The investigation was conducted in the karst-dominated terrain of Guangxi Zhuang Autonomous Region, Southwest China (20°54′-26°24′N, 104°28′-112°04′E; Figure 1 ). This geomorphologically complex area exhibits altitudinal gradients ranging from coastal plains (0 m) to montane systems (2141 m ASL), bisected by the Tropic of Cancer and bounded by tropical marine systems to the south. These latitudinal and topographic configurations engender a monsoonal climate regime with pronounced seasonality, manifesting in mean annual temperatures of 17.5-23.5°C and precipitation gradients from 841.2 mm (leeward basins) to 3387.5 mm (windward slopes). Nine standardized plots (200 m² each) were established across karst terrains, covering three vegetation succession stages: primary forests, secondary forests, and shrublands. This stratified design effectively captures karst ecosystem heterogeneity.

Longitudinal foliar sampling spanned July 2018 to September 2020 across all study plots. Within each plot, phyllosphere specimens were systematically collected from 8–15 dominant species, establishing a comprehensive karst flora spectral database comprising 301 samples representing 37 families, 59 genera, and 70 species. To ensure spatial representativeness, sampling followed triaxial orientation protocols (0°[N], 120°, and 240°) within the horizontal plane.

Spectral acquisition employed a high-resolution field spectroradiometer (Fieldspec4, ASD Inc., USA) with 3 nm VNIR (350–1000 nm) and 8 nm SWIR (1001–2500 nm) spectral resolution (Shah et al., 2019). Three photometric replicates per tree were obtained through standardized protocol: 1) periodic radiometric calibration (10-minute intervals) using integrated reference panels; 2) constrained by field operation limitations (4-hour battery endurance), two mature leaves per branch underwent non-destructive scanning; 3) branch-level spectral signatures were averaged to derive tree-specific reflectance profiles.

Post-spectral analysis, target leaves were immediately preserved in sterile bags (Whirl-Pak^®) under controlled conditions (ICERSICE940 incubator, 4°C). Samples underwent laboratory processing within 24 h: 1) oven-drying at 75°C to constant mass; 2) mechanical homogenization to 100-mesh particle size; 3) quantitative potassium determination via flame photometric analysis (Sherwood 410, ± 0.01 ppm detection limit) following standard digestion protocols (Reddy and Veeranki, 2013).

A total of 301 leaf samples were collected and analyzed for their total potassium content (expressed in units of 10 g/kg). The results showed that the potassium content ranged from 0.06 to 5.87, with a mean value of 0.81 ( Figure 2 ). The coefficient of variation was calculated to be 1.30, indicating a high degree of variability among the samples. This substantial variation provides a solid foundation for model development and accuracy evaluation in subsequent analysis.

Figure 3 illustrates the variations in spectral reflectance with different fractional differentiations. Compared to integer-order differentiations (0th, 1st, 2nd, and 3rd), fractional differentiation exhibits smaller amplitudes and smoother transitions. This gradual transformation maintains the detailed features of the spectral curves and prevents the abrupt fluctuations typically observed in integer-order differentiations. These results suggest that fractional differentiation, demonstrates greater advantages in the analyzing of complex experimental designs.

Figure 4 illustrates the distribution of absolute correlation coefficients between fractional differentiation spectra and leaf potassium content across fractional differentiation orders ranging from FD (0.0) to FD (3.0), with wavelengths spanning from 400 to 2500 nm. Before fractional differentiation (FD (0.0)), the spectral bands between 400–505 nm and 640–680 nm show significant correlation with leaf potassium content, though the correlation coefficients are relatively low. As the order of fractional differential (FD) increases—particularly between FD (1.5) and FD (3.0)—the spectral information in the ranges of 700–1100 nm and 1400–1800 nm shows stronger correlations with leaf potassium content, with most correlation coefficients exceeding 0.2. The maximum absolute correlation coefficient generally increases from FD (0.0) to FD (2.2), reaching a peak value of 0.46, before declining at higher orders. These findings highlight that selecting an appropriate fractional differentiation order, such as FD (2.2), can effectively improve the correlation between spectral features and the target variable in practical applications.

The performance of the Partial Least Squares Regression (PLSR) model under fractional differentiation is shown in Figure 5a . Across the FD range from 0.0 to 3.0, the R² values for the training set consistently exceed those of the validation set by approximately 0.2 to 0.3, suggesting the presence of a certain level of overfitting in the PLSR model. The validation set achieves its highest R² value of 0.51 when the fractional differentiation is set to 0.8. Although the model’s fitting accuracy is relatively low, it demonstrates stable performance without significant overfitting.

