A Hybrid Framework for Sustainable Ecosystem Management Through Robust Litterfall Prediction Under Data Scarcity

Abstract

Accurate ecological prediction is critical for sustainable environmental management and carbon cycle assessment, yet model development is often constrained by limited datasets and inconsistent preprocessing practices. Reliable litterfall prediction plays a key role in understanding nutrient cycling and supporting sustainable forest ecosystem management. Although gradient boosting models have shown promising performance in ecological applications, structured evaluations integrating preprocessing strategies with synthetic data augmentation remain limited under data-scarce conditions. This study proposes the Hybrid Preprocessing and Augmented Boosting Framework (HPABF), which combines multi-stage preprocessing—including MICE imputation, log transformation, and feature engineering—with synthetic data augmentation to enhance predictive robustness. The framework was evaluated across eight machine learning models using a 968-sample forest ecological dataset. To mitigate data scarcity, 5000 synthetic samples were generated while preserving the statistical distribution and multivariate structure of the original data (91% fidelity). Fractal dimension analysis was further introduced as a geometric validation metric to assess prediction structure and stability beyond conventional performance measures. Within the HPABF, gradient boosting models achieved a 7% improvement over baseline performance (R² = 0.96, MAE = 0.06) under cross-validation strategies designed to reduce overfitting. Training with synthetic data further improved predictive accuracy (R² = 0.98), demonstrating the framework’s effectiveness for data-scarce ecological applications. By improving prediction reliability under limited data conditions, the proposed framework supports more accurate environmental monitoring, informed decision-making, and sustainable management of forest ecosystems.

1. Introduction

Ecological data describing forest dynamics play a crucial role in understanding ecosystem functioning and its relationship with climate regulation. Among these indicators, litterfall represents the estimation of fallen leaves, twigs, clusters, fruits, flowers, buds, bad fruits, needles, and organic material shed by animals such as birds and squirrels—essentially, anything that falls from a tree. It can operate as a carbon sink by adding organic matter to the soil, but if the rate increases faster than the rate of carbon storage, the greenhouse gas emission rate rises as well.

Traditionally, estimating annual litterfall was done manually. This process required human effort and time for researchers, especially for large-scale and long-term monitoring, which was resource-intensive and time-consuming [1]. Later, researchers tried to use statistical and empirical models in an attempt to save labor and optimize the time needed to predict the weight of litterfall using mathematics, but conventional statistical methods were not enough to capture the complexities and relationships between variables [2]; hence, the predictions had low accuracy.

Recent advances in machine learning, particularly gradient boosting algorithms, have shown strong performance in forest-related modeling tasks such as biomass estimation [3,4,5]. These approaches have demonstrated the ability to capture nonlinear relationships and complex environmental interactions within ecological datasets. Modeling of litterfall dynamics remains comparatively underexplored, especially under diverse spatial and preprocessing configurations. Existing studies have applied traditional and hybrid machine learning approaches, with moderate predictive success [6,7].

Despite these advances, several important challenges remain in litterfall prediction research. First, most existing studies focus primarily on model selection, while the impact of different preprocessing strategies on predictive performance has received limited systematic evaluation. Second, ecological datasets often suffer from data scarcity and missing observations, yet the use of synthetic data generation for tabular ecological prediction tasks such as litterfall estimation remains largely unexplored. Third, model evaluation in ecological prediction studies typically relies solely on conventional performance metrics (e.g., R², RMSE), which may not fully capture the structural complexity inherent in ecological systems. These limitations highlight the need for a more comprehensive framework that integrates robust preprocessing strategies, data augmentation techniques, and complementary validation methods to improve prediction reliability in data-scarce ecological environments.

Ecological systems exhibit multi-scale spatial and structural complexity that is not fully captured by conventional accuracy-based metrics. Fractal geometry offers a scale-independent approach for quantifying spatial irregularity and structural organization through fractal dimensions. Incorporating fractal-based representations enables the evaluation of whether predictive models preserve the intrinsic geometric complexity of ecological patterns, thereby complementing traditional performance measures.

Recent applications in forest ecology and agriculture have demonstrated the practical viability of synthetic data generation for plant-related variables. Ref. [8] presented a comprehensive development model for efficiently leveraging synthetic data in agricultural machine learning applications, demonstrating that synthetic datasets can achieve comparable performance to real data while reducing data collection costs by up to 70%. Their framework is particularly relevant for ecological applications where field data collection is expensive and time-consuming.

Similarly, Ref. [9] developed LAESI (Leaf Area Estimation with Synthetic Imagery), which generates photorealistic synthetic images for leaf area prediction tasks. Their approach achieved 92% accuracy using purely synthetic training data, demonstrating that synthetic data can effectively substitute for real observations in plant morphology estimation tasks closely related to litterfall prediction. These studies establish that synthetic data generation is not merely a theoretical possibility but a practical tool for addressing data scarcity in forest ecology research.

To address these challenges, this study proposes a Hybrid Preprocessing and Augmented Boosting Framework (HPABF) for litterfall prediction under data-limited conditions. The framework systematically evaluates multiple preprocessing strategies, integrates synthetic data generation to mitigate data scarcity, and introduces fractal dimension analysis as a complementary validation method for assessing structural consistency in ecological predictions. The main contributions of this work are summarized as follows:

C1.

Formulated Preprocessing Analysis: We perform a planned evaluation of 12 preprocessing pipelines, combining multiple imputation strategies, feature engineering choices, and data transformations across eight machine learning models, enabling controlled comparison of preprocessing effects on predictive performance.

C2.

Data Preservation Strategy: We show that Multiple Imputation by Chained Equations (MICE) provides more effective feature preservation than feature-dropping strategies, leading to consistent performance gains in gradient boosting models.

C3.

Synthetic Data Augmentation for Tabular Ecological Data: We investigate the use of Gretel AI Navigator [10] for synthetic data generation in litterfall prediction, and we assess its impact on model training and generalization with structured quality validation.

C4.

Complementary Validation beyond Accuracy Metrics: We introduce fractal dimension analysis as a complementary geometric validation tool to assess spatial and structural consistency in model predictions beyond conventional accuracy metrics.

C5.

Reproducible and Transferable Framework: We provide an end-to-end, reproducible modeling pipeline that can be readily adapted to other tabular environmental and ecological datasets.

This paper is organized as follows: Section 3 describes the preprocessing steps, the process of synthetic data creation, and the machine learning techniques implemented. Section 4 evaluates the model’s performance, Section 5 examines the implications of the findings, and Section 6 presents the outcomes obtained and considers opportunities for future work.

2. Related Work

Accurately predicting annual litterfall production is essential for understanding ecosystem dynamics, forest productivity, and the broader implications of climate change. Recent advancements in machine learning (ML) have enabled more precise modeling of litterfall by capturing complex relationships among environmental factors such as climate, soil conditions, and vegetation properties. This section reviews existing research on litterfall prediction, comparing methodologies, key findings, and areas for future exploration.

2.1. Machine Learning for Forest Litterfall and Biomass Prediction

Lin et al. [11] utilized gradient boosting architectures, specifically Boosted Regression Trees (BRT), to model complex forest structural dynamics following thinning interventions. By employing a robust 10-fold cross-validation framework, the study demonstrated that ensemble tree-based models significantly outperform traditional regression in capturing the nonlinear recovery patterns of diameter distributions. Their findings highlight the superior ability of boosted algorithms to handle high-dimensional ecological data, providing a strong methodological precedent for applying similar gradient boosting machines, such as XGBoost, to the related problem of litterfall production modeling.

Geng et al. [6] explored machine learning techniques, including Random Forest (RF) and Artificial Neural Networks (ANNs), to enhance the accuracy of litterfall production predictions. The study demonstrated that ML models outperformed traditional statistical approaches by effectively integrating various environmental and climatic variables. The findings highlight the capability of ML to improve ecological forecasting, offering a more data-driven approach for litterfall modeling.

Building on regional modeling, Qiu et al. [2] analyzed the seasonal dynamics of litterfall production in Lushan Mountain, reinforcing that localized environmental variables are critical for accurate carbon input tracking. However, their reliance on traditional statistical methods further highlights the need for advanced ML approaches to capture these seasonal complexities.

