Application of mixed models, GGE biplot, ER analysis and machine learning for wheat genotype classification

Abstract

Accurate classification of wheat genotypes for adaptability and stability across diverse environments remains challenging in multi-environment trials. This study integrated mixed models, genotype plus genotype × environment interaction (GGE) biplot analysis, the Eberhart-Russell (ER) stability approach, and supervised machine learning to evaluate wheat genotype performance and improve ER-based classification. Seventy wheat genotypes were tested across 23 environments in Pakistan under the National Uniform Wheat Yield Trials (2023-2024). Genotype and environment effects were highly significant (p < 0.01), while genotype × environment interaction was significant (p < 0.05), confirming differential genotype responses. GGE biplot analysis identified interaction patterns, specific adaptation, and stable entries, whereas ER parameters classified genotypes into six stability classes. After SMOTE, PCA, and hyperparameter tuning, the optimized support vector machine achieved the best performance, with 94.4% accuracy and strong agreement with ER classes. This integrated framework supports the selection of stable, high-yielding wheat genotypes.

Keywords:
Multi-environment trials; genotype adaptability; yield stability; genotype × environment interaction; supervised learning

INTRODUCTION

Wheat (Triticum aestivum L.) is a major staple crop that plays a critical role in global food security, contributing substantially to human caloric and protein intake (Shiferaw et al. 2013). In countries such as Pakistan, it is central to both food systems and agricultural sustainability. Although conventional and modern breeding approaches, including genomic-assisted selection, have improved yield potential and stress tolerance (Crossa et al. 2017), the genetic base of cultivated wheat remains relatively narrow due to domestication bottlenecks and intensive selection, limiting available genetic diversity for further improvement (Rasheed et al. 2018). Increasing climate variability and environmental heterogeneity further limit genetic improvement and complicate the identification of elite genotypes with stable and broad adaptation (Mao et al. 2023). These challenges necessitate the use of more advanced analytical tools for effective genotype discrimination across diverse environments.

Evaluation of genotype performance across environments is typically conducted through multi-environment trials (METs), which enable assessment of yield potential and stability (Eberhart and Russell 1966). Classical approaches such as the Eberhart-Russell (ER) regression model quantify adaptability and stability through regression-based parameters, whereas genotype plus genotype × environment interaction (GGE) biplot analysis and mixed models facilitate interpretation of genotype × environment interaction (GEI) and partitioning of variation (Crossa 1990, Smith et al. 2001, Yan and Kang 2003). However, these methods are largely linear and descriptive, which may limit their capacity to capture complex and nonlinear GEI patterns commonly observed in MET data (Yang 2014).

Advanced statistical methods, including additive main effects and multiplicative interaction (AMMI) models (Gauch Junior 1988), factor-analytic mixed models (Smith et al. 2001), and nonparametric stability measures (Huehn 1990), have improved GEI characterization. Nevertheless, these approaches still rely on statistical assumptions and may be less effective in modeling high-dimensional and nonlinear relationships inherent in complex breeding datasets (Montesinos-López et al. 2021). These limitations have increased interest in data-driven approaches that can complement traditional methods.

Machine learning techniques offer the ability to model nonlinear relationships and extract patterns from complex datasets without strict parametric assumptions (Cortes and Vapnik 1995, Vapnik 1999). Among these, support vector machines (SVMs) have demonstrated strong performance in classification problems involving high-dimensional data (Mountrakis et al. 2011). Recent studies have demonstrated the usefulness of machine learning models for genotype classification and breeding-related prediction in complex biological datasets (Zhao et al. 2020, Sakeef et al. 2023). However, the integration of machine learning with established stability analysis frameworks remains limited.

Rather than replacing classical approaches, machine learning can complement them by improving classification accuracy and robustness. While ER, GGE biplot, and mixed models provide interpretable measures of genotype performance and stability (Crossa 1990, Yan and Kang 2003), machine learning algorithms can learn classification boundaries based on these outputs, enhance discrimination among similar genotypes, and better capture nonlinear GEI structures (Nascimento et al. 2013, Amaral et al. 2023). This integration is particularly relevant in wheat breeding, where environmental variability and overlapping genotype responses complicate classification and selection decisions.

