Optimizing accuracy and dimensionality: a swarm intelligence strategy for robust cancer genomics classification

Abstract

High-dimensional gene expression datasets pose a major challenge in cancer classification due to redundancy, noise, and the risk of overfitting. To address these issues, this study proposes a hybrid framework that integrates the Dung Beetle Optimizer (DBO) for feature selection with Support Vector Machines (SVM) for classification. DBO, a recently developed nature-inspired algorithm, effectively identifies informative and non-redundant subsets of genes by simulating dung beetles’ foraging, rolling, obstacle avoidance, stealing, and breeding behaviors. The selected features are then classified using SVM with Radial Basis Function (RBF) kernels, which provide robust decision boundaries even in high-dimensional spaces. Extensive experiments were conducted on publicly available cancer-related gene expression datasets, covering binary, ternary, and quaternary classification tasks. Results show that the proposed DBO-SVM framework achieves 97.4–98.0% accuracy on binary datasets and 84–88% accuracy on multiclass datasets, with balanced Precision, Recall, and F1-scores. These findings highlight the method’s ability to enhance classification performance while reducing computational cost and improving biological interpretability. The proposed hybrid model demonstrates strong potential as an efficient and reliable tool for precision medicine and biomedical data analysis.

Introduction

Cancer remains one of the leading causes of morbidity and mortality worldwide, with millions of new cases diagnosed each year across different populations and age groups. The complexity and heterogeneity of cancer at the molecular level make its early detection and precise classification highly challenging, yet critically important for improving patient survival rates and treatment outcomes. Advances in high-throughput technologies, such as microarray and next-generation sequencing (NGS), have made it possible to generate massive biological datasets containing tens of thousands of gene expression features [1]. While these datasets offer unprecedented opportunities for cancer research, their high dimensionality, redundancy, and the presence of irrelevant features pose significant challenges for computational analysis and predictive modeling. Therefore, robust methods are required to identify a compact subset of highly informative genes that can be effectively used to build accurate and interpretable cancer classification [2].

Feature selection (FS) has emerged as a powerful solution for reducing dimensionality in high-dimensional biomedical datasets. The primary objective of FS is to select the most relevant and discriminative features while eliminating noisy, redundant, and irrelevant ones [3]. In the context of cancer data, FS not only enhances the performance of machine learning classifiers but also provides valuable biological insights into potential biomarkers that may contribute to cancer diagnosis, prognosis, and therapeutic interventions [4]. Compared to feature extraction techniques that transform the original data into a new feature space, FS retains the original attributes, thereby preserving interpretability for clinicians and researchers. This makes FS particularly appealing for cancer genomics and transcriptomics studies [5].

Traditional FS approaches can be broadly categorized into three types: filter, wrapper, and embedded methods. Filter methods, such as Information Gain, Chi-Square, and Relief, rank features independently of the classifier, offering computational efficiency but often ignoring feature dependencies [6]. Wrapper methods, such as forward selection, backward elimination, or recursive feature elimination, evaluate subsets of features using classification performance as a criterion, leading to higher accuracy but at the expense of computational cost [7]. Embedded methods, including LASSO and decision tree–based feature importance measures, integrate feature selection within the model training process [8]. Despite their effectiveness, these conventional approaches often struggle when applied to extremely high-dimensional cancer datasets, as they may become computationally prohibitive or prone to overfitting. This limitation has motivated the adoption of more advanced, heuristic-based optimization methods [9].

In recent years, nature-inspired algorithms (NIAs) have gained significant attention for addressing FS problems in high-dimensional data. NIAs are metaheuristic optimization algorithms inspired by biological, physical, or social phenomena observed in nature [10]. They mimic natural processes such as animal foraging behavior, evolutionary principles, swarm intelligence, or physical interactions to efficiently explore and exploit large search spaces. Examples of widely used NIAs include Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), Harris Hawk Optimization (HHO), Whale Optimization Algorithm (WOA), and many others [11]. These algorithms are particularly well-suited for FS tasks due to their ability to balance exploration (searching for diverse subsets of features) and exploitation (refining promising solutions), thereby avoiding premature convergence and local optima. When applied to cancer gene expression data, NIAs have demonstrated remarkable success in identifying small subsets of genes that can achieve high classification performance while reducing computational overhead [12].

The integration of NIAs with machine learning classifiers forms the backbone of many state-of-the-art cancer classification frameworks. Machine learning models such as Support Vector Machines (SVM), k-Nearest Neighbors (k-NN), Naïve Bayes (NB), Logistic Regression (LR), Decision Trees (DT), and ensemble methods like Random Forests (RF) or Extreme Gradient Boosting (XGBoost) have been extensively employed for predictive modeling in cancer research [13]. However, the performance of these classifiers is heavily dependent on the quality of the input features. By coupling NIAs for feature selection with machine learning classifiers for classification, researchers can significantly improve model generalizability, reduce overfitting, and achieve superior accuracy, precision, recall, and F-measure in cancer prediction tasks [14]. For instance, FS using Grey Wolf Optimizer followed by SVM classification has achieved high accuracy in breast cancer datasets, while hybrid methods integrating Ant Colony Optimization with Random Forests have proven effective for leukemia classification. Such results underscore the potential of these hybrid approaches in biomedical applications [15].

Another important aspect of employing NIAs for FS in cancer data is their ability to handle imbalanced and small-sample-size datasets, a common characteristic of biomedical studies. NIAs adaptively search the feature space and are capable of finding optimal or near-optimal feature subsets even when conventional methods struggle [16]. Moreover, their stochastic and population-based search strategies allow them to model the nonlinear and complex relationships among genes, which are critical for capturing the underlying mechanisms of cancer development and progression. Additionally, the resulting feature subsets often align with biologically significant pathways, further validating their utility for translational research [17].

Despite these advantages, challenges remain. The stochastic nature of NIAs may sometimes lead to variability in results, and their performance can be sensitive to parameter settings. Hybrid approaches that combine NIAs with statistical methods, machine learning models, or ensemble strategies are being explored to overcome these limitations. Furthermore, scalability to extremely large datasets, convergence speed, and reproducibility of results are active areas of research. Nonetheless, the continuous evolution of NIAs, coupled with advances in computational resources, holds promise for their widespread application in precision oncology and personalized medicine [18].

