ABSTRACT The number of experiments that provides greater detail in the differentiation of common bean genotypes for grain physical traits and minerals in cluster analysis is not known. This study was undertaken to determine the number of experiments necessary to more accurately differentiate common bean genotypes for grain physical traits and minerals in cluster analyses. Seven traits of grain physical quality and the concentration of six minerals were evaluated in 17 common bean genotypes with carioca (9) and black (8) grains. Statistical analyses were performed in data obtained from one, two, three and four experiments. A significant genotype × experiment interaction occurred for all traits, except for the potassium concentration. Tocher’s and the unweighted pair group method with arithmetic mean (UPGMA) cluster analyses were efficient in differentiating common bean genotypes by grain type when the data obtained from one experiment were considered. However, the use of data obtained from four experiments made it possible to recognize differences regarding grain lightness and brightness as well as the other traits. Four experiments are need for the Tocher’s and the UPGMA cluster analyses to more accurately differentiate carioca and black bean genotypes for grain physical traits and minerals.

ABSTRACT: The selection of common bean (Phaseolus vulgaris L.) lines based on grain quality and mineral concentration traits will be more efficient if a minimum number of experiments is established. This study was carried out to determine whether grain quality and mineral concentration traits are significantly affected by the genotype × environment interaction; to estimate heritability and genetic gain in individual and combined experiments; and to select superior common bean lines considering a minimum number of experiments. A total of 17 common bean genotypes were evaluated in four experiments. Grain quality was determined through seven traits, and the concentration of six minerals was analyzed by acid digestion. Statistical analyses were completed using data obtained from both individual (I, II, III and IV) and combined (I and II; I, II and III; and I, II, III and IV) experiments. Except for the potassium concentration, all traits showed a significant genotype × environment interaction effect. Heritability and genetic gain estimates of grain quality and mineral concentration traits varied when the data were obtained from one or more experiments. Genetic gain may be inflated because of the data being based on one or two experiments. Four carioca bean (BRS MG Uai, LP 09-33, LEC 01-16 and Pérola) and four black bean (TB 02-19, CHP 04-239-52, TB 03-11 and IAC Netuno) genotypes were selected for their high grain quality and mineral concentration based on four experiments. Data from at least four experiments should be used to select common bean lines superior in grain quality and mineral concentration traits to increase the efficiency of simultaneous selection.

RESUMO O desenvolvimento de novas linhagens de feijão com caracteres que atendam a preferência dos consumidores aumenta a sua probabilidade de uso na alimentação. Os objetivos desse trabalho foram avaliar a variabilidade genética de linhagens e cultivares de feijão para caracteres da qualidade de grãos e concentração de minerais e selecionar as linhagens superiores usando o índice de soma de ranks com pesos econômicos diferenciados. Os experimentos foram conduzidos em duas épocas de cultivo para avaliar 17 genótipos de feijão. Os dez caracteres da qualidade de grãos e a concentração de sete minerais foram determinados em grãos crus. Efeito significativo para genótipo foi observado para 15 caracteres e interação genótipo x ambiente significativa foi constatada para 14 caracteres. Alta herdabilidade (≥ 60,00%) e estimativas de ganho genético favoráveis aos objetivos da seleção de linhagens de feijão de grãos claros e escuros superiores para a maioria dos caracteres da qualidade de grãos e concentração de minerais foram obtidas. As linhagens e cultivares de feijão apresentam variabilidade genética para todos os caracteres da qualidade de grãos e concentração de minerais, exceto para a concentração de cobre. Quatro genótipos de feijão carioca (LEC 04-16, Linhagem 110, UEM 266 e Pérola) e quatro genótipos de feijão preto (TB 17-03, SM 1510, BRS Intrépido e Fepagro Triunfo) são superiores para vários caracteres da qualidade de grãos e possuem alta concentração de potássio, fósforo, cálcio e ferro, evidenciando potencial de uso no melhoramento e na nutrição.

