Indirect selection for culinary quality and minerals in beans based on genotype × environment interaction

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.


INTRODUCTION
The breeding of common bean (Phaseolus vulgaris L.) for traits related to culinary quality-namely, color, cooking time, and grain size-and mineral concentration meets the demand of consumers who analyze the quality of grains in their purchases.For this reason, common bean breeding programs have started to put efforts into the development of new cultivars with high culinary quality and greater mineral concentrations.
Wide genetic variability has been described for color (CANCI et al., 2019;PARMAR et al., 2017), cooking time (GARCIA et al., 2012;PERINA et al., 2014;RIVERA et al., 2016), and mineral concentration (DELFINI et al., 2020;GOUVEIA et al., 2014;KATUURAMU et al., 2018;McCLEAN et al., 2017;SILVA et al., 2012;YEKEN et al., 2019) in grains of common bean genotypes.However, when common bean genotypes were evaluated in different experiments, culinary quality traits and/or mineral concentration showed a significant genotype × environment interaction effect (HOSSAIN et al., 2013;RIBEIRO et al., 2021a;STECKLING et al., 2017).These results indicate that common bean genotypes grown in diff erent environments (growing years, seasons, and/or locations) may exhibit variations in culinary quality traits and minerals.As a consequence, promising traits for indirect selection for culinary quality and minerals must diff er between growing environments, which makes the selection of superior common bean lines diffi cult.
Previous studies have shown that there is a correlation between culinary quality traits and/or minerals evaluated in common bean genotypes in experiments carried out in one (CANCI et al., 2019;PARMAR et al., 2017;SILVA et al., 2012), two (KATUURAMU et al., 2018;RIBEIRO et al., 2021b), three (HOSSAIN et al., 2013;McCLEAN et al., 2017;RIBEIRO et al., 2021a), or four (DELFINI et al., 2020) environments.Nonetheless, no study was found in the literature indicating the number of experiments that provide high coincidence in identifying significant correlations between culinary quality traits and/ or minerals in common bean lines.The hypothesis is that correlations between these traits have low coincidence when based on data obtained in one or two experiments.Thus, defining the minimum number of experiments that must be used in Pearson's linear correlation analysis will provide the breeding program with greater efficiency in indirect selection for culinary quality traits and minerals in common bean lines.
Therefore, the objectives of this study were: (1) to evaluate the correlations between traits related to culinary quality and minerals in common lines based on data from individual and combined experiments; (2) defi ne the minimum number of experiments that provide high coincidence in identifying signifi cant correlations in Pearson's linear correlation analysis; and (3) identify promising traits for indirect selection for culinary quality and minerals.

Description of experiments
The experiments were carried out in four growing seasons: 2016 rainy season (I), 2017 dry season (II), 2017 rainy season (III), and 2018 dry season (IV) at the campus of the Federal University of Santa Maria, located in Santa Maria, Rio Grande do Sul (RS), Brazil (29º42' S latitude, 53º49'W longitude, and 95 m altitude).The rainy-season crops were implemented between October and January and the dry-season crops from February to May, in agreement with the agricultural zoning of climatic risk for the common bean crop in RS.
The region has a humid subtropical climate and the soil is classified as a typic alitic Argisol (Hapludalf).All experiments were carried out using the conventional cultivation system (two plowing operations and one harrowing) and the fi eld area was maintained with the cultivation of black oat from June to September.
The experiments were established so as to meet the minimum requirements necessary for the release of new common bean cultivars for cultivation in Brazil (MAPA, 2006).Management practices (fertilizer application, control of weeds and insects) were Indirect selection for culinary quality and minerals in beans based on genotype × environment interaction implemented uniformly and in line with those adopted for common bean growing in Southern Brazil.Harvesting was carried out at the maturity stage (R9), without using agricultural machinery.The grains were kept refrigerated (temperature of 5 ºC and 75% relative humidity) until the beginning of the culinary quality and mineral evaluations.

Culinary quality and mineral evaluations
The culinary quality of the grains was analyzed based on color (L*, a*, and b* values), cooking traits (absorption, normal grains, and cooking time), and mass of 100 grains.Grain color was determined using a portable colorimeter.The value of L* indicated lightness, that is, the variation between black and white; a* measured the amplitude between green and red; and b* quantifi ed the shades between blue and yellow.
Cooking traits were evaluated in a sample of 25 grains that remained soaked in 50 mL of distilled water for 8 h, at room temperature (20 ± 2 ºC).Absorption was estimated by the following formula: [(weight of grains after soaking -weight of grains before soaking)/weight of grains before soaking] × 100.Normal grains were obtained by counting the number of grains that absorbed water after soaking relative to the total number of grains (normal and hard) and expressed in %.Cooking time was quantifi ed in a Mattson cooker with 25 plungers.The beans were uniformly distributed on the perforated depressions of the rack of the device and cooked in a similar way to that described by Ribeiro et al. (2021a).Mass of 100 grains was determined in three random samples of 100 grains representative of the usable area, with 13% average moisture.
The concentration of six minerals (potassium, phosphorus, calcium, magnesium, iron, and copper) was analyzed in 30 g of raw beans randomly collected from the usable area.The grains were ground until a fi ne and homogeneous fl our was obtained.A 0.5-g subsample of this fl our was used for the nitric-perchloric digestion process (MIYAZAWA et al., 2009).Mineral concentration was quantifi ed in an atomic absorption spectrophotometer, except for potassium, which was measured in a fl ame photometer, and phosphorus, which was determined in an optical emission spectrophotometer.