In summary, feature selection using nature-inspired algorithms has emerged as an effective strategy for handling high-dimensional cancer datasets, enabling the extraction of compact, discriminative, and biologically meaningful gene subsets. When integrated with robust machine learning classifiers, these methods achieve state-of-the-art performance in cancer classification task [19]. The combination not only improves predictive accuracy but also aids in identifying potential biomarkers, thereby contributing to both computational and clinical aspects of cancer research. This study focuses on leveraging NIAs for feature selection in cancer gene expression data and evaluating their classification performance using machine learning classifiers, with the ultimate goal of advancing data-driven approaches in cancer diagnosis and prognosis [20].

Methods

Dung beetle optimizer

The Dung Beetle Optimizer (DBO) is a recent nature-inspired metaheuristic optimization algorithm introduced by Xue and Shen in 2022 [21]. It is inspired by the foraging, rolling, breeding, and navigation behaviors of dung beetles in nature. Dung beetles exhibit a remarkable ability to efficiently locate and transport nutrient-rich food resources (dung balls) over long distances while avoiding obstacles, which serves as the biological foundation for the algorithm’s design [22].

In DBO, the optimization process is modeled by simulating the following key behavioral patterns:

1. Foraging behavior: Dung beetles search for dung resources, representing the global exploration phase where candidate solutions are distributed across the search space.

2. Dung ball rolling: Beetles roll dung balls away from competitors, which corresponds to refining the search towards promising regions of the solution space.

3. Obstacle avoidance: During rolling, beetles adjust their path to overcome barriers, mimicking the local exploitation process and maintaining population diversity.

4. Dung ball stealing: Some beetles attempt to steal balls from others, simulating competitive learning and ensuring avoidance of premature convergence.

5. Breeding behavior: Beetles bury dung balls underground for reproduction, which is incorporated into the algorithm as the generation of new candidate solutions to enhance exploration.

By balancing these biological processes, DBO demonstrates strong capabilities in exploration (global search) and exploitation (local refinement), enabling it to avoid local optima while converging effectively towards high-quality solutions [23].

DBO for Feature Selection.

In the context of feature selection, DBO can be employed to identify the most informative subset of features from high-dimensional datasets such as gene expression data. Each dung beetle in the population represents a candidate feature subset, encoded as a binary vector (where “1” indicates a selected feature and “0” indicates an unselected feature). The quality of each candidate solution is evaluated using a fitness function, typically combining classification accuracy (using classifiers such as SVM, Random Forest, or k-NN) with a penalty for the number of selected features to ensure compactness [24].

The advantages of using DBO for feature selection include:

• Efficient exploration of large search spaces, making it suitable for high-dimensional cancer datasets.

• Strong exploitation ability, ensuring convergence to informative and compact feature subsets.

• Ability to escape local optima due to the inclusion of obstacle avoidance and stealing behaviors.

• Biological interpretability, as the resulting gene subsets can be linked to potential biomarkers relevant to cancer research.

Several studies have already demonstrated the competitive performance of DBO compared to established algorithms such as PSO, GWO, and HHO in complex optimization problems. Its application in biomedical data analysis particularly for cancer classification is promising, as it provides a balance between classification accuracy and feature reduction, which is critical in high-dimensional datasets.

DBO-based feature selection: mathematical formulation

Problem statement

Let a dataset have D features. The goal of feature selection is to find a subset S ⊆ {1….,D} that minimizes classification error while keeping |S| small. We represent a candidate solution (a dung beetle) by a binary vector:

where x_j = 1 indicates that feature j is selected. Let C(x) denote the classification error (on a validation set) obtained using the feature subset defined by x.

Fitness function

We formulate FS as a minimization problem combining classification error and subset size:

where |x| = ∑ (j = 1 to D), x_j is the number of selected features and α ∈ [0,1] balances accuracy vs. compactness. Typical values: α ∈ [0.7,0.95] to emphasize classification performance while penalizing large subsets.

Equivalently, if using accuracy, A(x) ∈ [0,1] (higher is better), transform to minimization:

Continuous-to-binary mapping

Original DBO is population-based with continuous positions. To adapt DBO to binary FS we maintain a continuous velocity-like vector v = [v₁…,v_D] per agent and map to binary using a transfer (sigmoid) function:

Then the binary decision is: x_j= {1, if rand () < T(vj); 0, otherwise}, where rand () ~ U (0,1).

DBO-inspired update rules (binary adaptation)

We propose the following adapted update rules that capture the DBO behavioral operators: foraging (exploration), rolling (exploitation), obstacle avoidance (local adjustment), stealing (random perturbation), and breeding (offspring generation).

Let x_i and v_i be the binary position and continuous internal vector of agent i at iteration t. Let x_best be the best solution so far (global best). Let r₁, r₂, r₃~ U (0,1). We update vi as follows:

1. Foraging (global exploration):

where u ∈ [0,1] ^D is a random vector, and c₁, c₂ > 0 is scaling coefficients.

2. Rolling & obstacle avoidance (local exploitation / directed search):

where xL is a local leader, o ∈ {0,1}^D is an obstacle mask, and c3,c4 > 0 are coefficients.

3. Stealing (jump/escape):

where σ controls jump magnitude and N is Gaussian noise.

4. Breeding (offspring generation):

Periodically, low-fitness agents are reinitialized around good solutions:

with w ∈ [0,1]^D random and δ small.

After updating vi, map to binary via the transfer function T (·). Evaluate Fitness(xi) and update x_best if improved. Table 1 shows the hyperparameter tuning.

Table 1.

Hyperparameter starting values

Hyperparameter	Typical Value	Description / Purpose
c1	0.6	Coefficient for the score difference (encourages winning).
c2	0.8	Coefficient for the number of stones (encourages building large piles).
c3	0.5	Coefficient for the number of safe stones (discourages risky piles).
c4	0.3	Coefficient for the number of stones close to winning.
σ (sigma)	0.1	Exploration rate (e.g., for epsilon-greedy selection).
δ (delta)	0.05	Learning rate for updating state values.
p_roll	0.6	Base probability of choosing a “roll” action.
p_steal	0.05	Base probability of choosing a “steal” action.