As shown in Figures 5b–d , the RF, XGBoost, and MLP models all exhibit a marked discrepancy in R² values between the training and validation sets, reflecting a clear tendency toward overfitting. In comparison to RF and XGBoost, the MLP model demonstrates marginally superior validation performance, with a maximum R² of 0.46, outperforming RF (0.29) and XGBoost (0.38).

In summary, although the PLSR model has limited fitting accuracy in predicting leaf potassium content, it demonstrates good stability. The training set R² remains between 0.6 and 0.7, while the validation set R² stays between 0.3 and 0.5. In contrast, the RF, XGBoost, and MLP models perform well on the training set but poorly on the validation set, indicating potential overfitting. Therefore, among these four individual models, the PLSR model is the most suitable for estimating leaf potassium content.

The PLSR-RF model ( Figure 6a ) demonstrates strong fitting and generalization capabilities, as evidenced by its stable performance across most FD settings. The training set achieves consistently high R² values around 0.9, while the validation set maintains moderately high R² values ranging from approximately 0.75 to 0.89. Notably, within the FD range of 0.5 to 1.3, the validation performance improves sharply, with the R² value increasing from 0.01 to 0.77. The model achieves optimal performance at a fractional differentiation of FD (2.7), where the training set R² is 0.98, with MSE and MAE of 0.01 and 0.07, respectively. For the validation set, the R² value is 0.89, with MSE and MAE of 0.21 and 0.29, respectively.

The PLSR-XGBoost model shows significant fluctuations across different FD settings, particularly for the training set. Despite these fluctuations, the difference in R² values between the training and validation sets decreases significantly when the fractional differentiation exceeds 1.2 ( Figure 6b ). This indicates that the combined model effectively mitigates overfitting. When the fractional differentiation is set to FD (2.7), the model performance reaches its peak, with R², MSE, and MAE values are 0.99, 1.8*10^-5, and 0.003 for the training set, and 0.94, 0.1, and 0.22 for the validation set, respectively. These findings indicate that PLSR combined with XGBoost provides more stable predictions under higher fractional differentiation levels.

The PLSR-MLP model performs poorly at low fractional differentiation values (FD < 0.8), with validation R² remaining below 0.4 between FD (0.2) and FD (0.6). Notably, at FD (0.3), the model exhibits signs of underfitting, as indicated by similarly low performance on both the training and validation sets. This suggests that the MLP has limited adaptability to raw data or data processed with low-order fractional differentiation ( Figure 6c ). However, as FD increases, the model’s performance improves significantly. At FD (2.8), the R² values for both the training and validation sets reach 0.99 and 0.96, respectively, with MSE and MAE values of 0.01 and 0.05 for the training set, and 0.07 and 0.16 for the validation set, indicating excellent model performance at this optimal order.

Overall, the three combined models exhibit distinct responses to fractional differentiation. PLSR-RF improves with increasing FD but shows signs of overfitting. PLSR-XGBoost generalizes well when FD > 1.0, despite early instability. While PLSR-MLP achieves the highest accuracy in this study ( Figure 7 ), PLSR-XGBoost involves fewer hyperparameter adjustments, demonstrates high computational efficiency, and facilitates easy deployment Therefore, although PLSR-MLP is the optimal model in terms of predictive performance, PLSR-XGBoost may offer a more practical solution for real-world potassium prediction tasks, especially in scenarios with limited computational resources or where rapid deployment is required.

In this study, seven models, namely PLSR, RF, XGBoost, MLP, PLSR-RF, PLSR-XGBoost, and PLSR-MLP, were applied to predict the plant leaf potassium content using spectral differentiation transformation techniques in the karst region of Guangxi Province. The optimal fractional differentiation prediction results for each model are shown in Figure 7 . Based on the coefficient of determination (R²) on the validation sets, the top three models are PLSR-MLP (R²=0.96), PLSR-XGBoost (R²=0.94), and PLSR-RF (R²=0.89), respectively. In comparison, the RF model alone showed the worst performance, with an R² of only 0.29 on the validation sets.

Among these seven models, the PLSR-RF, PLSR-XGBoost, and PLSR-MLP models all effectively predict potassium content in plant leaves in the southwestern karst region. Relative to individual models, the three combined models exhibit improvements of 206%, 147%, and 108% in R² on the validation set, respectively. These substantial gains suggest that the combined modeling approach effectively mitigates overfitting and enhances generalization capability.

