Genetic divergence analyses for key agronomic traits in common bean breeding based on the number of experiments

ABSTRACT

The number of experiments used in genetic divergence analyses can influence the selection of parents with favorable traits. This study aimed to analyze the clustering patterns obtained from principal component and canonical variable analyses performed using data from one, two, three, and four experiments involving agronomic traits of common bean genotypes; to determine the minimum number of experiments required for efficient recognition of promising parents for use in crossing blocks; and to identify the most promising parents for crossing. To this end, 10 agronomic traits were evaluated in 11 common bean genotypes across four experiments. Analysis of variance, principal component analysis, and canonical variable analysis were implemented using data from individual experiments and combinations of two, three, and four experiments. Significant effects of genotype, experiment, and/or genotype × experiment interaction were observed for agronomic traits, supporting the differentiation of genotypes into groups based on genetic divergence. In both principal component and canonical variable analyses, the clustering pattern of genotypes varied with the number of experiments considered. In the principal component analyses, it was not possible to define a minimum number of experiments to identify promising parents. In the canonical variable analysis, using data from three experiments enabled more assertively recognition differences and similarities among common bean genotypes. The cross between CNFP 18552 and IPR Urutau is promising for obtaining recombinants with favorable agronomic traits.

Key words
Phaseolus vulgaris L.; genotype × experiment interaction; principal components; canonical variables; clustering pattern

INTRODUCTION

The common bean (Phaseolus vulgaris L.) is a staple food in Brazilian cuisine. The traditional feijoada, prepared with black beans, is widely known and appreciated around the world. To increase black common bean production in Brazil, which is currently concentrated in the southern states, it is necessary to develop cultivars with upright plant architecture, medium-sized grains (mass of 100 grains of 25 to 30 g), and high yield (Delfini et al. 2017, Pereira et al. 2019, Santos et al. 2022). This would enable the registration of new cultivars with highly valued agronomic traits adaptable to other regions of the country.

The main strategy employed by common bean breeding programs to generate genetic variability is the hybridization of parents with favorable traits. To accomplish this, it is first necessary to evaluate the available germplasm for agro-morphological traits of agricultural importance. Based on these data, it becomes possible to identify promising parents for multiple traits to be included in crossing blocks using multivariate analyses, particularly genetic divergence analyses.

The study of genetic divergence between genotypes makes it possible to identify hybrid combinations with a greater heterotic effect and greater heterozygosity (Cruz and Regazzi 1997). These authors recommended several multivariate methods to predict genetic divergence, including agglomerative methods, principal component analysis, and canonical variable analysis. Principal component analysis and canonical variable cluster analysis have the advantage of not depending on previously estimated dissimilarity measures. Both cluster analyses are simple to perform and interpret and therefore can be incorporated into the routine of the breeding programs for selecting promising parents.

Similarities and differences among common bean genotypes regarding key agronomic traits for breeding have been investigated through principal component analysis (Arteaga et al. 2019, Savic et al. 2019, Almeida et al. 2020, Long et al. 2020, Nkhata et al. 2020, Kouam et al. 2023, Mauceri et al. 2025, Prado-Garcia et al. 2025, Stoilova et al. 2025) and canonical variable analysis (Ceolin et al. 2006, Dique et al. 2022, Santos Neto et al. 2023, Kraeski et al. 2024). However, none of these studies have reported the minimum number of experiments required to achieve greater efficiency and/or repeatability in identifying parents with contrasting agronomic traits to be combined. For beans, no previous studies were found in the literature with principal component and canonical variable cluster analyses carried out in multiple experiments.

For the unweighted pair group method with arithmetic mean (UPGMA) and Tocher optimization analyses, the minimum number of experiments required is two and three, respectively (Ribeiro and Maziero 2022). This approach has enabled more accurate selection of common bean parents with favorable plant architecture and productivity traits. However, for principal component and canonical variable analyses, no references were found in the literature indicating the number of experiments needed to more efficiently define which parents should be included in crossing blocks. Our hypothesis was that using agronomic data obtained from multiple experiments allows for a more effective identification of the most promising parents for common bean breeding programs.

This study aimed to analyze the clustering patterns obtained from principal component and canonical variable analyses performed with data from one, two, three, and four experiments involving agronomic traits of common bean genotypes; to determine the minimum number of experiments required for efficient recognition of promising parents for use in crossing blocks; and to identify the most promising parents for crossing.

