Genetic diversity of corn cultivars through agronomic, physical, and chemical traits employing multivariate analysis, Bayesian approach, and artificial neural networks

ABSTRACT

The objective of this study was to evaluate the genetic diversity among 49 maize cultivars, including 43 popcorn cultivars, two common maize, two sweet maize, and two hominy maize, using multivariate statistical techniques to identify genetic groups and their implications for breeding. The experiment was conducted by a complete block design with randomized treatments and three replications. Agronomic, chemical, and physical traits were assessed, and statistical analyses included the Mahalanobis distance, multivariate analysis of variance, clustering methods such as unweighted pair-group method with arithmetic mean, modified Tocher, k-means, and Kohonen self-organizing maps, alongside Bayesian hierarchical clustering. Significant genetic variability (p 0.05) was observed, with Viçosa and Dow2B433PW showing the greatest divergence (910.60), while Xuxu Viçosa and Beija-Flor exhibited the closest genetic similarity (18.26). The trait pericarp thermal diffusivity contributed most to differentiation (24.36%), demonstrating its relevance for popcorn expansion capacity. The clustering methodologies efficiently classified genetic diversity, allowing the identification of promising genotypes for crosses. This study highlights the effectiveness of integrating traditional multivariate analyses with advanced artificial intelligence approaches, such as Kohonen maps and Bayesian clustering, for genetic diversity studies. Selecting genetically distant genotypes, such as Viçosa and Dow2B433PW, offers potential for heterotic gains, while closer genotypes like Xuxu Viçosa and Beija-Flor are valuable for preserving specific traits. These findings emphasize the importance of combining different statistical techniques to refine breeding strategies, optimize productivity, and enhance the adaptability and quality of maize cultivars under various conditions.

Key words
Zea mays L.; Mahalanobis distance; multivariate analysis; clustering; Kohonen

INTRODUCTION

Corn (Zea mays L.) stands out economically as an important crop, with various uses, ranging from human and animal nutrition to the high-tech industry (Nunes 2022). In this context, the demand for quality cultivars is high, increasingly depending on breeding programs to meet this need.

The success of corn breeding programs relies on efficiently identifying superior parents for segregating populations. Genetic divergence is crucial for heterosis expression and enables the grouping of genotypes, transforming a heterogeneous group into homogeneous clusters in a multivariate context. This facilitates crosses between contrasting genotypes and enhances selection gains (Alves et al. 2015). Such analyses are vital for hybridization, as selecting divergent parents boosts the heterotic effect, leading to superior progenies (Santos et al. 2020).

Genetic characterization of popcorn populations intended for breeding can be performed using agronomic traits and/or molecular markers. Molecular analysis has been applied to estimate the genetic divergence between popcorn lines (Dandolini et al. 2008, Leal et al. 2010, Eloi et al. 2012, Castro et al. 2022).

Genetic divergence can be assessed by employing multivariate techniques or predictive processes. Predictive processes of genetic divergence have received considerable emphasis because they do not require obtaining hybrids. They are based on differences between characteristics that have quantitative behavior, generally using dissimilarity measures such as the Mahalanobis distance and the Euclidean distance (Rao 1952).

The generalized Mahalanobis distance (D2) considers the correlation between variables from a dispersion matrix and is recommended for data from experimental designs, especially when there is a correlation between traits, enabling more consistent decisions (Cruz et al. 2011).

Cluster analyses aim to separate an original group of observations into several groups to obtain homogeneity in the group and heterogeneity between subgroups. This method depends on dissimilarity measures from quantitative and qualitative traits. The unweighted pair group method with arithmetic mean (UPGMA), the non-hierarchical k-means method, and the canonical variables method stand out among the clustering methods, aiming to evaluate similarity through graphical dispersion (Cruz et al. 2011).

Studies of genetic divergence have been also conducted using artificial neural networks. Artificial neural networks (ANNs) are computational techniques that present a model inspired by the human neural structure and acquire knowledge through experience (Haykin 2008). The main reasons for their use are: ANNs do not assume any type of data distribution a priori, unlike the traditional parametric statistical approach, which assumes data normality; and the ability to manipulate data acquired from different sources and with different levels of precision.

The ANN technique has been employed in studies of genetic diversity (Oliveira et al. 2013), with particular emphasis on the Kohonen self-organizing map model, aiming at genotype clustering and identification (Barbosa et al. 2011, Cardoso et al. 2021, Sá et al. 2022).

Among neural network models, Kohonen self-organizing maps (SOM) are indicated for grouping cultivars and recognizing patterns without requiring the researcher to apply prior knowledge of the material under study, in addition to providing support for updating or even formulating new theories about the problem (Barbosa et al. 2011).

Bayesian hierarchical clustering (BHC), based on the Dirichlet process mixture model, excels in creating an informative hierarchical cluster structure by employing Bayesian model selection instead of ad hoc distance metrics. This improves the quality and reliability of clusters, making BHC a promising tool for studying genetic diversity in maize. Unlike traditional methods like UPGMA or principal component analysis, BHC identifies genetic structures at multiple levels, revealing broad clusters tied to origin or adaptation and subtle subdivisions linked to historical crossings. These insights support genetic improvement programs and the conservation of maize diversity.

Studies on methodologies that enable the identification of more divergent and promising materials are fundamental for the genetic improvement of special corn and can help to obtain new cultivars adapted to different soil and climate conditions. The higher availability of cultivars can provide farmers with the possibility of adding value by selling the generated product and, consequently, contributing to an increase in the economy. In this sense, this study aimed to evaluate and compare the different statistical methodologies used to study genetic diversity.

MATERIAL AND METHODS

Genetic material and trial conditions

A total of 49 corn cultivars was evaluated, of which 43 consisted of popcorn cultivars from the genetic breeding program of the Universidade Estadual de Maringá (UEM), two common corn cultivars, two sweet corn cultivars, and two hominy corn cultivars (Table 1).

Table 1
Description of the cultivars used in the trial.

