Neural networks applied to plant breeding for predicting grain yield in common bean genotypes

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Therefore, identifying excellent genotypes for grain yield is a critical step in breeding programs. This study aimed to evaluate the performance of artificial neural networks in predicting common bean genotypes considering different grain yield ranges, using data obtained from multiple environments. The model was trained and tested with phenotypic variables to classify genotypes into grain yield categories (poor, medium, good, and excellent). The results indicated satisfactory performance, with an overall accuracy of 70%, as well as a higher discriminative capacity in the extreme classes, especially “excellent” and “poor.” The area under the curve reinforced the model’s effectiveness, with values above 0.90 for the “excellent” and “poor” classes, which are considered priorities in genotype recommendation and discard processes. Therefore, the use of neural networks proved to be a promising tool to support decision-making in common bean breeding, allowing efficient identification of promising genotypes and elimination of less productive ones during the final field evaluation stage. Phaseolus vulgaris L. Plant breeding Artificial intelligence Machine learning Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Common bean ( Phaseolus vulgaris L.) is a globally relevant crop, cultivated across a wide range of biomes and management systems, resulting in diverse environmental conditions and agronomic challenges (Gepts et al. 2008). Despite its socioeconomic and nutritional importance, the average grain yield of common bean often remains below its genetic potential due to the complex interaction among genotypes, environments, and management practices (Blair et al. 2010). In this context, the selection of excellent genotypes based on grain yield is a central goal in breeding programs, aiming to meet the growing food demand in a scenario of climate change and limited resources (Fita et al. 2015). Grain yield in common bean is a quantitative trait strongly influenced by environmental factors, which generates high phenotypic variability across locations and growing seasons (Assefa et al. 2019). This variability can mask the true performance of genotypes, making it difficult to consistently and efficiently identify excellent lines. Traditionally, genotype recommendation has been conducted using statistical analyses of stability and adaptability (Yan and Tinker 2006, Crossa et al. 2021). Although effective, these approaches often rely on linear assumptions that may not fully capture the complexity of phenotypic data under highly variable conditions. With the advancement of high-throughput phenotyping technologies and the increasing availability of agronomic data from multi-environment trials, more robust and flexible analytical methods have become indispensable. In this scenario, artificial intelligence, particularly artificial neural networks (ANNs), has emerged as a promising tool for modeling complex and nonlinear patterns in agricultural data (Liakos et al. 2018). Inspired by the functioning of the biological nervous system, ANNs are capable of learning from data, identifying nonlinear relationships among variables, and performing predictions or classifications with high accuracy (Haykin 2001, Goodfellow et al. 2016). In crops such as maize, wheat, and rice, ANNs have been successfully applied to yield prediction, disease detection, and genomic selection, often matching the performance of conventional statistical methods (Montesinos-López et al. 2018, Shook et al. 2021). However, in the context of common bean, studies employing ANNs for genotype prediction based on agronomic performance remain limited. Therefore, applying ANNs offers an opportunity to integrate multiple traits into a predictive model (Ma et al. 2019). This approach is particularly relevant for optimizing resources invested in field trials, reducing the number of genotypes evaluated in advanced stages, and increasing efficiency in identifying excellent lines (Khaki and Wang 2019). Thus, this study aimed to evaluate the performance of artificial neural networks in predicting common bean genotypes across different grain yield ranges using multi-environment data, thereby contributing to genotype classification in breeding programs. Materials and Methods Experimental setup and evaluation of phenotypic traits This study used data from the Value of Cultivation and Use (VCU) trials of common bean lines and cultivars conducted at the state and regional levels in southern Brazil, under the coordination of the Agricultural Research and Rural Extension Company of Santa Catarina (EPAGRI). The experiments were carried out in nine municipalities of Santa Catarina: Chapecó, Canoinhas, Campos Novos, Águas de Chapecó, Ponte Serrada, Xanxerê, Ituporanga, Urussanga, and Lages (Fig. 1 ). Evaluations were conducted over five consecutive growing seasons, from 2012/2013 to 2016/2017, totaling 36 experimental environments, since not all locations were assessed in every season. Thus, a total of 83 common bean genotypes were included in the data analysis. The experimental design adopted was a randomized complete block design with four replications per environment. Each experimental unit consisted of four 4-meter-long rows, spaced 0.45 meters apart, with a sowing density of 15 seeds per meter. Evaluations were performed on the useful area of each plot, composed of the two central rows, excluding the borders to minimize edge effects. In this study, no chemical control of diseases was applied in order to record the natural phenotypic expression of genotypes in response to pathogen occurrence across different growing environments in Santa Catarina. This approach made it possible to assess the tolerance or susceptibility of the tested genotypes under real field conditions, without interference from agrochemicals that could mask genetic responses. Only seed treatment with fungicides and insecticides was performed, following technical recommendations for the crop. Fertilization at planting and topdressing, along with pest management, were carried out according to technical guidelines, ensuring proper crop development and minimizing external factors that could affect yield. Nine phenotypic traits were measured (Table 1 ) to characterize the agronomic performance of common bean genotypes in terms of productivity, disease resistance, and phenological cycle. Grain yield was estimated based on the harvest from the useful area of each plot, consisting of the two central rows within the four that made up each experimental unit. Data were expressed in kilograms per hectare (kg ha⁻¹), with grain moisture corrected to 13%. This trait was considered an indicator of the genotypes’ final productivity. Two phenological traits were determined for each genotype to describe the crop cycle: (i) days to flowering, corresponding to the number of days from emergence until 50% of the plants in a plot presented open flowers, and (ii) days to harvest, corresponding to the number of days from emergence until harvest at physiological maturity. Table 1 Description of the phenotypic traits considered in this study for common bean genotypes in the Cultivar and Line Value (VCU) trials conducted in Santa Catarina Trait Description Unit of Measurement Scale Grain yield Grain production per plot, adjusted to 13% moisture kg ha⁻¹ Continuous Days to flowering Number of days from emergence to 50% of plants with open flowers Days Continuous Days to harvest Number of days from emergence to harvest at physiological maturity Days Continuous Thousand-grain weight Mass of 1,000 dry seeds at 13% moisture Grams (g) Continuous Common bacterial blight Percentage of leaf area affected by bacterial lesions caused by Xanthomonas phaseoli pv. phaseoli Diagrammatic scale 1–9 Ordinal Anthracnose – leaves Presence of dark necrotic lesions with reddish halo on leaves caused by Colletotrichum lindemuthianum Diagrammatic scale 1–9 Ordinal Anthracnose – pods Circular and depressed lesions on pods caused by the same pathogen Diagrammatic scale 1–9 Ordinal Angular leaf spot – leaves Angular lesions delimited by veins caused by Pseudocercospora griseola Diagrammatic scale 1–9 Ordinal Angular leaf spot – pods Depressed and angular lesions on pods caused by the same pathogen Diagrammatic scale 1–9 Ordinal Disease reactions were assessed for five different traits following the methodology described by Godoy et al. (1997), using specific diagrammatic scales for each pathogen: (i) common bacterial blight ( Xanthomonas phaseoli pv. phaseoli ), with severity visually estimated on leaves by considering the percentage of leaf area affected by typical bacterial lesions; (ii) anthracnose ( Colletotrichum lindemuthianum ), with severity evaluated separately in two plant organs: on leaves, by observing the presence of circular necrotic lesions with dark coloration and reddish halos, and on pods, by considering depressed, circular, dark-colored lesions; and (iii) angular leaf spot ( Pseudocercospora griseola ), also evaluated on two parts of the plant: on leaves, by verifying the presence of angular spots delimited by veins and ranging in color from light to dark brown, and on pods, by observing depressed, angular lesions. These measurements were recorded using diagrammatic scales ranging from 1 (absence of symptoms) to 9 (high severity), allowing standardized quantification of genotype tolerance. Data Analysis To classify common bean genotypes according to their productive performance across different environments, an approach based on artificial neural networks (ANN) was developed, using a feedforward architecture with multiple densely connected layers (Multilayer Perceptron, MLP). The model was implemented using the Keras library (with TensorFlow backend) in Python. Initially, grain yield was categorized into four discrete classes based on agronomic ranges: “poor” ( 2000–3000 kg ha⁻¹), and “excellent” (> 3000 kg ha⁻¹). This categorical variable was used as the response variable in the predictive models. As predictive