ABSTRACT The development of new common bean lines with traits that meet consumer preference increases their probability of use as food. The objectives of this work were to evaluate the genetic variability of common bean lines and cultivars for grain quality traits and mineral concentration and to select superior lines using the rank-sum index with differentiated economic weights. The experiments were carried out in two growing seasons to evaluate 17 common bean genotypes. The ten grain quality traits and the concentration of seven minerals were determined in raw grains. A significant effect for genotype was observed for 15 traits and a significant genotype x environment interaction was found for 14 traits. High heritability (≥ 60.00%) and genetic gain estimates favorable to the objectives of selection of superior light-and dark-grain common bean lines for most of grain quality traits and mineral concentration were obtained. The common bean lines and cultivars show genetic variability for all grain quality traits and mineral concentration, except for copper concentration. Four carioca (LEC 04-16, Linhagem 110, UEM 266 and Pérola) and four black (TB 17-03, SM 1510, BRS Intrépido and Fepagro Triunfo) common bean genotypes are superior for several grain quality traits and have high concentrations of potassium, phosphorus, calcium and iron, showing potential for use in breeding and nutrition.

ABSTRACT An approach to the number of experiments that should be used in correlation analyses aimed at increasing efficiency in indirect selection for grain yield is unprecedented for common bean (Phaseolus vulgaris L.). We hypothesize that trait correlation estimates vary in response to the growing environment. This study was undertaken to investigate the correlations between plant architecture and yield traits in common bean lines and to determine the minimum number of experiments required by Pearson’s linear correlation analysis to increase efficiency in indirect selection for grain yield. Seventeen common bean genotypes were evaluated for 17 agronomic traits in four experiments. Pearson’s linear correlation analyses were carried out using data from individual experiments and different combinations of growing seasons and years. Ten out of the 17 agronomic traits showed a significant genotype × environment interaction effect, meaning that common bean genotypes exhibited variation for most of the traits evaluated in different growing seasons and years, which resulted in changes in the correlation estimates between these traits. Pearson’s linear correlation estimates obtained between plant architecture and yield traits varied in significance, magnitude, and sign when data from individual experiments and combinations of growing seasons and years were considered. The number of grains per pod is the most promising agronomic trait used in indirect selection for grain yield in common bean lines. Data from at least three experiments should be used in Pearson’s linear correlation analysis to achieve greater efficiency in indirect selection for grain yield in common bean lines.

ABSTRACT Estimating the genetic gain obtained for technological quality traits over the years makes it possible to analyze whether the changes made meet consumer preferences, which represents an important innovation for common-bean breeding programs. The objectives of this study were to obtain genetic gain estimates for technological grain quality traits of common bean lines and investigate whether the modifications made were favorable in the context of sustainability and food and nutritional security for the coming generations. Twenty-four experiments were conducted between the years 2010 and 2022 and a total of 75 common bean lines were evaluated. Genetic gains of technological grain quality traits were determined by the Vencovsky’s (1988) method adapted for biennia. There was a significant effect of genotype for most traits evaluated, which shows the existence of genetic variability. Mass of 100 grains and water absorption had a negative genetic gain of -2.91% and -0.55% per year, respectively, indicating a reduction in these traits. Genetic gain was zero for L* value (lightness) and cooking time, denoting a plateau for these traits. Most of the common bean lines exhibit adequate L* values for carioca (L* ≥ 53) and black (L* ≤ 22) bean grains; a mass of 100 grains from 20 to 25 g; and fast cooking (≤ 25 min). The new common bean cultivars released for cultivation in the southern region of Brazil have high technological grain quality, being favorable in a context of sustainability and food and nutritional security for the coming generations.