Cultivars		Type	Genetic characterization	Origin
1.	Colombiana	Popcorn	Open-pollinated variety	UEM
2.	Composto Vanin	Popcorn	Open-pollinated variety	UEM
3.	Composto Matheus	Popcorn	Open-pollinated variety	UEM
4.	UNB 2UC5	Popcorn	Open-pollinated variety	UENF
5.	Composto Elizete	Popcorn	Open-pollinated variety	UEM
6.	PARA 170	Popcorn	Open-pollinated variety	CIMMYT
7.	CMS 42	Popcorn	Open-pollinated variety	EMBRAPA
8.	ARZM 07 049	Popcorn	Open-pollinated variety	CIMMYT
9.	URUG 298	Popcorn	Open-pollinated variety	CIMMYT
10.	SC 016	Popcorn	Open-pollinated variety	UEL
11.	PA 091	Popcorn	Open-pollinated variety	UEM
12.	Viviane	Popcorn	Open-pollinated variety	UEM
13.	RR 046	Popcorn	Open-pollinated variety	UEL
14.	Xuxu Viçosa	Popcorn	Open-pollinated variety	UEM
15.	Composto Márcia	Popcorn	Open-pollinated variety	UEM
16.	Beija-Flor	Popcorn	Open-pollinated variety	UFV
17.	Composto Gaúcha	Popcorn	Open-pollinated variety	UEM
18.	Composto Chico	Popcorn	Open-pollinated variety	UEM
19.	Composto misto	Popcorn	Open-pollinated variety	UEM
20.	PR 023	Popcorn	Open-pollinated variety	UEM
21.	PARA 172	Popcorn	Open-pollinated variety	CIMMYT
22.	ARZM 13050	Popcorn	Open-pollinated variety	CIMMYT
23.	Viçosa	Popcorn	Open-pollinated variety	UFV
24.	SE 013	Popcorn	Open-pollinated variety	UEM
25.	ARZM 05083	Popcorn	Open-pollinated variety	CIMMYT
26.	SAM	Popcorn	Open-pollinated variety	USA
27.	PA 038	Popcorn	Open-pollinated variety	UEM
28.	Composto Aelton	Popcorn	Open-pollinated variety	UEM
29.	BOZM 260	Popcorn	Open-pollinated variety	CIMMYT
30.	PA 79	Popcorn	Open-pollinated variety	UEM
31.	BOYA 462	Popcorn	Open-pollinated variety	CIMMYT
32.	UEM J1	Popcorn	Open-pollinated variety	UEM
33.	Barão Viçosa	Popcorn	Open-pollinated variety	UFV
34.	Composto Branco	Popcorn	Open-pollinated variety	UEL
35.	PR 009	Popcorn	Open-pollinated variety	UEL
36.	SC 002	Popcorn	Open-pollinated variety	UEL
37.	Popten	Popcorn	Single-cross hybrids	SEEMAX
38.	Poptop II	Popcorn	Single-cross hybrids	SEEMAX
39.	IAC 125	Popcorn	Single-cross hybrids	IAC
40.	RS 20	Popcorn	Open-pollinated variety	IPAGRO
41.	PR 017	Popcorn	Open-pollinated variety	UEL
42.	Zélia	Popcorn	Triple hybrid	PIONEER
43.	BRS Angela	Popcorn	Open-pollinated variety	EMBRAPA
44.	Dow2B433PW	Common	Triple hybrid	DOW
45.	DKB 290 PRO3	Common	Triple hybrid	DEKALB
46.	BR 402	Sweet	Open-pollinated variety	EMBRAPA
47.	IAC Doce Cubano	Sweet	Open-pollinated variety	IAC
48.	IAC Nelore	Hominy	Intervarietal hybrid	IAC
49.	IPR 119	Hominy	Double-cross hybrid	IAPAR

• UEM: Universidade Estadual de Maringá; UENF: Universidade Estadual do Norte Fluminense Darcy Ribeiro; CIMMYT: International Maize and Wheat Improvement Center; EMBRAPA: Brazilian Agricultural Research Corporation; UEL: Universidade Estadual de Londrina; UFV: Universidade Federal de Viçosa; SAM: South American Mushroom; IAC: Agronomic Institute of Campinas; IPAGRO: Agricultural Research Institute; IAPAR: Agronomic Institute of Paraná; USA: United States of America.

The experiment was conducted in September 2017, during the 2017/2018 season, at the Iguatemi Experimental Farm of the UEM, located in the Iguatemi district of Maringá, Paraná, Brazil (latitude 23°25’S, longitude 51°57’W, and altitude of 550 m). The region has an average annual rainfall of 1,500 mm and mean temperature of 19°C. The soil in the experimental area is classified as an Oxisol (Dystrophic Red Latosol).

The 49 cultivars were arranged in a complete block design with randomized treatments with three replications. The experimental plots consisted of two 5-m rows, spaced 0.90 m between rows and 0.2 m between plants. Then, the useful area of the plot was 9 m². Two seeds were sown per hole and thinned to five plants per meter 30 days after emergence, resulting in a density of 55,500 plants·ha^-1. Sweet corn cobs were protected to avoid the xenia effect (effect of pollen on seed development and traits).

The trial area was prepared by desiccating the cover crop (black oat Avena strigosa) and controlling the weeds with the application of paraquat (2 L·ha^-1). A total of 230 kg·ha^-1 of the NPK formula 08-20-20 was applied as base fertilization. The seeds of the trials were treated with insecticide (Cropstar). Two applications of nitrogen sources were carried out at the V4 and V8 stages of corn crop development, totaling 90 kg N·ha^-1.

The fall armyworm (Spodoptera frugiperda) was controlled with two sprays of insecticides whose active ingredient was flubendiamide at the dose of 70 mL cp·ha^-1 and beta-cyfluthrin + imidacloprid at the dose of 500 mL cp·ha^-1 at the stage V8 of crop development.

Evaluated traits

• The following traits were evaluated:

• Mean ear insertion height (EH): expressed in cm, obtained by the mean of measurements taken using a measuring tape from soil level to the insertion of the upper ear, in the six competitive plants of the plot;

• Mean plant height (PH): expressed in cm, obtained by the mean of measurements taken with a tape measure from soil level to the insertion of the flag leaf, in the six competitive plants of the plot, after tasseling;

• Stem diameter (SD): expressed in mm, obtained by averaging the measurements at the first node above the plant collar after tasseling, on the six competitive plants in the plot, using a digital caliper;

• Mean number of grain rows per ear (NGRe): mean number of grain rows per ear of 10 random ears from each plot;

• Mean number of grains per row (NGR): mean number of grains per row of 10 random ears from each plot;

• Number of ears (NE): obtained by the sum of all ears husked from each plot;

• Mean ear length (EL): expressed in cm, obtained by averaging the measurements from the basal part to the tip of the husked ear, conducted with a ruler on 10 random ears from each plot;

• Ear diameter (ED): expressed in mm, obtained by averaging the diameter of 10 random ears from each plot, measured in the central-basal region of the ear, using a caliper;

• 100-grain mass (M100): two samples of 100 grains from each plot were weighed on a precision scale, and the mean of the two samples was calculated;

• Grain yield (GY): expressed in kg·ha^-1, obtained by weighing the threshed grains of the plot corrected for a standard moisture of 13%;

• Expansion capacity (EC): expressed in mL·g^-1, obtained by the relationship between the volume of expanded popcorn and the mass of grains (30 g), using the mean of two samples per plot. The procedure to measure EC was performed when moisture levels between 12.5 and 13.5% were found in the samples, following the methodology described by Stipp et al. (2023);

• Mean grain length (GL): expressed in mm, obtained by averaging the distance measured from the tip to the base of the grain, in 50 grains from each plot, using a digital caliper;

• Mean grain width (GW): expressed in mm, obtained by averaging the distance measured from tip to tip of the widest part of the grain, in 50 grains from each plot, using a digital caliper;

• Mean grain thickness (GT): expressed in mm, obtained by averaging the distance measured between the two sides of the grain, in 50 grains from each plot, using a digital caliper;

• Mean pericarp thickness (PT): expressed in mm, obtained by the mean pericarp thickness measured using a micrometer. Five pericarp samples from each plot were measured in five regions of each pericarp sample (central and peripheral). The pericarps were manually removed after the grains were immersed in water for 6 hours. Subsequently, the pericarps were compressed between two glass plates for 12 hours and stored inside a glass chamber with blue silica, ensuring a flat shape and uniformity of moisture;

• Pericarp thermal diffusivity (PTD): expressed in m2·s^-1, determined by the open-cell photoacoustic technique. This technique consists of observing acoustic waves produced by a sample when heated by modulated light, using an electret microphone (Figs. 1 and 2). Five pericarp samples from each field plot were evaluated. The time for the heating cycles and capture of acoustic waves for each sample was approximately 15 minutes;

• Protein content (PC): grain samples from each plot were ground in a mill, using a sieve with a 0.50-mm opening.