variables, the categorical variables corresponding to distinct environments and genotypes were included, along with the agronomic traits: severity of common bacterial blight, anthracnose on leaves and pods, angular leaf spot on leaves and pods, 1000-grain weight, days to flowering, and days to harvest. Categorical variables were encoded using One-Hot Encoding, and continuous variables were standardized using z-score normalization through a ColumnTransformer. The dataset was partitioned into training (80%) and testing (20%) subsets in a stratified manner, preserving the proportional distribution of classes. The response variable was converted to one-hot format to ensure compatibility with the categorical cross-entropy loss function. The ANN architecture consisted of three hidden layers with 128, 64, and 32 neurons, respectively, all using the ReLU activation function. The output layer employed a softmax activation function with four neurons corresponding to the yield classes. Optimization was performed using the Adam algorithm with a learning rate of 0.001. The model was trained for 100 epochs, with a batch size of 32 samples and internal validation (validation split = 0.1). Mathematically, the neural network can be represented as follows: $$\:\widehat{y}=\text{softmax}({W}^{\left(L\right)}\cdot\:f({W}^{(L-1)}\cdot\:f(\cdots\:f({W}^{\left(1\right)}\cdot\:x+{b}^{\left(1\right)})\cdots\:\text{\hspace{0.17em}})+{b}^{(L-1)})+{b}^{\left(L\right)})$$ , where \(\:x\in\:{\mathbb{R}}^{p}\) is the input vector (predictor variables); \(\:{W}^{\left(l\right)}\) and \(\:{b}^{\left(l\right)}\) are the weights and biases of layer \(\:l\) ; \(\:f(\cdot\:)\) is the ReLU activation function in the hidden layers; \(\:\text{softmax}(\cdot\:)\) is the activation function of the output layer; and \(\:\widehat{y}\in\:{\mathbb{R}}^{4}\) represents the predicted probabilities for each yield class. To mitigate class imbalance effects, class weights inversely proportional to the observed frequencies were applied, following the balanced strategy from the Scikit-learn function class_weight.compute_class_weight. Model performance was monitored using metrics such as the area under the ROC curve (AUC) and recall for both training and validation sets. The learning curves of these metrics across epochs were analyzed to detect potential signs of overfitting or underfitting. After training, the model was evaluated on the test set. Probabilistic predictions were converted into predicted classes using the argmax function, and the results were compared with actual values using the confusion matrix and classification report, which included precision, recall, and F1-score for each class. Additionally, class-specific ROC curves were constructed, and the area under the curve (AUC) was calculated for each of the four yield categories, enabling a detailed evaluation of the model’s performance across different productivity levels. These curves demonstrated the model’s ability to distinguish yield levels under varying environmental and genotypic conditions. Results The performance metrics obtained for the prediction model used to estimate the quality of common bean genotypes based on qualitative yield categories (Table 2 ) indicate satisfactory performance of the adopted approach. Accuracy represents the proportion of correct predictions relative to the total number of predictions made by the model. In this study, the overall model accuracy (0.70) indicates a 70% success rate in classifications performed on the test dataset, reflecting a moderate generalization capacity. However, accuracy alone does not provide a complete view of the model’s performance, especially in contexts where different types of errors have distinct implications. Moreover, accuracy can be influenced by the class distribution within the dataset. In addition to accuracy, when performance was assessed individually by class, the precision, recall (sensitivity), and F1-score metrics revealed differences in predictive performance among the categories considered in this study. Precision, also known as positive predictive value, measures the proportion of positive predictions that were correct for each specific class. In the context of this study, precision was calculated individually for each class, indicating the reliability of the model when predicting that a genotype belongs to a specific category. Furthermore, recall, also known as sensitivity or true positive rate, measures the model’s ability to correctly identify all members of a specific class. Finally, the F1-score represents the harmonic mean between precision and recall, providing a single metric that balances both aspects of performance. Table 2 Performance metrics of the prediction model based on artificial neural networks, showing precision, recall, and F1-score for each class, along with the overall accuracy of the model Class Precision Recall F1-Score Poor 0.70 0.67 0.69 Medium 0.69 0.71 0.70 Good 0.66 0.65 0.66 Excellent 0.74 0.75 0.75 Overall Accuracy 0.70 The “excellent” class presented the best performance indices in terms of precision, recall, and F1-score, demonstrating approximately 75% efficiency of the model in predicting high-yielding genotypes (Table 2 ). This is particularly relevant for breeding programs, as it highlights the potential of the approach in identifying promising genotypes, with a low rate of false positives in this critical class. In other words, for every four genotypes classified as excellent by the model, three are truly excellent. The “poor” and “medium” classes showed intermediate performance, demonstrating the model’s capacity to adequately discriminate genotypes within these categories, which is important for avoiding misidentification of low-performing genotypes. On the other hand, the “good” class showed lower discriminative ability by the algorithm, as evidenced by its precision, recall, and F1-score values. This result is likely due to phenotypic overlap among adjacent yield ranges, which makes precise separation based on agronomic traits more difficult. The normalized confusion matrix (Fig. 2 ) provides a detailed visualization of the model’s predictive performance across the four yield categories: poor, medium, good, and excellent. The values represented correspond to relative proportions between the predictions made and the observed classes, allowing inferences about hit and error rates for each category. It can be observed that the highest values, corresponding to correct classification rates, are concentrated along the main diagonal of the matrix. These values corroborate the descriptive metrics previously presented, reinforcing the consistency of the results. The analysis of error dispersion among adjacent classes reveals that, in the classes of greatest interest for identifying excellent genotypes, some misclassifications occurred, where the model identified genotypes as good when they should have been classified as excellent. Despite these errors, more severe misclassifications, such as predicting poor or medium genotypes as good or excellent, occurred at very low frequencies. Certain inaccuracies are compatible with the continuous nature of the grain yield trait and with the process of transforming a continuous variable into qualitative classes, which imposes limits on the separation between adjacent phenotypic groups. Nevertheless, the results indicate satisfactory predictive performance, particularly in the extreme categories, which is of great interest in breeding programs, as it enables the prioritization of excellent genotypes and the elimination of low-performing ones. The ROC (Receiver Operating Characteristic) curves for the four yield classes were fitted (Fig. 3 ). These curves allow the evaluation of the model’s discriminative ability in terms of the relationship between the true positive rate (sensitivity) and the false positive rate across different decision thresholds. The curves for all classes were positioned above the reference line (diagonal), indicating predictive performance excellent to random classification. The area under the curve (AUC), which summarizes overall performance, ranged from 0.84 to 0.94, with higher values for the “poor” (AUC = 0.94) and “excellent” (AUC = 0.92) classes, followed by “medium” (0.87) and “good” (0.84). These results reinforce the effectiveness of the model in distinguishing genotypes belonging to the extreme yield categories, that is, those with poor or excellent agronomic performance. The lower AUC values observed for the “good” and “medium” classes reflect greater phenotypic overlap within these intermediate categories, making their distinction more difficult. The evolution of performance metrics over 100 training epochs, considering the training and test sets, is presented (Fig. 4 ). Accuracy, loss function, area under the ROC curve (AUC), and recall were evaluated, providing a comprehensive analysis of the algorithm’s learning process. In the training set, rapid convergence was observed (with accuracy above 0.95), an AUC close to 1, and high sensitivity within the first 30 epochs. The loss function showed a significant decrease, stabilizing at low values, indicating efficient model learning for the training data. In the validation set, the metrics suggested limitations in model generalization. Accuracy stabilized around 0.70, and AUC, after initially high values, declined to 0.86. The validation loss increased after an inflection point, indicating that the model prioritized patterns specific to the training set. Validation sensitivity stabilized at approximately 0.68. In summary, the model’s performance was satisfactory considering the complexity of the grain yield trait, especially in predicting the extreme productivity classes of common bean genotypes. This approach represents a complementary strategy for breeding programs, supporting decision-making during the identification of excellent genotypes in comparative trials. Discussion Application of artificial neural networks in predicting common bean genotypes The increasing complexity of breeding programs, particularly in self-pollinated crops such as common bean, has driven the adoption