The fractional differentiation is determined to be the optimal spectral transformation approach for all seven models ( Table 1 ). The application of fractional differentiation significantly enhances the models’ performance in estimating leaf potassium content. For the PLSR model, the optimal fractional differentiation is FD (0.8), resulting in a validation R² of 0.51, a marked improvement over the 0th order (R² = 0.26), 1st order (R² = 0.39), 2nd order (R² = 0.33), and 3rd order (R² = 0.35). The PLSR-RF model achieves its best performance at FD (2.7), with a validation R² of 0.89, significantly outperforming the 0th order (R² = 0.005), 1st order (R² = 0.58), 2nd order (R² = 0.82), and 3rd order (R² = 0.86).The PLSR-XGBoost model performs optimally at FD (2.7), with a validation R² of 0.94, significantly outperforming the 0th order (R² = 0.08), 1st order (R² = 0.58), 2nd order (R² = 0.83), and 3rd order (R² = 0.89). Finally, the PLSR-MLP model achieves its highest validation R² of 0.96 at FD (2.8), outperforming all integer orders from 0.0 to 3.0.

The results show that the optimal differentiation orders in all seven models are fractional rather than integer. This highlights the advantage of fractional differentiation in improving the accuracy and robustness of leaf potassium content estimation.

This study demonstrates that the spectral ranges of 700–1100 nm and 1400–1800 nm are critical for accurately estimating potassium content in plant leaves. Previous studies have identified the 964–1024 nm range as important for detecting potassium status in mature rubber tree leaves (Hu et al., 2024). In addition, specific wavelengths such as 720 nm and 1027 nm have been shown to play essential roles in predicting potassium content in rapeseed leaves (Zhang et al., 2013). The sensitive band in the 1400–1800 nm range identified in this study also aligns closely with the findings of Pimstein et al. (2011), further validating the relevance of this region for potassium estimation. Potassium is an essential ion in plant cells, involved in regulating osmotic pressure, activating enzymatic processes, and controlling stomatal dynamics (Nieves-Cordones et al., 2014; Yu et al., 2023). These physiological activities influence leaf cellular structure and water status, thereby indirectly affecting spectral reflectance. In the 700–1100 nm range, particularly within the near-infrared region (700–900 nm), spectral responses are strongly associated with internal leaf structure, which is sensitive to variations in tissue density and cellular arrangement. Since potassium plays a key role in water transport, cell turgor, and tissue development, changes in potassium levels can induce structural modifications that alter reflectance in this region (Lyu et al., 2023). Moreover, the short-wave near-infrared region (900–1100 nm) captures spectral signals related to leaf water content and biochemical composition, both of which are closely linked to potassium-mediated regulation (Dos Santos et al., 2023).

The presence of sensitive bands in the 1400–1800 nm range is closely linked to the various physiological roles of potassium in plant growth. Potassium influences leaf water transpiration by regulating stomatal opening, which in turn affects spectral reflectance (Lin et al., 2024). Consequently, potassium-sensitive bands are often found near the peak wavelengths of water absorption, such as 1450 nm and 1950 nm (Yu et al., 2023). However, some wavelengths farther from these water absorption peaks also show high sensitivity, likely due to changes in plant chemical composition and physiology under the unique environmental conditions of the karst regions. Previous studies have demonstrated significant differences in stoichiometric characteristics between plants in karst and non-karst regions (Zhang et al., 2019). Potassium is crucial for activating enzymes involved in starch, protein, and fat synthesis, as well as promoting the synthesis of plant hormones that regulate meristem growth (Amirruddin et al., 2020). These functions may contribute to the sensitive bands distanced from water absorption peaks. Therefore, the presence of such bands in the 1400–1800 nm range likely reflects potassium’s regulatory effects on physiological traits linked to long-term adaptation of plants to the karst environment.

Spectral data are often affected by instrument noise, environmental conditions, sample surface scattering, and background signals (Liu et al., 2023). Preprocessing techniques help mitigate these interferences, yielding a purer spectral signal that prevents the model from being affected by irrelevant signals and reduces errors (Li et al., 2025). Among these techniques, differentiation—particularly fractional differentiation—has emerged as a powerful method for capturing subtle spectral details and improving the accuracy of spectral-based estimations.

While traditional preprocessing techniques such as SNV and MSC effectively reduce scattering effects and smooth spectra, they are limited in handling high-noise spectral data (Oliveri et al., 2019). Differentiation processing of near-infrared spectra effectively removes noise while extracting subtle inflection points and spectral changes (Wang et al., 2018). Yang et al. (2022) demonstrated that applying differentiation to crop spectra significantly improves model prediction accuracy. Similarly, Shen et al. (2020) found that fractional differentiation significantly improves the accuracy of soil organic matter (SOM) content estimation. These studies highlight the significant advantages of differentiation in spectral preprocessing. Our findings similarly show that differentiation enhances the correlation between leaf potassium content and spectral reflectance, thereby improving estimation accuracy.