MATERIALS AND METHODS

Plant material

A total of 11 black common bean genotypes—seven lines and four commercial cultivars (BRS Esteio, BRS FP403, IPR Uirapuru, and IPR Urutau)—were analyzed for genetic divergence based on key agronomic traits for breeding. The lines and cultivars BRS Esteio and BRS FP403 were developed by the Brazilian Agricultural Research Corporation (Embrapa), whereas cultivars IPR Uirapuru and IPR Urutau were developed by the Paraná Rural Development Institute (IDR-PR). Considering that Embrapa and IDR-PR have released the largest number of black common bean cultivars available for cultivation in Brazil (MAPA 2025), the evaluated genotypes are representative of the genetic variability generated by these breeding programs. Additionally, all genotypes have a normal cycle (approximately 90 days) and mass of 100 grains ranging from 18 to 30 g.

Field experiments

Field experiments were carried out between 2022 and 2024 at the Federal University of Santa Maria, Rio Grande do Sul, Brazil (29°42’S latitude, 53°49’W longitude, and 95 m altitude). Sowing was performed manually in four seasons: 2022 rainy, 2023 dry, 2023 rainy, and 2024 rainy seasons.

The region’s climate is humid subtropical, with rainfall well distributed throughout the year. The soil is a typic alitic Argisol (Hapludalf), prepared for cultivation using the conventional system.

The experiments were conducted in a randomized block design with three replicates. Each plot comprised four 4-m rows, with a spacing of 0.5 m between rows and 48 plants per row. The two central rows constituted the usable area (4 m²).

Management practices were similar across experiments. Seeds were treated with the fungicide Maxim (Fludioxonil and Metalaxil-M) and the insecticide Cruiser®350 FS (Thiamethoxam). Fertilization consisted of 450 kg.ha^-1 of the 05-20-20 (N-P₂O₅-K₂O) formulation on the day of sowing and 70 kg.ha^-1 of nitrogen (urea) applied at the third fully expanded trifoliate leaf stage (V3).

During crop development, the insecticide Engeo^TM Pleno (Thiamethoxam and Lambda-cyhalothrin) was applied whenever a Diabrotica speciosa infestation of 5% or more was observed at the fully open primary leaf (V2) and/or V3 stages. Weeds were controlled by hoeing. No herbicides or fungicides were applied after the emergence of the common bean plants. Irrigation was carried out only when a water deficit was recorded after sowing or during the flowering stage (R6).

Agronomic characterization

A total of 10 key agronomic traits relevant to common bean breeding were evaluated in all experiments. At the maturity stage (R9), plants in the usable area were visually assessed using score scales for three traits. Lodging scale 1 analyzed the percentage of bent plants, assigning scores from 1 (upright plants) to 9 (prostrate plants) (CIAT 1987). Lodging scale 2 classified the degree of plant bending into categories ranging from 1 (0% of plants lodged) to 9 (91–100% of plants lodged) (Melo 2009). The general adaptation score was based on the overall appearance of the plants, considering the number of pods, degree of bending, and presence of disease symptoms in the pods, with scores from 1 (excellent) to 9 (very poor) (CIAT 1987).

Subsequently, 10 plants were randomly harvested from the usable area to determine the following traits: height of insertion of the first pod, height of insertion of the last pod, plant height, stem diameter, and number of nodes. The remaining plants from the usable plot and border rows were harvested separately and properly identified. After manual processing and impurity removal, grains obtained from the 10 plants and from the usable area were combined into a single sample. These grains were stored in paper bags, and their moisture content was standardized to 13% before assessing the mass of 100 grains and grain yield. The mass of 100 grains was measured by weighing three random subsamples of 100 grains from each replicate. Grain yield was quantified in 4 m² and extrapolated to kg.ha^-1.

Data analyses

Grain yield data from the 2023 rainy season experiment were corrected using the Covariance method—ideal stand (Schmildt et al. 2001)—, as the final plant stand was heterogeneous among plots. The following statistical analyses were carried out using Genes software (Cruz 2016): adjusting of grain yield, model assumptions, variance analyses, and cluster analyses.

The Shapiro-Wilk’s and Bartlett’s tests were applied to verify the normality and the homogeneity of residual variance, respectively. Subsequently, analyses of variance were undertaken for each individual experiment—2022 rainy (I), 2023 dry (II), 2023 rainy (III), and 2024 rainy (IV) seasons—and for the combinations of two (I and II), three (I, II, and III), and four (I, II, III, and IV) experiments. In the combined analyses of variance, performed with data from two, three, and four experiments, the genotype effect was considered fixed because all the genotypes accessed are pure lines and were previously selected for normal cycle and small to medium-sized black grains. However, the experiment effect was analyzed as random due to the meteorological conditions observed among the years, and growing seasons evaluated are representative of the range of growing conditions in the target region. The statistical significance of the genotype, experiment, and genotype × experiment interaction effects was analyzed through the F-test (p < 0.05).