of computational approaches capable of handling large data volumes and nonlinear relationships. The need to make decisions based on multiple environments, years, and traits has made complementary techniques, such as machine learning-based methods, increasingly valuable in assisting conventional approaches. In this context, artificial neural networks (ANNs) have emerged as a promising technique, especially for classification tasks and the prediction of agronomic performance under complex and heterogeneous conditions. This study demonstrated that an ANN-based model was able to predict common bean genotypes into four qualitative yield categories with an overall test accuracy of 70%, a performance consistent with that observed in similar studies applying artificial intelligence to crops such as wheat, rice, and maize (Montesinos-López et al. 2018, Shook et al. 2021). The best performance metrics were observed for the “excellent” and “poor” classes, indicating that the neural network could more accurately predict patterns associated with the extremes of the phenotypic grain yield spectrum. This ability is strategic in breeding programs since the correct identification of genotypes with high yield potential directly contributes to greater efficiency in identifying excellent genotypes and, consequently, in recommending cultivars with a higher likelihood of success across different agricultural environments (Allard 1961). Conversely, the reliable prediction of low-yielding genotypes is equally valuable, as it enables the early elimination of poor genotypes, thereby optimizing the allocation of experimental resources and reducing the time required for subsequent evaluation stages (Bhering et al. 2015). On the other hand, the relatively lower performance in the intermediate classes (“medium” and “good”) may be attributed to the overlap of phenotypic classes among genotypes with similar yields, a common phenomenon in quantitative traits such as grain yield. Additionally, the process of transforming continuous data into discrete categories may have introduced ambiguity at the boundaries between classes, reducing the model’s discriminative ability in such cases. Nevertheless, the confusion matrix derived from the test data predictions showed a predominance of correct classifications along the main diagonal, reinforcing that, despite these challenges, the neural network exhibited consistent performance. In this sense, the observed values indicate that the ANN was effective in distinguishing high- and low-yielding genotypes, even under the environmental variability inherent to the dataset used. The robustness of the model in response to environmental variation is particularly relevant in programs that rely on data collected across multiple sites and years, under distinct soil, climate, and management conditions. Similar findings were reported by González-Camacho et al. (2016), who demonstrated the superiority of neural networks over traditional regression methods for predicting performance across multiple environments, highlighting the potential of this approach to handle such complexity. Similarly, Corrêa et al. (2016) also observed high concordance between classical methods for measuring phenotypic adaptability and stability and the results generated by artificial neural networks, suggesting that these techniques can be used not only as classifiers but also as viable alternatives for evaluating genotype stability. Therefore, the application of artificial neural networks in predicting common bean genotypes represents an approach with the potential to increase the accuracy of identifying excellent or poor genotypes in breeding programs, contributing to the development of more productive cultivars adapted to the conditions of modern agriculture. Model robustness in response to environmental variability Grain yield in common bean is strongly influenced by environmental factors, making the prediction of genotypic performance across different locations and years a challenge for breeding programs (Bernal-Vasquez et al. 2014). This complexity arises from genotype-by-environment interaction, which can substantially alter the behavior of genotypes under varying environmental conditions. In this study, the artificial neural network (ANN) was trained and tested using data from multiple locations and growing seasons, thereby capturing a relevant portion of this variability. Despite the inclusion of environmental variation in the model, the results revealed the occurrence of overfitting, as indicated by the discrepancy between training accuracy (> 95%) and validation accuracy (~ 70%). This finding suggests that the model learned specific patterns from the training data but showed limited ability to generalize its performance to new contexts. Part of these limitations may be attributed to the nature of the data used for modeling. The use of morphological variables such as plant height, stem diameter, and insertion height of the first pod, although relevant, may not provide sufficient discriminatory power to accurately distinguish intermediate performance classes, particularly when dealing with a continuous quantitative trait such as grain weight per plant. This trait, being polygenic and influenced by multiple environmental factors (Costa-Neto et al. 2021), tends to follow an approximately normal distribution in the population, resulting in a higher concentration of individuals within intermediate ranges and greater genotypic diversity in these classes. Consequently, it is common to observe overlapping regions between adjacent performance categories, such as those classified as “moderate” and “good.” Such overlap complicates pattern definition, especially when subtle phenotypic differences are not effectively captured. This ambiguity can negatively affect learning algorithms such as neural networks, since the proximity of samples from different classes in multidimensional space may lead to inconsistent classification decisions. Additionally, even when the number of individuals per class is balanced, the way these individuals are distributed across the feature space may favor the prediction of extremes while hindering accurate prediction of genotypes with intermediate performance. The greater morphological homogeneity in the poor and excellent classes, associated with clearer physiological limitations or advantages, tends to generate more easily recognizable patterns for the model, whereas the genetic variability within intermediate classes results in more dispersed data clusters and less well-defined decision boundaries. To mitigate overfitting, one recommended strategy is the use of cross-validation structured by environment, as proposed by Burgueño et al. (2012). This type of validation accounts for the environmental origin of the experimental units, promoting a more realistic assessment of the model’s generalization capacity. Moreover, incorporating environmental variables such as temperature, precipitation, relative humidity, solar radiation, and vegetation indices can enhance the modeling of genotype-by-environment interaction (Costa-Neto et al. 2021). This approach has been widely applied in other crops to integrate environmental data into predictive genetic and phenotypic models, thereby improving prediction accuracy and robustness (Cooper et al. 2014). In this context, more sophisticated neural networks, such as those based on deep learning, offer new possibilities for handling the complexity of genetic and environmental data. These architectures can model nonlinear relationships and capture subtle spatial or temporal patterns that are difficult to detect using traditional methods (Gupta and Singh 2023). Therefore, the application of neural networks in common bean breeding may represent an important advancement, particularly during the early stages of selection when working with segregating populations. At this stage, the scarcity of seeds and the limited use of experimental designs often result in phenotypic data with greater variability and noise, requiring more robust models for the accurate identification of excellent genotypes. Strategic use of artificial neural networks in plant breeding The main contribution of this study lies in demonstrating the potential of artificial neural networks (ANNs) as a strategic technique to support the identification of excellent genotypes in common bean breeding programs. The model’s ability to discriminate high-yielding genotypes with an acceptable error rate positions neural networks as a viable and effective approach to assist decision-making in the final stages of breeding programs, particularly during testing, as evidenced in this study. This type of application aligns with the growing adoption of artificial intelligence techniques in agriculture, especially within the context of digital and precision agriculture (Kamilaris and Prenafeta-Boldú 2018). The use of ANNs stands out for their ability to model multiple complex nonlinear relationships between explanatory variables and agronomic responses, which is particularly valuable in biological systems and can be directly applied to plant breeding. By incorporating phenotypic data from multiple environments, these networks can predict patterns related to grain yield and other traits with a high degree of accuracy, even in the presence of environmental variability inherent to agricultural experiments. Thus, the use of ANNs provides an additional tool to help breeders make more assertive decisions regarding the identification of both promising and unpromising genotypes. Integrating neural networks with other statistical techniques can further enhance the efficiency of identifying excellent genotypes. For example, genotypes classified as “excellent” by the ANN can be jointly analyzed with phenotypic stability scores, such as those obtained from the Eberhart and Russell method or the AMMI model, allowing the identification of genotypes that are not only productive but also stable or adapted to different environmental conditions (Cruz et al. 2018, Yan and Kang 2003). This combined approach is strategic in breeding programs where production stability