The present study integrates mixed-model analysis, GGE biplot analysis, and Eberhart-Russell stability parameters with supervised machine learning algorithms. The objectives were to: i) evaluate wheat genotype adaptability and stability across diverse environments using mixed models, GGE biplot, and ER parameters, and ii) enhance ER-based genotype classification through machine learning models. This integrated approach bridges statistical stability analysis and data-driven classification, providing a novel and practical framework for genotype evaluation and selection in multi-environment trials.

MATERIAL AND METHODS

Plant material and experimental design

Seventy bread wheat genotypes (advanced lines and varieties), including two long-term check varieties, Pakistan-13 and Akbar-19, along with a composite local check, were evaluated across 23 environments during 2023-2024 cropping season (Rabi season: October-June) in National Uniform Wheat Yield Trials. Detailed passport information for each genotype is provided in Supplementary Table S1. The genotypes represented promising materials from provincial and federal research institutes, stations, and universities across Pakistan.

The test locations included Bahawalpur (L1), Rahim Yar Khan (L2), Muzaffargarh (L3), Dera Ghazi Khan (L4), Ranjanpur (L5), Faisalabad (L6), Bahawalnagar (L7), Okara (L8), Sahiwal (L9), Sargodha (L10), Khanewal (L11), Bhakkar (L12), Layyah (L13), Multan (L14), Hyderabad (L15), Sanghar (L16), Shaheed Benazirabad (L17), Thatta (L18), Lakki Marwat (L19), Nowshera (L20), Charsadda (L21), Dera Ismail Khan (L22), and Quetta (L23), representing diverse agro-ecological zones of Pakistan. Environmental descriptors such as latitude, rainfall, and soil type are provided in Supplementary Table S2.

Trials were conducted using an alpha-lattice design with two replications to control spatial heterogeneity (Patterson and Williams 1976). Each plot consisted of six rows, 5 m long with 30 cm spacing. Standard agronomic practices were followed at each location. Grain yield (t ha⁻¹) was recorded at physiological maturity by harvesting the central rows to minimize border effects. Grain weight was adjusted to standard moisture content and expressed in t ha⁻¹. Data were screened for outliers and standardized prior to machine learning analysis (Jolliffe and Cadima 2016).

Mixed model analysis of variance

A combined analysis of variance was performed using a mixed linear model to partition phenotypic variation into genotype (G), environment (E), and genotype × environment interaction (GEI) components (Yan and Kang 2003). Genotypes were treated as fixed effects, whereas environments and blocks within environments were treated as random factors (Crossa 1990). The model was presented in Equation 1:

Y_ijk= µ + G_i+ E_j+ GE_ij+ B_jk+ e_ijk (1)

where Y _ijk represents grain yield of i ^th genotype evaluated in j ^th environment and k ^th block; μ denotes overall mean; G _i denotes fixed effect of i ^th genotype; E _j is random effect of j ^th environment; GE _ij captures genotype × environment interaction effect; B _jk represents block effect nested within environment; and e _ijk is residual error. This approach provided precise estimation of GEI and facilitated decisions regarding broad or specific adaptation across environments (Yang 2014).

GGE biplot analysis

GGE biplot analysis was conducted using environment-centered data (G + GE), in which environmental main effects were removed to emphasize genotype performance and genotype × environment interaction (GEI), as recommended for cultivar evaluation (Yan and Kang 2003). This approach facilitates comparison of genotypes based on mean performance and stability across environments. Symmetrical scaling was also examined to validate the “which-won-where” pattern.

Singular value decomposition (SVD) of the genotype main effects plus genotype × environment interaction (G + GE) matrix was performed. The first two principal components were used to construct biplots for visualization of genotype performance, stability, and interaction patterns.

Eberhart-Russell stability analysis

Genotype stability and adaptability were evaluated using the Eberhart-Russell regression model (Eberhart and Russell 1966), as defined in Equation 2:

Y_ij= µ_i+ β_iI_j+ δ_ij (2)

where Y _ij is mean performance of genotype i in environment j; μᵢ is the overall mean of genotype i; Iⱼ is environmental index; and δ _ij denotes deviation from regression. Positive values of Iⱼ indicate favorable conditions, whereas negative values indicate unfavorable conditions.