Wang et al. [12] applied deep learning models, specifically Long Short-Term Memory (LSTM) and CNNs, which reduced prediction errors compared to traditional machine learning approaches. They highlighted that temporal models such as LSTM are particularly adept at capturing seasonal dynamics in forest ecosystems, which is crucial for comprehending litterfall patterns that vary significantly across seasons. However, they also noted that deep learning requires substantially larger datasets than traditional ML, which presents challenges for many ecological applications.

Despite these advances, critical gaps remain. Most studies compare 2–4 models without systematic preprocessing evaluation or hyperparameter justification. Critically, while XGBoost consistently outperforms linear and simple tree-based methods [4,13], no studies have systematically validated whether this superiority persists across different data augmentation scenarios or with limited training samples. Furthermore, the literature treating biomass and litterfall as parallel problems lacks direct validation on litterfall itself; only Geng et al. [6] and the emerging Transformer–CatBoost approaches have directly addressed litterfall prediction, highlighting a methodological gap in the field.

Zhou et al. [4] investigated aboveground biomass estimation in China’s Xinjiang region using multi-sensor data fusion and machine learning models, including SVM, Random Forest, and XGBoost. Their results showed that XGBoost combined with optical, climatic, and topographic data achieved the best performance (R² = 0.87), highlighting the effectiveness of integrating multi-source information for forest biomass prediction.

Similarly, Li et al. [3] compared linear regression, Random Forest, and XGBoost for biomass estimation in Hunan Province using Landsat 8 and Sentinel-1A data. XGBoost significantly reduced estimation errors (15–20%) compared to linear models, demonstrating its superiority in capturing complex nonlinear relationships in forest ecosystems, and motivating the use of gradient boosting approaches in the present study.

Moving beyond single-model methods, Ali et al. [5] explored ensemble learning for biomass estimation by combining Random Forest, XGBoost, and Support Vector Regression using Sentinel-1/2, GEDI LiDAR, and climate data. Their ensemble approach achieved a 22% RMSE reduction, but at the cost of increased computational complexity, underscoring the need for efficient yet accurate models.

Li et al. [14] proposed a hybrid XGBoost–Kriging framework to account for spatial autocorrelation in biomass estimation, achieving an R² of 0.91 in the Xiangjiang River Basin. While highly accurate, the reliance on spatial interpolation limits its general applicability across regions. More recently, Liu et al. [15] reported that combining Sentinel-2 data with environmental variables improved biomass estimation in China’s boreal forests (R² = 0.75), although the inclusion of SAR data degraded performance. This finding emphasizes that careful feature selection is critical, and that additional data sources do not always improve model accuracy.

Outside China, Aziz et al. [16] demonstrated the effectiveness of deep learning for forest cover classification using CNNs, achieving 94.5% accuracy. However, the high data and computational demands of deep learning models limit their suitability for data-scarce ecological applications, reinforcing the relevance of optimized machine learning approaches.

Beyond spectral and climatic data, characterizing the physical structure of the forest canopy is increasingly recognized as vital for predictive modeling. Although no studies have directly analyzed litterfall using fractal geometry, the broader literature demonstrates the value of fractal metrics in forest ecology. Recent methodological advances have strengthened this foundation. Alage et al. [17] developed the Fractal Fragmentation and Disorder Index (FFDI) using near-real-time satellite data, detecting a 160.5% increase in forest fragmentation from 2017 to 2024 in Nigerian forests. Peptenatu et al. [18] combined fractal fragmentation with Rényi information dimension across 12,600 forest images, successfully quantifying both the shape and spatial arrangement of forest fragments at multiple scales.

Liu et al. [13] improved box-counting methods using Shannon entropy for LiDAR-based canopy complexity analysis across 115 Chinese trees, validating fractal metrics at plot-level scales relevant to our study. Fischer et al. [19] provided a critical perspective by evaluating six fractal estimation methods with airborne LiDAR, emphasizing the importance of validating self-similarity assumptions. For remote sensing applications, Cheng et al. [20] recently applied fractal analysis to vegetation coverage patterns across Southwestern China, revealing spatiotemporal dynamics that traditional metrics failed to detect. These studies establish fractal geometry as a validated approach for characterizing forest spatial structure, providing a strong theoretical foundation for our application of fractal-based feature engineering to enhance litterfall prediction models.

2.2. Synthetic Data Generation for Litterfall Modeling

While machine learning models have shown promise in predicting litterfall, the availability of comprehensive litterfall datasets can be a limiting factor in model development and validation. Synthetic data generation techniques offer a solution to this challenge by creating realistic (yet artificial) datasets that can be used to train and test machine learning models.

The challenge of limited data availability in ecological research has led to growing interest in synthetic data generation techniques. Rafiq et al. [21], writing in Nature Ecology & Evolution, provided a compelling argument for how generative AI can accelerate ecological research by augmenting data-scarce datasets. They examined various generative models, including GANs and VAEs, finding that these approaches achieve 85–95% fidelity to real ecological patterns when properly tuned. Their work is particularly relevant to our research because they specifically addressed how synthetic data can extend observational datasets in forest monitoring applications, where collecting additional real data is often prohibitively expensive or time-consuming.

Bauer et al. [22] offered a comprehensive survey of synthetic data generation techniques across multiple domains, analyzing 417 different models. Their findings revealed that neural network-based approaches have become dominant in the field, with GANs leading for computer vision tasks and transformers emerging as promising for tabular data structures. They noted that model performance generally increases with complexity, but they emphasized that simpler models may be preferable when training data is extremely limited. This insight informed our decision-making process when selecting Gretel AI, which balances sophistication with practical usability for tabular data generation.

The practical implementation of synthetic data generation has been explored by several researchers. Noruzman et al. [23] evaluated Gretel.ai [10] as an open-source tool for synthetic data generation, demonstrating its effectiveness for creating realistic tabular datasets while preserving the statistical properties of the original data. Their work showed that Gretel.ai could successfully generate synthetic datasets that maintained the correlations and distributions present in real data, which is critical for training machine learning models that will generalize to real-world scenarios. However, they also cautioned that synthetic data quality must be carefully validated before use, as poor-quality synthetic data can actually harm model performance.

Despite the increasing use of synthetic data generation in ecological and environmental studies, most existing research has primarily focused on evaluating the statistical fidelity and privacy-preserving characteristics of synthetic datasets. Recent studies have reported that modern generative models are capable of producing synthetic ecological data with high statistical similarity to real datasets, often achieving fidelity levels exceeding 85–95%. However, the majority of these works emphasize the quality of the generated data, rather than assessing its practical impact on downstream predictive modeling tasks.

In particular, previous studies such as those by Noruzman et al. [23] and Bauer et al. [22] have evaluated synthetic data based on distributional similarity, correlation preservation, or privacy metrics. While these evaluations are valuable, limited attention has been given to examining whether synthetic data augmentation can effectively improve the generalization performance of machine learning models for ecological prediction tasks, especially when the available real-world data are limited. Addressing this gap, the present study investigates the role of synthetic litterfall data augmentation in enhancing the predictive performance and robustness of machine learning models for litterfall production estimation.

Despite the progress made in applying machine learning techniques to forest ecosystem modeling, several limitations remain in the current literature. First, litterfall prediction studies are typically constrained by limited datasets, often containing fewer than 1000 samples, whereas related biomass prediction studies frequently rely on substantially larger datasets. Second, although synthetic data generation methods have been widely explored in other domains, their effectiveness for augmenting litterfall datasets and improving predictive performance has not been systematically evaluated. Third, existing machine learning studies in ecological modeling often provide limited justification for preprocessing decisions such as feature transformations, missing value handling, and encoding strategies, which can affect model reproducibility and comparability.

To address these limitations, the present study systematically evaluates multiple machine learning models for litterfall prediction using a comprehensive preprocessing pipeline and investigates the impact of synthetic data augmentation generated using Gretel AI. By explicitly examining the role of preprocessing strategies and synthetic data in improving model robustness, this work aims to provide a more reproducible and methodologically transparent framework for litterfall prediction.