is as important as absolute yield, particularly in agricultural environments characterized by high variability. Moreover, the incorporation of molecular data can enable the use of ANNs in genomic prediction approaches, combining genomic, phenotypic, and environmental information within a predictive model. This integration can improve the accuracy of marker-assisted selection, thereby increasing the rate of genetic gain (Montesinos-López et al. 2019). Within this context, ANNs move beyond their role as classification tools to become models for predicting genotype performance in breeding programs. However, it is important to emphasize that the use of neural networks in plant breeding should not replace traditional experimental methods but rather complement them by providing additional support for more efficient decisions. The future of plant breeding will likely be shaped by the convergence of different data sources and analytical methodologies within an interdisciplinary framework that combines statistics, molecular biology, agronomy, and data science. This integrated approach has already been explored in several crops (Silva et al. 2014, Azevedo et al. 2015) and is expanding into animal breeding, with equally promising results (Okut et al. 2013). Therefore, the strategic adoption of neural networks and other machine learning techniques for appropriate situations represents an innovation with strong potential to enhance breeding efficiency. Conclusion Artificial neural networks demonstrated satisfactory performance in predicting common bean genotypes based on grain yield, using multiple agronomic traits and data from different environments. The model was particularly effective in identifying high- and low-performing genotypes, confirming its applicability for prioritizing excellent lines or eliminating poor ones. The ability to integrate multiple traits and capture nonlinear relationships makes this approach a valuable decision-support tool in plant breeding programs. Declarations Acknowledgments We thank the Foundation for Research and Innovation Support of the State of Santa Catarina (FAPESC), Coordination for the Improvement of Higher Education Personnel (CAPES) and the University of the State of Santa Catarina (UDESC) for granting scholarships and financial assistance in carrying out research projects. Data availability All data related to the analyses performed are available from the corresponding author upon reasonable request. Competing interests The authors declare that there is no conflict of interest. Funding This research was supported by the Coordination for the Improvement of Higher Education Personnel (CAPES) and the University of the State of Santa Catarina (UDESC). Author contributions All authors are listed in alphabetical order and contribute equally. Luan Tiago dos Santos Carbonari: Conceptualization, Methodology, Formal analysis, Writing-Original Draft. 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G., Busato, P., Moshou, D., Pearson, S., & Bochtis, D. (2018). Machine learning in agriculture: A review. Sensors, 18(8), 2674. Montesinos-López, A., Montesinos-López, O. A., Gianola, D., Crossa, J., & Hernández-Suárez, C. M. (2018). Multi-environment genomic prediction of plant traits using deep learners with dense architecture. G3: Genes, Genomes, Genetics, 8(12), 3813-3828. Montesinos-Lopez, O. A., Chavira-Flores, M., Kismiantini, Crespo-Herrera, L., Saint Piere, C., Li, H., Crossa, J. (2024). A review of multimodal deep learning methods for genomic-enabled prediction in plant breeding. Genetics, 228(4), iyae161. Montesinos-López, O. A., Montesinos-López, A., Crossa, J., de Los Campos, G., Alvarado, G., Suchismita, M., ... & Burgueño, J. (2017). Predicting grain yield using canopy hyperspectral reflectance in wheat breeding data. Plant methods, 13(1), 4. Okut, H., Wu, X. L., Rosa, G. J., Bauck, S., Woodward, B. W., Schnabel, R. D., ... & Gianola, D. (2013). Predicting expected progeny difference for marbling score in Angus cattle using artificial neural networks and Bayesian regression models. Genetics Selection Evolution, 45(1), 34. Shook, J., Gangopadhyay, T., Wu, L., Ganapathysubramanian, B., Sarkar, S., & Singh, A. K. (2021). Crop yield prediction integrating genotype and weather variables using deep learning. Plos one, 16(6), e0252402. Silva, G. N., Tomaz, R. S., Sant'Anna, I. D. C., Nascimento, M., Bhering, L. L., & Cruz, C. D. (2014). Neural networks for predicting breeding values and genetic gains. Scientia Agricola, 71, 494-498. Yan, W., Kang, M. S. (2002). GGE biplot analysis: a graphical tool for breeders, geneticists, and agronomists. CRC press. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 03 Jan, 2026 Reviews received at journal 25 Nov, 2025 Reviewers agreed at journal 17 Nov, 2025 Reviewers agreed at journal 14 Nov, 2025 Reviewers invited by journal 14 Nov, 2025 Editor assigned by journal 04 Nov, 2025 Submission checks completed at journal 04 Nov, 2025 First submitted to journal 04 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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10:12:17","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1614968,"visible":true,"origin":"","legend":"\u003cp\u003eNormalized confusion matrix obtained from the prediction of grain yield levels, these values represent the proportions of correct and incorrect predictions for each class\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8029028/v1/dc6cf69096975ddd5cb7013f.png"},{"id":96711433,"identity":"144d0a1e-15b7-40b3-8865-206b491a1e25","added_by":"auto","created_at":"2025-11-25 10:12:01","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":85423,"visible":true,"origin":"","legend":"\u003cp\u003eReceiver Operating Characteristic (ROC) curves for each grain yield prediction class, these curves show the true positive rate (TPR) as a function of the false positive rate (FPR) for the Poor, Medium, Good, and Excellent classes\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8029028/v1/47865befbe96aa7437bff77c.jpeg"},{"id":96706985,"identity":"2e248069-36f6-419e-85e5-9a8410c460c1","added_by":"auto","created_at":"2025-11-25 09:27:31","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":71560,"visible":true,"origin":"","legend":"\u003cp\u003eEvolution of the model’s performance metrics during training and validation over 100 epochs for bean genotype prediction, showing accuracy, loss, area under the ROC curve (AUC), and recall for both training and validation sets\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8029028/v1/11d4b3c353cf3e3bdd4047d4.jpeg"},{"id":96712911,"identity":"9d4a1709-cc0c-49f4-825a-796ded53af0b","added_by":"auto","created_at":"2025-11-25 10:17:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2092894,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8029028/v1/ba24f316-a019-474c-811d-d86bc3743302.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Neural networks applied to plant breeding for predicting grain yield in common bean genotypes","fulltext":[{"header":"Introduction","content":"\u003cp\u003eCommon bean (\u003cem\u003ePhaseolus vulgaris\u003c/em\u003e L.) is a globally relevant crop, cultivated across a wide range of biomes and management systems, resulting in diverse environmental conditions and agronomic challenges (Gepts et al. 2008). Despite its socioeconomic and nutritional importance, the average grain yield of common bean often remains below its genetic potential due to the complex interaction among genotypes, environments, and management practices (Blair et al. 2010). In this context, the selection of excellent genotypes based on grain yield is a central goal in breeding programs, aiming to meet the growing food demand in a scenario of climate change and limited resources (Fita et al. 2015).\u003c/p\u003e\u003cp\u003eGrain yield in common bean is a quantitative trait strongly influenced by environmental factors, which generates high phenotypic variability across locations and growing seasons (Assefa et al. 2019). This variability can mask the true performance of genotypes, making it difficult to consistently and efficiently identify excellent lines. Traditionally, genotype recommendation has been conducted using statistical analyses of stability and adaptability (Yan and Tinker 2006, Crossa et al. 2021). Although effective, these approaches often rely on linear assumptions that may not fully capture the complexity of phenotypic data under highly variable conditions.\u003c/p\u003e\u003cp\u003eWith the advancement of high-throughput phenotyping technologies and the increasing availability of agronomic data from multi-environment trials, more robust and flexible analytical methods have become indispensable. In this scenario, artificial intelligence, particularly artificial neural networks (ANNs), has emerged as a promising tool for modeling complex and nonlinear patterns in agricultural data (Liakos et al. 2018). Inspired by the functioning of the biological nervous system, ANNs are capable of learning from data, identifying nonlinear relationships among variables, and performing predictions or classifications with high accuracy (Haykin 2001, Goodfellow et al. 2016).\u003c/p\u003e\u003cp\u003eIn crops such as maize, wheat, and rice, ANNs have been successfully applied to yield prediction, disease detection, and genomic selection, often matching the performance of conventional statistical methods (Montesinos-L\u0026oacute;pez et al. 2018, Shook et al. 2021). However, in the context of common bean, studies employing ANNs for genotype prediction based on agronomic performance remain limited. Therefore, applying ANNs offers an opportunity to integrate multiple traits into a predictive model (Ma et al. 2019). This approach is particularly relevant for optimizing resources invested in field trials, reducing the number of genotypes evaluated in advanced stages, and increasing efficiency in identifying excellent lines (Khaki and Wang 2019).\u003c/p\u003e\u003cp\u003eThus, this study aimed to evaluate the performance of artificial neural networks in predicting common bean genotypes across different grain yield ranges using multi-environment data, thereby contributing to genotype classification in breeding programs.