Figure 1
Scheme for determining the pericarp thermal diffusivity through the open cell photoacoustic (OPC) technique.

Figure 2
Views of the apparatus used to determine the pericarp thermal diffusivity through open-cell photoacoustic, showing the (a) equipment in operation and (b) photoacoustic chamber with an electret microphone.

Statistical analyses

The multivariate analysis of variance and all other analyses were performed in the R statistical environment version 4.3.2 (R Core Team 2024).

The multivariate analysis of variance was developed in the R statistical environment, using the Multivariate Analysis package (Azevedo and Azevedo 2025). Multivariate Analysis is a package with multivariate analysis methodologies for experiment evaluation.

The genetic distance between the accessions evaluated in this study was estimated by the generalized Mahalanobis distance (D2). The Mahalanobis distances allowed the construction of a dendrogram using the UPGMA cluster analysis. The dendrogram was cut off using the method by Mojena (1977). The cophenetic correlation coefficient was estimated in this same environment, aiming to evaluate the efficiency of the UPGMA clustering method.

The k-means clustering method was also adopted to demonstrate the structure of populations depending on the evaluated traits. The k-means method was used with the within-cluster sum of squares algorithm, based on a data set of standardized means with mean = 0 and variance = 1 (Kassambara and Mundt 2016).

Clustering using the modified Tocher optimization method was performed by the Mahalanobis distance matrix, which identifies the pair of most similar individuals that form the initial group.

The analysis of canonical variables was conducted in such a way that the original variables (measured traits) were transformed into a new set, originating the canonical variables.

The relative importance of the traits was calculated using the method proposed by Singh (1981), which is based on the partition of the total Mahalanobis distance estimates considering all possible pairs of cultivars for the contribution referring to each evaluated trait.

The study of genetic dissimilarity implementing the SOM ANN technique, based on the model by Kohonen (1983), was performed using the Kohonen package and sound function. The SOM methodology was applied with the traditional unsupervised approach, according to the traits and needs of the study.

The training of the SOM was conducted through a trial-and-error process using the convergence graph provided by the Kohonen package, ensuring the network captured the nuances of the data. The initial parameters included 10,000 iterations, a grid configuration of three rows and two columns, and a hexagonal topology, which was chosen for its ability to allow smoother transitions and naturally represent clusters. The number of classes was determined using the Elbow test, contributing to an accurate and realistic organization of the evaluated data.

BHC was developed in the R statistical environment, using Bioconductor as an integrated platform for data analysis. The analysis was performed using the BHC package available in Bioconductor. The BHC package of Bioconductor (Savage et al. 2023) was essential for performing the agglomerative hierarchical clustering. This package guides choosing the “correct” number of clusters and uses Bayesian model selection to determine hierarchical structure rather than an ad-hoc distance metric, thereby increasing the quality of the resulting clusters (Sirinukunwattana et al. 2013).

RESULTS AND DISCUSSION

The multivariate analysis of variance revealed significant differences (p < 0.05) between the mean vectors of the treatments, highlighting the importance of multivariate approaches for a more precise understanding of the genetic diversity of the evaluated materials. This study focused on popcorn maize due to its expansion and quality traits, while the inclusion of common, sweet, and hominy maize cultivars provides a crucial comparative basis for assessing genetic divergences and heterotic potential.

The coefficients of variation were in agreement with the standards for trial with corn, indicating satisfactory precision, according to the classification proposed by Scapim et al. (1995).

The Mahalanobis distance, by accounting for correlations and variable redundancies through covariance or correlation matrices, effectively mitigates experimental noise and provides a robust and reliable metric for genotypic diversity in heterogeneous experiments. This method enables the integration of multiple traits, assisting in the identification of superior genotypes for genetic improvement programs. The significant genetic distance (910.60) between the popcorn maize variety Viçosa and the common maize hybrid Dow2B433PW highlights distinct genetic groups influenced by traits like PTD, PC, and GY. In contrast, the smaller genetic distance (18.26) observed between Xuxu Viçosa and Beija-Flor reflects their genetic similarity, attributed to a shared origin and common traits. Genetically distinct genotypes, such as Viçosa and Dow2B433PW, emerge as promising candidates for crosses aimed at generating heterotic offspring and enhancing genetic variability.

Studies on genetic diversity using the generalized Mahalanobis distance as a measure of dissimilarity for clustering analysis have been conducted in maize by Alves et al. (2015), resulting in four groups of cultivars; by Silva et al. (2016), forming 11 groups of cultivars; and by Nardino et al. (2017), identifying eight distinct groups of cultivars. The generalized Mahalanobis distance has been also employed in studies on other crops, such as rice (Benitez et al. 2011), bean (Cargnelutti Filho et al. 2008, Tavares et al. 2018), soybean (Rodrigues et al. 2017), and wheat (Condé et al. 2010).

Figure 3 shows the dendrogram obtained for cluster analysis using the UPGMA method, from the estimates of the generalized Mahalanobis distance. Five distinct groups can be identified. The number of groups was obtained according to the methodology proposed by Mojena (1977), with k = 1.25 and cut off point = 191.6141.

Figure 3
Dendrogram representing the genetic dissimilarity between 49 corn cultivars obtained by the unweighted pair group method with arithmetic mean based on the Mahalanobis generalized dissimilarity measure.

Group I (gray), formed by 40 out of the 49 analyzed cultivars, was efficient since all cultivars belonging to this group consist of popcorn individuals. Non-improved cultivars were grouped with improved cultivars, including two popcorn hybrids (Zélia and IAC 125).

Among the cultivars present in Group I, IAC 125 originated from SAM and IAC 64 lines and an advanced generation of an American hybrid, while the genotype Zélia originated from a triple hybrid from the company Pioneer. The variety BRS Angela is an improved genotype resulting from six cycles of recurrent intrapopulation selection in the CMS 43 popcorn composition, with white and round grains. The genotype RS 20 was developed by IPAGRO and UFVM2-Barão Viçosa. The improved genotype UNB 2UC5 originated from the crossing of the UNB-1 population with the popcorn variety Americana, whose selected progenies were crossed with a variety of yellow grains resistant to helminthosporiosis (Exserohilum turcicum). A population formed by resistant plants and yellow grains was obtained after two cycles of mass selection, which was backcrossed three times with the variety Americana and originated the UNB2U population. This population originated the genotype UNB 2UC5 after five selection cycles.

