Rice canopy images for panicle detection were gathered at the fields of the National Institute of Crop Science (NICS) in Wanju-gun, Republic of Korea, during the 2022 and 2023 growing seasons. High-resolution RGB images were acquired using two imaging systems: a fixed-position PTZ (Pan–Tilt–Zoom) camera (Hanwha Vision XNP-8300RW, South Korea) and a handheld camera (Sony DSC-RX0-M2, Japan). The experimental site and image acquisition equipment are shown in Supplementary Figure S1 .

The PTZ camera, mounted on a tower at a fixed height of 5 m, was used for time-series imaging. While the camera has pan-tilt-zoom capabilities, these were used only for initial framing of the plot; for all subsequent data acquisition, the camera remained in a fixed position to record nadir RGB images at 3840 × 2160 pixels, ensuring consistent imaging geometry. The PTZ camera, using the Wisenet WAVE (Hanwha Vision, South Korea) software, recorded images twice daily at 09:00 and 16:00. In contrast, the handheld camera captured images between 10:00 AM and 12:00 PM. This dataset, collected in 2022 and 2023, was used solely for training and validating the deep learning-based semantic segmentation models.

For the handheld camera, a specific visual alignment protocol was implemented to minimize human-induced variability. The camera was wirelessly tethered to a smartphone using the ‘Imaging Edge’ mobile application for real-time monitoring of the field of view. Four poles were used to clearly mark the corners of the 1 m² target quadrat within each plot. During image acquisition, the operator manually adjusted the camera’s position until the on-screen auxiliary gridlines visually aligned with the four corner poles of the quadrat. This procedure was repeated for every shot between 10:00 AM and 12:00 PM to ensure that the camera’s height, distance, and near-nadir viewing angle were kept as consistent as possible, resulting in a highly consistent pixel resolution of the target area across all images.

The entire dataset, collected from four rice cultivars (Nampyeong, Shindongjin, Dongjin-1, and Saeilmi), was used solely for training and validating the deep learning-based semantic segmentation models.

All acquired images underwent preprocessing for semantic segmentation training. OpenCV 4.9.0 (a Python-based image processing library) cropped the images to 512 × 512 pixels, improving computational efficiency and model performance. The rice panicle regions were then manually annotated as a single class using the LabelMe tool (Russell et al., 2008), after the heading stage. These annotations were converted into binary masks, in which 0 encoded background and 1 encoded panicles ( Figure 1 ). Image augmentation techniques (Shorten and Khoshgoftaar, 2019), including resizing, Gaussian noise addition, and random brightness and contrast adjustments ( Figure 1 ), were applied to improve model generalization and robustness. Specifically, the images were augmented with random brightness and contrast adjustments between 0.8 and 1.2, and were then upscaled (1.1–2.0) or downscaled (0.6–0.9) to vary size. This tripled the original dataset from 867 to 2,601 labeled images, producing greater diversity. This augmentation strategy simulated real-world variations in lighting, noise, and contrast, such as those caused by cloudy skies, shadows, and variable camera exposure, thereby enhancing model robustness at inference. Finally, the augmented dataset was divided into training, validation, and testing sets at a ratio of 7:2:1 to enable objective evaluation.

This study evaluated the rice panicle segmentation performance with two backbone networks and five established semantic-segmentation architectures. The backbone networks, ResNet-50 and ResNet-101 ( Supplementary Table S1 ), were selected for their capacity to extract hierarchical features and mitigate the vanishing gradient problem through residual learning. These pre-trained networks act as foundational feature extractors, providing rich, multi-scale representations essential for accurate pixel-level classification (He et al., 2016). The use of both ResNet-50 and ResNet-101 enabled comparison of the feature representation depth, with ResNet-101 potentially capturing finer details at the cost of increased computational resources. Five distinct semantic segmentation models were evaluated: DeepLabv3+ (Chen et al., 2018), U-Net (Ronneberger et al., 2015), PSPNet (Zhao et al., 2017), FPN (Lin et al., 2017), and LinkNet (Chaurasia and Culurciello, 2017) ( Supplementary Figure S2 ). These models were selected to represent a range of architectural designs and feature-processing strategies commonly employed in pixel-level classification, particularly in agricultural image analysis. DeepLabv3+ was chosen for its capacity to capture long-range contextual information via atrous convolution and the Atrous Spatial Pyramid Pooling (ASPP) module. U-Net, with its encoder–decoder structure and skip connections, was included for its success in biomedical image segmentation and adaptability to diverse image analysis tasks. PSPNet, which utilizes a pyramid scene parsing network, was assessed to examine how global context affects segmentation accuracy. FPN was incorporated to evaluate the benefits of multi-scale feature representations for improved object delineation. Finally, LinkNet, known for its efficiency and real-time applicability, was used to explore the potential for computationally efficient segmentation. By systematically combining each of the five segmentation models with both ResNet-50 and ResNet-101, this study sought the optimal deep learning configuration for accurate and efficient rice panicle segmentation under field conditions.