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eExperimental setup and evaluation of phenotypic traits\u003c/h2\u003e\u003cp\u003eThis study used data from the \u003cem\u003eValue of Cultivation and Use\u003c/em\u003e (VCU) trials of common bean lines and cultivars conducted at the state and regional levels in southern Brazil, under the coordination of the Agricultural Research and Rural Extension Company of Santa Catarina (EPAGRI). The experiments were carried out in nine municipalities of Santa Catarina: Chapec\u0026oacute;, Canoinhas, Campos Novos, \u0026Aacute;guas de Chapec\u0026oacute;, Ponte Serrada, Xanxer\u0026ecirc;, Ituporanga, Urussanga, and Lages (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eEvaluations were conducted over five consecutive growing seasons, from 2012/2013 to 2016/2017, totaling 36 experimental environments, since not all locations were assessed in every season. Thus, a total of 83 common bean genotypes were included in the data analysis. The experimental design adopted was a randomized complete block design with four replications per environment. Each experimental unit consisted of four 4-meter-long rows, spaced 0.45 meters apart, with a sowing density of 15 seeds per meter. Evaluations were performed on the useful area of each plot, composed of the two central rows, excluding the borders to minimize edge effects.\u003c/p\u003e\u003cp\u003eIn this study, no chemical control of diseases was applied in order to record the natural phenotypic expression of genotypes in response to pathogen occurrence across different growing environments in Santa Catarina. This approach made it possible to assess the tolerance or susceptibility of the tested genotypes under real field conditions, without interference from agrochemicals that could mask genetic responses. Only seed treatment with fungicides and insecticides was performed, following technical recommendations for the crop. Fertilization at planting and topdressing, along with pest management, were carried out according to technical guidelines, ensuring proper crop development and minimizing external factors that could affect yield. Nine phenotypic traits were measured (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) to characterize the agronomic performance of common bean genotypes in terms of productivity, disease resistance, and phenological cycle. Grain yield was estimated based on the harvest from the useful area of each plot, consisting of the two central rows within the four that made up each experimental unit. Data were expressed in kilograms per hectare (kg ha⁻\u0026sup1;), with grain moisture corrected to 13%. This trait was considered an indicator of the genotypes\u0026rsquo; final productivity. Two phenological traits were determined for each genotype to describe the crop cycle: (i) days to flowering, corresponding to the number of days from emergence until 50% of the plants in a plot presented open flowers, and (ii) days to harvest, corresponding to the number of days from emergence until harvest at physiological maturity.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDescription of the phenotypic traits considered in this study for common bean genotypes in the Cultivar and Line Value (VCU) trials conducted in Santa Catarina\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTrait\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDescription\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eUnit of Measurement\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eScale\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGrain yield\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eGrain production per plot, adjusted to 13% moisture\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ekg ha⁻\u0026sup1;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eContinuous\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDays to flowering\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNumber of days from emergence to 50% of plants with open flowers\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDays\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eContinuous\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDays to harvest\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNumber of days from emergence to harvest at physiological maturity\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDays\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eContinuous\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eThousand-grain weight\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMass of 1,000 dry seeds at 13% moisture\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eGrams (g)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eContinuous\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCommon bacterial blight\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePercentage of leaf area affected by bacterial lesions caused by \u003cem\u003eXanthomonas phaseoli\u003c/em\u003e pv. \u003cem\u003ephaseoli\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDiagrammatic scale 1\u0026ndash;9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eOrdinal\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAnthracnose \u0026ndash; leaves\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePresence of dark necrotic lesions with reddish halo on leaves caused by \u003cem\u003eColletotrichum lindemuthianum\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDiagrammatic scale 1\u0026ndash;9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eOrdinal\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAnthracnose \u0026ndash; pods\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCircular and depressed lesions on pods caused by the same pathogen\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDiagrammatic scale 1\u0026ndash;9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eOrdinal\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAngular leaf spot \u0026ndash; leaves\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAngular lesions delimited by veins caused by \u003cem\u003ePseudocercospora griseola\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDiagrammatic scale 1\u0026ndash;9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eOrdinal\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAngular leaf spot \u0026ndash; pods\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDepressed and angular lesions on pods caused by the same pathogen\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDiagrammatic scale 1\u0026ndash;9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eOrdinal\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eDisease reactions were assessed for five different traits following the methodology described by Godoy et al. (1997), using specific diagrammatic scales for each pathogen: (i) common bacterial blight (\u003cem\u003eXanthomonas phaseoli\u003c/em\u003e pv. \u003cem\u003ephaseoli\u003c/em\u003e), with severity visually estimated on leaves by considering the percentage of leaf area affected by typical bacterial lesions; (ii) anthracnose (\u003cem\u003eColletotrichum lindemuthianum\u003c/em\u003e), with severity evaluated separately in two plant organs: on leaves, by observing the presence of circular necrotic lesions with dark coloration and reddish halos, and on pods, by considering depressed, circular, dark-colored lesions; and (iii) angular leaf spot (\u003cem\u003ePseudocercospora griseola\u003c/em\u003e), also evaluated on two parts of the plant: on leaves, by verifying the presence of angular spots delimited by veins and ranging in color from light to dark brown, and on pods, by observing depressed, angular lesions. These measurements were recorded using diagrammatic scales ranging from 1 (absence of symptoms) to 9 (high severity), allowing standardized quantification of genotype tolerance.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003eData Analysis\u003c/h2\u003e\u003cp\u003eTo classify common bean genotypes according to their productive performance across different environments, an approach based on artificial neural networks (ANN) was developed, using a feedforward architecture with multiple densely connected layers (Multilayer Perceptron, MLP). The model was implemented using the Keras library (with TensorFlow backend) in Python. Initially, grain yield was categorized into four discrete classes based on agronomic ranges: \u0026ldquo;poor\u0026rdquo; (\u0026lt;\u0026thinsp;1000 kg ha⁻\u0026sup1;), \u0026ldquo;medium\u0026rdquo; (1000\u0026ndash;2000 kg ha⁻\u0026sup1;), \u0026ldquo;good\u0026rdquo; (\u0026gt;\u0026thinsp;2000\u0026ndash;3000 kg ha⁻\u0026sup1;), and \u0026ldquo;excellent\u0026rdquo; (\u0026gt;\u0026thinsp;3000 kg ha⁻\u0026sup1;). This categorical variable was used as the response variable in the predictive models. As predictive variables, the categorical variables corresponding to distinct environments and genotypes were included, along with the agronomic traits: severity of common bacterial blight, anthracnose on leaves and pods, angular leaf spot on leaves and pods, 1000-grain weight, days to flowering, and days to harvest. Categorical variables were encoded using One-Hot Encoding, and continuous variables were standardized using z-score normalization through a ColumnTransformer.\u003c/p\u003e\u003cp\u003eThe dataset was partitioned into training (80%) and testing (20%) subsets in a stratified manner, preserving the proportional distribution of classes. The response variable was converted to one-hot format to ensure compatibility with the categorical cross-entropy loss function. The ANN architecture consisted of three hidden layers with 128, 64, and 32 neurons, respectively, all using the ReLU activation function. The output layer employed a softmax activation function with four neurons corresponding to the yield classes. Optimization was performed using the Adam algorithm with a learning rate of 0.001. The model was trained for 100 epochs, with a batch size of 32 samples and internal validation (validation split\u0026thinsp;=\u0026thinsp;0.1).