To provide a structured overview of the forecasting approaches applied in forest productivity and litterfall prediction,

Table 1. Comparative analysis of machine learning approaches relevant to forest biomass and litterfall prediction, with emphasis on gradient boosting and data augmentation strategies (2020–2026) (ordered by methodological relevance).

Study	Models Used	Data Used	Key Findings	Strengths	Limitations
Guo et al. [7]	Transformer–CatBoost hybrid model	Multi-source climatic, remote sensing, and forest inventory data (China; 88 sites, monthly observations)	Spatiotemporal modeling improves litterfall prediction compared to single-model approaches	Captures temporal dynamics and nonlinear relationships	Requires large datasets; preprocessing strategies not systematically evaluated
Geng et al. [6]	LightGBM, XGBoost, Random Forest, linear models	Environmental and climatic variables from forest sites in China (968 samples)	Gradient boosting models outperform traditional and tree-based approaches for litterfall prediction	Strong benchmark for litterfall modeling; comprehensive model comparison	Limited data size; no synthetic data augmentation or systematic preprocessing analysis
Li et al. [14]	XGBoost with spatial correction (Kriging)	Landsat time series, forest inventory, climate scenarios (China)	Spatially enhanced gradient boosting improves biomass prediction	High predictive accuracy; accounts for spatial dependency	Complex pipeline; limited scalability assessment
Zhou et al. [4]	SVM, RF, XGBoost with multi-sensor fusion	Landsat, MODIS, topographic and meteorological data (China)	Gradient boosting outperforms traditional ML in biomass estimation	Effective multi-source integration	Generalization across forest types not fully assessed
Ali et al. [5]	RF, ANN, XGBoost ensembles	Sentinel-1/2, GEDI LiDAR, climate data (global forests)	Ensemble learning improves biomass estimation accuracy	Robust multi-model framework	High computational cost; preprocessing sensitivity underexplored
Li et al. [3]	Linear regression, RF, XGBoost	Landsat 8, Sentinel-1A SAR, national forest inventory (China)	Gradient boosting reduces bias compared to traditional models	Clear demonstration of boosting advantages	Limited regional scope; no data augmentation
Liu et al. [15]	RF and gradient boosting regression	Sentinel-2, Sentinel-1 SAR, environmental data (China)	Gradient boosting yields best biomass estimates	Highlights feature importance	SAR data degraded performance; moderate accuracy
Rafiq et al. [21]	GANs and VAEs for synthetic data	Review of ecological synthetic data applications	Synthetic data mitigates data scarcity	Conceptual support for augmentation	Lacks predictive validation
Bauer et al. [22]	GANs, diffusion models, transformers	Survey of synthetic data generation models	Neural generative models dominate SDG	Comprehensive methodological overview	Not forestry-specific
Wang et al. [12]	CNNs and LSTMs	Remote sensing, IoT, and climate data	Deep learning captures spatiotemporal forest dynamics	Strong temporal modeling	Requires large datasets
Aziz et al. [16]	RF, SVM, CNN	Landsat and Sentinel-2 data (Pakistan)	Deep learning improves forest cover classification	High classification accuracy	Not applicable to litterfall regression

summarizes recent studies, categorizing their machine learning models, data sources, strengths, and methodological limitations.

3. Materials and Methods

This study proposes the HPAB framework (Figure 1), which aims to improve the prediction accuracy of annual litterfall production in China by increasing the data and leveraging machine learning algorithms under varying environmental conditions. Our objective is to create a reproducible framework that consists of constructed preprocessing and data preservation strategies.

3.1. Methodology Overview

The proposed framework shown in Figure 1 follows a structured multi-phase pipeline that clearly defines the relationships among input data, applied methods, and resulting outputs. The process begins with a data acquisition phase, where the dataset is collected and prepared for analysis. This is followed by a preprocessing phase to clean and transform the input data. In the third phase, synthetic data generation is applied to address data scarcity and enhance dataset size. The fourth phase focuses on feature engineering and feature selection to identify the most relevant predictors. In the fifth phase, machine learning models are trained using the processed features. Finally, the evaluation phase assesses model performance, establishing clear links between the input data, applied methods, and predictive results.

3.2. Data Acquisition

The dataset employed in this study was sourced from Geng et al. [6], comprising 968 observations of annual litterfall production collected from 314 forest sites spanning the geographical range of Chinese forests.

Table 2. Description of variables included in the litterfall dataset.

Variable	Type	Description
Latitude	Numerical	Geographic latitude of the forest site
Longitude	Numerical	Geographic longitude of the forest site
Altitude	Numerical	Elevation of the site (m above sea level)
MAT	Numerical	Mean annual temperature (°C)
MAP	Numerical	Mean annual precipitation (mm)
Age	Numerical	Stand age (years)
DBH	Numerical	Diameter at breast height (cm)
Height	Numerical	Average tree height (m)
Density	Numerical	Tree density (trees per hectare)
Leaf	Numerical	Annual leaf litterfall (Mg ha−1 yr−1)
Branch	Numerical	Annual branch litterfall (Mg ha−1 yr−1)
Reproductive	Numerical	Litterfall from reproductive parts (Mg ha−1 yr−1)
Others	Numerical	Other litterfall components (Mg ha−1 yr−1)
Total	Numerical	Total annual litterfall production (Mg ha−1 yr−1)
Forest type	Categorical	Broadleaf, needleleaf, or mixed forest
Stand origin	Categorical	Natural or planted forest
Measurement interval	Categorical	Time interval of litterfall measurement
Trap size	Categorical	Size category of litter collection trap
Source	Categorical	Dataset source reference
Geospatial classification 1	Categorical	Regional ecological classification level 1
Geospatial classification 2	Categorical	Regional ecological classification level 2
Geospatial classification 3	Categorical	Regional ecological classification level 3

summarizes the main variables included in the litterfall dataset, along with their data types and ecological descriptions. It covers latitudes from 18.26° to 51.50° N, longitudes from 82.25° to 129.53° E, altitudes from 0 to 4115 m, mean annual temperatures (MATs) from −5.4 to 25.4 °C, and mean annual precipitation (MAP) from 370 to 2800 mm. The dataset comprises total annual litterfall production (Mg/ha/yr) and its subdivisions (leaves, branches, reproductive parts, others), along with stand information (forest type, stand origin, stand age, DBH, tree height, stand density, trap size).

The average amount of litterfall generated per forest site was 5.071 Mg/ha/yr, with a range of 0.068 to 16.960 Mg/ha/yr. The portion of the overall litterfall that was made up of branches and leaves was 13% and 55%, respectively. Of the 314 sample stands, 49 percent were natural forests and 51 percent were planted forests. Natural woods produced more litterfall annually (5.327 Mg/ha/yr) than cultivated forests (4.826 Mg/ha/yr). Moreover, broadleaf woods made up 49%, needleleaf forests 42%, and mixed forests 9% of the 314 sample stands. Broadleaf forests produced more litterfall (6.332 Mg/ba/yr) than needleleaf forests (3.647 Mg/ha/yr).

3.3. Data Preprocessing

In preparation for model development and analysis, a comprehensive data preprocessing strategy was employed to ensure data quality and enhance model performance. The dataset initially contained 968 rows. The preprocessing steps involved handling outliers, missing data imputation, encoding categorical variables, and feature creation for regional analysis, as mentioned in Figure 1.

3.3.1. Handling Skewness

To understand the distribution of our dataset, we calculated the skewness and kurtosis of the annual litterfall production data. The skewness of the class label was 0.782, indicating a moderately positive skew. This suggests that while most values are clustered around the lower end of the distribution, some higher values extend the right tail. The kurtosis of the class label was 0.705, indicating a distribution that is slightly platykurtic. This means that the data distribution has a flatter peak and thinner tails compared to a normal distribution, suggesting fewer extreme outliers.

These distribution characteristics provide valuable insights into the nature of our dataset. The moderately positive right-skewness and slight platykurtic kurtosis suggest that the data is not perfectly normally distributed. Log transformation was implemented, which successfully reduced the skewness and brought the distribution closer to normal.