Group II (purple) was the result of the grouping of sweet corn cultivars (BR 402 and IAC Doce Cubano), while Group III (blue) was formed by the two single-cross hybrids of popcorn (Popten and Poptop II). Group IV (red) presented only one genotype, Composto Vanin, a local open-pollinated variety. Group V (pink) included common corn hybrids (Dow2B433PW and DKB 290 PRO3) and hominy hybrids (IAC Nelore and IPR 119).

In contrast, BHC, a model-based clustering algorithm based on the Dirichlet process mixture model, led to the formation of four distinct groups (Fig. 4).

Figure 4
Dendrogram representing the Bayesian hierarchical clustering of 49 corn cultivars. The values shown in the branches represent the log-likelihood of joint.

Group B1 (red) gathered 32 out of the 49 evaluated cultivars, not including the improved cultivars BRS Angela and IAC 125, which were grouped in groups B3 and B4, respectively, unlike what was found in the UPGMA hierarchical grouping. Group B2 (blue) grouped the cultivars of common corn (Dow2B433PW and DKB 290 PRO3), hominy corn (IAC Nelore and IPR 119), and sweet corn (BR 402 and IAC Doce Cubano). Group B3 (yellow) had five popcorn cultivars, including BRS Angela and ARZM 05083, whereas group B4 (green) was formed by the simple popcorn hybrids Popten and Poptop II, the topcross hybrid IAC 125, the genotype SAM, and the cultivars RS 20 and Viviane.

Silva et al. (2016) evaluated the genetic dissimilarity between progenies of corn half-sibs and found group formation with isolated individuals when using the UPGMA method. Other authors also reported similar results with popcorn (Miranda et al. 2003, Faria et al. 2008, Resh et al. 2015), proving to be an interesting method for identifying and selecting lines with higher divergence for subsequent crossings.

The cophenetic correlation coefficient obtained from the UPGMA clustering was 0.8204 and significant (p ≤ 0.05), indicating a reliable representation of the genetic distances of the cultivars in the dendrogram. Silva et al. (2016), while studying dissimilarity in green maize progenies, observed a cophenetic correlation coefficient of 0.65 using the UPGMA method, which was also significant. This result is consistent with the findings of the present study, indicating that the data matrix showed a satisfactory fit in the graphical representation presented by the dendrogram.

The data variance was tested by the Elbow method relative to the number of clusters. An ideal value of k is one in which the increase in the number of clusters does not represent a significant value of gain. The Elbow method indicated that four groups would be ideal to represent the results of the present study under the evaluated traits.

The plot for k-means (Fig. 5), plotted for the first two principal components, explained 53.1% of the data variability. Cluster 1 included the cultivars PARA 170, URUG 298, PR 023, PARA 172, ARZM 13050, PA 038, BOZM 260, Boya 462, BR 402, and IAC Doce Cubano. Cluster 2 included the cultivars Colombiana, DOW2B433PW, DKB 290 PRO3, IAC Nelore, and IPR 119. Cluster 3 consisted of the cultivars Composto Matheus, ARZM 07049, SC 016, PA 091, RR 046, Composto Márcia, Composto Chico, Composto misto, SE 013, ARZM 05083, Composto Aelton, PA 79, UEM J1, Composto Branco, PR 009, SC 002, PR 017, and BRS Angela. Finally, cluster 4 included the cultivars Composto Vanin, UNB 2UC5, CMS 42, Viviane, Xuxu Viçosa, Beija-Flor, Composto Gaúcha, Viçosa, SAM, Barão Viçosa, Popten, Poptop II, IAC 125, RS 20, and Zélia.

Figure 5
Groups of cultivars considering the k-means algorithm, based on the studied traits.

Cluster 1 presented higher means for the traits of EH (121.25), NE (53.70), and oil content (6.73). Cluster 2 grouped cultivars with higher mean GL (11.04), GT (4.35), GW (8.14), M100 (29.17), EL (16.58), ED (47.77), NGRe (15.31), yield (5602.15), and starch content (77.70). On the other hand, cluster 3 grouped cultivars with higher means for the traits of PH (196.08), NGR (34.36), and SD (22.94), while cluster 4 consisted of the cultivars that had higher means for the traits of PC (10.98), PT (75.10), PTD (0.61), and EC (28.03).

The modified Tocher optimization method, based on the generalized Mahalanobis distance, allowed the classification of the 49 cultivars into five groups (Table 2). According to Cruz et al. (2014), the formation of these groups contributes to choosing parents, as the new combinations to be established must be based on the magnitude of their dissimilarities and the potential per se of the parents. Therefore, cultivars that belong to the same group have higher genetic similarity to each other.

Table 2
Grouping by the modified Tocher optimization method, according to the generalized Mahalanobis distance (D2) of 49 corn cultivars, based on 19 agronomic, chemical, and physical traits.

Group	Number of cultivars	% Number of cultivars	Cultivars
1	11	22,45	Composto Matheus, UNB2UC5, Composto Elizete, CMS 42, PA 091, Xuxu Viçosa, Beija-Flor, Composto Gaúcha, Composto Chico, Viçosa, Composto Aelton
2	31	63,27	Colombiana, PARA 170, ARZM 07049, URUG 298, SC 016, Viviane, RR 046, Composto Marcia, Composto Misto, PR 023, PARA 172, ARZM 13050, SE 013, ARZM 05083, SAM, PA 038, BOZM 260, PA 79, Boya 462, UEM J1, Barão Viçosa, Composto Branco, PR 009, SC 002, IAC 125, RS 20, PR 017, Zélia, BRS Angela, BR 402, IAC Doce Cubano
3	4	8,16	Dow2B433PW, DKB 290 PRO3, IAC Nelore, IPR 119
4	2	4,08	Popten, Poptop II
5	1	2,04	Composto Vanin

Rotili et al. (2012) and Silva et al. (2015) stated that the presence of groups with only one genotype indicates a wide genetic diversity, thus diverging more in terms of the other formed groups, facilitating the projection of improvement works and the identification of distinct cultivars for future crossings. Therefore, according to the modified Tocher clustering and the UPGMA method, Composto Vanin can be used in crosses with any genotype from the other groups, providing potential hybrids, as they are the result of contrasting parents.

Group I, obtained by the UPGMA method, and groups 1 and 2, by the modified Tocher method, presented the same cultivars, except for sweet corn cultivars, which were isolated in group II by the UPGMA method and incorporated into group 2 together with popcorn cultivars by the modified Tocher method. Group III, proposed by the UPGMA methodology, and group IV, by the modified Tocher method, presented the same cultivars, which also occurred with groups IV and V by the UPGMA and modified Tocher methods, respectively.