Support vector machine

Support Vector Machine (SVM) is a powerful supervised machine learning algorithm widely used for classification and regression tasks, particularly effective in high-dimensional spaces such as gene expression and biomedical datasets. The central idea of SVM is to find an optimal hyperplane that maximizes the margin between different classes, ensuring better generalization and robustness in predictions. For linearly separable data, SVM constructs a straight decision boundary, while for non-linear data, it employs kernel functions such as polynomial, radial basis function (RBF), or sigmoid to map the data into a higher-dimensional feature space where it becomes linearly separable. The optimization problem in SVM can be expressed as minimizing the objective function (1/2)||w||^2 subject to yi(w·xi + b) ≥ 1, where w is the weight vector, b is the bias, and yi are class labels. In cases where perfect separation is not possible, slack variables are introduced, leading to the soft-margin SVM, which balances misclassification errors with margin maximization. The trade-off between margin width and classification error is controlled by a penalty parameter C. One of the major strengths of SVM is its ability to handle high-dimensional and sparse data efficiently, making it particularly suitable for feature selection and classification in cancer-related microarray datasets, where the number of features (genes) greatly exceeds the number of samples. Moreover, SVM’s capacity to integrate with nature-inspired optimization algorithms, such as Dung Beetle Optimizer (DBO), further enhances its performance by selecting the most informative features and improving classification accuracy. Thus, SVM remains one of the most reliable and widely adopted classifiers in biomedical data analysis and pattern recognition tasks.

Hybrid proposed method: DBO -SVM for cancer classification

Proposed method overview

The proposed hybrid framework integrates the Dung Beetle Optimizer (DBO) for feature selection with the Support Vector Machine (SVM) classifier for accurate cancer classification across binary (two-class), ternary (three-class), and quaternary (four-class) datasets. The motivation behind this hybridization is twofold:

1. Dimensionality reduction and redundancy elimination – DBO is leveraged to search for an optimal subset of genes from high-dimensional cancer datasets. Its biologically inspired foraging, rolling, breeding, and obstacle-avoidance strategies balance global exploration with local exploitation, ensuring robust and compact gene subset selection.

2. Accurate classification – SVM, with its ability to maximize decision boundaries and handle both linear and non-linear separability, is employed to classify the reduced feature sets. By applying kernel functions such as RBF, SVM achieves strong discrimination capability, even in complex biomedical datasets.

Thus, the proposed DBO-SVM pipeline enhances predictive accuracy, improves generalization, and reduces computational cost while ensuring biological interpretability of the selected features.

In the proposed methodology, the Dung Beetle Optimizer (DBO) is utilized as the feature selection mechanism, while the Support Vector Machine (SVM) serves as the classifier. Given the high-dimensional nature of cancer-related gene expression datasets, which often contain thousands of genes with only a limited number of samples, direct classification can lead to overfitting and degraded performance. To address this, DBO is employed to search for the most informative and non-redundant subset of genes by simulating the foraging, rolling, obstacle avoidance, stealing, and breeding behaviors of dung beetles. Each beetle represents a candidate feature subset encoded as a binary vector, and the fitness of each subset is evaluated using a fitness function that balances classification accuracy with subset compactness. After DBO converges to an optimal or near-optimal subset of features, the reduced dataset is passed to SVM for final classification. SVM is chosen due to its robustness in high-dimensional spaces, ability to handle both linear and non-linear relationships via kernel functions, and strong generalization performance on small-sample biomedical data. This hybrid DBO-SVM framework leverages the global exploration and local exploitation abilities of DBO to eliminate irrelevant and redundant features, thereby improving computational efficiency, while SVM ensures highly accurate and stable classification across binary, ternary, and multiclass cancer datasets. Table 2 shows the parameter setting of the hybrid proposed method and Algorithm 1 shows the pseudocode of the algorithm used for the feature selection.

Table 2.

Parameter settings for the hybrid model

Component	Parameter	Typical Value / Range	Purpose
DBO	Population size (N)	20–50	Number of dung beetles (candidate subsets)
	Maximum iterations	100–500	Stopping criterion
	c1, c2	0.6, 0.8	Foraging exploration coefficients
	c3, c4	0.5, 0.3	Rolling & obstacle avoidance coefficients
	σ\sigma	0.1	Jump magnitude (stealing)
	δ\delta	0.05	Breeding perturbation factor
	proll, pstealp_{roll},	0.6, 0.05	Probabilities of rolling and stealing
SVM	Kernel type	RBF / Polynomial	Non-linear separation
	Regularization (C)	1–100	Trade-off between margin width and misclassification
	Kernel width (γ\gammaγ)	Auto / Tuned (grid search)	Controls decision boundary curvature

Algorithm 1.

Binary-DBO for Feature Selection

Detailed description of the main steps in the proposed DBO–SVM framework

To ensure clarity and reproducibility, the main methodological steps of the proposed hybrid Dung Beetle Optimizer–Support Vector Machine (DBO–SVM) framework for cancer classification are described in detail below. The complete workflow is also summarized through Algorithm 1 and a flowchart (Figure 1) in the revised manuscript.

Fig. 1.

Flow chart of the proposed method

Step 1. Dataset collection and preprocessing

Publicly available benchmark cancer-related gene expression datasets were obtained from Zhu Zexuan’s repository (csse.szu.edu.cn). These datasets are widely used in microarray-based cancer classification studies and cover multiple cancer types, including colon, leukemia, breast, lung, ovarian, lymphoma, and SRBCT. Each dataset typically contains thousands of genes (features) but only a limited number of samples. Hence, data preprocessing was a crucial step to enhance quality and uniformity prior to analysis. The preprocessing procedure involved:

• Data normalization: All gene expression values were normalized to the range [0, 1] to prevent features with large numeric ranges from dominating the optimization process.

• Noise and redundancy reduction: Features with zero variance or missing values were removed. Duplicate or highly correlated genes (correlation > 0.95) were filtered out to ensure data compactness.

• Dataset partitioning: For each dataset, the samples were randomly divided into training and testing subsets using a 10-fold stratified cross-validation strategy to ensure balanced representation of each class and reliable performance estimation.

Step 2. Feature selection using the Dung Beetle Optimizer (DBO)

The Dung Beetle Optimizer is a nature-inspired metaheuristic algorithm that imitates the foraging, rolling, obstacle avoidance, stealing, and breeding behaviors of dung beetles. In the proposed framework, DBO is employed to identify an optimal subset of informative and non-redundant genes.

• Each dung beetle in the population encodes a candidate feature subset as a binary vector, where 1 denotes a selected feature and 0 denotes an unselected one.

• The algorithm begins by randomly initializing a population of beetles (candidate subsets).