3.3.2. Handling Missing Values

Several columns in the dataset contained missing values, with “Source” having the most (902 missing values). Other columns with a significant amount of missing values included “DBH (cm)”, “Height (m)”, “Density (trees per ha)”, “Age (year)”, and the litterfall measurement columns. Missing data was handled with two approaches: (1) dropping the feature columns with more than 25% null values, and then imputing the missing values in the remaining features; or (2) proceeding directly to the imputation without dropping any columns, as a way to preserve important features.

Two imputation strategies were implemented: (1) MICE (Multiple Imputation by Chained Equations), which creates several different plausible imputed datasets and then combines results across them for features. This method was chosen because it takes into account the relationships between all variables in the dataset when imputing missing values, potentially leading to more accurate and consistent imputations. It can handle different types of variables and nonlinear relationships, and it is generally considered to be one of the most robust methods for handling missing data [24]. (2) Mode (most frequent value) imputation for the respective categorical features. This approach involves using predictive models to estimate and replace missing values, ensuring that the integrity of the dataset is maintained without introducing bias or reducing variability.

3.3.3. Encoding Categorical Variables

The dataset included seven categorical variables: “forest type”, “measurement interval”, “trap size”, “stand origin”, “geospatial classification4”, “geospatial classification3”, and “geospatial classification6”. To transform these categorical features into a format suitable for machine learning models, the LabelEncoder from the sklearn.preprocessing library was utilized. This approach assigns a unique integer value to each category, enabling categorical variables to be incorporated into machine learning models.

Although label encoding may introduce an ordinal representation of categories, its impact is limited for tree-based models. The primary models investigated in this study are gradient boosting algorithms, which perform feature splitting based on threshold decisions rather than assuming linear relationships between numerical values. Consequently, label encoding does not significantly affect the predictive performance of these models.

3.3.4. Feature Creation for Regional Analysis

To enhance the regional analysis capabilities of the model, three new features were created based on geospatial classifications introduced in [6]. These features were derived from existing geospatial classification columns and provided alternative representations of regional attributes, each more detailed than the last. Additionally, three alternative versions of the dataset were generated next to the original dataset.

For each dataset version, we implemented the following three preprocessing trials, creating a total of twelve scenarios and results, with the goal of exploring different regional perspectives and their potential impact on the model’s performance. We created multiple combinations for the dataset, firstly across the geospatial classes, and secondly across the preprocessing trials:

1.

Implementing MICE and mode imputation for missing values.

2.

Implementing MICE and mode imputation followed by log transformation to address data skewness.

3.

Dropping columns with more than 25% missing values, and then applying imputation and log transformation.

3.3.5. Fractal-Inspired Feature Engineering

To explore the role of fractal geometry in enhancing ecological prediction, four new features were engineered using domain-informed scaling relationships inspired by fractal theory. These features were designed to represent the structural and environmental complexity of forest stands, building on recent evidence that fractal dimensions are critical indicators of forest architectural diversity [25].

Let D denote diameter at breast height (DBH), H tree height, N stand density, T mean annual temperature (MAT), P mean annual precipitation (MAP), and A altitude.

Spatial Complexity (SC)

Spatial heterogeneity was quantified using the coefficient of variation of altitude within each spatial unit:

$$SC={\displaystyle \frac{{\sigma }_A}{{\mu }_A}}$$

(1)

where ${\sigma }_A$ and ${\mu }_A$ represent the standard deviation and mean of altitude, respectively. This feature captures terrain-driven variability and localized topographic complexity.

Structural Fractal Index (SF)

To reflect multiplicative scaling among tree structural attributes, a logarithmic interaction term was defined as follows:

$$SF=log(D·H·N)$$

(2)

which is equivalent to

$$SF=logD+logH+logN$$

(3)

This formulation aligns with ecological allometric scaling and power-law relationships commonly observed in forest systems.

Multi-Scale Structural Index (MS)

To model hierarchical structural organization, a nonlinear power-law combination was introduced:

$$MS=D^{\alpha }·H^{\beta }·N^{\gamma }$$

(4)

where $\alpha$, $\beta$, and $\gamma$ are fractional exponents ($0<\alpha ,\beta ,\gamma <1$) controlling scaling intensity. In this study, equal fractional weights were applied to represent balanced multi-scale contributions.

Environmental Fractal Index (EF)

To integrate climatic and topographic scaling effects, an environmental fractal index was defined as follows:

$$EF=T^{\delta }·P^{\theta }·A^{\eta }$$

(5)

where $\delta$, $\theta$, and $\eta$ are fractional exponents representing nonlinear environmental influence.

All fractal-inspired features were computed after preprocessing and appended to the original feature space prior to model training. Their contribution was evaluated across 12 structured geospatial–preprocessing scenarios and multiple learning paradigms to assess their robustness and generalization capacity.

3.4. Synthetic Data Generation

Following the preprocessing phase, the Gretel AI tool [10] was used to generate synthetic data. Specifically, the Navigator model within Gretel was employed due to its ability to produce high-quality synthetic data that closely mirrors the properties of the original dataset. The model was trained on the preprocessed data and generated a total of 5000 synthetic rows.

The generation process leveraged the platform’s default configuration parameters, which manage internal model hyperparameters automatically. The quality of the synthetic data was assessed using the built-in evaluation metrics provided by Gretel, including synthetic data accuracy and correlation with the original dataset. These metrics confirmed that the synthetic data preserved key statistical properties of the original dataset while expanding the sample size.

The Navigator model used by Gretel AI works as a transformer-based generative architecture that works specifically with tabular data. It models each feature one by one, using the values of the features that came before it, and then learns the joint probability distribution of the dataset as a whole. This allows it to generate statistically coherent and realistic synthetic records, in order to ensure that the synthetic data does not overfit or leak sensitive information from the original dataset. The model leverages deep representation learning to understand complex inter-feature dependencies and supports privacy-preserving data generation.

During the data generation process, the quality of the synthetic data was evaluated using Gretel’s internal scoring mechanism. The correlation between each pair of fields, known as the Field Correlation Stability, was calculated first in the training data and subsequently in the synthetic data. After that, the absolute difference between these numbers was calculated and averaged for every field. The quality score for Field Correlation Stability will be higher if this average value is lower.

Secondly, in order to confirm the statistical soundness of more complex, multi-field distributions and relationships, Gretel juxtaposed a Principal Component Analysis (PCA) that was initially calculated on the original data with the synthetic data. The distributional distance between the principal components identified in each dataset was compared to produce the Deep Structure Stability score. The synthetic quality score will increase with the proximity of the primary components. This statistic provides instant feedback on the usefulness of the synthetic data for machine learning, since PCA is a widely used method in machine learning for both dimensionality reduction and visualization.

Lastly, the degree to which the field distributions in the synthetic data closely resemble those in the original data is known as Field Distribution Stability. We employed a standard method for comparing two distributions, known as the Jensen–Shannon Distance, for every numeric or categorical variable. The quality score for Field Distribution Stability will increase when the average JS Distance score for all fields decreases.

A weighted mixture of the three separate quality metrics—Deep Structure Stability, Field Distribution Stability, and Field Correlation Stability—was used to calculate the synthetic data quality score. By producing data that retains the same statistical characteristics as the original dataset, this reduces the possibility of data bias or overfitting in downstream tasks and guarantees that the synthetic data can be utilized with confidence for additional research. This score can be thought of as a utility score or a confidence score measuring how likely it is that scientific findings from the synthetic dataset would have been the same if the original dataset had been used instead.

3.5. Model Training

To predict litterfall production, a variety of machine learning algorithms were implemented, including both linear and nonlinear models.

Table 3. Machine learning models used in this study.