RESUMO Estimativas de ganho genético para caracteres da qualidade tecnológica obtidas ao longo dos anos permitem analisar se as mudanças realizadas atendem a preferência dos consumidores, o que representa uma importante inovação para os programas de melhoramento de feijão. Os objetivos deste trabalho foram obter estimativas de ganho genético para caracteres da qualidade tecnológica de grãos em linhagens de feijão e analisar se as modificações efetuadas foram favoráveis em um contexto de sustentabilidade e de segurança alimentar e nutricional das próximas gerações. Um total de 24 experimentos foram conduzidos entre os anos de 2010 a 2022, avaliando 75 linhagens de feijão. O ganho genético dos caracteres da qualidade tecnológica foi determinado pelo método de Vencovsky (1988), adaptado para biênios. Efeito significativo para genótipo foi observado para a maioria dos caracteres, evidenciando que há variabilidade genética. Massa de 100 grãos e absorção de água apresentaram ganho genético negativo de -2,91% e de -0,55% por ano, respectivamente, indicando redução nestes caracteres. Ganho genético nulo foi constatado para o valor de L* (luminosidade) e para tempo de cozimento, evidenciando um platô nesses caracteres. A maioria das linhagens de feijão apresenta valores de L* adequados para grãos carioca (L* ≥ 53) e preto (L* ≤ 22), massa de 100 grãos de 20 a 25 g e cozimento rápido (≤ 25 min). As novas cultivares de feijão lançadas para o cultivo na região Sul do Brasil têm alta qualidade tecnológica, sendo favoráveis em um contexto de sustentabilidade e de segurança alimentar e nutricional das próximas gerações.

ABSTRACT The determination of the number of experiments required to achieve high coincidence in identifying significant correlations between culinary quality traits and/or mineral concentrations is unprecedented for common bean. The objectives of this study were to evaluate correlations between culinary quality traits and minerals in common bean lines considering data from individual and combined experiments; define the minimum number of experiments that provide high coincidence in identifying significant correlations; and identify promising traits for indirect selection. For this, seven traits related to culinary quality and the concentration of six minerals in grains of 17 common bean genotypes were evaluated. Pearson’s linear correlation analysis was performed on data obtained from four individual experiments and six combinations of experiments. Twelve of the 13 evaluated traits showed a significant genotype × environment interaction effect, indicating that the common bean genotypes exhibited differences in culinary quality and mineral concentration when these were determined in different experiments. Pearson’s linear correlation coefficients vary in significance, sign, and/or magnitude for the traits analyzed in individual and combined experiments. The use of data from three experiments provides a high coincidence percentage in identifying significant correlations in Pearson’s linear correlation analysis. Common bean lines with high culinary quality and greater mineral concentration can be indirectly selected based on higher L* values (grain lightness) and higher calcium concentrations.

RESUMO A caracterização da divergência genética de cultivares de feijão para vários caracteres relacionados a arquitetura de planta e produtividade de grãos é inédita. Os objetivos desse estudo foram avaliar se cultivares de feijão de diferentes tipos de grãos diferem para 12 caracteres da arquitetura de planta e para produtividade de grãos, estudar as correlações entre esses caracteres, analisar a divergência genética dessas cultivares e selecionar as cultivares superiores para esses caracteres. Um total de 22 cultivares de feijão com os tipos de grãos mais produzidos no Brasil foram avaliadas em duas épocas de cultivo. A arquitetura de planta foi analisada por 12 caracteres e a produtividade de grãos foi determinada na maturação. Efeitos significativos de genótipo e de interação genótipo x ambiente foram obtidos, portanto há variabilidade genética para todos os caracteres avaliados. Vários caracteres da arquitetura de planta foram correlacionados, entretanto nenhum foi altamente correlacionado com a produtividade de grãos. Os comprimentos do primeiro e do segundo entrenós apresentam maior importância na diferenciação entre as cultivares de feijão. As análises de componentes principais e de Tocher resultaram na formação de quatro e de sete grupos de cultivares, respectivamente. Os dois métodos são eficientes na análise da divergência genética, no entanto o método de Tocher é mais informativo. As cultivares de feijão BRS Campeiro, SCS 205 - Riqueza, BRS Esteio, IAC Imperador e Guapo Brilhante apresentam um alto potencial de produtividade de grãos, mas apenas as cultivares BRS Campeiro, BRS Esteio e Guapo Brilhante têm arquitetura de planta ereta.