\u003c/p\u003e\u003cp\u003eMathematically, the neural network can be represented as follows:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\widehat{y}=\\text{softmax}({W}^{\\left(L\\right)}\\cdot\\:f({W}^{(L-1)}\\cdot\\:f(\\cdots\\:f({W}^{\\left(1\\right)}\\cdot\\:x+{b}^{\\left(1\\right)})\\cdots\\:\\text{\\hspace{0.17em}})+{b}^{(L-1)})+{b}^{\\left(L\\right)})$$\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:x\\in\\:{\\mathbb{R}}^{p}\\)\u003c/span\u003e\u003c/span\u003eis the input vector (predictor variables); \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}^{\\left(l\\right)}\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{b}^{\\left(l\\right)}\\)\u003c/span\u003e\u003c/span\u003eare the weights and biases of layer \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:l\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:f(\\cdot\\:)\\)\u003c/span\u003e\u003c/span\u003eis the ReLU activation function in the hidden layers; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{softmax}(\\cdot\\:)\\)\u003c/span\u003e\u003c/span\u003eis the activation function of the output layer; and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\widehat{y}\\in\\:{\\mathbb{R}}^{4}\\)\u003c/span\u003e\u003c/span\u003erepresents the predicted probabilities for each yield class. To mitigate class imbalance effects, class weights inversely proportional to the observed frequencies were applied, following the \u003cem\u003ebalanced\u003c/em\u003e strategy from the Scikit-learn function class_weight.compute_class_weight. Model performance was monitored using metrics such as the area under the ROC curve (AUC) and recall for both training and validation sets. The learning curves of these metrics across epochs were analyzed to detect potential signs of overfitting or underfitting. After training, the model was evaluated on the test set. Probabilistic predictions were converted into predicted classes using the argmax function, and the results were compared with actual values using the confusion matrix and classification report, which included precision, recall, and F1-score for each class. Additionally, class-specific ROC curves were constructed, and the area under the curve (AUC) was calculated for each of the four yield categories, enabling a detailed evaluation of the model\u0026rsquo;s performance across different productivity levels. These curves demonstrated the model\u0026rsquo;s ability to distinguish yield levels under varying environmental and genotypic conditions.\u003c/p\u003e\u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eThe performance metrics obtained for the prediction model used to estimate the quality of common bean genotypes based on qualitative yield categories (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) indicate satisfactory performance of the adopted approach. Accuracy represents the proportion of correct predictions relative to the total number of predictions made by the model. In this study, the overall model accuracy (0.70) indicates a 70% success rate in classifications performed on the test dataset, reflecting a moderate generalization capacity. However, accuracy alone does not provide a complete view of the model\u0026rsquo;s performance, especially in contexts where different types of errors have distinct implications. Moreover, accuracy can be influenced by the class distribution within the dataset.\u003c/p\u003e\u003cp\u003eIn addition to accuracy, when performance was assessed individually by class, the precision, recall (sensitivity), and F1-score metrics revealed differences in predictive performance among the categories considered in this study. Precision, also known as positive predictive value, measures the proportion of positive predictions that were correct for each specific class. In the context of this study, precision was calculated individually for each class, indicating the reliability of the model when predicting that a genotype belongs to a specific category. Furthermore, recall, also known as sensitivity or true positive rate, measures the model\u0026rsquo;s ability to correctly identify all members of a specific class. Finally, the F1-score represents the harmonic mean between precision and recall, providing a single metric that balances both aspects of performance.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePerformance metrics of the prediction model based on artificial neural networks, showing precision, recall, and F1-score for each class, along with the overall accuracy of the model\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eClass\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePrecision\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRecall\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eF1-Score\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePoor\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.67\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.70\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGood\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.66\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.66\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eExcellent\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.74\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.75\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOverall Accuracy\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e0.70\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe \u0026ldquo;excellent\u0026rdquo; class presented the best performance indices in terms of precision, recall, and F1-score, demonstrating approximately 75% efficiency of the model in predicting high-yielding genotypes (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). This is particularly relevant for breeding programs, as it highlights the potential of the approach in identifying promising genotypes, with a low rate of false positives in this critical class. In other words, for every four genotypes classified as excellent by the model, three are truly excellent.\u003c/p\u003e\u003cp\u003eThe \u0026ldquo;poor\u0026rdquo; and \u0026ldquo;medium\u0026rdquo; classes showed intermediate performance, demonstrating the model\u0026rsquo;s capacity to adequately discriminate genotypes within these categories, which is important for avoiding misidentification of low-performing genotypes. On the other hand, the \u0026ldquo;good\u0026rdquo; class showed lower discriminative ability by the algorithm, as evidenced by its precision, recall, and F1-score values. This result is likely due to phenotypic overlap among adjacent yield ranges, which makes precise separation based on agronomic traits more difficult.\u003c/p\u003e\u003cp\u003eThe normalized confusion matrix (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) provides a detailed visualization of the model\u0026rsquo;s predictive performance across the four yield categories: poor, medium, good, and excellent. The values represented correspond to relative proportions between the predictions made and the observed classes, allowing inferences about hit and error rates for each category. It can be observed that the highest values, corresponding to correct classification rates, are concentrated along the main diagonal of the matrix. These values corroborate the descriptive metrics previously presented, reinforcing the consistency of the results.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe analysis of error dispersion among adjacent classes reveals that, in the classes of greatest interest for identifying excellent genotypes, some misclassifications occurred, where the model identified genotypes as good when they should have been classified as excellent. Despite these errors, more severe misclassifications, such as predicting poor or medium genotypes as good or excellent, occurred at very low frequencies. Certain inaccuracies are compatible with the continuous nature of the grain yield trait and with the process of transforming a continuous variable into qualitative classes, which imposes limits on the separation between adjacent phenotypic groups. Nevertheless, the results indicate satisfactory predictive performance, particularly in the extreme categories, which is of great interest in breeding programs, as it enables the prioritization of excellent genotypes and the elimination of low-performing ones.\u003c/p\u003e\u003cp\u003eThe ROC (Receiver Operating Characteristic) curves for the four yield classes were fitted (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). These curves allow the evaluation of the model\u0026rsquo;s discriminative ability in terms of the relationship between the true positive rate (sensitivity) and the false positive rate across different decision thresholds. The curves for all classes were positioned above the reference line (diagonal), indicating predictive performance excellent to random classification. The area under the curve (AUC), which summarizes overall performance, ranged from 0.84 to 0.94, with higher values for the \u0026ldquo;poor\u0026rdquo; (AUC\u0026thinsp;=\u0026thinsp;0.94) and \u0026ldquo;excellent\u0026rdquo; (AUC\u0026thinsp;=\u0026thinsp;0.92) classes, followed by \u0026ldquo;medium\u0026rdquo; (0.87) and \u0026ldquo;good\u0026rdquo; (0.84). These results reinforce the effectiveness of the model in distinguishing genotypes belonging to the extreme yield categories, that is, those with poor or excellent agronomic performance. The lower AUC values observed for the \u0026ldquo;good\u0026rdquo; and \u0026ldquo;medium\u0026rdquo; classes reflect greater phenotypic overlap within these intermediate categories, making their distinction more difficult.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe evolution of performance metrics over 100 training epochs, considering the training and test sets, is presented (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Accuracy, loss function, area under the ROC curve (AUC), and recall were evaluated, providing a comprehensive analysis of the algorithm\u0026rsquo;s learning process. In the training set, rapid convergence was observed (with accuracy above 0.95), an AUC close to 1, and high sensitivity within the first 30 epochs. The loss function showed a significant decrease, stabilizing at low values, indicating efficient model learning for the training data.