Differentiation includes both integer-order and fractional differentiation (Jin and Wang, 2022). Integer-order differentiation typically involves the first and second differentiations. However, the large intervals between these first and second differentiations result in significant differences between the nth and (n+1)th differentiation curves. This limitation causes integer-order differentiation to overlook finer spectral details (Anon, 2020). In contrast, fractional differentiation can extract detailed spectral information over smaller intervals while minimizing the introduction of excessive high-frequency noise (Zununjan et al., 2024; Song et al., 2023). The advantages of fractional differentiation stem from its unique mathematical structure, which, through the Grünwald-Letnikov definition, achieves a generalized difference structure, smooth attenuation, and long memory effects (Scherer et al., 2011). This enables fractional differentiation to more accurately capture spectral detail variations in data with complex background noise. Ge et al. (2022) demonstrated that fractional differentiation is highly effective for processing hyperspectral data in soil salinization risk assessment, with models using fractional differentiation proving more stable than those using integer-order differentiation. This conclusion from Ge et al. (2022) aligns with our findings, where fractional differentiation outperformed integer-order differentiation in estimating potassium content in plant leaves in the karst region.

However, the application of fractional differentiation also presents challenges. Low-order differentiation transformations provide limited improvement in correlation, while higher-order differentiation does not significantly enhance correlation coefficients between spectral reflectance and potassium content. Additionally, the optimal fractional differentiation varies across models, and similar studies on nutrient inversion in plant leaves suggest that the best fractional differentiation should be chosen based on the specific model being used.

The results indicate that the RF, XGBoost, and MLP models generally exhibit overfitting ( Figure 5 ). Due to their strong nonlinear fitting abilities (Bentéjac et al., 2021), these models tend to capture noise and irrelevant features when handling high-dimensional data, resulting in overfitting (Ying, 2019).

Common methods to control overfitting include dimensionality reduction, regularization, cross-validation, feature selection (Barbosa et al., 2024), and ensemble models. Several studies have explored the application of these methods in controlling overfitting. For example, Teresa et al. (2022) showed that dimensionality reduction effectively addresses over-parameterization in deep learning. Du et al. (2024) estimated rapeseed growth parameters using an ensemble learning algorithm, achieving better performance than individual machine learning models. For dimensionality reduction, we employed a PLS-based PCA method to extract latent variables that are highly correlated with the target variable. These latent variables were used as input features for the RF, XGBoost, and MLP models, effectively reducing the risk of overfitting in complex datasets.

In addition, hyperparameter optimization is a crucial strategy for mitigating overfitting and improving model generalization (Bischl et al., 2023). By tuning parameters such as the number of estimators, learning rate, and maximum tree depth (for RF and XGBoost), or the number of hidden layers and neurons (for MLP), models can better balance bias and variance. In this study, we employed grid search combined with cross-validation to optimize the key hyperparameters of each model, thereby reducing overfitting and enhancing predictive robustness. These findings are consistent with previous studies, which have demonstrated that well-tuned models generally outperform those using default configurations, particularly in high-dimensional datasets (Quan, 2024).

Combining dimensionality reduction with machine learning shows great potential for predicting nutrient content in plant leaves. For instance, Mahajan et al. (2024) used a PLSR-based machine learning model to predict potassium content in cashew leaves, achieving an R² of 0.66. Zhou et al. (2024) combined PCA with machine learning to predict cadmium content in lettuce leaves, obtaining an R² of 0.92 for the validation set. In our study, potassium content estimation in karst plants achieved an R² of 0.96 in the prediction set. This result confirms the effectiveness of PLS-based dimensionality reduction for retrieving leaf nutrient content across multiple species. This approach provides a valuable reference for future research.

In summary, combined machine learning models effectively control overfitting and enhance prediction performance. However, our research is limited to the leaf scale, and further validation is needed for their effectiveness in controlling overfitting when applied to UAV or satellite platforms. Future studies should explore the applicability of these models at larger scales and with higher-resolution data to comprehensively assess their generalization and practical value. Moreover, selecting the best model should not rely solely on prediction accuracy; factors such as model complexity, training time, and computational cost must also be taken into account to ensure the model’s feasibility and efficiency in real-world applications.