Training parameters were tuned to standardize the input data and ensure stable learning. The image size was fixed at 512 × 512 pixels, the batch size was set to 8 to balance memory usage with optimization stability, and each model was trained for 200 epochs with a learning rate of 0.0001 to ensure gradual, stable improvement. Training was conducted on a system featuring an NVIDIA Quadro RTX 5000 GPU (16 GB), an Intel Xeon Gold 6226R CPU, and 256 GB of RAM. The operating system was Windows 11, with CUDA 12.5 for GPU acceleration, Python 3.9, and PyTorch 2.2.2 serving as the deep-learning framework ( Table 1 ). Model validation and testing were conducted on the same system to ensure consistency.

To evaluate the rice panicle detection performance, an independent evaluation dataset, separate from the training set, was used. Various metrics, including pixel accuracy, precision, recall, F1 score, and intersection over union (IoU), were used to assess the performance of the model comprehensively of the model comprehensively (Equations 1-5). Pixel accuracy denotes the proportion of correctly classified pixels among all pixels for evaluating the overall accuracy of the model. Precision is the proportion of actual panicle pixels among those predicted as panicles by the model, thus indicating the panicle prediction accuracy of the model. Recall is the proportion of actual panicle pixels correctly identified by the model; it is used to evaluate the panicle detection capability of the model. The F1 score, which is the harmonic mean of the precision and recall, combines both metrics. IoU is the ratio between the intersection area and the union area of the actual and predicted panicle regions, thus indicating the accurate segmentation ability of the model. These metrics are crucial to evaluating the rice panicle detection performance of the model from various aspects and determining its applicability to real-world environments. The equations for the metrics are as follows:

where TP (true positive) denotes the number of pixels correctly classified as panicle, FP (false positive) denotes pixels incorrectly classified as panicle, FN (false negative) signifies panicle pixels incorrectly classified as background, and TN (true negative) represents background pixels correctly classified as background. These metrics offer a comprehensive evaluation of the overall segmentation performance of the models.

To apply the trained segmentation models and build a yield prediction framework, separate time-series panicle coverage experiments were conducted in 2023 and 2024 at the National Institute of Crop Science (NICS), Republic of Korea, under both field and soil–bin conditions. Field transplantation occurred on June 7 and June 26, 2023, and on June 8, 2024. The transplantation on June 26, 2023, was designated late transplantation (LT). Soil bins (1 m × 1 m × 0.5 m) were placed outdoors, and transplantation occurred on June 9, 2023, and June 10, 2024. The primary cultivar was Nampyeong, with Dongjin-1, Shindongjin, and Saeilmi included in the 2024 experiments. Nitrogen was applied at three rates (0, 98.8, and 197.6 kg ha^-¹), with treatments varying by year, environment (field or soil bin), and cultivar. Nitrogen was split into three doses following the Korean standard cultivation method in Korea: 50% as a basal dressing before transplantation, 20% as a tillering fertilizer 20 days after transplanting, and the final 30% as a panicle fertilizer at the panicle formation stage. Each experimental unit consisted of a 1 m² plot containing 28 hills. To analyze the relationship between the time-series panicle coverage and yield components, post-harvest measurements of the panicle number (PN), grain number (GN), number of grains per panicle (GNP), 1000-grain weight (TGW), and filled grain ratio (FGR) were conducted.