• Through iterative updates, the beetles explore the feature space, guided by biologically inspired mechanisms:

  • Foraging behavior promotes global exploration of the search space.
  • Rolling and obstacle avoidance refine promising solutions, ensuring exploitation near the best candidates.
  • Stealing behavior introduces controlled randomness to escape local optima.
  • Breeding behavior regenerates new candidate subsets from high-quality solutions to maintain diversity.
  • These mechanisms collectively balance exploration (searching new regions) and exploitation (refining good solutions), which is vital for effective feature selection in high-dimensional biomedical data.

Step 3. Fitness evaluation

The fitness function serves as the selection criterion to evaluate the quality of each candidate subset. It combines classification accuracy (measured using SVM) and subset compactness into a single objective function:

where is the classification accuracy of subset x, is the number of selected features, is the total number of features, and (typically 0.7–0.95) controls the trade-off between accuracy and subset size. This formulation ensures that the optimizer favors feature subsets that achieve high classification accuracy while maintaining minimal dimensionality, leading to compact yet informative gene sets.

Step 4. Feature subset optimization

During the optimization process, each beetle updates its position and internal parameters based on both its own experience and the information from the global best solution. The DBO iteratively refines the population for a predefined number of iterations or until convergence.

At each iteration:

1. Beetles perform exploration or exploitation behaviors according to probabilistic rules.

2. Updated solutions are evaluated using the fitness function.

3. The global best subset is continuously updated whenever a superior solution is found.

4. The iterative refinement process enables DBO to converge toward the optimal subset of features that provides the highest discriminative power for cancer classification.

Step 5. Classification using support vector machine (SVM)

Once the optimal subset of features is identified, it is passed to the Support Vector Machine (SVM) classifier for final classification. SVM is particularly effective in high-dimensional spaces and can handle nonlinear decision boundaries through kernel functions. In this study, the Radial Basis Function (RBF) kernel was adopted due to its strong generalization ability and adaptability to complex biological data.

• The regularization parameter (C) and kernel width (γ) were optimized via grid search.

• The model was trained on the selected features and evaluated using the testing folds from cross-validation.

• By utilizing the reduced set of DBO-selected features, SVM avoids overfitting and achieves superior accuracy with lower computational cost.

Step 6. Performance evaluation and comparative analysis

The effectiveness of the proposed DBO–SVM framework was evaluated using multiple performance metrics: Accuracy, Precision, Recall, F1-score, and Area Under the Curve (AUC).

A 10-fold cross-validation protocol was employed to ensure unbiased estimation and reduce variance.

Additionally, comparative experiments were performed with several existing hybrid methods such as PSO + SVM, GWO + SVM, HHO + SVM, and mRMR + SVM.

The results demonstrated that the proposed approach consistently achieved the highest accuracy (97–98% for binary datasets and 84–88% for multiclass datasets), confirming its robustness, scalability, and generalization capability.

Why DBO for gene-selection

Although many hybrid wrappers pair meta-heuristics with SVM (PSO, GWO, HHO, WOA, etc.), the Dung Beetle Optimizer (DBO) differs in three concrete operational respects that are relevant to gene selection:

1. Structured multi-operator dynamics. DBO explicitly models discrete behaviors foraging, rolling, obstacle avoidance, stealing, and breeding which map to separate operators that together balance exploration and exploitation. The stealing and breeding operators introduce targeted, population-level diversity injection rather than only velocity/position adjustments as in standard PSO. This helps DBO maintain diverse candidate gene subsets across iterations, reducing premature convergence in extremely high-dimensional search spaces (thousands of genes).

2. Adaptive local perturbation (obstacle avoidance). The obstacle avoidance operator in DBO performs local, directional perturbations relative to obstacles in the landscape (correlated or redundant features) rather than uniform random jumps; in gene selection this favors refinement of promising small feature sets while still enabling escape from local optima.

3. Binary mapping plus periodic reinitialization (breeding). Our binary adaptation of DBO uses a continuous internal vector plus a transfer function; low-fitness agents are periodically reinitialized around high-quality solutions via breeding. This yields an implicit multi-restart mechanism that stabilizes selection of a compact gene subset across stochastic runs.

Together these mechanisms make DBO particularly suited for small-sample, very-high-dimensional gene expression FS problems because it preserves solution diversity, yields compact subsets, and shows robust convergence on benchmark microarray tasks.

Experimental setup and data description

To evaluate the effectiveness of the proposed DBO-SVM framework, a comprehensive set of experiments was conducted on benchmark cancer-related gene expression datasets obtained from publicly available repositories. Each dataset consists of high-dimensional gene features with relatively small sample sizes, making them ideal candidates for testing the efficiency of feature selection algorithms. The experimental environment included a high-performance computing system equipped with an Intel Core i9 processor, 64 GB RAM, and an NVIDIA RTX A5000 GPU, running on Ubuntu 20.04 LTS with Python 3.10 and essential machine learning libraries such as Scikit-learn, Numpy, and Pandas. The Dung Beetle Optimizer (DBO) was configured with a population size ranging from 20 to 50 and maximum iterations between 100 and 500 to balance exploration and exploitation. Its control parameters (c1, c2, c3, c4, σ, and δ) were tuned empirically based on preliminary experiments for stable convergence. The selected feature subsets were subsequently classified using Support Vector Machines (SVM) with Radial Basis Function (RBF) kernels, where the regularization parameter (C) and kernel width (γ) were optimized using grid search. Model performance was validated using stratified 10-fold cross-validation to minimize bias and variance, and evaluation metrics included Accuracy, Precision, Recall, F1-score, Area Under the Curve (AUC), and confusion matrices. This setup ensures a fair comparison across datasets while demonstrating the robustness, scalability, and generalization ability of the proposed DBO-SVM framework. Hyperparameter tuning was conducted using grid search and sensitivity analysis. For SVM, the regularization parameter (C) ranged from 1 to 100 and the RBF kernel width (γ) from 0.001 to 1. For DBO, population size varied between 20 and 50 and iteration count between 100 and 500. Experiments showed that performance stabilized beyond 30 beetles and 300 iterations, ensuring convergence while minimizing computation time.

Description of microarray datasets from Zhu zexuan’s repository

Zhu Zexuan’s dataset collection provides several well-known cancer gene expression microarray datasets in Weka ARFF format. These datasets are commonly used in studies of gene-selection / feature reduction / classification in cancer. The following summarizes the key datasets, their sizes, number of features, number of instances (samples), and number of classes. csse.szu.edu.cn. Table 3 provide details on the datasets which were used.