\u003c/p\u003e\u003cp\u003eIn the validation set, the metrics suggested limitations in model generalization. Accuracy stabilized around 0.70, and AUC, after initially high values, declined to 0.86. The validation loss increased after an inflection point, indicating that the model prioritized patterns specific to the training set. Validation sensitivity stabilized at approximately 0.68. In summary, the model\u0026rsquo;s performance was satisfactory considering the complexity of the grain yield trait, especially in predicting the extreme productivity classes of common bean genotypes. This approach represents a complementary strategy for breeding programs, supporting decision-making during the identification of excellent genotypes in comparative trials.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e"},{"header":"Discussion","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003eApplication of artificial neural networks in predicting common bean genotypes\u003c/h2\u003e\u003cp\u003eThe increasing complexity of breeding programs, particularly in self-pollinated crops such as common bean, has driven the adoption of computational approaches capable of handling large data volumes and nonlinear relationships. The need to make decisions based on multiple environments, years, and traits has made complementary techniques, such as machine learning-based methods, increasingly valuable in assisting conventional approaches. In this context, artificial neural networks (ANNs) have emerged as a promising technique, especially for classification tasks and the prediction of agronomic performance under complex and heterogeneous conditions.\u003c/p\u003e\u003cp\u003eThis study demonstrated that an ANN-based model was able to predict common bean genotypes into four qualitative yield categories with an overall test accuracy of 70%, a performance consistent with that observed in similar studies applying artificial intelligence to crops such as wheat, rice, and maize (Montesinos-L\u0026oacute;pez et al. 2018, Shook et al. 2021). The best performance metrics were observed for the \u0026ldquo;excellent\u0026rdquo; and \u0026ldquo;poor\u0026rdquo; classes, indicating that the neural network could more accurately predict patterns associated with the extremes of the phenotypic grain yield spectrum. This ability is strategic in breeding programs since the correct identification of genotypes with high yield potential directly contributes to greater efficiency in identifying excellent genotypes and, consequently, in recommending cultivars with a higher likelihood of success across different agricultural environments (Allard 1961).\u003c/p\u003e\u003cp\u003eConversely, the reliable prediction of low-yielding genotypes is equally valuable, as it enables the early elimination of poor genotypes, thereby optimizing the allocation of experimental resources and reducing the time required for subsequent evaluation stages (Bhering et al. 2015). On the other hand, the relatively lower performance in the intermediate classes (\u0026ldquo;medium\u0026rdquo; and \u0026ldquo;good\u0026rdquo;) may be attributed to the overlap of phenotypic classes among genotypes with similar yields, a common phenomenon in quantitative traits such as grain yield. Additionally, the process of transforming continuous data into discrete categories may have introduced ambiguity at the boundaries between classes, reducing the model\u0026rsquo;s discriminative ability in such cases. Nevertheless, the confusion matrix derived from the test data predictions showed a predominance of correct classifications along the main diagonal, reinforcing that, despite these challenges, the neural network exhibited consistent performance.\u003c/p\u003e\u003cp\u003eIn this sense, the observed values indicate that the ANN was effective in distinguishing high- and low-yielding genotypes, even under the environmental variability inherent to the dataset used. The robustness of the model in response to environmental variation is particularly relevant in programs that rely on data collected across multiple sites and years, under distinct soil, climate, and management conditions. Similar findings were reported by Gonz\u0026aacute;lez-Camacho et al. (2016), who demonstrated the superiority of neural networks over traditional regression methods for predicting performance across multiple environments, highlighting the potential of this approach to handle such complexity.\u003c/p\u003e\u003cp\u003eSimilarly, Corr\u0026ecirc;a et al. (2016) also observed high concordance between classical methods for measuring phenotypic adaptability and stability and the results generated by artificial neural networks, suggesting that these techniques can be used not only as classifiers but also as viable alternatives for evaluating genotype stability. Therefore, the application of artificial neural networks in predicting common bean genotypes represents an approach with the potential to increase the accuracy of identifying excellent or poor genotypes in breeding programs, contributing to the development of more productive cultivars adapted to the conditions of modern agriculture.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003eModel robustness in response to environmental variability\u003c/h2\u003e\u003cp\u003eGrain yield in common bean is strongly influenced by environmental factors, making the prediction of genotypic performance across different locations and years a challenge for breeding programs (Bernal-Vasquez et al. 2014). This complexity arises from genotype-by-environment interaction, which can substantially alter the behavior of genotypes under varying environmental conditions. In this study, the artificial neural network (ANN) was trained and tested using data from multiple locations and growing seasons, thereby capturing a relevant portion of this variability. Despite the inclusion of environmental variation in the model, the results revealed the occurrence of overfitting, as indicated by the discrepancy between training accuracy (\u0026gt;\u0026thinsp;95%) and validation accuracy (~\u0026thinsp;70%). This finding suggests that the model learned specific patterns from the training data but showed limited ability to generalize its performance to new contexts.\u003c/p\u003e\u003cp\u003ePart of these limitations may be attributed to the nature of the data used for modeling. The use of morphological variables such as plant height, stem diameter, and insertion height of the first pod, although relevant, may not provide sufficient discriminatory power to accurately distinguish intermediate performance classes, particularly when dealing with a continuous quantitative trait such as grain weight per plant. This trait, being polygenic and influenced by multiple environmental factors (Costa-Neto et al. 2021), tends to follow an approximately normal distribution in the population, resulting in a higher concentration of individuals within intermediate ranges and greater genotypic diversity in these classes.\u003c/p\u003e\u003cp\u003eConsequently, it is common to observe overlapping regions between adjacent performance categories, such as those classified as \u0026ldquo;moderate\u0026rdquo; and \u0026ldquo;good.\u0026rdquo; Such overlap complicates pattern definition, especially when subtle phenotypic differences are not effectively captured. This ambiguity can negatively affect learning algorithms such as neural networks, since the proximity of samples from different classes in multidimensional space may lead to inconsistent classification decisions. Additionally, even when the number of individuals per class is balanced, the way these individuals are distributed across the feature space may favor the prediction of extremes while hindering accurate prediction of genotypes with intermediate performance. The greater morphological homogeneity in the poor and excellent classes, associated with clearer physiological limitations or advantages, tends to generate more easily recognizable patterns for the model, whereas the genetic variability within intermediate classes results in more dispersed data clusters and less well-defined decision boundaries.\u003c/p\u003e\u003cp\u003eTo mitigate overfitting, one recommended strategy is the use of cross-validation structured by environment, as proposed by Burgue\u0026ntilde;o et al. (2012). This type of validation accounts for the environmental origin of the experimental units, promoting a more realistic assessment of the model\u0026rsquo;s generalization capacity. Moreover, incorporating environmental variables such as temperature, precipitation, relative humidity, solar radiation, and vegetation indices can enhance the modeling of genotype-by-environment interaction (Costa-Neto et al. 2021). This approach has been widely applied in other crops to integrate environmental data into predictive genetic and phenotypic models, thereby improving prediction accuracy and robustness (Cooper et al. 2014).\u003c/p\u003e\u003cp\u003eIn this context, more sophisticated neural networks, such as those based on deep learning, offer new possibilities for handling the complexity of genetic and environmental data. These architectures can model nonlinear relationships and capture subtle spatial or temporal patterns that are difficult to detect using traditional methods (Gupta and Singh 2023). Therefore, the application of neural networks in common bean breeding may represent an important advancement, particularly during the early stages of selection when working with segregating populations. At this stage, the scarcity of seeds and the limited use of experimental designs often result in phenotypic data with greater variability and noise, requiring more robust models for the accurate identification of excellent genotypes.