Statistical analyses
The data obtained in each of the four experiments were subjected to individual analysis of variance.For absorption and normal grains, the data were 5 .0 + x -transformed, in which x corresponds to the trait value, and cooking time was converted to s.The signifi cance level was checked by the F test at 5% probability, and the homogeneity of residual variances was evaluated by Hartley's maximum F test.
Combined analysis of variance was performed considering all effects as random, except for the genotype eff ect, which was fi xed.The F test at 5% probability was also used to identify signifi cant traits.The phenotypic correlation matrix generated in combined analysis of variance was used for multicollinearity diagnostics.In this analysis, the condition number (CN) was associated with a collinearity class (weak, moderate or strong, and severe), based on the classifi cation table by Montgomery, Peck and Vining (2012 For this, the phenotypic correlation matrix generated in analysis of variance of experiment I was used to undertake the correlation analysis of experiment I.The same procedure was adopted for correlation analysis of the other individual and combined experiments.The significance of correlation coefficients was analyzed by Student's t test, at 5% probability.All statistical analyses were performed in Genes software (CRUZ, 2016).

Individual and combined analysis of variance
Residual variances were heterogeneous for b* value, normal grains, and iron concentration.These traits required correcting the degrees of freedom of the error and of the genotype × environment interaction, as proposed by Cruz (2016).This procedure allowed obtaining homogeneous residual variances (highest/lowest residual mean square < 7) for all traits and conducting combined analysis of variance.
Seven of the 13 evaluated traits exhibited a significant genotype effect (Table 1), indicating the existence of genetic variability for most of the culinary quality traits and minerals determined in the common bean lines and cultivars.Great genetic diversity has also been described for grain traits in common bean genotypes, namely, color (CANCI et al., 2019;PARMAR et al., 2017), cooking (RIVERA et al., 2016), and mineral concentration (GOUVEIA et al., 2014;S I LVA et al., 2012;YEKEN et al., 2019).However, all traits related to culinary quality and the concentration of five minerals showed a significant genotype × environment interaction effect, similarly to what was reported for common bean genotypes evaluated in different environments (RIBEIRO et al., 2021a;STECKLING et al., 2017).These results demonstrate that common bean lines and cultivars grown in different years, seasons, and/or locations may vary in traits related to culinary quality and minerals.Thus, when a significant genotype × environment interaction effect occurs, the identification of promising traits for use in indirect selection for culinary quality and minerals is expected to be different for each growing environment.
The common bean lines and cultivars did not differ in terms of potassium concentration, that is, the genotype and genotype × environment interaction effects were not significant for this mineral.For this reason, potassium concentration values were not included in Pearson's linear correlation analyses.In addition, severe multicollinearity was observed (CN = 5,698.14)based on the classification table by Montgomery, Peck and Vining (2012).To achieve weak collinearity (CN < 100), highly correlated traits, traits with a greater weight in the last eigenvectors, and traits showing greater variance inflation factors were excluded before Pearson's linear correlation analysis.This prevents multicollinear variables from implicitly receiving a greater weight in Pearson's linear correlation analysis and results in the correct interpretation of results (CRUZ; CARNEIRO, 2014).Therefore, the traits of b* and a* values and normal grains were also not included in Pearson's linear correlation analyses.