This section details the first step of our yield prediction framework: RGB image collection and preprocessing. The overall process, described in the following sections, involved (1) extracting panicle coverage from these images, (2) fitting the time-series data to a piecewise function to derive dynamic parameters (Section 2.7), and (3) using these parameters as inputs for machine learning models to predict final yield (Section 2.8). High-resolution RGB images were captured at intervals of 3–7 days throughout the growing season using a Sony DSC-RX0-M2 camera to document all key growth stages. For this study, which focuses on panicle coverage, the images taken from the heading onwards were used, as panicles are the primary subject of segmentation. The images were acquired between 10:00 AM and 12:00 PM, with the camera aimed at the center of the yield survey plot and leveled with the ground to minimize distortion. The captured RGB images were cropped to encompass a 1 m² area demarcated by the four corner poles within the plot, ensuring consistency in yield component measurements and reducing variability from inconsistent sampling. These cropped images were then resized to 1536 × 1536 pixels, nine times the model input size of 512 × 512 pixels, to ensure dataset uniformity ( Figure 1 ). For the yield estimation study, an aggregate of 1,956 time-series images was acquired over multiple observation dates. These images were collected from 152 distinct plots (20 field plots in 2023, and 132 plots, including 80 field and 52 soil-bin plots in 2024). Panicle coverage was calculated by dividing each 1536 × 1536 image into nine 512 × 512 pixel tiles. The deep learning model then processed each sub-image to estimate the panicle coverage for that segment. The overall panicle coverage was determined by dividing the estimated panicle area by the total image area as (Equation 6).

where PC denotes the panicle coverage (%), PA represents the panicle area of the image, and BA denotes the background area of the image. The estimated panicle coverage values from all nine segments were averaged to derive coverage per unit area ( Figure 1 ). Representative resized images after the 2023 and 2024 treatments appear in Supplementary Figure S3 to demonstrate the structure and quality of the dataset. Based on the performance evaluation presented in Section 3.2, the DeepLabv3+ model with a ResNet-101 backbone, which achieved the highest mIoU (0.82), was selected as the final model. This model was then used to segment all time-series images for the subsequent yield prediction analysis.

The time-series panicle coverage data obtained from the segmented images were fit to a piecewise function (Equation 7) designed to model the growth and decline phases of the rice panicles, as shown in Figure 2 . The function comprises a sigmoidal growth phase and a quadratic decline phase, seamlessly connected at the transition point. The function is expressed below.

where K represents the maximum panicle coverage observed during the growth phase; g determines the growth rate, influencing the steepness of the sigmoidal curve. The parameter d₀ defines the point of maximum growth rate (inflection point), and d₁ marks the transition point between the growth and decline phases. Lastly, a controls the curvature of the quadratic decline, dictating how rapidly the panicle coverage decreases after d₁ . This piecewise function enables precise modeling of rice panicle dynamics, capturing the rapid increase during the heading stage and subsequent decline during senescence. The parameters derived from this model (K, g, d₀, d₁ , and a) provide quantitative insights into panicle development under varying environmental and experimental conditions. These fitted parameters served to compare treatment effects on rice growth and yield. The parameters of this piecewise function for each experimental plot were determined by fitting the model to the time-series panicle coverage data using the non-linear least squares method. The optimization was performed using a scientific computing library (e.g., the curve_fit function from the SciPy library in Python). A key step in this process was providing robust initial guesses for the parameters to ensure stable convergence of the algorithm; these were estimated from the observed data trends for each plot. The goodness-of-fit for each resulting curve was then evaluated using the coefficient of determination (R²).

Machine learning models were developed for predicting the rice yield and its components using five parameters (K, g, d₀ , a, d₁ ) extracted from a piecewise function fitted to the time-series panicle coverage data collected in 2023 and 2024. The models included partial least squares regression (PLSR), XGBoost regressor (XGBR), random forest regressor (RFR), and gradient boosting regressor (GBR).

The models were selected based on their documented performance in similar predictive modeling tasks in agricultural research. PLSR captures the linear relationship between the input and output variables, exhibiting stable predictive performance even under multicollinearity (Wold et al., 2001). RFR is an ensemble model that enhances the predictive performance by combining multiple decision trees (Breiman, 2001), whereas GBR and XGBR are boosting-based ensemble models that increase predictive accuracy by sequentially training weak learners (Friedman, 2001; Chen and Guestrin, 2016). The scikit-learn library serves primarily for model training and prediction.

Hyperparameter optimization was conducted for each model using GridSearchCV. Specifically, the PLSR model was set to n_components = 3, the RFR model with n_estimators = 100, and both the GBR and XGBR models with n_estimators = 100 and learning_rate = 0.05. The model performance was assessed using leave-one-out cross-validation (LOOCV). The root mean squared error (RMSE) and coefficient of determination (R²) served as evaluation as evaluation metrics (Equations 8, 9). Tree SHapley Additive exPlanations (Tree SHAP) analysis was performed to clarify the RFR and boosting-based models (XGBR, GBR). The RMSE equals the square root of the mean squared difference between the predicted and actual values, calculated as

where y i denotes the actual values, y ^ i denotes the predicted values, and n is the number of data points. The coefficient of determination (R²) is the proportion of the variance in the actual values that is predictable from the predicted values, calculated as

where y ¯ represents the mean of the actual values.