ABSTRACT The characterization of genetic divergence in common bean cultivars for various traits related to plant architecture and grain yield is unprecedented. This study proposes to determine whether common bean cultivars of different grain types differ for 12 traits of plant architecture and grain yield; examine the correlations between these traits; analyze the genetic divergence of these cultivars; and select superior cultivars for these traits. A total of 22 common bean cultivars with the grains types most produced in Brazil were evaluated in two growing seasons. Plant architecture was analyzed based on 12 traits, and grain yield was determined at maturity. Significant genotype and genotype × environment interaction effects were obtained, indicating the existence of genetic variability for all evaluated traits. Several plant architecture traits were correlated, but none was highly correlated with grain yield. Firstand second-internode lengths are more important in differentiating common bean cultivars. Principal component and Tocher’s analyses resulted in the formation of four and seven groups of cultivars, respectively. Both methods are efficient in analyzing genetic divergence; however, Tocher's method is more informative. Cultivars BRS Campeiro, SCS 205 - Riqueza, BRS Esteio, IAC Imperador and Guapo Brilhante have a high grain yield potential, but only BRS Campeiro, BRS Esteio and Guapo Brilhante have upright plant architecture.

ABSTRACT The selection of common bean lines with intermediate cycle, upright plant architecture and high grain yield is an important goal of breeding programs. This study proposes to examine the genetic diversity of common bean genotypes for agronomic traits, select superior genotypes for traits that provide high agronomic performance and define promising crosses. Seventeen common bean genotypes were evaluated in two growing seasons in 2019. A total of 17 agronomic traits were determined, which comprised the cycle, 12 traits related to plant architecture and four traits related to production. All traits exhibited a significant genotype × environment interaction, except for lodging and insertion of the first pod. Tocher's and the unweighted pair group method with arithmetic mean (UPGMA) cluster analyses resulted in the formation of three groups of genotypes. Tocher and UPGMA analyses do not allow identifying differences between the superior genotypes of high agronomic performance. Cultivars Fepagro Triunfo and Fepagro Garapiá and lines SM 1510 and Linhagem 110, selected by the multiplicative index, stand out for different agronomic traits. The cross between cultivars Fepagro Triunfo and Fepagro Garapiá (superior agronomic traits) is recommended for the breeding program. Recombiants with high agronomic performance could be setected from the tested hybrid combinations.

RESUMO O desenvolvimento de linhagens de feijão com cozimento rápido e biofortificadas para minerais representa uma importante inovação nos programas de melhoramento. Os objetivos deste trabalho foram avaliar se linhagens elite de feijão Mesoamericano diferem para tempo de cozimento e concentração de minerais e selecionar linhagens com cozimento rápido e biofortificadas para minerais. Os experimentos foram conduzidos em duas épocas de cultivo, possibilitando a avaliação de 16 genótipos de feijão. O tempo de cozimento foi determinado em um cozedor de Mattson e a concentração de minerais foi analisada por digestão ácida. Os dados obtidos foram submetidos às análises de: variância individual, variância conjunta, agrupamento pelo teste de Scott-Knott e índice de seleção (multiplicativo). Efeito significativo da interação genótipo x ambiente foi observado para o tempo de cozimento e concentração de potássio, ferro, zinco e cobre. Apenas para a concentração de fósforo não se observou variabilidade genética entre as linhagens. A classificação das melhores linhagens de feijão não foi igual para todos os caracteres avaliados nos diferentes ambientes, quando se usou o teste de Scott-Knott. A aplicação do índice multiplicativo possibilita a seleção das linhagens superiores para todos os caracteres: DF 07-11, DF 08-21, DF 08-20 e DF 08-28. Essas linhagens de feijão apresentam cozimento muito rápido (até 15 min), alta concentração de potássio (> 12,00 g kg-1 de matéria seca - MS) e os maiores valores médios de concentração de microminerais e serão selecionadas pelo programa de melhoramento.