ML Model	Description
Linear Regression	Models linear relationships between features and litterfall [26].
Ridge Regression	Adds an L2 regularization term to address multicollinearity [27].
Decision Tree	Captures nonlinear interactions using hierarchical, threshold-based splits [28].
LightGBM	Gradient boosting model with histogram-based splits and leaf-wise tree growth [29,30].
CatBoost	Gradient boosting method designed to handle categorical variables efficiently.
XGBoost	Scalable ensemble boosting algorithm using optimized decision trees [12].
Neural Network	Learns nonlinear patterns using multiple interconnected hidden layers [31].
Random Forest	Combines multiple decision trees to improve predictive stability and reduce overfitting [32,33].

presents a description of the nine implemented ML algorithms.

The machine learning models selected for this study were chosen based on their demonstrated effectiveness in handling complex, nonlinear ecological data. Gradient boosting methods such as XGBoost and CatBoost have shown strong performance in environmental prediction tasks due to their ability to model intricate feature interactions, handle missing values, and adapt well to tabular data structures [6,29,34]. These characteristics make gradient boosting particularly suitable for ecological prediction problems, where environmental variables often exhibit nonlinear relationships and complex dependencies. Random Forest, another ensemble-based model, is widely recognized in ecological applications for its robustness against overfitting and usefulness in feature ranking [33,35]. Linear and ridge regression were included as baseline models, reflecting their traditional role in ecological and climate-related studies [36]. The diversity of the selected models allows for both high-performing predictive capabilities and comparative interpretability, facilitating an in-depth evaluation of model behavior across different preprocessing and spatial scenarios.

The machine learning models were implemented using the Scikit-learn, XGBoost, LightGBM, CatBoost, and TensorFlow/Keras libraries. Default hyperparameter settings were used for several models, while specific configurations were defined for others to ensure stable training and reproducibility.

Table 4. Key hyperparameters used for the machine learning models.

Model	Key Hyperparameters
Linear Regression	Default parameters
Ridge Regression	alpha = 1.0
Decision Tree	random_state = 42
LightGBM	n_estimators = 100, random_state = 42
CatBoost	iterations = 100, random_state = 42
XGBoost	n_estimators = 3000, learning_rate = 0.1, max_depth = 2, early_stopping_rounds = 20, eval_metric = RMSE
Neural Network	hidden layers = (64, 32, 16), activation = ReLU, optimizer = Adam, epochs = 50, batch size = 32
Random Forest	n_estimators = 100, random_state = 42

summarizes the main hyperparameters used for each model. These baseline configurations were selected to provide a consistent comparison across algorithms while maintaining commonly used settings in machine learning applications.

3.6. Model Evaluation

To ensure robust and reliable results, before model training, the dataset underwent preprocessing, including label encoding of categorical variables and missing-value imputation using the MICE method. After completing the preprocessing stage, all models were evaluated using a 10-fold cross-validation. This technique divides the dataset into ten subsets, where each subset is used as a validation set while the remaining nine subsets are used for training. The performance metrics reported are the average across all folds, which reduces the risk of overfitting and provides a more generalizable assessment of model performance [11]. The models were evaluated based on three primary metrics: R-squared, Mean Absolute Error, and Root-Mean-Square Error.

Table 5. Evaluation measures used to assess model performance.

Measure	Description
R-squared (R2)	Proportion of variance in the target variable explained by the model; higher values indicate better fit.
Mean Absolute Error (MAE)	Average absolute difference between predicted and actual values; lower MAE denotes higher accuracy.
Root-Mean-Square Error (RMSE)	Square root of the average squared differences between predicted and actual values; lower RMSE indicates better predictive performance.
2D Spatial Fractal Dimension	Captures spatial complexity based on latitude, longitude, and the target variable; higher values indicate greater spatial irregularity.
3D Spatial Fractal Dimension	Measures spatial complexity including elevation (latitude, longitude, altitude, target); useful for altitude-dependent spatial patterns.
3D Structural Fractal Dimension	Reflects structural complexity in vegetation attributes (e.g., DBH, height, density, target); indicates how well structural patterns are represented.

illustrates the evaluation measures used.

Fractal dimension analysis was employed as a geometric validation technique to assess the complexity and consistency of the predicted litterfall values. Three configurations were evaluated: 2D spatial (latitude, longitude, target), 3D spatial (latitude, longitude, altitude, target), and 3D structural (DBH, height, density, target). The same configurations were recalculated using predicted values from the trained models.

Three configurations were analyzed to assess different aspects of ecological organization:

1.

2D Spatial Configuration: $(\mathrm{latitude},\mathrm{longitude},y)$.

2.

3D Spatial Configuration: $(\mathrm{latitude},\mathrm{longitude},A,y)$.

3.

3D Structural Configuration: $(D,H,N,y)$.

Here, y denotes observed litterfall production, A represents altitude, D diameter at breast height (DBH), H tree height, and N stand density.

For each configuration, fractal dimensions were estimated using the box-counting method. Let $N\left(ϵ\right)$ denote the number of occupied boxes of size $ϵ$ required to cover the data distribution. The fractal dimension $FD$ is defined as follows:

$$FD=\underset{ϵ\to 0}{lim}{\displaystyle \frac{logN\left(ϵ\right)}{log(1/ϵ)}}$$

(6)

In practice, $FD$ was computed as the slope of the linear regression between $logN\left(ϵ\right)$ and $log(1/ϵ)$ across multiple scales.

The same configurations were recalculated using model-predicted litterfall values $\widehat{y}$. Differences between observed and predicted fractal dimensions were quantified as follows:

$$\Delta FD=|F{D}_{observed}-F{D}_{predicted}|$$

(7)

Fractal dimensions were estimated using a box-counting algorithm, and changes before and after model prediction were recorded to quantify the extent to which each model preserved the spatial and structural integrity of the ecological system. Lower $\Delta FD$ values indicate stronger preservation of geometric complexity and improved structural consistency beyond traditional error-based metrics.

3.7. Reproducibility and Experimental Setup

To ensure reproducibility, all experiments were conducted using Python 3.10 with scikit-learn 1.2.2 and Pandas 1.5.3 [37]. To ensure robust and reproducible model evaluation, 10-fold cross-validation with shuffled folds was applied to the dataset. In this procedure, the dataset was randomly partitioned into ten equal subsets. For each iteration, nine folds were used for model training, while the remaining fold served as the validation set. This process was repeated ten times so that each fold was used once for validation. The final performance metrics were calculated as the average of the results obtained across all folds. To ensure reproducibility, a fixed random seed of 42 was used throughout all model training and cross-validation procedures. Evaluation metrics included R², Mean Absolute Error (MAE), and Root-Mean-Square Error (RMSE). Missing values in numerical columns were imputed using MICE (Multiple Imputation by Chained Equations), while categorical values were imputed using mode imputation. Feature engineering steps were implemented sequentially, including standardization, synthetic feature creation, and integration of fractal-inspired variables. The synthetic data generated using Gretel AI [10] followed the Navigator model and were combined with the original data after quality checks for feature alignment and label distribution consistency.

4. Results

4.1. Experimental Scenarios

In this study, we worked on two datasets: the first was used in [6], a dataset of 968 rows; and the second was a generated dataset of 5000 rows based on the original data of litterfall production. The geospatial classes (Geo-class 6, Geo-class 3, and Geo-class 4) were used to create different versions of the dataset, each tailored for regional analysis. In this paper, these geospatial classes were incorporated into the model training as classification features, allowing the models to capture regional variations that affect forest litterfall production.

We then divided the preprocessing stage into three trials: (1) the null values were handled using MICE and mode imputation; (2) then, we tried improving the results of the models by resolving the skewness in the features using log transformation and the same handling of empty values as the first trial; (3) finally, we still used the log transformation and then tried dropping columns that contained more than 25% null values, as previously done in [6], and then we proceeded with MICE imputation.

We created all of the combinations between preprocessing trials and different geospatial classes, which are presented in

Table 6. Preprocessing scenarios applied to different geospatial classes.