Genotypes were classified into six Eberhart-Russell stability classes based on regression coefficient (β _i ) and stability parameter deviation from regression (σ² _dᵢ ) (Table 3). Genotypes with 0.90 ≤ β _i ≤ 1.10 were considered widely adapted, those with β _i > 1.10 adapted to favorable environments, and those with β _i < 0.90 adapted to unfavorable environments. Stability was defined as σ² _dᵢ ≈ 0 (stable) and σ² _dᵢ > 0 (unstable). These classes were used as reference labels for machine learning classification, following Nascimento et al. (2013).

Machine learning classification and model evaluation

Supervised machine learning algorithms, including support vector machine (SVM), artificial neural network (ANN), random forest (RF), decision tree (DT), and k-nearest neighbors (KNN), were used to classify wheat genotypes into ER stability classes. The input features consisted of genotype mean grain yield across 23 environments, resulting in 23 environment-specific variables per genotype derived from multi-environment trial data. These features capture genotype × environment interaction patterns and provide a high-dimensional representation of genotype performance across diverse environments.

Prior to model training, all features were standardized using z-score normalization. Model performance was evaluated using stratified 10-fold cross-validation, ensuring proportional representation of ER classes in training and validation subsets. Performance metrics were calculated according to Equations 3 to 6:

$Accuracy=\frac{TP+TN}{TP+TN+FP+FN}$(3)

$Precision=\frac{TP}{TP+FP}$(4)

$F1Score=2\times \frac{Precision\times Recall}{Precision+Recall}$(5)

Cohen’s Kappa = $k=\frac{P_0-P_e}{1-P_e}$(6)

where TP, TN, FP, and FN denote true positives, true negatives, false positives, and false negatives, respectively. Pₒ represents the observed agreement, and Pₑ represents the expected agreement due to chance. Cohen’s kappa provides a robust measure of classification performance beyond simple accuracy, particularly under class imbalance (Fawcett 2006). Balanced accuracy was calculated as the average recall across classes to account for class imbalance.

Class imbalance correction and model optimization

Class imbalance among ER stability classes was addressed using the synthetic minority over-sampling technique (SMOTE) with k = 3 nearest neighbors and an oversampling rate of 2 (Chawla et al. 2002). SMOTE was applied exclusively to the training data within each fold to prevent data leakage. Class distributions before and after SMOTE are presented in Figure 1b. Dimensionality reduction was performed using principal component analysis (PCA) applied after SMOTE on the training data. Principal components explaining 90% of the total variance were retained to reduce feature redundancy and improve computational efficiency (Jolliffe 2002). Model optimization focused on SVM due to its superior baseline performance, although all models were initially evaluated under identical conditions to ensure fair comparison. Hyperparameters were tuned using grid search over a logarithmically spaced range of cost parameter (C) and kernel parameter (γ) values for the radial basis function (RBF) kernel. The optimal combination (C = 1.8, γ = 0.015625) was selected based on cross-validated accuracy (Lin et al. 2003).

Figure 1
Integrated analytical workflow and machine-learning optimization for Eberhart-Russell-based wheat genotype classification: (a) ER stability and machine-learning classification workflow; (b) ER class distribution before and after SMOTE; and (c) cross-validated SVM accuracy across C and gamma combinations.

Software and implementation

All statistical and machine learning analyses were conducted in R using the packages e1071, caret, class, rpart, randomForest, nnet, smotefamily, dplyr, and ggplot2. GGE biplots were generated using GEA-R software. The complete analytical workflow is illustrated in Figure 1a.