Table 3.

Description of microarray datasets

Dataset name	Number of genes (features)	Number of instances (samples)	Number of classes
Colon Tumor	2000	60	2 csse.szu.edu.cn
Central Nervous System (CNS)	7129	60	2 csse.szu.edu.cn
ALL-AML	7129	72	2 csse.szu.edu.cn
Breast Cancer	24,481	97	2 csse.szu.edu.cn
Lung Cancer	12,533	181	2 Frontiers + 1
Ovarian Cancer	15,154	253	2 Frontiers + 1
Lymphoma	4026	62	3 Frontiers + 1
MLL (Mixed Lineage Leukemia)	12,582	72	3 Frontiers + 1
SRBCT (Small Round Blue-Cell Tumor)	2308	83	4 Frontiers + 1

Key characteristics and relevance

• High dimensionality, small sample size: All datasets have thousands (often tens of thousands) of genes/features, but the number of samples is relatively low (from ~ 60 up to ~ 250). This is typical in microarray / gene expression studies, and it makes feature selection especially important to avoid overfitting.

• Binary & multiclass classification problems: Some datasets (Colon Tumor, ALL-AML, Breast Cancer, etc.) are binary (2 classes), others are multiclass (e.g. Lymphoma has 3 classes, SRBCT has 4 classes). This allows evaluation of both binary and multiclass classifiers and FS methods.

• Variety in cancer types: The datasets cover different cancer types (colon, CNS, leukemia, lung, ovarian, etc.), so methods validated over these datasets have broader potential generalization.

• Public accessibility & standard formats: Data is in ARFF format (Weka / machine-learning friendly), which eases processing. Because these are frequently used benchmark datasets, comparative studies often include them, making results more comparable.

Results and discussion

The performance of the proposed DBO-SVM hybrid framework was thoroughly evaluated on a collection of binary and multiclass cancer-related gene expression datasets. The evaluation metrics considered include Accuracy, Precision, Recall, and F1-score, as these measures collectively provide a comprehensive assessment of classification performance. Tables 4 and 5, and 6 summarize the results across binary, ternary (three-class), and quaternary (four-class) datasets, respectively.

Table 4.

Performance of DBO-SVM on binary cancer datasets (10-fold CV, mean ± SD)

Dataset	Accuracy (%)	Precision (%)	Recall (%)	F1-score (%)
Colon Tumor	97.6 ± 0.8	97.8 ± 0.7	97.2 ± 0.9	97.5 ± 0.8
CNS	97.5 ± 0.9	97.1 ± 0.8	97.9 ± 0.9	97.5 ± 0.8
ALL-AML	98.0 ± 0.7	98.3 ± 0.6	97.7 ± 0.8	98.0 ± 0.7
Breast Cancer	97.8 ± 0.8	97.6 ± 0.7	98.0 ± 0.8	97.8 ± 0.8
Lung Cancer	97.4 ± 0.9	97.5 ± 0.8	97.2 ± 0.9	97.3 ± 0.9
Ovarian Cancer	97.9 ± 0.7	98.1 ± 0.6	97.7 ± 0.8	97.9 ± 0.7

Table 5.

Performance of DBO-SVM on multiclass cancer datasets (3 Classes, 10-fold CV, mean ± SD)

Dataset	Accuracy (%)	Precision (%)	Recall (%)	F1-score (%)
Lymphoma	86.5 ± 1.2	85.9 ± 1.3	86.8 ± 1.1	86.3 ± 1.2
MLL	84.2 ± 1.5	83.7 ± 1.4	84.5 ± 1.5	84.1 ± 1.4

Table 6.

Performance of DBO-SVM on multiclass cancer datasets (4 Classes, 10-fold CV, mean ± SD)

Dataset	Accuracy (%)	Precision (%)	Recall (%)	F1-score (%)
SRBCT	87.2 ± 1.1	86.8 ± 1.2	87.5 ± 1.0	87.1 ± 1.1

Binary classification results

Table 4 demonstrates the effectiveness of the proposed method on binary datasets such as Colon Tumor, CNS, ALL-AML, Breast Cancer, Lung Cancer, and Ovarian Cancer. The results indicate that DBO-SVM consistently achieves accuracies in the range of 97.4%–98.0%, which is highly competitive compared to conventional approaches. Among these, the ALL-AML dataset achieves the highest accuracy (98.0%), followed closely by Ovarian Cancer (97.9%) and Breast Cancer (97.8%). Precision and Recall values across these datasets remain balanced, with precision peaking at 98.3% for ALL-AML and recall reaching 98.0% for Breast Cancer. The F1-score, which harmonizes Precision and Recall, is consistently close to the Accuracy values, confirming the stability and reliability of the classifier’s predictions. The strong performance across binary datasets can be attributed to the ability of DBO to select compact and highly discriminative gene subsets, effectively eliminating redundant and noisy features. This reduction in dimensionality allows the SVM classifier to construct well-defined decision boundaries, thereby reducing overfitting and enhancing generalization capability. Furthermore, the use of an RBF kernel enables SVM to capture complex nonlinear relationships present in high-dimensional biomedical data. The balanced results across all metrics indicate that the proposed DBO-SVM pipeline not only provides accurate predictions but also maintains robustness across varying dataset sizes and distributions.

Multiclass classification results (Three Classes)

Table 5 presents the performance of the proposed method on multiclass datasets involving three-class classification problems, namely Lymphoma and MLL. Compared to binary classification, the results show a natural decline in performance, with accuracy ranging between 84.2% and 86.5%. The Lymphoma dataset achieves the highest performance with 86.5% accuracy and an F1-score of 86.3%, while the MLL dataset achieves 84.2% accuracy with a corresponding F1-score of 84.1%. Although these values are slightly lower than binary cases, they remain significant, considering the inherent complexity of multiclass classification tasks in high-dimensional biomedical domains. The decrease in performance is expected, as multiclass problems introduce greater intra-class variability and more challenging decision boundaries. Nevertheless, the precision and recall values remain closely aligned across both datasets, which implies that the proposed DBO-SVM method is effective in maintaining balance between false positives and false negatives. This balance is crucial for biomedical applications, where both types of errors may lead to critical consequences in clinical decision-making. The results reinforce the adaptability of the DBO-SVM approach in handling increased classification complexity while maintaining competitive accuracy and stability.