Multicollinearity diagnostics were performed using the phenotypic correlation matrix from each individual and combined analysis of variance. The degree of multicollinearity was evaluated by the condition number, as proposed by Montgomery et al. (2021).

Principal component and canonical variable cluster analyses were conducted for the four individual experiments (I; II; III; and IV) and for the combinations of two (I and II), three (I, II, and III), and four (I, II, III, and IV) experiments conducted in sequential crops. The other possible combinations from data from two and three experiments were not implemented, because the main objective of this study was to determine the minimum number of experiments required for recognition of promising parents.

Both cluster analyses were performed using genotype means obtained in one, two, three or four experiments. Phenotypic data were standardized using z-scores (mean = 0; variance = 1) to prevent traits with larger scales or higher variance from disproportionately influencing the principal component and canonical variable cluster analyses, ensuring equal contribution of all traits. Seven scatter plots were generated for principal component analyses and seven for canonical variable analyses, allowing the assessment of clustering patterns among black common bean genotypes for agronomic traits based on the number of experiments. No clustering algorithm was applied to delimit the groups. The ellipses were prepared by visual inspection of the genotypes of each group, in a similar way that is made in a dendrogram.

The minimum number of experiments required for selection of black bean genotypes for use in crossing blocks was established by the three criteria: total variance explained by the first two principal components; total variance explained by the first two canonical variables; and concordance of cluster structures across individual experiments (I; II; III; and IV) and combinations of two, three, and four experiments by the adjusted Rand index (Hubert and Arabie 1985). This statistical analysis was carried out in R software using the ‘mcclust’ package.

RESULTS AND DISCUSSION

Analysis of variance and partitioning of phenotypic variation

The assumptions of randomness and normality were met in all individual and combined analyses of variance. However, for height of insertion of the first pod determined with data from two, three, and four experiments, heterogeneous residual variance was detected. Consequently, for this trait the degrees of freedom for error and genotype × experiment interaction were adjusted to meet the assumption of homogeneity of residual variances, as recommended by Cruz (2016). This methodology enabled the implementation of all combined analyses of variance for 10 agronomic traits.

Significant differences were observed for the genotype source of variation across all traits (Table 1). However, the genotypes differed for general adaptation score only in the II and IV experiments and for plant height in all individual and combined experiments. Thus, the evaluated genotypes exhibited genetic variability for agronomic traits, confirming the presence of genetic diversity in common bean (Pereira et al. 2019, Kraeski et al. 2024, Mauceri et al. 2025, Prado-Garcia et al. 2025, Stoilova et al. 2025) with potential for use in breeding programs. To this end, identifying parents with multiple favorable traits for inclusion in crossing blocks can be effectively accomplished using multivariate analyses, particularly genetic divergence analysis.

Table 1
Mean squares from the analysis of variance for the traits of lodging scale 1 (LS1), lodging scale 2 (LS2), general adaptation score (GAS), height of insertion of the first pod (HIFP, cm), height of insertion of the last pod (HILP, cm), plant height (PH, cm), stem diameter (SD, mm), number of nodes (NN), mass of 100 grains (M100G, g), and grain yield (YIELD, kg·ha^-1) obtained of 11 black bean genotypes evaluated in the 2022 rainy (I), 2023 dry (II), 2023 rainy (III), and 2024 rainy (IV) seasons and for the combinations of two (I and II), three (I, II, and III), and four (I, II, III, and IV) experiments.