RESULTS AND DISCUSSION

Combined analysis of variance and genotype × environment interaction

The combined analysis of variance (ANOVA) for grain yield of 70 wheat genotypes evaluated across 23 locations revealed highly significant effects (p < 0.01) of genotype and environment, while the genotype × environment interaction (GEI) was significant at the 5% level (p < 0.05) (Table 1). Environmental effects accounted for the largest proportion of variation (53.4%), highlighting the strong influence of site-specific conditions on wheat productivity. GEI explained 21.1% of total variation, confirming differential genotype responses across environments, consistent with earlier MET studies (Yan and Kang 2003, Mohammadi and Amri 2008). Genotypic effects contributed 3.98%, while experimental error accounted for 20.3%. The substantial GEI component underscores the need for complementary stability analyses such as mixed models, GGE biplots, and ER statistics to support genotype selection across heterogeneous environments.

Table 1
Combined analysis of variance for wheat grain yield across 23 locations

Sources of variation	df	SS	MS	F-value	P-value	Total SS (%)
Replication	1	3.09	3.0897	7.16	0.007	0.09
Block (Rep.)	12	7.12	0.593	1.38	0.169	0.21
Genotype (G)	69	134.97	1.956	4.54**	< 0.001	3.98
Environment (E)	22	1811.08	82.322	191.12**	< 0.001	53.44
G × E	1518	715.62	0.4714	1.09*	0.037	21.12
Error	1597	687.88	0.431			20.30
Total	3219	3388.92				100

• * and ** indicate significance at p < 0.05 and p < 0.01, respectively.

GGE biplot analysis of genotype performance and stability

The GGE biplot (Figure 2), derived from the first two principal components of the environment-centered (G + GE) matrix, explained 36.50% of the total (G + GE) variation, with 22.99% attributed to PC1 and 13.51% to PC2. In the which-won-where view (Figure 2a), the polygon formed by the outermost genotypes revealed pronounced crossover genotype × environment interaction, indicating that genotype ranking changed across environments and that no single genotype was superior under all test conditions. The distribution of environments across sectors suggested three main groups. The left-upper sector was won by G45 and included L15, L17, and L2. A second, larger group occupied the left-lower sector and was won by G44, including L9, L14, L3, L11, L10, L6, L22, L8, L21, L19, and L20. A third group was represented by L5 in the lower sector, which was won by G17. The remaining polygon sectors did not contain test environments, indicating that their corresponding vertex genotypes were not winners in the evaluated environments. These findings are consistent with previous studies showing that GGE biplot analysis is effective for identifying crossover GEI, specifically adapted genotypes, and sector-based environmental grouping in wheat multi-environment trials (Yan and Tinker 2006, Mujahid et al. 2011).

Figure 2
GGE biplot analysis illustrating: (a) mega-environment delineation and winning genotypes (which-won-where), (b) genotype mean performance and stability, and (c) discriminativeness vs. representativeness of test environments.

In the mean performance-stability view (Figure 2b), genotypes located farther along the positive direction of the average environment coordinate (AEC) abscissa had higher mean yield, whereas those with smaller projections onto the AEC ordinate were more stable across environments. In the discriminativeness-representativeness view (Figure 2c), environments farther from the origin were more discriminating, while those with smaller angles relative to the average environment axis were more representative, indicating their usefulness for efficient genotype evaluation. The GGE biplot confirmed substantial crossover GEI, revealed sector-based environmental grouping, and provided useful support for identifying specifically adapted and relatively stable wheat genotypes across diverse agro-ecological conditions in Pakistan (Mujahid et al. 2011).

ER-based stability classification of wheat genotypes

The Eberhart-Russell (ER) model classified wheat genotypes into six stability classes based on regression coefficient (β _i ) and deviation from regression (σ² _dᵢ ) (Table 2 and Table 3). Genotypes with 0.90 ≤ β _i ≤ 1.10 and σ² _dᵢ ≈ 0 were considered stable and widely adapted, whereas genotypes with β _i > 1.10 or β _i < 0.90 were considered specifically adapted to favorable or unfavorable environments, respectively. Among the evaluated genotypes, 14 (20.0%) were classified as stable and widely adapted (Class 3), 11 (15.7%) as stable and adapted to favorable environments (Class 2), and 7 (10.0%) as stable under unfavorable environments (Class 1). The remaining genotypes were classified as unstable but adapted to unfavorable (Class 4; 15.7%), favorable (Class 5; 18.6%), or broad (Class 6; 20.0%) environments. This distribution revealed marked differences in genotype response across environments, confirming the importance of identifying both broadly adapted and specifically adapted materials in wheat improvement programs. Stable and widely adapted genotypes are particularly useful for general cultivation, whereas specifically adapted genotypes may be more suitable for targeted recommendation under defined environmental conditions.