Correlation analysis using data from individual experiments
Pearson's linear correlation coeffi cients varied in signifi cance, sign, and/or magnitude for the diff erent traits evaluated in individual experiments (Table 2).Additionally, the number of signifi cant correlations ranged from two (experiment III) to six (experiments I, II, and IV), showing that the correlation estimates were not constant in the four experiments.Correlation estimates between culinary quality traits determined in common bean genotypes were variable (PERINA et al., 2014) and not signifi cant (GARCIA et al., 2012) when evaluated in diff erent growing locations and seasons.On the other hand, the obtained correlation estimates between minerals were diff erent in experiments with common bean genotypes conducted in three locations (ZILIO; SOUZA; COELHO, 2017) and in eight combinations of growing years, seasons, and locations (DIAS et al., 2021).Therefore, the results of Pearson's linear correlation analysis will be specifi c for the common bean genotypes evaluated in the year, season, and location in which the experiment was carried out.Two significant correlations were common only to experiments I and II, namely, mass of 100 grains and phosphorus concentration; and calcium concentration and magnesium concentration.Therefore, there was low coincidence between correlations that were signifi cant when Pearson's linear correlation analysis was performed using data from individual experiments.This can be attributed to the fact that 12 of the 13 evaluated traits showed a signifi cant genotype × environment interaction (Table 1).Thus, most of the culinary quality traits and minerals determined in common bean genotypes showed variation depending on the growing environment, and this also altered the correlations that were signifi cant in each of the experiments (Table 2).These results confi rm the hypothesis that identifying promising traits for indirect selection for culinary quality and minerals in common bean lines should consider the genotype × environment interaction eff ect to increase the chances of a successful selection.

Correlation analysis using data from two experiments
Most of Pearson's linear correlation coeffi cients varied in signifi cance, sign, and/or magnitude for the traits evaluated in the tested combinations of two experiments (Table 3), similarly to what was observed for individual experiments (Table 2).The lowest number of signifi cant correlations was identifi ed when Pearson's linear correlation analysis was performed using data from experiments II and IV (one), and the highest number, using data from experiments I and III (six) (Table 3).This shows that the eff ect of growing years and seasons infl uenced the signifi cance level of correlations between culinary quality traits and minerals.Previous studies using average data from experiments carried out in two growing years found that the cooking quality traits of common bean grains were not correlated (CICHY; WIESINGER; MENDOZA, 2015) and that correlations between minerals were predominantly of low (KATUURAMU et al., 2018) or high (RIBEIRO et al., 2021b) magnitude in common bean genotypes.Therefore, the use of average data from two experiments, involving combinations of growing years and/or seasons, may lead to errors in the identifi cation of promising traits for indirect selection for culinary quality traits and minerals in common bean lines.
Only three signifi cant correlations were coincident for the diff erent combinations of two experiments tested: L* value and absorption (I and III; and III and IV); magnesium concentration and copper concentration (I and III; and III and IV); and calcium concentration and magnesium concentration (I and II; I and III; and II and IV).No signifi cant correlation coincided for the four combinations of experiments tested.Thus, the use of average data from two experiments resulted in low coincidence in obtaining signifi cant correlations between culinary quality traits and minerals in common bean genotypes, similarly to what was observed in the present study when data from individual experiments were considered (Table 2).These fi ndings show that the use of data from one or two experiments in Pearson's linear correlation analysis does not allow for high coincidence in identifying signifi cant correlations between culinary quality traits and minerals.To increase the effi ciency of indirect selection for culinary quality traits and minerals in common bean lines, it is necessary to identify the minimum number of experiments to be used in Pearson's linear correlation analysis.