Experiment	LS1	LS2	GAS	HIFP	HILP	PH	SD	NN	M100G	YIELD
Genotype
I	3.09*	1.85*	2.07ns	41.49*	116.18*	253.21*	0.26ns	3.07*	4.91ns	444,063.69*
II	4.68*	3.94*	5.55*	6.23ns	76.01*	189.65*	0.93*	0.79ns	6.26*	206,180.29*
III	0.90ns	0.76ns	1.32ns	45.67ns	66.75ns	129.18*	0.93ns	1.35ns	8.90*	79,264.26ns
IV	7.49*	10.83*	10.14*	8.74ns	379.83*	537.87*	4.05*	3.47*	18.49*	1,569,208.19*
I and II	6.05*	4.18ns	2.87ns	35.23ns	154.78*	382.13*	0.92*	2.43ns	8.76*	195,425.44ns
I, II, and III	3.80ns	2.49ns	2.03ns	70.01*	155.71*	365.71*	0.74ns	2.44ns	12.82*	211,098.42ns
I, II, III, and IV	3.37ns	3.57ns	3.45ns	66.41*	377.60*	675.80*	1.59ns	4.18*	19.40*	847,029.13ns
Experiment
I and II	122.73*	167.04*	87.51*	1,008.86*	955.62*	1,519.10*	4.84*	47.94*	716.76*	3,445,026.02*
I, II, and III	110.86*	152.27*	74.31*	1,412.67*	2,965.33*	4,465.70*	6.30ns	46.02*	371.37*	1,726,134.30*
I, II, III, and IV	73.95*	101.64*	49.84*	1,007.01*	2,711.57*	4,421.16*	54.21*	41.04*	329.10*	3,530,616.76*
Genotype × Experiment
I and II	1.73ns	1.61ns	4.75*	12.50*	37.41ns	60.72ns	0.26ns	1.43ns	2.41ns	454,818.54*
I, II and III	2.44*	2.03*	3.46*	11.69ns	51.62ns	103.16*	0.69ns	1.38ns	3.62ns	259,204.91*
I, II, III, and IV	4.26*	4.60*	5.21*	16.24ns	87.06*	144.70*	1.53*	1.50ns	6.39*	483,895.77*

• ^ns
  Non-significant;
• ^*
  significant by F test at 0.05 probability.

In the combined analyses of variance, the experiment source of variation was significant for 96.67% of the traits determined in two, three, and four experiments. Significant experiment effects have also been reported for many key agronomic traits used in selection (Delfini et al. 2017, Nkhata et al. 2020, Santos et al. 2022). In our study, the experiment contributed most to phenotypic variation in 73.33% of the traits analyzed based on data from two, three, and four experiments (Table 2). This confirms that meteorological conditions, particularly precipitation, mean air temperature, relative humidity, and solar radiation recorded during the growing seasons (Figs. 1a–1d), influenced the expression of several agronomic traits. Therefore, using data from a single experiment in genetic divergence analyses provides limited information for defining the most promising parents to be combined. This is because most key agronomic traits in common bean breeding are quantitatively inherited (Ramalho et al. 2024) and thus vary with the growing experiment.

Table 2
Minimum (Min), maximum (Max), mean values, standard deviation (SD), and partition of phenotypic variation in the genotype (PVG), environment (PVE), and genotype × environment interaction (PVG×E) for the traits of lodging scale 1 (LS1), lodging scale 2 (LS2), general adaptation score (GAS), height of insertion of the first pod (HIFP, cm), height of insertion of the last pod (HILP, cm), plant height (PH, cm), stem diameter (SD, mm), number of nodes (NN), mass of 100 grains (M100G, g), and grain yield (YIELD, kg·ha^-1) obtained of 11 black bean genotypes evaluated in the 2022 rainy (I), 2023 dry (II), 2023 rainy (III), and 2024 rainy (IV) seasons and for the combinations of two (I and II), three (I, II, and III), and four (I, II, III, and IV) experiments.