ABSTRACT Developing fast-cooking, mineral-biofortified common bean lines represents an important innovation for breeding programs. Thus, this study was conducted to determine whether elite Mesoamerican common bean lines differ for cooking time and mineral concentration and to select fast-cooking, mineral- biofortified lines. The experiments were carried out in two growing seasons, in which 16 common bean genotypes were evaluated. Cooking time was determined using a Mattson cooker, and the minerals were analyzed by acid digestion. The resulting data were subjected to individual analysis of variance, combined analysis of variance, clustering by the Scott-Knott test, and selection index (multiplicative). There was a significant genotype × environment interaction effect for cooking time and the concentrations of potassium, iron, zinc and copper. Only the phosphorus concentration showed no genetic variability between the common bean lines. The ranking of the best common bean lines differed for all traits examined in the different environments, according to the Scott-Knott test. The use of the multiplicative selection index allows selecting superior common bean lines for all traits, namely, DF 07-11, DF 08-21, DF 08-20 and DF 08-28. These lines exhibit a very short cooking time (up to 15 min), high potassium concentration (> 12.00 g kg-1 of dry matter) and the highest mean values of micromineral concentration, and will thus be selected by the breeding program.

ABSTRACT: Simultaneous selection for various agronomic traits, cooking time and mineral concentration are major challenges for common-bean (Phaseolus vulgaris L.) breeding programs. The authors of this study proposed to analyze genetic gain estimates obtained by direct and indirect selection using selection indices and economic weights for 13 traits, and to determine the most efficient selection strategy for the simultaneous selection of fast cooking, mineral-biofortified common bean cultivars with high agronomic performance. For this purpose, three experiments were carried out in different growing seasons to evaluate 49 common bean cultivars of different grain types. Agronomic performance was evaluated based on six traits; cooking time was determined using a Mattson cooker; and the concentration of six minerals was analyzed in samples of raw grains. Significant genotype × environment interaction or genotype effects were observed for all traits, indicating the existence of genetic variability. Direct selection resulted in high genetic gain estimates for individual traits, but caused undesirable changes in one or more of the traits under selection. The classic, base, desired-gains and rank-sum selection indices tested with six economic weights do not provide genetic gain estimates favorable to the selection of all traits. The multiplicative index is the best selection strategy for use in the breeding program when aiming at the simultaneous selection of fast cooking, mineral-biofortified common bean cultivars with high agronomic performance.

Resumo O objetivo deste trabalho foi avaliar a precisão experimental de dez estatísticas, na avaliação de caracteres relacionados à qualidade tecnológica, em linhagens de feijão-comum (Phaseolus vulgaris). Dezessete experimentos foram realizados, entre 2010 e 2019, com 116 genótipos de feijão de diferentes tipos de grãos. A qualidade tecnológica foi quantificada para os seguintes caracteres: massa de 100 grãos, valor de luminosidade do grão (L*), absorção e tempo de cozimento. Obteve-se um efeito de genótipo significativo em 100% dos experimentos quanto ao valor de L* e à massa de 100 grãos, em 76,92% quanto à absorção e em 94,12% quanto ao cozimento. O valor de L* e a massa de 100 grãos foram determinados com alta precisão experimental por todas as estatísticas. A absorção e o tempo de cozimento mostraram alta precisão experimental, quando analisados pelas seguintes estatísticas: valor do teste F para genótipo (Fc), coeficiente de variação genética (CVG), coeficiente de variação relativa (CVR), herdabilidade (h2) e acurácia seletiva (AS). As estatísticas Fc, CVG, CVR, h2 e AS propiciaram alta precisão experimental na avaliação de caracteres da qualidade tecnológica em linhagens de feijão. A acurácia seletiva é a estatística mais apropriada, para selecionar linhagens de feijão superiores quanto à qualidade de grãos e de cozimento em programas de melhoramento.

Abstract The objective of this work was to evaluate the experimental precision of ten statistics in the evaluation of characters related to the technological quality of common bean (Phaseolus vulgaris) lines. Seventeen experiments were carried out between 2010 and 2019, with 116 common bean genotypes of different types of grain. Technological quality was determined for the following characters: mass of 100 grains, grain lightness value (L*), absorption, and cooking time. A significant genotype effect was obtained in 100% of the experiments for L* value and mass of 100 grains, in 76.92% for absorption, and in 94.12% for cooking time. The L* value and mass of 100 grains were determined with a high experimental precision by all statistics. Absorption and cooking time showed a high experimental precision, when analyzed by the following statistics: F-test value for genotype (Fc), genetic variation coefficient (GVC), relative variation coefficient (RVC), heritability (h2), and selective accuracy (SA). The statistics Fc, GVC, RVC, h2, and SA provided a high experimental precision in the evaluation of the characters related to technological quality in common bean lines. Selective accuracy is the most appropriate statistics to select superior common bean lines for grain and cooking quality in breeding programs.