To assess the effects of the experimental factors on the parameters derived from the piecewise function (K, g, d₀ , a, and d₁ ), an analysis of variance (ANOVA) was performed using the statsmodels library in Python. Due to differences in the experimental design between the two years, the data for each year were analyzed separately. For the 2023 data, a one-way ANOVA was used to test the effect of the different treatment levels, which included nitrogen rates and transplantation dates. For the 2024 data, a three-way ANOVA was conducted to test the main effects of nitrogen, cultivar, and location, as well as their two-way interaction effects. All effects were considered statistically significant at p < 0.05.

The comprehensive methodology, visually summarized in Figure 1 , is structured into two main components. The left panel details the development and validation of the deep learning model for panicle segmentation, while the right panel illustrates how this trained model is subsequently applied within a time-series analysis pipeline to extract dynamic growth parameters and, ultimately, to predict rice yield and its components using machine learning regression.

The training and validation performance of five semantic segmentation models—DeepLabv3+, PSPNet, U-Net, FPN, and LinkNet—was evaluated using two different backbone architectures, ResNet-50 and ResNet-101. Both training loss and validation accuracy were monitored over 200 epochs to analyze the convergence trends ( Supplementary Figure S4 ).

Across all models and backbones, the training loss consistently decreased, whereas the validation accuracy increased and subsequently stabilized as epochs increased. Models using ResNet-101 generally exhibited a slightly higher validation accuracy than ResNet-50, reflecting the enhanced feature extraction capabilities of the deeper backbone. Although the convergence patterns varied across the models, all achieved stable, low validation loss by the end of training. U-Net demonstrated the fastest initial stabilization, whereas other models, such as PSPNet, required more epochs to achieve similar final loss values.

This analysis confirms that all five segmentation models with both ResNet-50 and ResNet-101 backbones successfully converged, exhibiting decreasing training loss and stable validation accuracy. These results emphasize the effectiveness of these architectures in segmenting rice panicle images, with variations in convergence speed and final accuracy depending on the specific model and backbone combination.

To evaluate the performance of the models trained with two backbones (ResNet-50 and ResNet-101) and five semantic segmentation models (U-Net, FPN, LinkNet, PSPNet, and DeepLabv3+), the performance metrics were calculated using a test image set ( Table 2 ). These metrics included the pixel accuracy, precision, recall, F1-score, and mean IoU (mIoU), offering a comprehensive overview of the segmentation quality and performance of each model.

Among the models with the ResNet-50 backbone, DeepLabv3+ attained the highest mIoU (0.81), F1-score (0.88), and pixel accuracy (0.99). LinkNet also scored well with an mIoU of 0.81 and an F1-score of 0.87. PSPNet had the lowest mIoU (0.61) among the models employing ResNet-50. Among the models with the ResNet-101 backbone, DeepLabv3+ again recorded the highest mIoU (0.82) and an F1-score of 0.88. LinkNet ranked second with an mIoU of 0.81 and an F1-score of 0.88. Across all models, the use of ResNet-101 generally resulted in a modest improvement in the recall and mIoU over that of ResNet-50, although the magnitude of this improvement varied.

A visual inspection of the segmentation results ( Supplementary Figure S5 ) showed that despite these differences in the numerical metrics, the qualitative performance of panicle detection was generally high across all models. All models segmented the panicle regions, with DeepLabv3+ and LinkNet showing slightly better quantitative results, particularly in terms of the mIoU.

These findings indicate that although the numerical performance metrics highlight subtle differences between the models, practical model selection may depend on the computational efficiency, task-specific requirements, or hardware constraints rather than significant differences in the segmentation capability. DeepLabv3+ and LinkNet emerge as strong candidates due to their consistently high performance across both backbones. Future research should prioritize evaluating the robustness of these models across diverse datasets and environmental conditions to optimize their application to real-world tasks.