Silva et al. (2009) evaluated the diversity of 25 popcorn cultivars, 10 of which are common to this study (Zélia, BRS Angela, IAC 125, Composto Aelton, SE 013, Viçosa, CMS 42, Composto Matheus, PA 091, and PR 023) and observed that the cultivars in common were grouped similarly when using the Tocher optimization method. The cultivars Zélia, BRS Angela, IAC 125, Composto Aelton, SE 013, Viçosa, CMS 42, and Composto Matheus, grouped in group I by Silva et al. (2009), were also grouped in group II of this study, except for Composto Matheus, Composto Aelton, and CMS 42, which were grouped in group I of this study along with eight other cultivars, including the genotype PA 091, which was allocated alone in group IV by Silva et al. (2009). These results demonstrate that the cultivars are grouped efficiently, showing the real association between genotypic values.

The first two out of the 19 canonical variables explained 58.5% of the total variation, the first reaching 38.3% and the second 20.2% (Fig. 6). In this sense, the variability manifested between corn cultivars can be partially explained, thus allowing the interpretation of the phenomenon with considerable simplification, as the first two canonical variables explained more than half of the contained variation.

Figure 6
Dispersion of scores relative to two canonical variables (Can1 and Can2).

The low variance observed in the first canonical variables suggests that the evaluated traits may not have been sufficient to effectively discriminate the genetic diversity among the 49 popcorn cultivars studied. It is possible that the current descriptors exhibit redundancy or high correlation, limiting differentiation potential, and that other traits not included in the analysis, such as the leaf area index–previously identified as influential in corn variability by Simon et al. (2012)–could be more sensitive in highlighting subtle genetic differences among cultivars.

The common corn cultivars Dow2B433PW and DKB 290 PRO3 and the hominy cultivars IAC Nelore and IPR 119 remained isolated through the dispersion of scores relative to the two canonical variables (CV1 and CV2), but these cultivars were grouped using the modified Tocher optimization method. Groups I and II, obtained by the modified Tocher optimization method, were close in the score dispersion plane, with the genotype Colombiana isolated relative to the other cultivars belonging to group II. The genotype Colombiana is an open-pollinated variety from Colombia, which differed from other varieties due to the variability existing in cultivars of different origins. This trait is very interesting, consisting of a great alternative in crossing with cultivars from other groups in generating variability, also allowing the acquisition of popcorn cultivars with desirable traits. The genotype BOZM 260, from Bolivia, and the genotype URUG 298, from Uruguay, are interesting due to their very different origins from the other corn cultivars in this study, which allows to assume that they would be an interesting possibility in obtaining variability when crossed with cultivars from other groups.

The single-cross hybrids of popcorn Popten and Poptop II were close in the plane, corroborating the modified Tocher analysis. However, the genotype Composto Vanin, isolated by the modified Tocher optimization method in group V, is close to the Poptop II genotype in the genotype scatterplot. Thus, Tocher’s clustering methods and canonical variables were partially in agreement with each other.

All multivariate methodologies used in this study grouped the cultivars Xuxu Viçosa and Viçosa into the same group, which proved to be efficient, as the genotype Xuxu Viçosa is an improvement of Viçosa, with only one mass selection cycle.

The cultivars ARZM 07049, ARZM 13050, and ARZM 05083 are open-pollinated varieties originating from indigenous cultivars of Paraguay. The multivariate techniques allowed the cultivars to be grouped into the same group, showing the efficiency of the used techniques. These cultivars can be viable alternatives when crossing with cultivars from other groups to generate variability and obtain popcorn cultivars with desirable traits.

The ANN technique, using the Kohonen SOM method, allowed the formation of all six pre-established classes with three rows and two columns for command, also enabling the formation of four groups (Fig. 7).

Figure 7
Kohonen self-organizing map for six classification classes and the four groups formed using an artificial neural network.

Therefore, the cultivars were organized into different classes represented by hexagons. It shows the number of cultivars arranged in each of the classes. Nearby classes, that is, those that constitute space boundaries, there are cultivars with similarity to the neighboring class, while the most divergent classes constitute the regions of extremes, and intermediate classes (second neighbors) are in the center of the map.

Classes 1 and 4 (marked in light green) were made up of seven cultivars each. Class 2 (marked in red) contains four cultivars. Classes 3 and 5 (marked in purple) have 12 and 11 cultivars, respectively, and class 6 (marked in green) contains eight out of the 49 cultivars. Regarding the four groups, group I was formed by the cultivars present in class 1, group II was formed by the cultivars present in class 2, group III was formed by the cultivars present in class 3, and group IV was formed by the cultivars present in classes 4, 5, and 6.

Group/class 1 was formed by foreign open-pollinated cultivars and sweet corn cultivars with similarity in having higher influences on the traits of EH, PH, and oil content. Group/Class 2 was formed by hybrids of common corn and hominy corn, which show higher similarity in terms of yield traits and starch content. Group/Class 3 was made up of the single-cross hybrid popcorn cultivars Poptop and Popten II, triple hybrid IAC 125, and some open-pollinated varieties, including Xuxu Viçosa, Viçosa, Barão de Viçosa, SAM, Viviane, UNB 2UC5, and ARZM 05083, showing a certain similarity for the highest means of EC, PTD, PT, and PC. Group 4, formed by classes 4, 5, and 6, is composed of open-pollinated varieties of popcorn with higher similarities, mainly for the traits of NGR, SD, and EL.

The number of cultivars was variable in each group, with group IV showing the largest number of cultivars. This difference in the number of cultivars within each group is related to the variation in the evaluated traits.

The groups found by the Kohonen SOM partially agree with the results obtained by the hierarchical multivariate analysis methods UPGMA and canonical variables, and with higher agreement with the results obtained by the non-hierarchical k-means clustering.

The differences in groups occur because ANN have a non-linear structure that can capture deeper and more complex characteristics of the data, whether quantitative or qualitative, which is not always possible when using traditional statistical techniques, according to Galvão et al. (1999).

The formation of genetically distinct groups maximizes heterosis, making the selection of genotypes with large genetic distances essential for enhancing variability in crosses. Genotypes such as Composto Vanin, Composto Matheus, UNB 2UC5, Xuxu Viçosa, Beija-Flor, and Viçosa, which exhibit high genetic diversity, are valuable for improving stress resistance and broadening the genetic base for heterosis-focused breeding programs. These genotypes can be crossed with commercial hybrids (Dow2B433PW and DKB 290 PRO3) to enhance productivity or with popcorn maize hybrids (Poptop II and Popten) to maintain popcorn quality while increasing environmental stress resistance. Commercial hybrids and maize sweet and hominy hybrids demonstrate advantages in resource efficiency, uniformity, and resistance, making them suitable for crosses aimed at adapting genotypes to diverse cultivation conditions. Popcorn hybrids such as Poptop II and Popten, with high expansion yield and grain quality, could be crossed with open-pollinated varieties to enhance pest resistance while preserving grain quality or with common maize hybrids to combine productivity and resilience while retaining desirable popcorn traits.