Table 2
Mean grain yield, Eberhart-Russell regression coefficient (βᵢ), deviation from regression (σ² _dᵢ ), adaptability, stability status, and ER-based classification of wheat genotypes across environments

Entry #	Genotype name	Mean yield (t ha⁻¹)	β i	σ² dᵢ	Adaptability	Stability	ER class
G1	TWS-15110	4.439	1.21	0.23	Favorable	Unstable	Class 5
G2	KT-06	4.490	1.09	0.10	Wide	Unstable	Class 6
G3	DF-1708	4.747	1.30	0.06	Favorable	Unstable	Class 5
G4	181601	4.572	0.78	0.08	Unfavorable	Unstable	Class 4
G5	CTHN-162056	4.699	1.03	0.15	Wide	Unstable	Class 6
G6	V.SR-6026	4.602	0.94	0.07	Wide	Unstable	Class 6
G7	TRB-14-116	4.570	0.89	0.12	Unfavorable	Unstable	Class 4
G8	18C117	4.673	0.96	0.15	Wide	Unstable	Class 6
G9	WV-1195	4.190	0.66	0.00	Unfavorable	Stable	Class 1
G10	15BT001	4.266	0.63	0.00	Unfavorable	Stable	Class 1
G11	AUP-1411815	4.250	0.99	0.00	Wide	Stable	Class 3
G12	PR-137	4.534	0.71	0.08	Unfavorable	Unstable	Class 4
G13	MY-291-4	4.651	0.97	0.07	Wide	Unstable	Class 6
G14	TWS 17060	4.651	0.94	0.09	Wide	Unstable	Class 6
G15	SN-005	4.932	1.13	0.00	Favorable	Stable	Class 2
G16	10136	4.576	1.01	0.00	Wide	Stable	Class 3
G17	RUSTAM-20	4.576	0.68	0.22	Unfavorable	Unstable	Class 4
G18	HYT-100-47	4.912	0.92	0.12	Wide	Unstable	Class 6
G19	TRB-2-103	4.884	0.99	0.00	Wide	Stable	Class 3
G20	PR-138	4.681	1.19	0.07	Favorable	Unstable	Class 5
G21	EV-18102	4.549	0.60	0.07	Unfavorable	Unstable	Class 4
G22	SWB-9	4.391	0.95	0.00	Wide	Stable	Class 3
G23	Pakistan-13	4.461	1.11	0.00	Favorable	Stable	Class 2
G24	TWS 1849	4.451	0.89	0.21	Unfavorable	Unstable	Class 4
G25	HYT-100-74	4.708	0.83	0.29	Unfavorable	Unstable	Class 4
G26	CTHN-172114	4.668	1.24	0.22	Favorable	Unstable	Class 5
G27	PR-139	4.684	1.21	0.00	Favorable	Stable	Class 2
G28	KT-24	4.459	1.03	0.00	Wide	Stable	Class 3
G29	NR-546	4.725	0.94	0.00	Wide	Stable	Class 3
G30	V-7	3.883	0.68	0.00	Unfavorable	Stable	Class 1
G31	NBW-231	4.129	1.11	0.07	Favorable	Unstable	Class 5
G32	V-19308	4.859	1.24	0.00	Favorable	Stable	Class 2
G33	V.MPT-14	4.440	0.79	0.00	Unfavorable	Stable	Class 1
G34	NR-550	4.683	1.22	0.00	Favorable	Stable	Class 2
G35	SWB-13	4.016	0.85	0.10	Unfavorable	Unstable	Class 4
G36	PR-141	4.296	0.99	0.00	Wide	Stable	Class 3
G37	180059	4.593	0.65	0.06	Unfavorable	Unstable	Class 4
G38	V-18352	4.650	0.94	0.08	Wide	Unstable	Class 6
G39	NRL-1825	4.294	1.13	0.00	Favorable	Stable	Class 2
G40	WV-1197	4.802	0.90	0.00	Wide	Stable	Class 3
G41	17 FJ 10	4.378	1.25	0.00	Favorable	Stable	Class 2
G42	BF 1807	4.829	1.15	0.00	Favorable	Stable	Class 2
G43	PR-142	4.510	1.13	0.00	Favorable	Stable	Class 2
G44	WAL-10	4.717	1.17	0.14	Favorable	Unstable	Class 5
G45	HYT-70-16	4.933	1.25	0.00	Favorable	Stable	Class 2
G46	Akbar-19	4.732	1.31	0.00	Favorable	Stable	Class 2
G47	NRL-1812	4.625	1.25	0.14	Favorable	Unstable	Class 5
G48	NW-9	4.334	1.03	0.05	Wide	Unstable	Class 6
G49	KT-22	4.593	1.04	0.06	Wide	Unstable	Class 6
G50	V-19347	4.893	0.92	0.00	Wide	Stable	Class 3
G51	PR-143	4.371	0.99	0.22	Wide	Unstable	Class 6
G52	TRB-4-138	4.633	0.79	0.05	Unfavorable	Unstable	Class 4
G53	MY-409-4	4.336	0.82	0.00	Unfavorable	Stable	Class 1
G54	SWB-11	4.321	0.90	0.06	Wide	Unstable	Class 6
G55	NR-577	4.448	0.92	0.00	Wide	Stable	Class 3
G56	DN-139	4.435	1.09	0.25	Wide	Unstable	Class 6
G57	PR-144	4.149	1.01	0.00	Wide	Stable	Class 3
G58	NBW-232	4.526	1.18	0.08	Favorable	Unstable	Class 5
G59	HYT-100-76	4.758	1.12	0.11	Favorable	Unstable	Class 5
G60	18BT017	4.234	0.90	0.00	Wide	Stable	Class 3
G61	V-17086	4.496	1.10	0.00	Wide	Stable	Class 3
G62	NR-556	4.429	1.11	0.06	Favorable	Unstable	Class 5
G63	18C124	4.605	1.11	0.05	Favorable	Unstable	Class 5
G64	WRSIJ-03	4.217	0.84	0.00	Unfavorable	Stable	Class 1
G65	SN-010	4.311	1.07	0.00	Wide	Stable	Class 3
G66	NR-549	4.691	1.16	0.05	Favorable	Unstable	Class 5
G67	AUP-1413015	4.681	1.33	0.10	Favorable	Unstable	Class 5
G68	SWB-12	4.164	0.89	0.26	Unfavorable	Unstable	Class 4
G69	NR-552	4.793	1.11	0.15	Favorable	Unstable	Class 5
G70	Local Check	4.506	0.74	0.00	Unfavorable	Stable	Class 1