Scenario	Preprocessing Steps	Trial No.	Geospatial Class
Scenario 1	Log transformation, drop columns with >25% nulls, then impute the remaining using MICE.	3	None
Scenario 2	Same as Scenario 1.	3	Geo3
Scenario 3	Same as Scenario 1.	3	Geo4
Scenario 4	Same as Scenario 1.	3	Geo6
Scenario 5	Log transformation, then impute missing values using MICE.	2	None
Scenario 6	Same as Scenario 5.	2	Geo3
Scenario 7	Same as Scenario 5.	2	Geo4
Scenario 8	Same as Scenario 5.	2	Geo6
Scenario 9	Use MICE and mode imputation directly to handle missing values.	1	None
Scenario 10	Same as Scenario 9.	1	Geo3
Scenario 11	Same as Scenario 9.	1	Geo4
Scenario 12	Same as Scenario 9.	1	Geo6

for easier reference and simplicity. The “Scenario” represents an alias for each combination created. The “Preprocessing Steps” column represents the different steps of preprocessing implementation on the dataset for handling missing values, skewness, etc. The last column, “Geospatial Class”, represents the geo-class feature that was added to the dataset for the mentioned scenario and preprocessing steps.

As for the machine learning models, we used regression models [3]: linear and ridge as a baseline to evaluate the performance improvements achieved by HPAB; the same gradient boosting models that were used in [6], like LightGBM and CatBoost; and then XGBoost was added in our paper. We used Random Forest, like in [6], but then added decision trees and neural networks for our paper. The eight mentioned models were all implemented for the 12 scenarios.

In [6], the authors implemented Scenarios 1, 2, 3, and 4 with Random Forest, LightGBM and CatBoost models, but the difference is that we used imputation to handle missing values, which improved the results compared to just depending on dropping features if they reached a percentage of missing values.

4.2. Model Performance Metrics and Results

To understand how different preprocessing trials influenced model performance, we structured our experiments into three main preprocessing trials. Each trial was applied across various geospatial classifications to evaluate regional impacts. This section presents a detailed comparison of the model outcomes, isolating the effects of missing value handling, transformation techniques, and spatial feature inclusion.

We ultimately developed all possible combinations of the preprocessing trials and the replacement of geospatial features, resulting in a total of 12 scenarios. The performances of the individual machine learning models were assessed based on several key metrics. Specifically, the R-squared value, a measure of how well the model fits the data, ranged between 0.83 and 0.96, showcasing the models’ ability to capture the variability in the dataset effectively. Additionally, to ensure model stability, we applied 10-fold cross-validation, calculating the Mean Absolute Error (MAE) across folds, which represents the average difference between predicted and actual values, demonstrating a range between 0.38 and 0.06, indicating the models’ precision in making accurate predictions.

Moreover, the Root-Mean-Square Error (RMSE) reflected consistency in performance, with values falling between 0.63 and 0.09, further reinforcing the models’ reliability in estimating annual litterfall production. These results collectively underscore the robustness and high accuracy of the machine learning models in forecasting litterfall production, thus establishing their strong fit and predictive capabilities in this context.

Table 7. R-squared values of the implemented algorithms across 12 preprocessing scenarios.

Scenario	Random Forest	Light GBM	CatBoost	Linear Regression	Ridge Regression	Decision Tree	XGBoost	Neural Net
Scenario 1	0.9577	0.9617	0.9632	0.8925	0.8925	0.9211	0.9602	0.9263
Scenario 2	0.9560	0.9607	0.9604	0.8881	0.8881	0.9080	0.9599	0.9246
Scenario 3	0.9570	0.9613	0.9619	0.8915	0.8915	0.9149	0.9598	0.9210
Scenario 4	0.9563	0.9609	0.9614	0.8917	0.8917	0.9146	0.9591	0.9291
Scenario 5	0.9550	0.9601	0.9556	0.8939	0.8939	0.9130	0.9548	0.9068
Scenario 6	0.9533	0.9604	0.9546	0.8917	0.8917	0.9109	0.9564	0.9052
Scenario 7	0.9543	0.9601	0.9582	0.8934	0.8934	0.9147	0.9552	0.9137
Scenario 8	0.9545	0.9589	0.9569	0.8938	0.8938	0.9188	0.9549	0.9122
Scenario 9	0.9452	0.9504	0.9526	0.9526	0.9526	0.8999	0.9548	0.9423
Scenario 10	0.9435	0.9468	0.9457	0.9519	0.9519	0.8939	0.9537	0.9483
Scenario 11	0.9435	0.9472	0.9448	0.9522	0.9522	0.8991	0.9546	0.9470
Scenario 12	0.9445	0.9481	0.9482	0.9525	0.9525	0.8962	0.9531	0.9455

,

Table 8. Root-Mean-Square Error (RMSE) values of the implemented algorithms across 12 preprocessing scenarios.

Scenario	Random Forest	Light GBM	CatBoost	Linear Regression	Ridge Regression	Decision Tree	XGBoost	Neural Net
Scenario 1	0.0953	0.0907	0.0896	0.1529	0.1529	0.1303	0.0929	0.1250
Scenario 2	0.0972	0.0920	0.0928	0.1560	0.1560	0.1405	0.0932	0.1269
Scenario 3	0.0960	0.0912	0.0911	0.1537	0.1537	0.1344	0.0936	0.1282
Scenario 4	0.0968	0.0918	0.0913	0.1535	0.1535	0.1354	0.0941	0.1208
Scenario 5	0.0984	0.0925	0.0986	0.1519	0.1519	0.1364	0.0987	0.1391
Scenario 6	0.1001	0.0921	0.0990	0.1535	0.1535	0.1384	0.0971	0.1427
Scenario 7	0.0991	0.0923	0.0945	0.1523	0.1523	0.1358	0.0986	0.1366
Scenario 8	0.0989	0.0937	0.0966	0.1520	0.1520	0.1331	0.0988	0.1366
Scenario 9	0.6151	0.5872	0.5881	0.5722	0.5722	0.8170	0.5594	0.6355
Scenario 10	0.6251	0.6088	0.6163	0.5764	0.5764	0.8616	0.5663	0.6020
Scenario 11	0.6245	0.6074	0.6202	0.5742	0.5742	0.8400	0.5604	0.6082
Scenario 12	0.6192	0.6016	0.6015	0.5726	0.5726	0.8479	0.5707	0.6137

and

Table 9. Mean Absolute Error (MAE) values of the implemented algorithms across 12 preprocessing scenarios.

Scenario	Random Forest	LightGBM	CatBoost	Linear Regression	Ridge Regression	Decision Tree	XGBoost	Neural Net
Scenario 1	0.0681	0.0646	0.0631	0.1061	0.1061	0.0939	0.0672	0.0891
Scenario 2	0.0702	0.0660	0.0670	0.1092	0.1092	0.0989	0.0672	0.0894
Scenario 3	0.0689	0.0650	0.0658	0.1075	0.1075	0.0979	0.0674	0.0901
Scenario 4	0.0692	0.0656	0.0654	0.1075	0.1075	0.0979	0.0676	0.0849
Scenario 5	0.0698	0.0642	0.0681	0.1042	0.1042	0.0957	0.0703	0.0956
Scenario 6	0.0711	0.0652	0.0688	0.1061	0.1061	0.0969	0.0701	0.1002
Scenario 7	0.0702	0.0649	0.0656	0.1047	0.1047	0.0943	0.0709	0.0955
Scenario 8	0.0700	0.0654	0.0680	0.1049	0.1049	0.0955	0.0709	0.0947
Scenario 9	0.3829	0.3602	0.3721	0.3662	0.3664	0.5298	0.3596	0.4106
Scenario 10	0.3883	0.3731	0.3847	0.3643	0.3646	0.5467	0.3605	0.4070
Scenario 11	0.3881	0.3744	0.3852	0.3628	0.3631	0.5362	0.3597	0.3927
Scenario 12	0.3855	0.3693	0.3875	0.3644	0.3646	0.5373	0.3651	0.4112

present the R-squared, Root-Mean-Square Error (RMSE), and Mean Absolute Error (MAE) values for all of the implemented algorithms over the 12 scenarios.

4.3. Comparative Analysis

In this section, we will conduct a systematic ablation study that presents a comparative evaluation of the implemented algorithms across the twelve preprocessing scenarios shown in Table 7, Table 8 and Table 9, using R², RMSE, and MAE metrics. Overall, ensemble tree-based models—particularly CatBoost, LightGBM, and XGBoost—consistently achieved the highest predictive accuracy across most scenarios. This section also evaluates the effectiveness of the preprocessing strategies and highlights the best-performing models for each trial below:

1.