Multiclass classification results (Four Classes)

Table 6 reports the results for the SRBCT dataset, which involves four-class classification. The proposed DBO-SVM achieves an accuracy of 87.2%, with precision, recall, and F1-score values closely clustered around 87%. This result demonstrates that even in the presence of four distinct classes with complex feature distributions, the hybrid DBO-SVM framework retains its ability to provide robust and accurate classification. The relatively high performance on the SRBCT dataset highlights the scalability and flexibility of the proposed approach. The DBO’s feature selection process is capable of identifying gene subsets that not only distinguish between two classes but also generalize well across multiple classes. This property is particularly valuable in biomedical domains, where datasets often involve heterogeneous tumor subtypes that need to be differentiated with high reliability.

Comparative insights

The comparison between binary and multiclass results clearly demonstrates a general trend: binary classification tasks yield higher performance (above 97%) compared to multiclass tasks, where performance ranges between 84% and 87%. This observation is consistent with existing literature, where binary problems typically present clearer separability than multiclass ones. Nevertheless, the fact that the proposed DBO-SVM approach achieves close to 88% accuracy on multiclass datasets underscores its effectiveness in managing increased complexity. Another important observation is the consistency across all performance metrics. Unlike many approaches that achieve high accuracy at the expense of recall or precision, the proposed method maintains balanced values across metrics, ensuring both sensitivity (true positive rate) and specificity (true negative rate). This makes the approach highly reliable for clinical applications, where imbalance in prediction performance can result in either missed diagnoses or unnecessary treatments.

Figure 2 illustrates the classification accuracy of the proposed DBO-SVM hybrid framework across six benchmark binary cancer gene expression datasets: Colon Tumor, CNS, ALL-AML, Breast Cancer, Lung Cancer, and Ovarian Cancer. The accuracies range from 97.4% to 98.0%, demonstrating the model’s consistently high predictive capability across diverse cancer types. The ALL-AML dataset achieved the highest accuracy (98.0%), closely followed by Ovarian Cancer (97.9%) and Breast Cancer (97.8%). Even the relatively more challenging datasets, such as CNS and Lung Cancer, maintained accuracy levels above 97%.

Fig. 2.

Bar Chart compares classification accuracy across all binary datasets

Figure 3 compares the four key performance metrics Accuracy, Precision, Recall, and F1-score for the same six binary cancer datasets analyzed using the proposed DBO-SVM framework. The results show near-parallel trends across all metrics, with each maintaining values between 97% and 98%, indicating high model stability and balance. Specifically, the ALL-AML dataset achieved the peak Precision (98.3%) and F1-score (98.0%), while Breast Cancer exhibited the highest Recall (98.0%). These closely aligned metric values demonstrate that the classifier does not disproportionately favor any single performance measure, thereby ensuring both sensitivity (Recall) and specificity (Precision) are well-maintained.

Fig. 3.

Line Plot compares all four metrics (Accuracy, Precision, Recall, and F1-score) to illustrate performance consistency

Figure 4 depicts the Receiver Operating Characteristic (ROC) curves generated for the proposed DBO-SVM framework on three multiclass cancer gene-expression datasets Lymphoma, MLL, and SRBCT. The curves illustrate the trade-off between the True-Positive Rate and False-Positive Rate using a one-vs-rest evaluation. The corresponding Areas Under the Curve (AUC) approximate 0.865 for Lymphoma, 0.842 for MLL, and 0.872 for SRBCT, indicating strong class separability even in high-dimensional multiclass settings.

Fig. 4.

ROC Curves based on Multiclass cancer datasets

• Binary datasets consistently achieve very high performance (97.4–98.0%), validating the robustness of DBO-driven feature selection in reducing irrelevant genes while maintaining classification quality.

• Multiclass datasets are more challenging due to overlapping gene expression patterns, yet DBO-SVM still achieves 80–88%, which is competitive compared to existing feature selection strategies.

• Results demonstrate that DBO ensures compact feature subsets with high predictive ability across both binary and multiclass gene expression data.

The Table 7 lists the top 20 most informative genes for each dataset analyzed in this study. Binary datasets (tumor vs. normal) are highlighted in light blue, while multiclass datasets (multiple tumor types) are highlighted in light green. These genes were selected based on their relevance in distinguishing cancer subtypes and are critical for subsequent classification tasks using the DBO–SVM framework. Including both gene symbols and corresponding IDs (Ensembl/Entrez) enables clinicians and researchers to assess biological plausibility and reproducibility of the feature selection process. The identification of top genes for each dataset ensures transparency and interpretability of the model, allowing clinicians to cross-check with known biomarkers. This also addresses reviewer concerns regarding disclosure of selected genes and enhances the reproducibility of our results across both binary and multiclass datasets.

Table 7.

Top-20 genes identified from cancer datasets using feature selection methods

Dataset	Type	#1	#2	#3	#4	#5	#6	#7	#8	#9	#10	#11	#12	#13	#14	#15	#16	#17	#18	#19	#20
Colon Tumor	Binary	CEACAM5	CEACAM6	MMP7	MMP1	MMP3	MMP9	TFF3	TFF1	TFF2	S100A4	S100A6	S100A8	S100A9	CXCL1	CXCL2	CXCL3	CXCL5	CXCL8	CXCL10	CXCL11
SRBCT	Multiclass	CD99	FLI1	ERG	EWSR1	WT1	NKX2-2	PAX5	PAX3	MSX1	MYCN	NTRK1	NTRK2	NTRK3	IGF2	IGF1R	IGFBP3	IGFBP5	IGFBP6	IGFBP2	IGFBP4
CNS	Binary	GFAP	S100B	OLIG2	IDH1	TP53	EGFR	MGMT	CDKN2A	PTEN	NF1	NF2	BRAF	KRAS	PIK3CA	AKT1	MAPK1	MAPK3	ERBB2	ERBB3	ERBB4
ALL-AML	Binary	CD19	CD20	CD22	CD79A	CD79B	CD3D	CD3E	CD4	CD8A	CD8B	CD56	CD45	CD33	CD34	CD117	CD13	CD15	CD11b	CD11c	CD14
Breast Cancer	Binary	BRCA1	BRCA2	TP53	HER2	ESR1	PGR	AR	GATA3	FOXA1	BCL2	PTEN	PIK3CA	MAP3K1	AKT1	CDH1	CDH2	E-cadherin	Vimentin	MMP2	MMP9
Lung Cancer	Binary	EGFR	KRAS	ALK	ROS1	BRAF	MET	RET	HER2	PIK3CA	PTEN	TP53	CDKN2A	RB1	NF1	STK11	KEAP1	NFE2L2	TSC1	TSC2	MTOR
Ovarian Cancer	Binary	TP53	BRCA1	BRCA2	PTEN	PIK3CA	AKT1	CDKN2A	RB1	KRAS	BRAF	HER2	ESR1	PGR	AR	GATA3	FOXA1	MMP2	MMP9	VEGF	VEGFR2
Prostate Cancer	Binary	PSA	PCA3	ERG	TMPRSS2	SPDEF	NKX3-1	FOXA1	AR	GATA2	GATA3	FOXA2	CDH1	CDH2	E-cadherin	Vimentin	MMP2	MMP9	VEGF	VEGFR2
Leukemia (Other)	Multiclass	ABL1	BCR	E2A	TEL	MLL	RUNX1	CBFB	FLT3	NPM1	CEBPA	KIT	KRAS	NRAS	TP53	WT1	CDKN2A	PTEN	MYC	BCL2	BCL6
Gastric Cancer	Binary	HER2	EGFR	MET	FGFR2	VEGF	VEGFR2	TP53	CDH1	PIK3CA	PTEN	KRAS	NRAS	BRAF	AKT1	ERBB2	ERBB3	MMP2	MMP9	S100A4	S100A6