RESUMO A caracterização da diversidade genética de genótipos de feijão para vários caracteres agronômicos permite selecionar parentais promissores e identificar genótipos de alto desempenho agronômico. Nesse contexto, foram objetivos desse trabalho avaliar a diversidade genética de variedades locais e cultivares de feijão para 14 caracteres agronômicos, estudar as correlações entre esses caracteres, definir cruzamentos promissores e selecionar genótipos com alto desempenho agronômico. Um total de 49 genótipos de feijão foram avaliados em três épocas de cultivo, sendo 37 variedades locais e 12 cultivares de feijão. Efeito significativo da interação genótipo x ambiente ou de genótipo foi observado para todos os caracteres agronômicos e isso possibilita o estudo da divergência genética. Vários caracteres da arquitetura de planta foram correlacionados, enquanto que a produtividade de grãos mostrou alta correlação com a inserção da última vagem (r = 0,74), o número de vagens por planta (r = 0,74) e a massa de 100 grãos (r = - 0,64). O método de agrupamento Vizinho mais Distante separou os genótipos de feijão em dois grupos Mesoamericano e Andino, pois a massa de 100 grãos apresentou a maior contribuição para a diferenciação entre os genótipos. O método de Tocher foi mais informativo e dividiu os genótipos de feijão em 12 grupos. Os seguintes cruzamentos são recomendados Vagem Roxa × IPR Juriti, Vagem Roxa × Macanudo, Fepagro Triunfo × IPR Juriti, Fepagro Triunfo × Macanudo, Guapo Brilhante × IPR Juriti e Guapo Brilhante × Macanudo. Os genótipos de feijão Fepagro Triunfo, IPR Juriti, Guapo Brilhante, BRS Campeiro e Vagem Roxa apresentam alto desempenho agronômico e deverão ser selecionados pelo programa de melhoramento.

ABSTRACT The characterization of genetic diversity in common bean genotypes for various agronomic traits enables the selection of promising parents and the identification of genotypes with high agronomic performance. The present study proposes to evaluate the genetic diversity of common bean landraces and cultivars for 14 agronomic traits; examine the correlations between these traits; define promising crosses; and select genotypes with high agronomic performance. A total of 49 common bean genotypes were evaluated in three growing seasons, consisting of 37 landraces and 12 common bean cultivars. Significant effects of genotype × environment interaction or genotype were observed for all agronomic traits, thereby allowing the study of genetic divergence. Several plant-architecture traits were correlated with each other, whereas grain yield was highly correlated with insertion of the last pod (r = 0.74), number of pods per plant (r = 0.74) and mass of 100 grains (r =-0.64). The furthest-neighbor method separated the common bean genotypes into two groups, Mesoamerican and Andean, and mass of 100 grains showed the greatest contribution to the differentiation between the genotypes. Tocher's method was more informative and divided the common bean genotypes into 12 groups. The following crosses are recommended: Vagem Roxa × IPR Juriti, Vagem Roxa × Macanudo, Fepagro Triunfo × IPR Juriti, Fepagro Triunfo × Macanudo, Guapo Brilhante × IPR Juriti, and Guapo Brilhante × Macanudo. The common bean genotypes Fepagro Triunfo, IPR Juriti, Guapo Brilhante, BRS Campeiro and Vagem Roxa have high agronomic performance and should thus be selected by the breeding program.