• βᵢ represents the regression coefficient describing genotype responsiveness to environmental variation, whereas σ² _dᵢ represents the deviation from regression used as the stability parameter in the Eberhart-Russell model. Genotypes with βᵢ < 0.90 were classified as adapted to unfavorable environments, those with 0.90 ≤ βᵢ ≤ 1.10 as widely adapted, and those with βᵢ > 1.10 as adapted to favorable environments. Genotypes with σ² _dᵢ values approximately equal to zero were considered stable, whereas those with positive σ² _dᵢ values were considered unstable. ER classes were assigned using the original parameter estimates; values shown in the Table are rounded for presentation.

Table 3
Distribution of wheat genotypes across Eberhart-Russell (ER) stability classes

ER class	ER stability parameters*	Description	Total genotypes	Genotypes above mean yield
I	σ²dᵢ ≈ 0, β i < 0.90	High stability, adapted to unfavorable environments	7 (10.0)	0 (0.0)
II	σ²dᵢ ≈ 0, β i > 1.10	High stability, adapted to favorable environments	11 (15.7)	7 (18.4)
III	σ²dᵢ ≈ 0, 0.90 ≤ β i ≤ 1.10	High stability, widely adapted	14 (20.0)	5 (13.2)
IV	σ²dᵢ > 0, β i < 0.90	Low stability, adapted to unfavorable environments	11 (15.7)	8 (21.1)
V	σ²dᵢ > 0, β i > 1.10	Low stability, adapted to favorable environments	14 (20.0)	10 (26.3)
VI	σ²dᵢ > 0, 0.90 ≤ β i ≤ 1.10	Low stability, widely adapted	13 (18.6)	8 (21.1)
Total	-	-	70 (100)	38 (54.3)