The contribution of 19 agronomic, chemical, and physical traits to genetic diversity was assessed using Singh (1981) method based on the Mahalanobis distance. PTD had the highest relative contribution (24.36%) to cultivar differentiation, playing a key role in temperature response and grain quality. According to Incropera and Dewitt (1992), this trait explains popcorn expansion due to the pericarp’s rapid thermal reaction. It significantly influences genetic divergence and aids parental line selection for hybrids with high expansion volumes. Marker-assisted selection enables early identification of superior lines, while advanced phenotyping and optimized post-harvest practices help maintain and improve grain quality across the production chain.

The traits PC, GY, and mean EH (12.95, 9.22, and 7.43%, respectively) presented a relatively important contribution to diversity.

Rotili et al. (2012) analyzed the contribution of traits to diversity in a genetic diversity study with corn cultivars and observed that yield presented the highest contribution to diversity. It agrees with the results found in this study, in which the yield of grains showed a relatively important contribution to the diversity in the evaluated cultivars.

Arnhold et al. (2010) studied the selection of popcorn lines based on performance and genetic diversity and observed that expansion capacity presented the highest relative contribution to genetic dissimilarity. Melo et al. (2017) studied selection strategies between popcorn half-sibling progenies and found that expansion capacity also presented the highest index of relative importance over diversity, corroborating the results obtained in the present study, showing that expansion capacity is a trait of great importance for the relative contribution to genetic dissimilarity.

According to the Singh method, the traits mean EL (1.02%) and NE (0.80%) presented the lowest contributions to genetic diversity, being suggested as variables that could be discarded, as they would be uninformative due to relative contribution estimates of small magnitudes.

Kage et al. (2013) studied 82 cultivars of corn and observed that PH and EIH were the traits that most contributed to genetic divergence, with 30.60 and 16.65%, respectively. Moreover, the traits GY (8.70%), NGR (6.14%), number of grains per ear (1.96%), and EL (1.48%) presented lower contributions. According to Nagalakshmi et al. (2010), the contribution depends mainly on the cultivars used in the study and the environmental influences on the trait.

Different clustering techniques, such as Kohonen SOM, BHC, and UPGMA hierarchical clustering, revealed fundamental differences despite some similarities. Kohonen maps minimize intra-group variance and maximize inter-group variance, offering precise identification of specific traits like PTD and EC. Bayesian clustering accommodates greater statistical heterogeneity by focusing on latent factors, while UPGMA groups similar cultivars together. These methods demonstrated that hybrids like Popten and Poptop II, as well as common, sweet, and hominy maize, form homogeneous groups based on agronomic traits and commercial value. In contrast, open-pollinated varieties exhibited greater genetic diversity, highlighting their potential for crosses that enhance variability. Variations in clustering patterns, as seen with Composto Vanin, Viçosa, and Barão Viçosa, emphasize the importance of combining different approaches to optimize genetic improvement strategies.

CONCLUSION

The evaluated corn cultivars exhibit significant genetic variability, with Viçosa and Dow2B433PW demonstrating the greatest divergence, suggesting a high potential for heterotic gains in breeding programs. The efficiency of multivariate methodologies in classifying genetic diversity was confirmed, with Bayesian clustering and Kohonen neural networks complementing traditional statistical techniques.

Among the studied traits, PTD (24.36%) played a crucial role in differentiation, making it a valuable criterion for selecting parental lines aimed at enhancing popcorn EC. Conversely, the number of ears (0.80%) had the least impact, indicating limited utility in diversity assessments. These findings provide essential insights for breeding strategies, facilitating the selection of genetically distant parent lines to maximize heterosis and ensuring the incorporation of traits that contribute to yield, resilience, and market quality. The integration of advanced statistical and artificial intelligence methods enhances the precision of genetic classification, optimizing the identification of promising genotypes for hybrid development and genetic improvement initiatives.

ACKNOWLEDGMENTS

The authors would like to thank Universidade Estadual de Maringá for their support.

• How to cite: Rocha, F. L. M., Zeni Neto, H., Alves, A. V., Maioli, M. F. S. D., Churata, B. G. M., Faria, M. V., Amaral Júnior, A. T. and Scapim, C. A. (2025). Genetic diversity of corn cultivars through agronomic, physical, and chemical traits employing multivariate analysis, Bayesian approach, and artificial neural networks. Bragantia, 84, e20240247. https://doi.org/10.1590/1678-4499.20240247
• FUNDING
  Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
  Finance code 001

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available on request from the corresponding author.

