal environment, plotted over the abscissa AEC, and indicates the estimate of the magnitude of the main effect of genotypes (G) versus the main effect of the G × E interaction. Thus, the further the genotype is from this line, the greater its performance variability (less stability). Consequently, the smaller its distance from the origin, the greater the performance stability of the genotype (Yan, 2011).

It is observed that G1 average yield was higher than the general average of the group of genotypes evaluated, but its stability was lower. In contrast, G2 was classified as stable. In addition, G11 presented yield above the general average and greater performance stability, due to the smaller extension of its vector. The other genotypes obtained grain yield below the general average, among which, G3, G4 and G5 presented the greatest stability (Figure 2).

Figure 3 presents the Biplot entitled “Discriminative vs. Representative”, in which the higher the value of PC1, the greater the discrimination ability of the variable. On the other hand, the smaller the angle formed between the variable and the line representing the circle formed by the arrow, in other words, the smaller the PC2, the greater the representativeness (Yan and Kang, 2019). This assessment aims to identify environments suitable for the effective selection of superior genotypes, that is, the environment is endowed with greater capacity for genotype discrimination and representativeness.

Figure 3
GGE Biplot of discrimination and representativeness between environments, Rio de Janeiro, 2018-2019. Genotypes: G1 (BRS Esteio), G2 (BRS FP 403), G3 (IPR Tuiuiu), G4 (IPR Uirapuru), G5 (CNFP 16379), G6 (CNFP 16380), G7 (CNFP 16383), G8 (CNFP 16384), G9 (CNFP 16404), G10 (CNFP 16416) and G11 (CNFP 16459). Environments: A1 (Campos dos Goytacazes 2018), A2 (Campos dos Goytacazes 2019), A3 (Macaé 2018), A4 (Macaé 2019) and A5 (Italva 2019).

Figure 3 shows that A5 (Italva, 2019) is the environment that most discriminated the genotypes, that is, the one with the highest vector for grain yield, while the A2 environment, presented the smallest vector, that is, it provided little or no information on differences between genotypes.

Figure 3 also shows that the representative environments can represent the others. In this scenario, those presenting small angles with the average environment axis are more representative than those with larger angles. Therefore, it is observed that A4 was the most representative environment, in other words, the one forming the smallest angle with the average environment axis, followed by environments A2 and A3. On the other hand, environments A5 and A1 presented the largest angles, that is, they were rated with the lowest representativeness (Figure 3).

Figure 3 reveals that, despite having been classified as the one with the greatest discriminating power, the environment A5 had low representation among the evaluated environments. The opposite is observed in the environment A2 (Campos dos Goytacazes 2019), which presented lower discriminating power, but obtained, on the other hand, the highest representativeness among the environments. Finally, environments A3 (Macaé 2018) and A4 (Macaé 2019) were discriminative, that is, they presented yields higher than the general average, in addition to being representative, that is, they presented smaller angles with the medium axis of the environment, so they were considered closer to an ideal location for recommending superior adapted genotypes, focused on higher grain yields.

The ideotype is configured as an ideal hypothetical model of a plant within a given species, and is used as a reference during the assessment of different genotypes (Figure 4). Its classification is graphically defined by its vector length in PC1 (high yield) and PC2 (high stability), oriented by a point located in the center of the concentric circles. The genotype is considered ideal when it has a long projection on PC1 and a smaller projection on PC2, located as close as possible to the center of the first concentric circle. Therefore, the genotypes closest to this limit are the closest to the “ideal”. In other words, they presented better performance, greater stability and better adaptability, compared to those that are further away (Yan and Kang, 2019).

Figure 4
GGE Biplot representing the 'Ideotype' for grain yield of black bean genotypes, Rio de Janeiro, 2018-2019. Genotypes: G1 (BRS Esteio), G2 (BRS FP 403), G3 (IPR Tuiuiu), G4 (IPR Uirapuru), G5 (CNFP 16379), G6 (CNFP 16380), G7 (CNFP 16383), G8 (CNFP 16384), G9 (CNFP 16404), G10 (CNFP 16416) and G11 (CNFP 16459). Environments: A1 (Campos dos Goytacazes 2018), A2 (Campos dos Goytacazes 2019), A3 (Macaé 2018), A4 (Macaé 2019) and A5 (Italva 2019).

The genotype G1 (BRS Esteio), positioned in the first concentric circle, was the closest genotype to an ideotype (Figure 4), showed high stability and productivity, proving to be a promising genotype for grain production in the state of Rio de Janeiro. Genotype G2 (BRS FP 403), in the second concentric circle, stood out for presenting similar performance to the ideal genotype in terms of grain yield and phenotypic stability.

4. Conclusion

The significant G × A interaction for grain yield reflected a differential performance of the genotypes in the different environments evaluated.

The genotypes BRS Esteio, BRS FP 403 and CNFP 16459 presented higher productivity, compared to the general average and were considered the ones with the best adaptation. Furthermore, these genotypes expressed broad adaptability under different environmental conditions and high performance stability.

The genotype BRS Esteio was classified as the ideotype. It presented a predictable behavior, was responsive to environmental variations and its performance was above the general average. The Macaé (2019) environment better discriminated the genotypes and was more representative.

Thus, the methodologies of Eberhart and Russell (1966), Lin and Binns (1988) and GGE Biplot proved to be effective and concordant in identifying superior black bean genotypes.

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Publication Dates

• Publication in this collection
  31 Jan 2025
• Date of issue
  2024

History

• Received
  03 May 2024
• Accepted
  01 Nov 2024