Table 3 lists the fitted parameters (K, g, d₀, a, d₁) for various treatment conditions in 2023 and 2024. Through analysis of variance (ANOVA), we confirmed that factors such as nitrogen level, transplantation date, and rice variety had a statistically significant effect on the dynamics of panicle development, as quantified by these parameters ( Supplementary Table S2 ).

Across both years, K (maximum panicle coverage) generally increased with higher nitrogen levels, affirming the critical role of nitrogen. For instance, in the 2023 field experiment, K increased from 0.2512 under no nitrogen (23-F-0N) to 0.3060 with nitrogen addition (23-F-9N). The parameter g (growth rate) also tended to rise with nitrogen application in most cases, such as in the 2024 Nampyeong variety field experiment, where it rose from 0.3098 (0N) to 0.3667 (9N), indicating accelerated growth.

The timing of key developmental stages also shifted. The time of maximum growth rate (d₀ ) advanced under higher nitrogen levels, shifting from 9.94 days (23-F-0N) to 8.67 days (23-F-9N) in the 2023 field data. Similarly, the start of the decline phase (d₁ ) was advanced in parallel, occurring at 27.01 days compared to 28.07 days. The curvature of the post-peak decline (a) showed varied responses, though it marginally increased with higher nitrogen in some treatments.

The piecewise function demonstrated reliable performance in capturing panicle dynamics across diverse conditions, with the goodness-of-fit R² values remaining high, nearly all above 0.98.

To investigate the influence of nitrogen, transplantation date, and varietal factors on the panicle coverage dynamics, the time-series changes in the panicle coverage were plotted under different treatment conditions, and the data were fitted to the piecewise function ( Figure 3 ).

As confirmed by our ANOVA results, nitrogen treatment had a statistically significant effect on panicle coverage dynamics ( Table 3 ), a trend visually represented in Figure 3A . Higher nitrogen level (9N) led to a higher maximum panicle coverage (K) of 0.2663 compared to 0.2220 under the no-nitrogen control (0N). This suggests that nitrogen promotes panicle growth and development. The quadratic curvature parameter (a), however, showed only slight changes with nitrogen treatment, where it remained constant (0.0003) across all treatments.

The effects of the transplantation date and nitrogen availability were also apparent ( Figure 3B ). Late transplantation (LT) under no-nitrogen conditions resulted in a lower maximum panicle coverage (K), decreasing from 0.2512 (0N) to 0.2081 (0N-LT). Contrary to the baseline treatment, the transition to the decline phase (d₁ ) was also earlier in the LT group. With sufficient nitrogen, the adverse effect of late transplantation on K was offset, with K values of 0.3060 (9N) and 0.3078 (9N-LT) being nearly identical.

Significant differences in panicle coverage dynamics were observed among cultivars, and these responses were influenced by nitrogen availability, as indicated by the significant main effects of cultivar and nitrogen ( Table 3 ) and shown in Figures 3C, D . Under the 9N condition, Saeilmi achieved one of the highest K values (0.2782) but had a slower growth rate (g = 0.2695), whereas Dongjin-1 showed the fastest growth rate (g = 0.4606) but a more moderate K value (0.2500). These results underscore the intricate interplay of genetics with management practices. These results reveal the complex interplay of nitrogen availability, transplantation timing, and genetic factors in determining the panicle coverage dynamics. The findings emphasize the importance of considering these factors in optimizing nitrogen management and variety selection for rice production.

A Pearson correlation analysis was performed to investigate the linear relationship between the five parameters derived from the piecewise function (K, g, d₀ , a, and d₁ ) and the key yield components ( Figure 4 ). The analysis identified several significant correlations.

Among the parameters, K (maximum panicle coverage) showed the strongest positive correlation with Yield (r = 0.87, p < 0.001), GN (grain number) (r = 0.85, p < 0.001), and PN (panicle number) (r = 0.70, p < 0.001), highlighting its dominant role in determining final crop yield. Interestingly, K displayed a significant negative correlation with TGW (1000-grain weight) (r = -0.47, p < 0.001).

The timing parameters also revealed strong relationships. The time of maximum growth rate (d₀ ) was strongly negatively correlated with Yield (r = -0.62, p < 0.001) and especially with FGR (filled grain ratio) (r = -0.71, p < 0.001). Similarly, the transition point to the decline phase (d₁ ) showed a strong negative correlation with Yield (r = -0.57, p < 0.001) and FGR (r = -0.69, p < 0.001). Taken together, these findings underscore the intricate interplay between genetic factors (cultivar) and management practices (nitrogen, transplantation timing) in determining panicle coverage dynamics, emphasizing the importance of an integrated approach for optimizing rice production.