REFERENCES

• Alves, B. M., Cargnelutti Filho, A., Burin, C., Toebe, M. and Silva, L. P. (2015). Divergência genética em milho transgênico em relação à produtividade de grãos e à qualidade nutricional. Ciência Rural, 45, 884-891. https://doi.org/10.1590/0103-8478cr20140471
  » https://doi.org/10.1590/0103-8478cr20140471
• Arnhold, E., Silva, R. G. and Viana, J. M. (2010). Seleção de linhagens S5 de milho-pipoca com base em desempenho e divergência genética. Acta Scientiarum. Agronomy, 32, 279-283. https://doi.org/10.4025/actasciagron.v32i2.3886
  » https://doi.org/10.4025/actasciagron.v32i2.3886
• Azevedo, A. M. and Azevedo, M. A. (2025). Pacote ‘MultivariateAnalysis’. Pacote R versão 0.4.
• Barbosa, C. D., Viana, A. P., Silva, S., Quintal, R. and Pereira, M. G. (2011). Artificial neural network analysis of genetic diversity in Carica papaya L. Crop Breeding and Applied Biotechnology, 11, 224-231. https://doi.org/10.1590/S1984-70332011000300004
  » https://doi.org/10.1590/S1984-70332011000300004
• Benitez, L. C., Rodrigues, I. C., Arge, L. W., Ribeiro, M. V. and Braga, E. J. (2011). Análise multivariada da divergência genética de genótipos de arroz sob estresse salino durante a fase vegetativa. Revista Ciência Agronômica, 42, 409-416. https://doi.org/10.1590/S1806-66902011000200021
  » https://doi.org/10.1590/S1806-66902011000200021
• Cardoso, D. B. O., Medeiros, L. A., Carvalho, G. D., Pimentel, I. M., Rojas, G. X., Souza, L. A., Souza, G. M. and Sousa, L. B. (2021). Uso de inteligência computacional na divergência genética de algodoeiro colorido. Jornal de Biociências, 37, e37007. https://doi.org/10.14393/BJ-v37n0a2021-53634
  » https://doi.org/10.14393/BJ-v37n0a2021-53634
• Cargnelutti Filho, A., Ribeiro, N. D., Reis, R. C., Souza, J. R. and Jost, E. (2008). Comparação de métodos de agrupamento para o estudo da divergência genética em cultivaes de feijão. Ciência Rural, 38, 2138-2145. https://doi.org/10.1590/S0103-84782008000800008
  » https://doi.org/10.1590/S0103-84782008000800008
• Castro, C. R., Gonçalves, L. S., Pinto, R. J., Scapim, C. A., Baba, V. Y., Zeffa, D. M. and Kuki, M. C. (2022). Genetic diversity and diallel analysis of elite popcorn lines. Revista Ciência Agronômica, 53, e20207698. https://doi.org/10.5935/1806-6690.20220017
  » https://doi.org/10.5935/1806-6690.20220017
• Condé, A. B., Coelho, M. A., Fronza, V. and Souza, L. V. (2010). Divergência genética em trigo de sequeiro por meio de caracteres morfoagronômicos. Revista Ceres, 57, 762-767. https://doi.org/10.1590/S0034-737X2010000600010
  » https://doi.org/10.1590/S0034-737X2010000600010
• Cruz, C. D., Carneiro, P. C. and Regazzi, A. J. (2014). Modelos biométricos aplicado ao melhoramento genético (3 ed.). Viçosa: UFV.
• Cruz, C. D., Ferreira, F. M. and Pessoni, L. A. (2011). Biometria aplicada ao estudo da diversidade genética. Visconde do Rio Branco: Suprema.
• Dandolini, T. S., Scapim, C. A., Amaral Júnior, A. T., Mangolin, C. A., Machado, M. F., Mott, A. S. and Lopes, A. D. (2008). Genetic divergence in popcorn lines detected by microsatellite markers. Crop Breeding and Applied Biotechnology, 8, 313-320. Retrieved from https://www.researchgate.net/publication/273074966_Genetic_divergence_in_popcorn_lines_detected_by_microsatellite_markers
  » https://www.researchgate.net/publication/273074966_Genetic_divergence_in_popcorn_lines_detected_by_microsatellite_markers
• Eloi, I. B., Mangolin, C. A., Scapim, C. A., Gonçalves, C. S. and Machado, M. F. (2012). Selection of high heterozygosity-popcorn varieties in Brazil based on SSR markers. Genetics and Molecular Research, 11, 1851-1860. Retrieved from https://www.researchgate.net/profile/Carlos-Scapim/publication/230623837_Selection_of_high_heterozygosity_popcorn_varieties_in_Brazil_based_on_SSR_markers/links/560fd4c908ae48337518087c/Selection-of-high-heterozygosity-popcorn-varieties-in-Brazil-based-on-SSR-markers.pdf
  » https://www.researchgate.net/profile/Carlos-Scapim/publication/230623837_Selection_of_high_heterozygosity_popcorn_varieties_in_Brazil_based_on_SSR_markers/links/560fd4c908ae48337518087c/Selection-of-high-heterozygosity-popcorn-varieties-in-Brazil-based-on-SSR-markers.pdf
• Faria, V. R., Viana, J. M., Sobreira, F. M. and Silva, A. C. (2008). Seleção recorrente recíproca na obtenção de híbridos interpopulacionais de milho pipoca. Pesquisa Agropecuária Brasileira, 43, 1749-1755. https://doi.org/10.1590/S0100-204X2008001200015
  » https://doi.org/10.1590/S0100-204X2008001200015
• Galvão, C. O., Valença, M. J., Vieira, V. P., Diniz, L. S., Lacerda, E. G., Carvalho, A. C. and Ludemir, T. B. (1999). Sistemas inteligentes: Aplicações a recursos hídricos e ciências ambientais. Porto Alegre: UFRGS/ABRH.
• Haykin, S. (2008). Neural networks and learning machines. Hamilton: Pearson Prentice Hall.
• Incropera, F. P. and Dewitt, D. P. (1992). Fundamentos de transferência de calor e de massa. Rio de Janeiro: Guanabara Koogan.
• Kage, U., Madalageri, D., Malakannavar, L. and Ganagashetty, P. (2013). Genetic diversity studies in newley derived inbred lines of maize (Zea mays L.). Molecular Plant Breeding, 4, 77-83. Retrieved from https://www.researchgate.net/publication/264785520_Genetic_Divergence_Study_in_Newly_Derived_Inbred_Lines_of_Maize_Zea_mays
  » https://www.researchgate.net/publication/264785520_Genetic_Divergence_Study_in_Newly_Derived_Inbred_Lines_of_Maize_Zea_mays
• Kassambara, A. and Mundt, F. (2016). Factoextra: extract and visualize the results of multivariate data analyses. R Package Version 1.0.7. Available at: https://CRAN.R-project.org/package=factoextra Accessed on: June 3, 2025.
  » https://CRAN.R-project.org/package=factoextra
• Kohonen, T. (1983). Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43, 59-69. https://doi.org/10.1007/BF00337288
  » https://doi.org/10.1007/BF00337288
• Leal, A. A., Mangolin, C. A., Amaral Júnior, A. T., Gonçalves, L. S., Scapim, C. A., Mott, A. S., Eloi, I. B. O., Cordovés, V. and Silva, M. F. P. (2010). Efficiency of RAPD versus SSR markers for determining genetic diversity among popcorn lines. Genetics and Molecular Research, 9, 9-18. Retrieved from https://pubmed.ncbi.nlm.nih.gov/20082266/
  » https://pubmed.ncbi.nlm.nih.gov/20082266/
• Melo, A. V., Colombo, G. A., Vale, J. C., Santana, W. D. and Fernandes, M. S. (2017). Estratégias de seleção entre progênies meio-irmãos de milho-pipoca no cerrado Tocantinense. Revista Brasileira de Teconologia Aplicada nas Ciências Agrárias, 10, 41-50. https://doi.org/10.5935/paet.v10.n01.04
  » https://doi.org/10.5935/paet.v10.n01.04
• Miranda, G. V., Coimbra, R. R., Godoy, C. L., Souza, L. V., Guimarães, L. J. and Melo, A. V. (2003). Potencial de melhoramento e divergência genética de cultivares de milho-pipoca. Pesquisa Agropecuária Brasileira, 38, 681-688. https://doi.org/10.1590/S0100-204X2003000600003
  » https://doi.org/10.1590/S0100-204X2003000600003