	LS1	LS2	GAS	HIFP	HILP	PH	SD	NN	M100G	YIELD
Experiment I
Min	2.00	2.00	1.00	14.40	35.00	41.40	5.79	10.90	17.44	494.00
Max	7.00	5.00	6.00	29.00	64.20	78.50	7.92	15.60	24.22	2,042.13
Mean	3.48	2.73	3.57	20.52	48.79	63.12	6.96	13.27	21.19	1,263.90
SD	1.25	0.94	1.20	4.04	7.75	10.18	0.55	1.28	1.89	413.85
PVG	61.52	64.97	45.00	79.26	60.46	76.42	27.26	58.22	42.97	81.02
Experiment II
Min	3.00	3.00	2.00	10.30	27.70	38.20	4.92	12.70	24.29	356.40
Max	8.00	8.00	9.00	19.50	54.70	72.50	8.62	16.80	31.84	1,522.22
Mean	6.21	5.91	5.88	12.70	41.18	53.53	6.42	14.97	27.78	806.97
SD	1.60	1.49	1.62	2.11	6.12	9.49	0.72	0.94	1.72	300.43
PVG	57.47	55.70	66.47	43.88	63.45	65.80	56.21	27.72	66.32	71.38
Experiment III
Min	5.00	4.00	4.00	15.00	38.00	52.75	4.67	10.60	18.27	758.65
Max	9.00	9.00	9.00	42.50	81.78	94.90	8.95	15.00	28.70	1,950.48
Mean	6.97	6.82	6.39	25.70	60.02	76.68	7.29	12.70	23.39	1,053.58
SD	1.21	1.07	1.32	6.41	11.48	11.02	0.94	1.23	2.60	252.18
PVG	19.10	20.52	23.64	34.72	15.82	33.22	33.11	28.10	41.20	38.95
Experiment IV
Min	2.00	2.00	2.00	13.50	28.50	48.00	6.98	9.60	14.48	395.29
Max	9.00	9.00	9.00	29.80	83.63	111.10	12.81	15.25	27.18	2,830.80
Mean	5.48	5.03	5.09	16.83	59.43	77.67	9.35	12.53	20.98	1,578.57
SD	2.05	2.19	2.11	3.61	12.56	16.47	1.50	1.42	2.75	762.19
PVG	55.80	70.80	71.04	20.99	75.22	61.95	56.37	54.08	76.53	84.41
Experiments I and II
Min	2.00	2.00	1.00	10.30	27.70	38.20	4.92	10.90	17.44	356.40
Max	8.00	8.00	9.00	29.00	64.20	78.50	8.62	16.80	31.84	2,042.13
Mean	4.85	4.32	4.73	16.61	44.98	58.32	6.69	14.12	24.48	1,035.43
SD	1.98	2.02	1.83	5.08	7.92	10.89	0.69	1.41	3.77	426.33
PVG	23.77	15.70	13.25	21.04	37.98	49.53	29.84	18.80	9.46	16.54
PVE	48.22	62.72	40.31	60.25	23.45	19.69	15.65	37.11	77.45	29.16
PVG×E	6.79	6.05	21.87	7.46	9.18	7.87	8.58	11.07	2.61	38.50
Experiments I, II, and III
Min	2.00	2.00	1.00	10.30	27.70	38.20	4.67	10.60	17.44	356.40
Max	9.00	9.00	9.00	42.50	81.78	94.90	8.95	16.80	31.84	2,042.13
Mean	5.55	5.15	5.28	19.64	50.00	64.44	6.89	13.65	24.12	1,041.48
SD	2.02	2.12	1.85	7.00	11.64	13.93	0.83	1.50	3.45	376.02
PVG	9.49	5.66	6.08	14.56	11.73	19.23	11.10	11.02	10.98	15.23
PVE	55.37	69.10	44.49	58.78	44.70	46.97	18.84	41.58	63.62	24.91
PVG×E	12.17	9.20	20.70	4.87	7.78	10.85	20.63	12.52	6.21	37.41
Experiments I, II, and IV
Min	2.00	2.00	1.00	10.30	27.70	38.20	4.67	9.60	14.48	356.40
Max	9.00	9.00	9.00	42.50	83.63	111.10	12.81	16.80	31.84	2,830.80
Mean	5.54	5.12	5.23	18.94	52.35	67.75	7.51	13.37	23.33	1,175.75
SD	2.02	2.13	1.91	6.43	12.52	15.64	1.48	1.55	3.55	549.71
PVG	6.31	6.01	7.21	12.26	18.40	21.10	5.50	13.21	11.73	21.40
PVE	41.48	51.33	31.30	55.76	39.64	41.41	56.31	38.89	59.71	26.76
PVG×E	23.92	23.24	32.73	6.59	12.73	13.55	15.88	14.20	11.59	36.67

Figure 1
Meteorological data on rainfall (mm), average temperature (°C), humidity (%), and radiation (MJ m^-2) recorded in the (a) 2022 rainy, (b) 2023 dry, (c) 2023 rainy, and (d) 2024 rainy seasons, collected in the eighth district at the Santa Maria Meteorology Station, located at the Federal University of Santa Maria (29°42’S, 53°43’W and 95 m of altitude), Rio Grande do Sul, Brazil.

Only the number of nodes showed no significant genotype × experiment interaction (Table 1). For all other traits, a significant genotype × experiment interaction was observed in the combined analyses of variance implemented with data from two, three, and/or four experiments. Similarly, previous studies have demonstrated that many important agronomic traits for common bean breeding exhibit a significant genotype × experiment interaction (Delfini et al. 2017, Arteaga et al. 2019, Santos et al. 2022). These findings indicate that the agronomic performance of common bean genotypes varies across growing experiments.