• Values in parentheses represent percentages (%). Overall mean yield = 4.533 t ha⁻¹. β _i represents the regression coefficient describing genotype responsiveness to environmental variation, whereas σ² _dᵢ denotes the deviation from regression used as the stability parameter in the Eberhart-Russell model. Genotypes with β _i < 0.90 were classified as adapted to unfavorable environments, those with 0.90 ≤ β _i ≤ 1.10 as widely adapted, and those with β _i > 1.10 as adapted to favorable environments. Genotypes with σ² _dᵢ values approximately equal to zero were considered stable, whereas those with positive σ² _dᵢ values were considered unstable.

Machine learning-based classification of stability classes

The ER-based stability classes were used as reference labels to evaluate the performance of supervised machine learning models under complex genotype × environment interaction (GEI) conditions. Among the evaluated machine learning models, support vector machine showed the best baseline performance, with 45.45% accuracy and Cohen’s κ of 0.33, followed by k-nearest neighbors (36.36%), while random forest, decision tree, and artificial neural network showed lower performance (Table 4). The generally modest baseline accuracy across models may be attributed to class imbalance, overlap among classes, and the inherent complexity of GEI in multi-environment data. Even under these conditions, the superior baseline performance of SVM agrees with previous reports describing its suitability for nonlinear and high-dimensional classification problems (Cortes and Vapnik 1995, Kuhn and Johnson 2013). Based on this initial comparison, SVM was selected for further optimization. Unlike the ER approach, which depends on predefined thresholds, the machine learning approach learns class boundaries from GEI-derived features, thereby providing greater flexibility for classification under complex response patterns.

Table 4
Integrated machine learning performance for Eberhart-Russell-based wheat genotype classification

Model or stage	Overall accuracy (%)	95% CI (%)	Cohen’s kappa	P-value
Baseline model comparison
SVM	45.45	16.75-76.62	0.33	0.035
KNN	36.36	10.93-69.21	0.23	0.123
RF	18.18	2.28-51.78	0.01	0.621
DT	27.27	6.02-60.97	0.14	0.322
ANN	9.09	0.23-41.28	−0.11	0.89
Stepwise SVM optimization
Baseline SVM	45.45	16.75-76.62	0.33	0.035
SVM + SMOTE	63.64	30.79-89.07	0.56	0.035
SVM + SMOTE + PCA	72.73	39.03-93.98	0.67	< 0.001
Optimized SVM	94.40	86.20-98.40	0.93	< 0.001
ER Class	Support	Precision (%)	F1-score (%)	Balanced accuracy (%)
Class-wise performance of optimized SVM
Class 1	18	100	100	100
Class 2	9	100	90	90
Class 3	12	90	92	98
Class 4	9	100	100	100
Class 5	12	90	92	98
Class 6	11	100	90	91

• CI = confidence interval; SVM = support vector machine; KNN = k-nearest neighbors; RF = random forest; DT = decision tree; ANN = artificial neural network; SMOTE = Synthetic Minority Over-sampling Technique; PCA = principal component analysis. Support indicates the number of samples in each ER class after SMOTE-based balancing.