Regression plots illustrated the predictive performance of the four models (PLSR, RFR, GBR, and XGBR) in predicting the yield and yield components based on the five parameters derived from the piecewise function ( Supplementary Figure S6 ). The models were evaluated using LOOCV; each plot shows the relationship between the actual (x-axis) and predicted values (y-axis). The red diagonal line represents the ideal 1:1 relationship (perfect prediction), and the blue line represents the regression line fitted to the data.

The results demonstrate different accuracies depending on the model and yield component. RFR and XGBR showed high predictive performance for Yield and GN, with points clustered closely around the 1:1 line, indicating good agreement between the predicted and observed values. PLSR and GBR also showed reasonably good predictions for Yield and GN, although with slightly greater scatter. For PN, all models showed moderate prediction accuracy, with RFR and XGBR performing marginally better than PLSR and GBR. In contrast, the predictions for GNP and TGW showed lower accuracy across all models, as evidenced by the increased scatter around the 1:1 line. This reflects a greater inherent variability in these traits, in addition to limitations in the ability of the models to capture them based solely on the piecewise function parameters. The FGR predictions showed moderate accuracy, with RFR and XGBR again demonstrating slightly better performances than those of PLSR and GBR.

Table 4 summarizes the predictive performances of the four regression models (PLSR, RFR, GBR, and XGBR) based on the R² and RMSE values for the yield and yield components: GN, PN, GNP, TGW, and FGR.

Regarding the R² values, RFR and XGBR consistently demonstrated superior performance for the key components, such as Yield (R² = 0.890 for both) and GN (R² = 0.870 and 0.820, respectively). GBR also achieved strong results for Yield, GN, and PN, with its performance comparable to that of RFR for these components. PLSR performed relatively well for Yield (R² = 0.820) and GN (R² = 0.750) but underperformed in components such as the GNP (R² = 0.210) and TGW (R² = 0.440), highlighting its limitations in capturing complex, nonlinear relationships.

Considering the RMSE values, RFR and XGBR recorded lower RMSE values for Yield (RMSE = 60.83 and 61.16, respectively) and GN (RMSE = 2527.82 and 2943.32, respectively), indicating their reliability in reducing the prediction errors. Conversely, PLSR displayed higher RMSE values across most components, particularly GN (RMSE = 3521.43) and Yield (RMSE = 75.69), reaffirming its limited predictive capability when compared with that of the nonlinear models. GBR generally performed similarly to XGBR in terms of the RMSE, particularly for Yield, GN, and PN.

These results emphasize the strengths of nonlinear models such as RFR and XGBR in handling complex traits and achieving better prediction accuracy for the yield components. However, traits such as the GNP and TGW consistently recorded lower R² values and higher RMSE across all models, suggesting the inherent difficulty in predicting these components with the available data.

Figure 5 ; Supplementary Figure S7 presents the SHapley Additive exPlanations (SHAP) value analysis for the RFR model, detailing the contribution of each parameter in the piecewise function (K, g, d₀ , a, d₁ ) to the prediction of the yield and yield components. Each point on the plot represents a single data point, with its position on the x-axis indicating the SHAP value (effect on the model output) and its color representing the feature value (red for high, blue for low).

Regarding the yield prediction, K (maximum panicle coverage) showed the greatest mean absolute SHAP value and therefore the most significant overall influence, with high values of K (red points) consistently associated with positive SHAP values (increased yield prediction); d₀ (time of maximum growth rate) was also found to be essential for yield prediction.

Regarding the GN, K was again the dominant predictor, followed by d₀ and d₁ , whereas K and d₁ were the most important for the PN. The GNP was the most affected by d₁ and K, whereas the TGW was the most influenced by K, d₁ , and d₀ . The parameters d₁ and d₀ had the strongest influence on the FGR, with a higher value of d₁ (a delayed transition to the decline phase) and a lower value of d₀ (delayed onset of the maximum growth rate) generally associated with a higher FGR. The growth rate (g) and curvature of the decline (a) consistently showed lesser importance across all yield components.

This SHAP analysis confirmed that the parameters derived from the piecewise function, particularly K, d₀ , and d₁ , provide valuable insights into the factors driving the yield and its components. The visual representation of the feature importance facilitates a more nuanced understanding of the predictions made by the model than a simple examination of the overall model performance metrics.