Therefore, the clustering pattern obtained in genetic divergence analyses is expected to differ if the experiment is repeated in another year(s), season(s), or growing location(s). Therefore, principal component and canonical variable analyses based on data from a single experiment may lead to errors in identifying contrasting parents for agronomic traits. To overcome this limitation, the use of data from two experiments for UPGMA analysis and from three experiments for Tocher’s optimization method was suggested (Ribeiro and Maziero 2022). This approach has enabled greater repeatability in recognizing common bean parents with favorable plant architecture and productivity traits for inclusion in crossing blocks. However, for principal component and canonical variable analyses, no references were found regarding the minimum number of experiments that should be conducted. This information is important for more accurate definition of parents with desirable agronomic traits to be combined in breeding programs.

Principal component analysis based on the number of experiments

A condition number of 1,725.61 was observed in the multicollinearity diagnostic analysis, which indicates severe multicollinearity, according to Montgomery et al. (2021). However, the degree of multicollinearity does not alter the classification of common bean genotypes into groups in the principal component and canonical variable cluster analyses (Ribeiro et al. 2026). These analyses assess genetic dissimilarity between genotypes through graphical dispersion on two Cartesian axes (Cruz and Regazzi 1997). As a result, it is not necessary to exclude highly correlated traits prior to these cluster analyses.

Principal component analyses performed with data from individual experiments, the first two principal components explained between 56.83 (23 rainy) and 76.16% (24 rainy) of the total variation (Figs. 2a–2d). Lower percentages of variation have been reported in studies of genetic divergence involving principal components for agro-morphological traits in common bean genotypes evaluated in a single experiment (Almeida et al. 2020, Long et al. 2020). In studies by Almeida et al. (2020) and Long et al. (2020) and in the present one, the first two principal components did not account for 80% of the total variation, which is the minimum threshold suggested by Cruz and Regazzi (1997) for adequately representing genetic diversity in two-dimensional scatter plots. Despite this limitation, differences and similarities among common bean genotypes for agronomic traits were still distinguishable in the principal component analyses based on data from a single experiment.

Figure 2
Scatter plots obtained for the first two principal components performed for key agronomic traits to common bean breeding obtained of 11 black bean genotypes evaluated in the (a) 2022 rainy, (b) 2023 dry, (c) 2023 rainy, and (d) 2024 rainy seasons and for the combinations of (e) two, (f) three, and (g) four experiments. Total variance explained by the first two principal components for each biplot was: (a) 67.69%, (b) 62.53%, (c) 56.83%, (d) 76.16%, (e) 69.29%, (f) 64.14%, and (g) 68.72%.

However, when principal component analyses were executed using data from individual experiments, the clustering pattern of the genotypes varied (Figs. 2a–2d). Since the common bean genotypes were evaluated in the same experimental area under similar management conditions, the differences in meteorological conditions recorded across the four growing seasons (Figs. 1a–1d), and the incidence of diseases and insects may partially justify the variation in clustering patterns. In the 2022 rainy season, the lowest rainfall and the lowest average air temperature were observed at the beginning of vegetative growth (Fig. 1a). The 2023 dry-season crop differed from the others due to higher rainfall, lower solar radiation, and lower average air temperature toward the end of the reproductive cycle (Fig. 1b). In the 2023 rainy season, rainfall was well distributed throughout the crop cycle (Fig. 1c), while in the 2024 rainy season, rainfall was reduced at the end of the reproductive cycle, and a higher percentage of relative humidity was recorded during most of the crop’s development cycle (Fig. 1d). These differences in meteorological conditions directly impacted the genotype performance across growing seasons, contributing to the genotype × environment interaction and to the non-uniform clustering patterns seen across the four experiments (Figs. 2a–2d).

Based on data from two, three, and four experiments, the percentage contribution of the first two principal components to total variation was more homogeneous (64.14 to 69.29%) (Figs. 2e–2g). A lower percentage of total variation explained by the first two principal components has been reported when using average data from two experiments for genetic divergence analysis of common bean genotypes for agronomic traits (Arteaga et al. 2019, Savic et al. 2019, Nkhata et al. 2020, Kouam et al. 2023, Mauceri et al. 2025). However, when the average data from three experiments were analyzed, the first two principal components accounted for a percentage of total variation similar to that found in the current study (Prado-Garcia et al. 2025, Stoilova et al. 2025). These results indicate that greater consistency in the clustering pattern of common bean genotypes for agronomic traits can be achieved when principal component analyses are conducted with a larger number of experiments.

Nonetheless, using data from two, three, and four experiments resulted in the formation of four (Fig. 2e), five (Fig. 2f), and six (Fig. 2g) genotype groups, respectively. Only one group, consisting of cultivar IPR Urutau, was consistently present across all cluster analyses based on principal components from the combined experiments (two, three, and four). IPR Urutau stood out from the other genotypes by exhibiting the highest values for the mass of 100 grains and grain yield, despite the variations in meteorological conditions among the four growing seasons (Figs. 1a–1d). Therefore, IPR Urutau represents a promising parent to be included in controlled crosses aimed at increasing the mass of 100 grains and grain yield in new black common bean lines.