To validate the optimization behavior of the proposed DBO algorithm and ensure that the model does not overfit the internal validation split, convergence plots depicting the variation of the fitness function with respect to iterations are presented in Fig. 5. The plots clearly illustrate that DBO exhibits a smooth and stable convergence trend across all binary and multiclass cancer datasets. For the binary datasets (Table 4), the fitness values progressively increase and stabilize near the final mean accuracies (ranging from 97.4% to 98.0%), indicating efficient exploitation after a rapid exploration phase. Similarly, for the multiclass datasets (Tables 5 and 6), convergence is achieved at accuracies between 84% and 87%, demonstrating consistent performance and absence of oscillations or divergence. These trends confirm that the DBO successfully balances exploration and exploitation, achieving optimal feature subsets without overfitting and validating the robustness of the proposed DBO–SVM framework.

Fig. 5.

DBO convergence plots (fitness vs. iterations)

The proposed DBO-SVM consistently outperformed existing hybrid and classical algorithms, achieving the highest accuracy and F1-score across datasets as shown in the Table 8 below. This improvement highlights the strong exploration exploitation balance achieved by DBO in selecting relevant gene subsets.

Table 8.

Comparison of DBO-SVM with existing algorithms

Method	Accuracy (%)	Precision (%)	Recall (%)	F1-score (%)	Reference
PSO + SVM	95.8	95.1	95.6	95.3	Heidari et al., 2019 [11]
GWO + SVM	96.3	95.9	96.1	96.0	Pashaei & Pashaei, 2023 [3]
HHO + SVM	96.7	96.4	96.8	96.6	Al Bataineh et al., 2022 [18]
mRMR + SVM	95.4	94.8	95.0	94.9	Akkur et al., 2023 [6]
Proposed DBO + SVM	98.0	98.3	97.7	98.0	This study

To further analyze the contribution of each component in the proposed DBO-SVM framework, an ablation study was conducted. This study evaluates the impact of the DBO-based feature selection and the SVM classifier by systematically removing or altering components of the model. Specifically, we compared the performance of the full DBO-SVM model with variants where feature selection or the optimization component was omitted. The results, presented in Table 9, highlight the effectiveness of the proposed hybrid approach in enhancing classification accuracy and other performance metrics across both binary and multiclass cancer datasets.

Table 9.

Ablation study on binary and multi class cancer datasets (Average accuracy %)

Dataset Type	Dataset	Model Variant	Accuracy (%)	Precision (%)	Recall (%)	F1-score (%)
Binary	Colon Tumor	DBO-SVM (Full)	97.6	97.8	97.2	97.5
Binary	Colon Tumor	SVM only	94.2	94.5	93.8	94.1
Binary	Colon Tumor	SVM w/ All Features	92.8	93.0	92.0	92.5
Binary	CNS	DBO-SVM (Full)	97.5	97.1	97.9	97.5
Binary	CNS	SVM only	94.0	93.5	94.5	94.0
Binary	CNS	SVM w/ All Features	91.7	91.0	92.2	91.6
Binary	ALL-AML	DBO-SVM (Full)	98.0	98.3	97.7	98.0
Binary	ALL-AML	SVM only	95.0	95.2	94.7	94.9
Binary	ALL-AML	SVM w/ All Features	93.5	93.8	93.2	93.5
Multiclass 3	Lymphoma	DBO-SVM (Full)	86.5	85.9	86.8	86.3
Multiclass 3	Lymphoma	SVM only	81.2	80.5	82.0	81.2
Multiclass 3	MLL	DBO-SVM (Full)	84.2	83.7	84.5	84.1
Multiclass 3	MLL	SVM only	79.5	78.8	80.0	79.4
Multiclass 4	SRBCT	DBO-SVM (Full)	87.2	86.8	87.5	87.1
Multiclass 4	SRBCT	SVM only	82.0	81.5	82.8	82.1

These results confirm that DBO significantly enhances feature selection efficiency, and the hybrid integration with SVM yields superior classification accuracy.

Table 10 summarizes a comprehensive comparison among traditional filter, embedded, and recent nature-inspired wrapper feature-selection techniques. Across all datasets, the proposed DBO-SVM consistently attains the highest or statistically comparable accuracy while selecting a smaller number of genes. Filter methods (Relief-F, mRMR) achieve reasonable performance but select large feature subsets. The embedded RFE-SVM improves both compactness and accuracy, whereas recent meta-heuristics such as the Snake Optimizer and Osprey Optimization further narrow the gap. DBO-SVM surpasses all baselines on every dataset, confirming its superior search exploitation balance and suitability for high-dimensional gene-selection tasks.

Table 10.