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eStrategic use of artificial neural networks in plant breeding\u003c/h3\u003e\n\u003cp\u003eThe main contribution of this study lies in demonstrating the potential of artificial neural networks (ANNs) as a strategic technique to support the identification of excellent genotypes in common bean breeding programs. The model\u0026rsquo;s ability to discriminate high-yielding genotypes with an acceptable error rate positions neural networks as a viable and effective approach to assist decision-making in the final stages of breeding programs, particularly during testing, as evidenced in this study. This type of application aligns with the growing adoption of artificial intelligence techniques in agriculture, especially within the context of digital and precision agriculture (Kamilaris and Prenafeta-Bold\u0026uacute; 2018).\u003c/p\u003e\u003cp\u003eThe use of ANNs stands out for their ability to model multiple complex nonlinear relationships between explanatory variables and agronomic responses, which is particularly valuable in biological systems and can be directly applied to plant breeding. By incorporating phenotypic data from multiple environments, these networks can predict patterns related to grain yield and other traits with a high degree of accuracy, even in the presence of environmental variability inherent to agricultural experiments. Thus, the use of ANNs provides an additional tool to help breeders make more assertive decisions regarding the identification of both promising and unpromising genotypes.\u003c/p\u003e\u003cp\u003eIntegrating neural networks with other statistical techniques can further enhance the efficiency of identifying excellent genotypes. For example, genotypes classified as \u0026ldquo;excellent\u0026rdquo; by the ANN can be jointly analyzed with phenotypic stability scores, such as those obtained from the Eberhart and Russell method or the AMMI model, allowing the identification of genotypes that are not only productive but also stable or adapted to different environmental conditions (Cruz et al. 2018, Yan and Kang 2003). This combined approach is strategic in breeding programs where production stability is as important as absolute yield, particularly in agricultural environments characterized by high variability.\u003c/p\u003e\u003cp\u003eMoreover, the incorporation of molecular data can enable the use of ANNs in genomic prediction approaches, combining genomic, phenotypic, and environmental information within a predictive model. This integration can improve the accuracy of marker-assisted selection, thereby increasing the rate of genetic gain (Montesinos-L\u0026oacute;pez et al. 2019). Within this context, ANNs move beyond their role as classification tools to become models for predicting genotype performance in breeding programs.\u003c/p\u003e\u003cp\u003eHowever, it is important to emphasize that the use of neural networks in plant breeding should not replace traditional experimental methods but rather complement them by providing additional support for more efficient decisions. The future of plant breeding will likely be shaped by the convergence of different data sources and analytical methodologies within an interdisciplinary framework that combines statistics, molecular biology, agronomy, and data science. This integrated approach has already been explored in several crops (Silva et al. 2014, Azevedo et al. 2015) and is expanding into animal breeding, with equally promising results (Okut et al. 2013). Therefore, the strategic adoption of neural networks and other machine learning techniques for appropriate situations represents an innovation with strong potential to enhance breeding efficiency.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eArtificial neural networks demonstrated satisfactory performance in predicting common bean genotypes based on grain yield, using multiple agronomic traits and data from different environments. The model was particularly effective in identifying high- and low-performing genotypes, confirming its applicability for prioritizing excellent lines or eliminating poor ones. The ability to integrate multiple traits and capture nonlinear relationships makes this approach a valuable decision-support tool in plant breeding programs.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe thank the Foundation for Research and Innovation Support of the State of Santa Catarina (FAPESC), Coordination for the Improvement of Higher Education Personnel (CAPES) and the University of the State of Santa Catarina (UDESC) for granting scholarships and financial assistance in carrying out research projects.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data related to the analyses performed are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that there is no conflict of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was supported by the Coordination for the Improvement of Higher Education Personnel (CAPES) and the University of the State of Santa Catarina (UDESC).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll authors are listed in alphabetical order and contribute equally. Luan Tiago dos Santos Carbonari: Conceptualization, Methodology, Formal analysis, Writing-Original Draft. Carlos Zacarias Joaquim Júnior, Marissa Prá de Souza, Charlene Barboza Bussolaro and Carina Lopes Djadjo: Conceptualization, Methodology and Formal analysis. Jefferson Luís Meirelles Coimbra, Altamir Frederico Guidolin and Sydney Antonio Frehner Kavalco: Data Curation, Writing-Review and Editing, Funding acquisition. All authors read and approved the final manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAllard, R. W. (1960). Principles of plant breeding. John Wiley \u0026amp; Sons.\u003c/li\u003e\n\u003cli\u003eAssefa, T., Assibi Mahama, A., Brown, A. V., Cannon, E. K., Rubyogo, J. C., Rao, I. M., ... \u0026amp; Cannon, S. B. (2019). A review of breeding objectives, genomic resources, and marker-assisted methods in common bean (Phaseolus vulgaris L.). Molecular Breeding, 39(2), 20.\u003c/li\u003e\n\u003cli\u003eAzevedo, A. 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S., Sant\u0026apos;Anna, I. D. C., Nascimento, M., Bhering, L. L., \u0026amp; Cruz, C. D. (2014). Neural networks for predicting breeding values and genetic gains. Scientia Agricola, 71, 494-498.\u003c/li\u003e\n\u003cli\u003eYan, W., Kang, M. S. (2002). GGE biplot analysis: a graphical tool for breeders, geneticists, and agronomists. CRC press.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"indian-journal-of-genetics-and-plant-breeding","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Indian Journal of Genetics and Plant Breeding](https://link.springer.com/journal/44489)","snPcode":"44489","submissionUrl":"https://submission.springernature.com/new-submission/44489/3","title":"Indian Journal of Genetics and Plant Breeding","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Phaseolus vulgaris L., Plant breeding, Artificial intelligence, Machine learning","lastPublishedDoi":"10.21203/rs.3.rs-8029028/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8029028/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCommon bean is a crop of great socioeconomic importance for several developing countries, being fundamental to food security. Therefore, identifying excellent genotypes for grain yield is a critical step in breeding programs. This study aimed to evaluate the performance of artificial neural networks in predicting common bean genotypes considering different grain yield ranges, using data obtained from multiple environments. The model was trained and tested with phenotypic variables to classify genotypes into grain yield categories (poor, medium, good, and excellent). The results indicated satisfactory performance, with an overall accuracy of 70%, as well as a higher discriminative capacity in the extreme classes, especially \u0026ldquo;excellent\u0026rdquo; and \u0026ldquo;poor.\u0026rdquo; The area under the curve reinforced the model\u0026rsquo;s effectiveness, with values above 0.90 for the \u0026ldquo;excellent\u0026rdquo; and \u0026ldquo;poor\u0026rdquo; classes, which are considered priorities in genotype recommendation and discard processes. Therefore, the use of neural networks proved to be a promising tool to support decision-making in common bean breeding, allowing efficient identification of promising genotypes and elimination of less productive ones during the final field evaluation stage.\u003c/p\u003e","manuscriptTitle":"Neural networks applied to plant breeding for predicting grain yield in common bean genotypes","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-25 09:27:26","doi":"10.21203/rs.3.rs-8029028/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-01-03T18:06:21+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-25T07:21:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"303960319493124616299720632184558731541","date":"2025-11-17T06:37:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"321043655697928846755539031720896857990","date":"2025-11-14T17:17:03+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-14T08:00:18+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-05T04:10:44+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-05T04:09:55+00:00","index":"","fulltext":""},{"type":"submitted","content":"Indian Journal of Genetics and Plant Breeding","date":"2025-11-04T12:42:59+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"indian-journal-of-genetics-and-plant-breeding","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Indian Journal of Genetics and Plant Breeding](https://link.springer.com/journal/44489)","snPcode":"44489","submissionUrl":"https://submission.springernature.com/new-submission/44489/3","title":"Indian Journal of Genetics and Plant Breeding","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"c97b4617-ad13-4db1-b871-597ef56485a9","owner":[],"postedDate":"November 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-01-21T17:53:31+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-25 09:27:26","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8029028","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8029028","identity":"rs-8029028","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}