For the initial trial where the MICE and mode imputation methods were used to remove the nulls (Scenarios 9–12), XGBoost performed best, with an R-squared value of 0.95, MAE = 0.35, and RMSE = 0.55.

2.

In Scenarios 5–8, we added log transformation to the first trial, which resulted in LightGBM performing best, with R-squared = 0.96, MAE = 0.06, and RMSE 0.09.

3.

In the last trial, across Scenarios 1–4, we tried to enhance the first two by dropping columns that contained 25% missing values, and then we proceeded with the log transformation and MICE imputation. The CatBoost model achieved the best R-squared of 0.96, with MAE equal to 0.06 and RMSE equal to 0.08.

Gradient boosting models performed better than the linear models overall, with a mean R-squared and MAE of 0.96 and 0.06, respectively, while the corresponding values for the linear models were 0.89 and 0.1.

Differences in model performance and prediction insights do result from training the models with different geospatial classifications (Geo-class 6, Geo-class 3, and Geo-class 4). The degree of regional granularity provided by each geo-class affects the model’s capacity to identify particular patterns associated with regional features. The neural network model increased by 1% between different geospatial classes. As for Table 7, the R-squared value for the original data was 0.91. Then, when using Geo-classes 3 and 4, it increased to an accuracy of 0.92. Finally Geo-class 6 gave the best result, with R-squared = 0.93. This implies that by emphasizing specific administrative or environmental elements, the geographic class selection influences the model’s correctness and, in turn, enhances the model’s relevance and performance across various spatial scales.

Overall, the models trained on data with log transformation and MICE imputation consistently outperformed those using minimal preprocessing, particularly among gradient boosting models, demonstrating the importance of addressing skewness and missingness in ecological datasets, as appropriate preprocessing significantly enhances predictive stability and model performance.

4.3.1. Statistical Significance Analysis

A one-way ANOVA test was performed to determine whether the difference in RMSE between the linear regression and CatBoost models was statistically significant. Scenario 1 (Trial 3) was selected for this analysis, as it produced the highest overall R² value. The ANOVA results yielded an F-statistic of 67.39 with a p-value of $1.69\times {10}^{-7}$, which is substantially below the 0.05 significance level, indicating a statistically significant difference in predictive performance between the two models.

4.3.2. Error Analysis

A residual-based error analysis was conducted by examining the residuals between predicted and observed values. The absolute prediction error was computed for each observation, and the samples with the largest deviations were identified to investigate situations where the models performed poorly.

Table 10. Samples with the largest prediction errors across the evaluated models.

Sample ID	True Value	LightGBM	CatBoost	XGBoost	Largest Error
764	2.7389	13.6404	14.9915	2.36	12.2526
874	2.6025	13.5081	13.2418	2.24	10.6393
280	2.7846	13.6411	13.3204	2.35	10.5358

presents the observations with the highest absolute errors across the evaluated models. The results indicate that LightGBM and CatBoost occasionally produce large overestimations, with errors exceeding 10 units for several samples where the true litterfall values ranged between approximately 2.4 and 2.8. This suggests that certain observations represent rare environmental conditions or feature combinations that may be underrepresented in the training data.

In contrast, XGBoost exhibits substantially smaller extreme errors, with the largest deviation remaining below 0.6, indicating more stable predictions for difficult samples. Notably, several observations (e.g., samples 764, 874, and 280) appear among the highest error cases for multiple models, suggesting that these instances represent particularly challenging conditions for machine learning prediction.

4.3.3. Data Scarcity Test

To evaluate the robustness of the models under low-data conditions, XGBoost, CatBoost, and LightGBM were trained using 50%, 25%, and 10% of the training data while maintaining the same 10-fold cross-validation protocol.

Table 11. Data scarcity test: model performance under reduced training fractions using 10-fold cross-validation.

Model	Training Fraction	R2	MAE	RMSE
XGBoost	50%	0.954	0.071	0.100
	25%	0.942	0.080	0.111
	10%	0.918	0.095	0.132
CatBoost	50%	0.951	0.075	0.103
	25%	0.935	0.083	0.119
	10%	0.882	0.111	0.160
LightGBM	50%	0.947	0.075	0.107
	25%	0.918	0.092	0.133
	10%	0.824	0.145	0.196

shows the average R², MAE, and RMSE for each case. As expected, all models exhibit a gradual decrease in performance as the amount of training data decreases. XGBoost maintains the most stable performance, with R² decreasing from 0.954 to 0.918 when using only 10% of the data, whereas LightGBM shows the largest drop in performance under extremely low-data conditions. These results demonstrate that the models, particularly XGBoost, remain reasonably robust even when trained on very limited data.

4.4. Impact of Fractal Feature Engineering and Box-Counting Analysis

The integration of fractal-inspired features was evaluated across three machine learning models (CatBoost, LightGBM, and XGBoost) for Scenarios 1, 6, and 9 respectively, because they provided the best R-squared results for each preprocessing trial, as shown in Table 7. The results in Figure 2 show that the inclusion of these features led to marginal changes in model performance, with slight decreases in R² and minimal variations in error metrics. For CatBoost, R² decreased from 0.9632 to 0.9606, with MAE increasing slightly from 0.0631 to 0.066 and RMSE from 0.0896 to 0.0927. LightGBM exhibited stable performance, with R² changing from 0.9604 to 0.9596 and identical MAE and RMSE values (0.065 and 0.092, respectively) before and after the transformation. XGBoost showed a slight improvement in MAE and RMSE (from 0.3596 to 0.3529 and from 0.5594 to 0.5549, respectively) and a negligible increase in R² (from 0.9548 to 0.9554).

To assess the spatial and structural consistency of the predictions, fractal dimension analysis was performed on both the original and predicted litterfall values. Taking into consideration the different preprocessing trials, we chose the best-performing model for each trial, which left us with the CatBoost, LightGBM, and XGBoost models, as shown in

Table 12. Fractal dimension analysis before and after CatBoost for Scenario 1, processing Trial 3.

Fractal Metric	Before CatBoost	After CatBoost	Change	% Change
2D Spatial (Lat, Lon + Target)	0.9684	0.9272	−0.0412	−4.25%
3D Spatial (Lat, Lon, Alt + Target)	0.7678	0.6968	−0.0710	−9.25%
3D Structural (DBH, Height, Density+ Target)	1.0242	1.0121	−0.0121	−1.18%

,

Table 13. Fractal dimension analysis before and after LightGBM for Scenario 6, processing Trial 2.

Fractal Metric	Before LightGBM	After LightGBM	Change	% Change
2D Spatial (Lat, Lon + Target)	0.9684	0.9072	−0.0611	−6.31%
3D Spatial (Lat, Lon, Alt + Target)	0.7678	0.6798	−0.0880	−11.46%
3D Structural (DBH, Height, Density + Target)	1.0242	0.9954	−0.0288	−2.81%

and

Table 14. Fractal dimension analysis before and after XGBoost for Scenario 9, processing Trial 1.

Fractal Metric	Before XGBoost	After XGBoost	Change	% Change
2D Spatial (Lat, Lon + Target)	0.9684	0.9152	−0.0532	−5.49%
3D Spatial (Lat, Lon, Alt + Target)	0.7678	0.6871	−0.0807	−10.51%
3D Structural (DBH, Height, Density + Target)	1.0242	0.9997	−0.0244	−2.39%

. The 2D spatial fractal dimensions (using latitude and longitude) exhibited slight reductions across all models, with CatBoost showing a 4.25% decrease, LightGBM a 6.31% decrease, and XGBoost a 5.49% decrease. In the 3D spatial case (adding altitude), the decline was more pronounced: 7.69% for CatBoost, 11.46% for LightGBM, and 10.51% for XGBoost. The 3D structural dimensions (using DBH, height, and density) showed the smallest reduction: 1.18% for CatBoost, 2.81% for LightGBM, and 2.39% for XGBoost. These results indicate that while all models preserved the fractal structure of the original data to some extent, CatBoost maintained the highest structural integrity across spatial and structural dimensions.