Correlation analysis using data from three and four experiments
Three correlations showed signifi cance when data from three or four experiments were used.Two of these correlations were coincident in magnitude and sign, namely, L* value and absorption; and calcium concentration and magnesium concentration (Table 4).However, there was no signifi cant correlation between calcium concentration and magnesium concentration in common bean genotypes when Pearson's linear correlation was performed with average data from three    HOSSAIN et al., 2013;McCLEAN et al., 2017).
These results indicate that correlation estimates between culinary quality traits and minerals determined in common bean genotypes evaluated in different growing years and seasons may be different from those obtained in different growing locations.This can be explained by the fact that the genotype × year and genotype × season interactions are more important than the genotype × location interaction when the genotype × environment interaction is decomposed (TORGA et al., 2013).The observed differences between common bean genotypes grown in different years can be attributed to climatic factors (temperature, precipitation, relative humidity, among others) and biotic factors (diseases, pests, and weeds), whereas differences between growing seasons can be explained by climatic and biotic factors and management practices.Therefore, the differences between growing years and seasons contributed to the fact that the correlation estimates between culinary quality traits and minerals of the common bean genotypes were not 100% coincident in the 10 correlation analyses tested (Tables 2, 3, and 4).
The correlation between L* value and absorption was signifi cant in fi ve correlation analyses, that is, it was coincident in 50% of the tested correlation analyses.Additionally, the correlation between calcium concentration and magnesium concentration was signifi cant in seven correlation analyses, which corresponds to 70% coincidence in the tested correlation analyses.These two correlations revealed, with a high coincidence percentage (≥ 50%), that common bean lines with light grains (higher L* value) showed a higher absorption percentage and that an increase in calcium concentration will result in an increase in magnesium concentration.In this way, common bean lines with better culinary quality and higher mineral concentration can be indirectly selected based on higher L* values and higher calcium concentrations.The other correlations between culinary quality traits and minerals showed a low coincidence percentage in individual and combined experiments and, as such, are not promising for the identifi cation of traits to be used in indirect selection.
A total of 36 correlations between pairs of culinary quality traits and minerals were evaluated; Indirect selection for culinary quality and minerals in beans based on genotype × environment interaction however, 33 correlations were not significant when Pearson's linear correlation analysis was performed using data from three or four experiments (Table 4).When the correlation between two traits is not significant, there are no linked genes or pleiotropic effects, i.e., the genetic values of the traits are independent (BALESTRE et al., 2013).Therefore, the lack of association between most of the culinary quality traits and minerals evaluated suggests ease of selection of superior common bean lines.
It was not possible to defi ne the number of experiments that provide 100% coincidence in the identifi cation of correlated pairs of culinary quality traits and minerals in Pearson's linear correlation analysis from the database used in this study.However, the use of data from three and four experiments resulted in 66.66% coincidence in the identifi cation of two positive correlations: L* value and absorption (r = 0.50 and 0.51, respectively); and calcium concentration and magnesium concentration (r = 0.72 and 0.62, respectively).Experiments conducted in three (HOSSAIN et al., 2013;McCLEAN et al., 2017) or four (DELFINI et al., 2020) environments identifi ed important correlations between culinary quality traits and/ or minerals in common bean genotypes.Despite this, no previous study was found in the literature determining the minimum number of experiments to be used in Pearson's linear correlation analysis that allow for high coincidence in the identifi cation of signifi cant correlations between culinary quality traits and/or minerals in common bean lines.
In the present study, 92.31% of the culinary quality traits and mineral concentrations determined in the common bean genotypes exhibited a signifi cant genotype × environment interaction eff ect (Table 1).This led to variations in the signifi cance, sign, and/or magnitude of Pearson's linear correlation coeffi cients obtained in individual and combined experiments (Tables 2, 3, and 4).The use of data from three experiments resulted in 66.66% coincidence in the identifi cation of signifi cant correlations when compared with Pearson's linear correlation analysis applied to data from four experiments (Table 4).Therefore, it is recommended to use data from at least three experiments in Pearson's linear correlation analysis for culinary quality traits and minerals.This allows the identifi cation of promising traits for indirect selection for culinary quality traits and minerals in common bean lines with high coincidence, which will increase the effi ciency of the breeding program in the selection process.

CONCLUSIONS
1. Correlations between culinary quality traits and minerals vary in signifi cance, magnitude, and/or sign when Pearson's linear correlation analysis is performed using data from individual and combined experiments; 2. The use of data from three experiments results in a high coincidence percentage in identifying signifi cant correlations in Pearson's linear correlation analysis; 3. Selection for higher L* values (grain lightness) and higher calcium concentrations is recommended in the indirect selection of common bean lines with high culinary quality and greater mineral concentrations.
). Pearson's linear correlation analysis was carried out with the data obtained in each of the four individual experiments: 2016 rainy season (I), 2017 dry season (II), 2017 rainy season (III), and 2018 dry season (IV); and for six combinations of experiments (I and II; I and III; II and IV; III and IV; I, II, and III; and I, II, III, and IV).
-1 DM) obtained in 17 common bean genotypes evaluated in four experiments carried out from 2016 to 2018

Table 2 -
Pearson's correlation coefficients obtained between the traits of L* value, absorption (ABS), cooking time (TIME), Signifi cant by the t test at 0.05 probability.ns Not signifi cant Indirect selection for culinary quality and minerals in beans based on genotype × environment interaction *

Table 3 -
Pearson's correlation coeffi cients obtained between the traits of L* value, absorption (ABS), cooking time (TIME), mass of 100 grains (M100G), and concentrations of phosphorus (P), calcium (Ca), magnesium (Mg), iron (Fe), and copper (Cu) obtained in 17 common bean genotypes evaluated in the experiments I and II (2016 rainy and 2017 dry seasons), I and III (2016 rainy and 2017 rainy seasons), II and IV (2017 dry and 2018 dry seasons), and III and IV (2017 rainy and 2018 dry seasons) *Signifi cant by the t test at 0.05 probability.ns Not signifi cant

Table 4 -
Pearson's correlation coeffi cients obtained between the traits of L* value, absorption (ABS), cooking time (TIME), mass of 100 grains (M100G), and concentrations of phosphorus (P), calcium (Ca), magnesium (Mg), iron (Fe), and copper (Cu) obtained in 17 common bean genotypes evaluated in the experiments I, II and III (2016 rainy, 2017 dry and 2017 rainy seasons) and I, II, III and IV (2016 rainy, 2017 dry, 2017 rainy and 2018 dry seasons) *Signifi cant by the t test at 0.05 probability.ns Not signifi cant locations (