The instability of the clustering patterns among individual and combined experiments was quantitatively confirmed by the adjusted Rand index (Table 3). Comparisons between the four-experiment analysis (G) and the individual experiments (A–D) showed a low number of observed concordant pairs (1 to 7), values very close to those expected by chance (1.96 to 5.89), resulting in adjusted Rand index values near 0 or negative (-0.11 to 0.08). This indicated weak agreement among grouping structures for principal components when experiments were analyzed separately. Among the combined analyses, the comparison between four and two experiments (G versus E) showed the highest agreement, with adjusted Rand index value (0,44), which can be interpreted as a moderate agreement (Hubert and Arabie 1985). Overall, these results reinforce the strong influence of experiment variation on genotype discrimination and support the need to evaluate genotypes across multiple experiments to obtain more consistent clustering patterns.

Table 3
Adjusted Rand index (ARI) and its components for groups formed in the principal component analysis using the first two components in the (a) 22 rainy, (b) 23 dry, (c) 23 rainy, and (d) 24 rainy seasons and in the combinations of (e) two, (f) three, and (g) four experiments.

Comparison	Observed pairs	Expected by chance	Maximum	ARI
G versus A	7	5.89	22.50	0.07
G versus B	2	2.13	11.00	-0.01
G versus C	1	1.96	10.50	-0.11
G versus D	3	2.29	11.50	0.08
G versus E	7	2.62	12.50	0.44
G versus F	2	1.96	10.50	0.01

In the current study, no agreement was observed among the genotype groups formed in the principal component analyses performed using data from the four individual experiments, nor from combinations of two, three, or four experiments. This can be justified by the fact that principal component analysis is based on total covariance, without considering residual covariance (Cruz and Regazzi 1997). Consequently, it was not possible to define the minimum number of experiments required for principal component analyses based on this dataset. These results highlight the challenges in selecting parents with promising agronomic traits for crossing blocks in a climate change scenario. This is because cultivation under highly variable meteorological, as observed in this study, demands that breeders evaluate accessions across multiple experiments before selecting promising parents for crossing. This practice increases the costs, labor, and time necessary for the release of new common bean cultivars.

Analysis of canonical variables based on the number of experiments

The first two canonical variables explained 61.60 to 89.64% of the total variation, depending on the growing season (Figs. 3a–3d). Similarly, previous studies have shown that the percentage contribution of the first two canonical variables is not constant (ranging from 72.61 to 80.91%) for agronomic traits of common bean genotypes assessed in different locations and growing years (Ceolin et al. 2006). In our study, the percentage contribution of the first two canonical variables was also not uniform for data from two, three, and four experiments (Figs. 3e–3g). A high percentage of explanation by the first two canonical variables (≥ 66.70%) for the total variation was also reported for agro-morphological traits of common bean evaluated in a single (Fisseha et al. 2018, Dique et al. 2022, Kraeski et al. 2024) and two (Santos Neto et al. 2023) experiments. Canonical variable analyses have the advantage over principal component analyses of considering existing residual correlations between genotype means (Cruz and Regazzi 1997), generating more robust results. The practical implication, as observed in this study, is that the proportion of total variation explained by the first two canonical variables (Figs. 3a–3g) was higher than that explained by the first two principal components in most of the individual and combined experiments (Figs. 2a–2g).

Figure 3
Scatter plots obtained for the first two canonical variables performed for key agronomic traits to common bean breeding obtained of 11 black bean genotypes evaluated in the (a) 2022 rainy, (b) 2023 dry, (c) 2023 rainy, and (d) 2024 rainy seasons and for the combinations of (e) two, (f) three, and (g) four experiments. Total variance explained by the first two canonical variables for each biplot was: (a) 89.64%, (b) 61.61%, (c) 68.88%, (d) 77.21%, (e) 71.54%, (f) 65.59%, and (g) 74.76%.

Different genotype groups were formed when canonical variable analyses were performed using data from one, two, three, and four experiments (Figs. 3a–3g). The number and composition of these groups changed when canonical variable analysis was implemented on agronomic data evaluated in carioca common bean lines in individual experiments (Ceolin et al. 2006). These findings confirm that prevailing meteorological conditions can modify the clustering pattern of common bean genotypes in experiments conducted across different years, seasons, and locations, emphasizing the need for breeding programs to interpret such results carefully.