Resumo O objetivo deste trabalho foi avaliar a variabilidade genética de genótipos de feijão (Phaseolus vulgaris) de diferentes tipos de grãos quanto à concentração de macro e microminerais, bem como selecionar genótipos superiores pelo índice multiplicativo. Um total de 22 genótipos de feijão foi avaliado em experimentos conduzidos nas estações seca e chuvosa. A concentração de seis minerais (potássio, fósforo, magnésio, ferro, zinco e cobre) foi determinada, e o índice multiplicativo foi aplicado a experimentos individuais e combinados. Houve efeito significativo da interação genótipo x ambiente sobre a concentração de todos os minerais, e, quando o efeito de genótipo foi decomposto em tipos de grãos, os genótipos diferiram quanto à concentração de três ou mais minerais. Há variabilidade genética na concentração de macro e microminerais nos genótipos de feijão comum avaliados nas estações seca e chuvosa. Nos experimentos combinados, são observados altas estimativas de herdabilidade (≥ 62,60%) e maior ganho genético total (283,59%). O índice multiplicativo aplicado a experimentos combinados possibilita a seleção de genótipos de feijão superiores dos seguintes tipos de grãos: vermelho (Amendoim comprido e Light Red Kidney), rajado ('BRS Executivo' e 'Hooter') e carioca ('IPR Siriri'), que apresentam alta concentração de fósforo e ferro; Amendoim comprido também se destaca pela alta concentração de potássio.

Abstract The objective of this work was to evaluate the genetic variability of common bean (Phaseolus vulgaris) genotypes of different grain types as to macro- and micromineral concentrations, as well as to select superior genotypes by the multiplicative index. A total of 22 common bean genotypes were evaluated in experiments carried out in the dry and rainy seasons. The concentration of six minerals (potassium, phosphorus, magnesium, iron, zinc, and copper) was determined, and the multiplicative index was applied to individual and combined experiments. There was a significant effect of the genotype × environment interaction on the concentration of all minerals, and, when the genotype effect was decomposed into grain types, the genotypes differed as to the concentration of three or more minerals. There is genetic variability in the concentration of macro- and microminerals in the common bean genotypes evaluated in the dry and rainy seasons. In the combined experiments, high heritability estimates (≥ 62.60%) and a greater total genetic gain (283.59%) are observed. The multiplicative index applied to combined experiments allows the selection of superior common bean genotypes of the following grain types: red (Amendoim comprido and Light Red Kidney), cranberry ('BRS Executivo' and 'Hooter'), and carioca ('IPR Siriri'), which have high phosphorus and iron concentrations; Amendoim comprido also stands out for its high potassium concentration.

RESUMO A análise da divergência genética e a seleção combinada para várias características físicas dos grãos é inédita para cultivares de feijão. Os objetivos desse trabalho foram avaliar a variabilidade genética de cultivares de feijão para 12 características físicas dos grãos, estudar as correlações entre essas características, analisar a divergência genética e selecionar cultivares de feijão superiores. Dois experimentos foram conduzidos em 2019, sendo avaliadas 22 cultivares de feijão de diferentes tipos de grãos. Efeitos significativos de genótipo, tipo de grão e interação genótipo x ambiente foram obtidos para todas as características físicas dos grãos, evidenciando variabilidade genética. Alta correlação foi observada entre comprimento e largura dos grãos (r = 0,844), grãos normais e absorção (r = 0,796) e absorção e tempo de cozimento (r = -0,651). Os valores de L* (claridade dos grãos) e a* (variação entre as tonalidades verde a vermelho) mostraram maior contribuição para a diferenciação entre as cultivares de feijão. Nas análises de variáveis canônicas e de ligação média dento de grupo com média aritmética foram formados quatro e três grupos de cultivares, respectivamente. As duas análises de agrupamento são eficientes para separar as cultivares de feijão em grupos homogêneos pelos valores de L* e a*, sendo que a análise de variáveis canônicas fornece informações mais detalhadas. As cultivares de feijão cranberry BRS Executivo, BRS MG Realce e Hooter e as cultivares de feijão preto IPR Tiziu, BRS Esteio e Guapo Brilhante apresentam características físicas de grãos superiores e serão selecionadas pelo programa de melhoramento.