Optimization and performance of the SVM model

Optimization markedly improved SVM performance. Class imbalance across ER stability classes was addressed using the Synthetic Minority Over-sampling Technique (SMOTE), resulting in a more balanced class distribution (Figure 1b). Principal component analysis (PCA) reduced data dimensionality by retaining components that explained 90% of the total variance, thereby minimizing redundancy and improving computational efficiency. Grid search identified the optimal SVM parameters as cost parameter (C) = 1.8 and kernel parameter γ = 0.015625 (Figure 1c). Model accuracy improved progressively from 45.45% in the baseline model to 63.64% after SMOTE and to 72.73% after PCA, reaching 94.40% after hyperparameter tuning, with a 95% confidence interval of 86.20-98.40% and κ = 0.93 (Table 4). These results showed strong agreement between optimized SVM predictions and the ER-based stability classes. The marked improvement in performance highlights the importance of combining class balancing, feature reduction, and parameter tuning when applying machine learning methods to complex biological datasets. However, the high predictive accuracy should be interpreted with some caution, as performance estimates may be influenced by dataset size, class structure, and preprocessing strategy. Even so, the observed gain is consistent with previous studies showing that class balancing, dimensionality reduction, and hyperparameter optimization can improve classification performance in challenging datasets (Chawla et al. 2002, Jolliffe 2002, Lin et al. 2003).

Class-wise evaluation further supported the effectiveness of the optimized model (Table 4). Precision and F1 scores were high for most stability classes, with slightly lower values for Classes 3 and 5, possibly due to greater heterogeneity and partial overlap in genotype responses within these groups. Agreement between SVM predictions and ER classifications ranged from 90% to 100%, indicating stable performance across classes. These results suggest that the optimized model was not only accurate overall, but also reliable in distinguishing among ER-based stability groups.

Comparison with previous studies and implications for wheat breeding

The strong performance of SVM in the present study agrees with its established ability to model nonlinear relationships and handle high-dimensional data, as described by Cortes and Vapnik (1995) and Vapnik (1999). Similar findings have been reported in plant science, where SVM has shown strong predictive performance in classification tasks involving complex biological datasets. For example, Sakeef et al. (2023) reported the usefulness of machine learning for plant genotype classification, while Khan et al. (2024) showed superior SVM performance in wheat genotype classification under nonlinear feature interactions. Zhao et al. (2020) further demonstrated the applicability of SVM in genomic prediction. The high accuracy obtained in the present study (94.40%) further indicates that SVM is well suited for modeling complex GEI patterns in multi-environment trials, where overlapping and nonlinear genotype responses are common. In contrast, the lower performance of DT and RF may be associated with diffuse class boundaries and heterogeneous response structures, whereas the weaker performance of ANN may reflect the relatively small dataset and the greater data requirements of neural network models for stable training (Kuhn and Johnson 2013). The integration of ER-based stability classification with machine learning provided a biologically interpretable and practically useful framework for genotype evaluation in wheat. Further validation using larger and more diverse multi-environment datasets would strengthen confidence in the robustness and wider relevance of this approach for wheat breeding.

CONCLUSION

This study combined mixed models, GGE biplot analysis, the ER stability method, and supervised machine learning algorithms to evaluate wheat genotypes across diverse environments. The results confirmed significant GEI, highlighting the importance of stability analysis for reliable genotype selection. Mixed-model and GGE biplot analyses provided complementary information on genotype performance and environmental discrimination, whereas ER parameters enabled classification of genotypes according to adaptability and stability.

Among the evaluated machine learning models, SVM showed the best performance. After optimization using SMOTE, PCA, and hyperparameter tuning, the SVM model achieved 94.4% accuracy and strong agreement with the ER-based stability classes. These findings indicate that machine learning can complement classical stability analysis for genotype classification under complex GEI conditions.

From a breeding perspective, this combined approach offers a practical and biologically interpretable means of identifying genotypes with desirable yield performance, stability, and adaptability across environments. Although the analysis was based on grain yield and a moderate dataset, the results support the potential usefulness of this approach in wheat breeding. Future studies should incorporate larger datasets, multi-trait information, genomic predictors, and independent validation to further strengthen its robustness and broader applicability.

Data Availability Statement

The datasets generated and/or analyzed in this study are available from the corresponding author upon reasonable request.

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Correspondence

* Email: [e-mail]

SCIENTIFIC EDITOR:

Luiz Antônio dos Santos Dias

Publication Dates

• Publication in this collection
  25 Sept 2026
• Date of issue
  2026

History

• Received
  03 Feb 2026
• Accepted
  04 May 2026
• Published
  11 June 2026