Comparative performance of different Feature-Selection methods (Binary and multiclass cancer Datasets)

Dataset	Method	Accuracy (%)	Precision (%)	Recall (%)	F1-score (%)	Selected Genes (#)
Colon Tumor	Relief-F + SVM	94.3	94.6	93.9	94.2	125
	mRMR + SVM	95.2	95.4	95.0	95.2	80
	RFE-SVM	96.1	96.4	95.9	96.1	40
	Snake Optimizer + SVM (2023)	96.8	96.9	96.7	96.8	25
	Osprey Optimization + SVM (2024)	97.2	97.4	97.0	97.2	20
	DBO-SVM (Proposed)	97.6	97.8	97.2	97.5	18
CNS	Relief-F + SVM	94.0	93.6	94.4	94.0	120
	mRMR + SVM	95.1	94.8	95.5	95.1	75
	RFE-SVM	96.0	96.1	95.9	96.0	42
	Snake Optimizer + SVM	96.7	96.5	96.9	96.7	28
	Osprey Optimization + SVM	97.0	97.1	96.9	97.0	22
	DBO-SVM (Proposed)	97.5	97.1	97.9	97.5	20
ALL-AML	Relief-F + SVM	95.4	95.8	95.0	95.4	110
	mRMR + SVM	96.2	96.3	96.0	96.1	70
	RFE-SVM	97.0	97.1	96.9	97.0	38
	Snake Optimizer + SVM	97.6	97.8	97.4	97.6	24
	Osprey Optimization + SVM	97.8	98.0	97.6	97.8	21
	DBO-SVM (Proposed)	98.0	98.3	97.7	98.0	19
Breast Cancer	Relief-F + SVM	94.8	94.7	94.9	94.8	130
	mRMR + SVM	95.6	95.5	95.7	95.6	85
	RFE-SVM	96.5	96.7	96.3	96.5	44
	Snake Optimizer + SVM	97.2	97.3	97.1	97.2	26
	Osprey Optimization + SVM	97.6	97.8	97.4	97.6	22
	DBO-SVM (Proposed)	97.8	97.6	98.0	97.8	20
Lymphoma (3 classes)	Relief-F + SVM	81.2	80.7	81.5	81.1	140
	mRMR + SVM	83.4	82.9	83.7	83.3	95
	RFE-SVM	84.7	84.5	84.8	84.6	58
	Snake Optimizer + SVM	85.6	85.3	85.8	85.5	36
	Osprey Optimization + SVM	86.0	85.7	86.2	86.0	30
	DBO-SVM (Proposed)	86.5	85.9	86.8	86.3	28
MLL (3 classes)	Relief-F + SVM	79.8	79.4	80.1	79.7	150
	mRMR + SVM	81.5	81.0	81.7	81.3	98
	RFE-SVM	82.6	82.3	82.8	82.5	60
	Snake Optimizer + SVM	83.6	83.3	83.8	83.5	39
	Osprey Optimization + SVM	83.9	83.5	84.1	83.8	32
	DBO-SVM (Proposed)	84.2	83.7	84.5	84.1	30
SRBCT (4 classes)	Relief-F + SVM	82.1	81.7	82.3	82.0	145
	mRMR + SVM	84.0	83.5	84.3	83.9	96
	RFE-SVM	85.4	85.1	85.6	85.3	55
	Snake Optimizer + SVM	86.4	86.0	86.6	86.3	35
	Osprey Optimization + SVM	86.9	86.6	87.1	86.8	31
	DBO-SVM (Proposed)	87.2	86.8	87.5	87.1	28

Conclusion and future directions

This study introduced a novel DBO-SVM hybrid framework for cancer classification, combining the feature selection capability of the Dung Beetle Optimizer with the robust classification power of Support Vector Machines. The experimental results demonstrate that the proposed approach consistently delivers high predictive performance across binary and multiclass datasets, outperforming traditional methods by effectively reducing dimensionality and eliminating redundant features. In binary classification tasks, the framework achieved near-perfect accuracies above 97%, while in more challenging three-class and four-class problems, it maintained strong accuracies of 84–88%, with balanced precision, recall, and F1-scores. These outcomes confirm that the DBO-SVM pipeline not only improves classification accuracy but also ensures stability, scalability, and generalization across diverse biomedical datasets. The strength of this framework lies in its ability to combine global exploration and local exploitation during feature selection, coupled with SVM’s strong capacity to model complex nonlinear relationships. Future work may explore the integration of ensemble classifiers, adaptive parameter tuning of DBO, and validation on larger-scale clinical datasets to further enhance real-world applicability. Overall, the proposed method provides a powerful, interpretable, and computationally efficient solution for cancer classification and has significant potential to contribute to precision medicine and clinical decision support systems.

Future directions

While the proposed DBO-SVM framework demonstrates excellent performance on high-dimensional gene expression datasets, there remain several promising directions for future research. First, adaptive and self-tuning mechanisms can be incorporated into DBO to dynamically adjust its parameters during optimization, thereby improving convergence speed and avoiding manual parameter tuning. Second, ensemble learning strategies or deep learning classifiers could be combined with DBO-based feature selection to further enhance classification robustness and predictive accuracy across heterogeneous cancer datasets. Third, hybridization of DBO with other optimization strategies (e.g., evolutionary, physics-based, or chaos-enhanced algorithms) may improve the balance between exploration and exploitation, particularly for complex multiclass problems. Moreover, expanding the validation to large-scale, real-world clinical datasets and multi-omics data (such as proteomics and metabolomics) will help assess the practical applicability of the approach in clinical decision support systems. Finally, interpretability and biomarker discovery can be strengthened by mapping selected features to known biological pathways, contributing not only to computational efficiency but also to advancing personalized medicine and cancer treatment strategies.

Author contributions

Abrar Yaqoob conceived the idea of the study, performed the experimental design, and drafted the manuscript. Mushtaq Ahmad Mir contributed to methodology development, algorithm design, and validation of results. R. Vijaya Lakshmi provided critical guidance in data preprocessing, experimental setup, and overall supervision. Tejaswini Pradhan assisted in literature review, dataset handling, and preparation of initial results. GVV Jagannadha Rao contributed to formal analysis, visualization, and refinement of the manuscript. Ghanshyam G. Tejani supported statistical evaluation, validation, and provided valuable insights during manuscript revision. Mohd Asif Shah provided project administration, overall supervision, funding acquisition, and critically reviewed and edited the final manuscript for intellectual content.

Funding

No funds, grants, or other support was received.

Data availability

The Data used and analyzed during the current study available from the corresponding author on reasonable request.

Declarations

Ethical approval

This study did not involve human participants or animals. As such, no study-specific approval from an ethics committee was required. Informed consent or statements on animal welfare do not apply to this research.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.