ABSTRACT Genetic divergence analysis and combined selection for various physical grain traits are unprecedented for common bean cultivars. The objectives of this study were to examine the genetic variability of common bean cultivars for 12 physical grain traits; study the correlations between these traits; analyze the genetic divergence; and select superior common bean cultivars. Two experiments were carried out in 2019 in which 22 common bean cultivars of different grain types were evaluated. Significant effects of genotype, grain type and genotype × environment interaction were obtained for all physical grain traits, indicating the existence of genetic variability. High correlations were observed between grain length and width (r = 0.844), normal grains and uptake (r = 0.796) and uptake and cooking time (r = -0.651). The L* (grain lightness) and a* (variation between green and red hue) values had a greater contribution to the differentiation between common bean cultivars. Four and three groups of cultivars were formed by the analyses of canonical variables and unweighted pair group method with arithmetic mean, respectively. Both cluster analyses are efficient in separating the cultivars into homogeneous groups based on the L* and a* values, although the canonical variables analysis provides more detailed information. The cranberry bean cultivars BRS Executivo, BRS MG Realce and Hooter and the black bean cultivars IPR Tiziu, BRS Esteio and Guapo Brilhante have superior physical grain traits and will thus be selected by the breeding program.

RESUMO Os grãos de feijão apresentam grande variabilidade genética para os caracteres da qualidade tecnológica, concentração de minerais e compostos bioativos. Por isso, o estudo das correlações entre esses caracteres em linhagens de feijão de diferentes grupos gênicos proporciona avanços no programa de biofortificação. Para tanto, duas populações homozigotas recombinantes de feijão Mesoamericano e Andino foram avaliadas em geração F5:7. A qualidade tecnológica foi analisada pela massa de 100 grãos e pela coloração dos grãos determinada em um colorímetro pelos valores de L* (branco ao preto), a* (verde a vermelho) e b* (azul a amarelo). A concentração de seis minerais e de compostos bioativos (fitatos e compostos fenólicos) foi avaliada e usada para caracterizar a composição nutricional das linhagens. As linhagens de feijão avaliadas diferiram para todos os caracteres da qualidade tecnológica e para a concentração de minerais e de compostos bioativos, exceto para a concentração de zinco nas linhagens de feijão Andino. A coloração dos grãos (valores de L*, a* e b*) apresentou alta correlação com a maioria dos minerais avaliados e com os fitatos em feijão Mesoamericano. Em feijão Andino, a coloração dos grãos (valores de L*, a* e b*) foi correlacionada com as concentrações de potássio, magnésio, ferro e compostos fenólicos. A composição nutricional das linhagens de feijão de diferentes classes de grãos é variável: feijão preto apresenta as maiores concentrações de potássio, fósforo, cálcio, zinco e fitatos; feijão carioca se destaca pela alta concentração de magnésio; feijão rajado tem maior concentração de potássio, magnésio e ferro.

ABSTRACT The common bean exhibits wide genetic variability for technological quality traits, mineral concentrations, and bioactive compounds. For this reason, investigating the correlations between those traits in common bean lines of different gene pools contributes to the progress of biofortification programs. In the present study, two recombinant inbred line populations of Mesoamerican and Andean common bean were evaluated at the F5:7 generation. Technological quality was evaluated based on mass of 100 grains and seed coat color, which was determined using a colorimeter that analyzed the L* (white to black), a* (green to red) and b* (blue to yellow) values. The concentration of six minerals and bioactive compounds (phytates and phenolic compounds) was evaluated and used to characterize the nutritional composition of the lines. The evaluated common bean lines differed (p ≤ 0.05) for all technological quality traits, mineral concentrations, and bioactive compounds, except for the zinc concentration in Andean beans. Seed coat color (L*, a*, and b* values) was highly correlated with most of the evaluated minerals and with the phytates in Mesoamerican beans. In Andean beans, seed coat color (L*, a*, and b* values) was correlated with the concentrations of potassium, magnesium, iron, and phenolic compounds. The nutritional composition of common bean lines of different classes is variable: black beans have higher concentrations of potassium, phosphorus, calcium, zinc, and phytates; carioca beans stand out with high magnesium concentration; and cranberry beans have higher concentrations of potassium, magnesium, and iron.