However, when using data from three or four experiments, the black common bean genotypes were grouped into five clusters with identical composition (Figs. 3f and 3g). Only one genotype was assigned to each of groups 1 (CNFP 18552), 2 (BRS Esteio), 3 (IPR Urutau), and 4 (CNFP 17968). These genotypes were the most divergent from the others in terms of key agronomic traits relevant to breeding. Line CNFP 18552 exhibited lower lodging, greater plant height, and a larger stem diameter. Line CNFP 17968 had the lowest plant height and the lowest mass of 100 grains. Cultivars BRS Esteio and IPR Urutau were superior in grain yield; however, only IPR Urutau showed higher mass of 100 grains across all growing seasons—a trait highly valued in common bean marketing. Group 5 included all remaining genotypes.

The adjusted Rand index (Table 4) supported the clustering patterns obtained from the canonical variable analyses (Figs. 3a–3g). Agreement between the four-experiment analysis (G) and the individual experiments (A–D) was low to moderate, with adjusted Rand index values ranging from -0.03 to 0.28 (Table 4). In G versus A, the number of observed pairs (15) slightly exceeded the value expected by chance (11.07), whereas in G versus B the observed and expected values were similar (5 versus 5.35), indicating lack of consistent grouping. In contrast, the comparison between G (four experiments) versus F (three experiments) showed perfect concordance (adjusted Rand index = 1.00), with the number of observed pairs (21) reaching the maximum possible value. This result quantitatively confirms that canonical variable analyses using data from three or four experiments agreed 100% in the formation of genotype groups that differ for several key agronomic traits for the improvement of black-grained beans.

Table 4
Adjusted Rand index (ARI) and its components for groups formed in the canonical variable analysis based on the first two canonical variables in the (a) 22 rainy, (b) 23 dry, (c) 23 rainy, and (d) 24 rainy seasons and in the combinations of (e) two, (f) three, and (g) four experiments.

Comparison	Observed pairs	Expected by chance	Maximum	ARI
G versus A	15	11.07	25.00	0.28
G versus B	5	5.35	17.50	-0.03
G versus C	7	4.58	16.50	0.20
G versus D	7	4.58	16.50	0.20
G versus E	1	6.49	19.00	0.28
G versus F	21	8.02	21.00	1.00

In this study, using data from four experiments did not alter the clustering pattern obtained from canonical variable analyses using data from three experiments. Therefore, data from three experiments are sufficient for conducting canonical variable analyses of key agronomic traits in common bean breeding. With data from three experiments, it was possible more assertively distinguish differences and similarities among genotypes in the canonical variable analyses, despite the limited number of genotypes accessed. Based on these results, a cross between CNFP 18552 and IPR Urutau is recommended to obtain recombinants combining upright plant architecture, higher mass of 100 grains, and high grain yield.

CONCLUSION

The clustering pattern of common bean genotypes varies according to the number of experiments used in principal component and canonical variable analyses.

For principal component analyses, it was not possible to establish a minimum number of experiments necessary to identify promising parents for inclusion in crossing blocks.

The use of data from three experiments enables recognition differences and similarities among common bean genotypes in canonical variable analysis in a more assertive way.

The cross between CNFP 18552 and IPR Urutau is recommended for developing recombinants with favorable agronomic traits.

ACKNOWLEDGMENTS

Not applicable.

• How to cite:
  Ribeiro, N. D., Argenta, H. S., Lago, L. P. and Ferreira, J. I. (2026). Genetic divergence analyses for key agronomic traits in common bean breeding based on the number of experiments. Bragantia, 85, e20250273. https://doi.org/10.1590/1678-4499.20250273
• FUNDING
  Conselho Nacional de Desenvolvimento Científico e Tecnológico
  Grant No.: 303895/2023-3
  Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
  Grant No.: 88881.844984/2023-01
  Fundação de Amparo a Pesquisa do Estado do Rio Grande do Sul
  Grant No.: 25/2551-0000730-5
• DECLARATION OF USE OF ARTIFICIAL INTELLIGENCE TOOLS
  Any artificial intelligence tool was used in the preparation of the manuscript.

DATA AVAILABILITY STATEMENT

All data were generated or analyzed in this study.

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Edited by

• Section Editor:
  Alberto Cargnelutti Filho https://orcid.org/0000-0002-8608-9960

Publication Dates

• Publication in this collection
  10 July 2026
• Date of issue
  2026

History

• Received
  11 Dec 2025
• Accepted
  24 Mar 2026