• Mojena, R. (1977). Métodos de agrupamento hierárquico e regras de parada: uma avaliação. The Computer Journal, 20, 359-363.
• Nagalakshmi, R. M., Kumari, R. U. and Boranayaka, M. B. (2010). Assessment of genetic diversity in cowpea (Vigna unguiculata). Eletronic Journal of Plant Breeding, 3, 1327092. https://doi.org/10.1080/23311932.2017.1327092
  » https://doi.org/10.1080/23311932.2017.1327092
• Nardino, M., Baretta, D., Carvalho, I. R., Follmann, D. N., Ferrari, M., Pelegrini, A. J., Szareski, V. J., Konflanz, V. A., and Souza, V. Q. (2017). Divergência genética entre genótipos de milho (Zea mays L.) em ambientes distintos. Revista Ciências Agrárias, 40, 164-174. https://doi.org/10.19084/RCA16013
  » https://doi.org/10.19084/RCA16013
• Nunes, J. L. (2022). Milho: comercialização. Available at: https://www.agrolink.com.br/culturas/milho/informacoes/comercializacao_361415.html Accessed on: June 3, 2025.
  » https://www.agrolink.com.br/culturas/milho/informacoes/comercializacao_361415.html
• Oliveira, A. C. L., Pasqual, M., Pio, L. A. S., Lacerda, W. S. and Silva, O. S. (2013). Use of mathematical modeling (artificial neural networks) in classification of banana autotetraploid (musa acuminata colla). Bioscience Journal, 29, 617-622. Retried from https://seer.ufu.br/index.php/biosciencejournal/article/view/14128/12503
  » https://seer.ufu.br/index.php/biosciencejournal/article/view/14128/12503
• Rao, C. R. (1952). Advanced statistical methods in biometric research. Willey.
• R Core Team (2024). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna: R Core Team. Available at: https://www.r-project.org/ Accessed on: June 3, 2025.
  » https://www.r-project.org/
• Resh, F. S., Scapim, C. A., Mangolin, C. A., Machado, M. F., Amaral Júnior, A. T., Ramos, H. C. and Vivas, M. (2015). Diversidade genética de genótipos de pipoca utilizando análise molecular. Genetics and Molecular Research, 14, 9829-9840. Retrived from https://pubmed.ncbi.nlm.nih.gov/26345916/
  » https://pubmed.ncbi.nlm.nih.gov/26345916/
• Rodrigues, J. I., Arruda, K. M., Cruz, C. D., Barros, E. G., Piovesan, N. D. and Moreira, M. A. (2017). Genetic divergence of soybean genotypes in relation to grain components. Ciência Rural, 47, e20151258. https://doi.org/10.1590/0103-8478cr20151258
  » https://doi.org/10.1590/0103-8478cr20151258
• Rotili, E. A., Cancellier, L. L., Dotto, M. A., Peluzio, J. M. and Carvalho, E. V. (2012). Divergência genética em genótipos de milho no estado do Tocantins. Revista Ciência Agronômica, 43, 516-521. https://doi.org/10.1590/s1806-66902012000300014
  » https://doi.org/10.1590/s1806-66902012000300014
• Sá, L. G., Azevedo, A. M., Albuquerque, C. J. B., Valadares, N. R., Brito, O. G., Fernandes, A. C. G. and Aspiazú, I. (2022). Mapas auto-organizáveis de Kohonen no estudo da dissimilaridade genética entre cultivares e genótipos de soja. Pesquisa Agropecuária Brasileira, 57, e02722. Retrieved from https://apct.sede.embrapa.br/index.php/pab/article/view/27089
  » https://apct.sede.embrapa.br/index.php/pab/article/view/27089
• Santos, W. F., Maciel, L. C., Júnior, B. L., Peluzio, J. M., Sodré, L. Ferreira Júnior, O. J., Oliveira, M., Silva, M. S. And Barbosa, A. S. (2020). Genetic divergence in corn genotypes for high and low phosphorus in Pará, Brazil. Annual Research & Review in Biology, 35, 82-90. https://doi.org/10.9734/arrb/2020/v35i530227
  » https://doi.org/10.9734/arrb/2020/v35i530227
• Savage, R., Cooke, E., Darkins, R. and Xu, Y. (2023). BHC: Bayesian Hierarchical Clustering. Retrieved from https://bioconductor.org/packages//2.13/bioc/manuals/BHC/man/BHC.pdf
  » https://bioconductor.org/packages//2.13/bioc/manuals/BHC/man/BHC.pdf
• Scapim, C. A., Carvalho, C. G. and Cruz, C. D. (1995). Uma proposta de classificação dos coeficientes de variação para a cultura do milho. Pesquisa Agropecuária Brasileira, 30, 683-686. Retrieved from https://apct.sede.embrapa.br/index.php/pab/article/view/4353
  » https://apct.sede.embrapa.br/index.php/pab/article/view/4353
• Silva, D. F., Jesus Coelho, C., Romanek, C., Gardingo, J. R., Silva, A. R., Graczyki, B. L., Oliveira, E. A. T. and Matiello, R. R. (2016). Dissimilaridade genética e definição de grupos de recombinação em progênies de meios-irmãos de milho verde. Bragantia, 75, 401-410. https://doi.org/10.1590/1678-4499.343
  » https://doi.org/10.1590/1678-4499.343
• Silva, K. C., Silva, K. P., Carvalho, E. V., Rotili, E. A., Afférri, F. S. and Peluzio, J. M. (2015). Divergência genética de genótipos de milho com e sem adubação nitrogenada em cobertura. Revista Agro@Mbiente On-Line, 9, 102-110. https://doi.org/10.18227/1982-8470ragro.v9i2.2142
  » https://doi.org/10.18227/1982-8470ragro.v9i2.2142
• Silva, T. A., Pinto, R. J., Scapim, C. A., Mangolin, C. A., Machado, M. D. and Carvalho, M. S. (2009). Genetic divergence in popcorn cultivars using microsatellites in bulk genomic DNA. Crop Breeding and Applied Biotechnology, 9, 30-35. Retrieved from https://www.researchgate.net/publication/273232278_Genetic_divergence_in_popcorn_genotypes_using_microsatellites_in_bulk_genomic
  » https://www.researchgate.net/publication/273232278_Genetic_divergence_in_popcorn_genotypes_using_microsatellites_in_bulk_genomic
• Simon, G. A., Kamada, T. and Monteiro, M. (2012). Divergência genética em milho de primeira e segunda safra. Semina: Ciências Agrárias, 33, 449-458. https://doi.org/10.5433/1679-0359.2012v33n2p449
  » https://doi.org/10.5433/1679-0359.2012v33n2p449
• Singh, D. (1981). The relative importance of characters affecting genetic divergence. Indian Journal of Genetics and Plant Breeding, 41, 237-245.
• Sirinukunwattana, K., Savage, R. S., Bari, M. F., Snead, D. R. and Rajpoot, N. M. (2013). Bayesian Hierarchical Clustering for studying cancer gene expression data with unknown statistics. PLos One, 8, e75748. https://doi.org/10.1371/journal.pone.0075748
  » https://doi.org/10.1371/journal.pone.0075748
• Stipp, O. J., Possatto Junior, O., Rossi, E., Rosa, J. C., Uhdre, R. S., Rizzardi, D. A., Freitas, P. S. L. and Barth Pinto, R. J. (2023). Agricultural traits and popping expansion of the popcorn hybrid IAC 125 under different plant densities and irrigation water depth levels. Acta Scientiarum Agronomy, 46, e62929. https://doi.org/10.4025/actasciagron.v46i1.62929
  » https://doi.org/10.4025/actasciagron.v46i1.62929
• Tavares, T. C., Souza, S. A., Lopes, M. B., Veloso, D. A. and Fidelis, R. R. (2018). Divergência genética entre cultivares de feijão comum cultivados no estado do Tocantins. Revista de Agricultra Neotropical, 5, 76-82. https://doi.org/10.32404/rean.v5i3.1892
  » https://doi.org/10.32404/rean.v5i3.1892

Edited by

• Section Editor:
  Gabriel Constantino Blain https://orcid.org/0000-0001-8832-7734

Publication Dates

• Publication in this collection
  07 July 2025
• Date of issue
  2025

History

• Received
  23 Oct 2024
• Accepted
  05 May 2025