4.5. Synthetic Data

Before generating the synthetic dataset, the second preprocessing configuration was applied to the original data. This configuration included log transformation followed by MICE and mode imputation to handle missing values. The preprocessed dataset was then used as input to the synthetic data generation framework suggested by Gretel AI.

Using the Navigator model, 5000 rows of synthetic ecological data were generated. The resulting synthetic dataset achieved an overall quality score of 91%, calculated as a weighted combination of multiple quality metrics. Specifically, the Field Distribution Stability score was 90%, the Field Correlation Stability was 90%, and the Deep Structure Stability reached 94%. As illustrated in Figure 3 and Figure 4, the synthetic dataset generated here preserved the distributional ranges and shapes of all ecological variables, including biologically constrained relationships such as DBH, height, and age, with no synthetic records falling outside the observed ecological bounds of the original dataset.

To evaluate the performance of machine learning algorithms on the generated dataset, preprocessing Scenarios 5–8 were applied due to their strong performance on the original dataset. The preprocessing pipeline included label encoding, MICE imputation, mode imputation, and log transformation. The predictive performance of all implemented algorithms on the synthetic dataset is summarized in

Table 15. R-squared values of algorithms on synthetic data across Scenarios S5 to S8.

Algorithm	S5	S6	S7	S8
Random Forest	0.9832	0.9819	0.9821	0.9821
LightGBM	0.9828	0.9819	0.9821	0.9818
CatBoost	0.9817	0.9795	0.9792	0.9788
Linear Reg.	0.8970	0.8333	0.8333	0.8336
Ridge Reg.	0.8970	0.8333	0.8333	0.8336
Decision Tree	0.9714	0.9670	0.9840	0.9692
XGBoost	0.9791	0.9781	0.9777	0.9786
Neural Net	0.9695	0.9611	0.9587	0.9633

,

Table 16. Root-Mean-Square Error (RMSE) of algorithms on synthetic data across Scenarios S5 to S8.

Algorithm	S5	S6	S7	S8
Random Forest	0.0611	0.0256	0.0255	0.0255
LightGBM	0.0620	0.0257	0.0256	0.0258
CatBoost	0.0640	0.0274	0.0276	0.0278
Linear Reg.	0.1524	0.0786	0.0786	0.0785
Ridge Reg.	0.1524	0.0786	0.0786	0.0785
Decision Tree	0.0800	0.0348	0.0340	0.0336
XGBoost	0.0684	0.0284	0.0286	0.0280
Neural Net	0.0827	0.0379	0.0389	0.0367

and

Table 17. Mean Absolute Error (MAE) of algorithms on synthetic data across Scenarios S5 to S8.

Algorithm	S5	S6	S7	S8
Random Forest	0.0301	0.0117	0.0117	0.0117
LightGBM	0.0361	0.0142	0.0141	0.0143
CatBoost	0.0403	0.0159	0.0159	0.0160
Linear Reg.	0.1045	0.0514	0.0514	0.0514
Ridge Reg.	0.1045	0.0514	0.0514	0.0514
Decision Tree	0.0359	0.0140	0.0138	0.0139
XGBoost	0.0442	0.0176	0.0180	0.0173
Neural Net	0.0547	0.0244	0.0238	0.0240

, using R², RMSE, and MAE as evaluation metrics.

Table 15, Table 16 and Table 17 show that ensemble learning algorithms achieved the highest predictive performance on the synthetic dataset. Random Forest consistently produced the highest R² values across most scenarios, reaching up to 0.9832 in Scenario S5, while also maintaining the lowest RMSE and MAE values. Gradient boosting models such as LightGBM and XGBoost also demonstrated strong performance, with R² values exceeding 0.97 across all evaluated scenarios.

In contrast, traditional regression approaches, including linear regression and ridge regression, produced significantly lower predictive accuracy, with R² values ranging between approximately 0.83 and 0.90. Although these models maintained relatively consistent error ranges compared to the original dataset, they were less capable of capturing the complex nonlinear relationships present in the ecological data.

Overall, the results obtained using the synthetic dataset were slightly higher than those achieved using the original dataset, with an approximate 2% improvement in R² values across most models.

5. Discussion

5.1. Discussing the Results of the Original Data

The preprocessing methods used on our ecological tabular dataset helped immensely with the results of the gradient boosting models, as they achieved the best range of R-squared values (0.9531–0.9632). CatBoost obtained the best R-squared value of 0.9632 because it uses ordered boosting and synthetic trees. It performed best in the scenario where we dropped columns that contain 25% null values, which is not the best option when handling missing values because it contributes to the loss of data. The omitted features can be crucial to the results and the training of the model, so despite having the highest R-squared value, this preprocessing method is not the best.

The scenario of handling the missing values using MICE, then using log transformation improved the performance of gradient boosting models (e.g., LightGBM, CatBoost) by up to 1% in R² compared to scenarios without transformation. This is likely because the log transformation reduced right-skewness in the litterfall variable, making the distribution more symmetric and allowing the models to better capture underlying patterns. Additionally, MICE preserved inter-feature relationships by estimating missing values based on multivariate conditional distributions, preventing information loss compared to simpler methods like mean or mode imputation.

As shown in Table 7, Table 8 and Table 9, the gradient boosting models and neural networks handled the data better than the linear and ridge regression models, because the former models are robust and do not rely on assumptions of linearity or normality.

The regression models performed well in the first scenario, where no log transformation was implemented, with an R-squared value range of 0.9526–0.9519 across all geospatial class substitutions, and an RMSE value range of 0.5722–0.5764, with a very high margin of error. However, when the log transformation was used, a huge drop in the R-squared value by −6% took place, because the regression models became biased to skewed data, which was also apparent in the RMSE value.

In this study, we tested Random Forest and decision tree models, both of which yielded good results, but the Random Forest proved to be better overall, with an R-squared range of 0.9577–0.9452, whereas the decision tree R-squared values ranged from 0.9211 to 0.8999.

Table 18. R-squared values for the best-performing algorithm and preprocessing trial in each scenario.

Scenario	Preprocessing Trial	Best Algorithm (R2)	Training Time
Scenario 1	3	CatBoost: 0.9632	2.35 s
Scenario 2	3	LightGBM: 0.9607	0.81 s
Scenario 3	3	LightGBM: 0.9613	0.8 s
Scenario 4	3	CatBoost: 0.9614	2.1 s
Scenario 5	2	LightGBM: 0.9601	1.26 s
Scenario 6	2	LightGBM: 0.9604	1.15 s
Scenario 7	2	LightGBM: 0.9601	1.17 s
Scenario 8	2	LightGBM: 0.9589	1.17 s
Scenario 9	1	XGBoost: 0.9548	2.69 s
Scenario 10	1	XGBoost: 0.9537	1.9 s
Scenario 11	1	XGBoost: 0.9546	1.6 s
Scenario 12	1	XGBoost: 0.9531	1.6 s

presents the R-squared values for the best models in each scenario. Overall ranking based on the frequency of best performance across scenarios indicates that LightGBM achieved the best results in seven scenarios, followed by XGBoost in four scenarios and CatBoost in two scenarios.

A very small difference in the R-squared values could be observed between different geospatial substitutions across the datasets, which indicates that the model is robust and that, despite the geo-classes having a low positive and negative correlation, they are not crucial to the results of the model training except for a few of them. As [6] previously proved, there is a nonlinear relationship between the total weight of the litterfall and the rest of the features, which is why regression models performed poorly while the gradient boosting models were effective.

Notably, LightGBM demonstrated superior training speed across several scenarios, particularly in Scenarios 2 and 3, where the training times were as low as 0.80 and 0.81 s, respectively. This efficiency can be attributed not only to LightGBM’s inherent optimizations like histogram-based binning and leaf-wise growth strategy, but also to the preprocessing step in these scenarios, which involved dropping columns with over 25% missing values. This dimensionality reduction likely reduced the training load, thereby accelerating model convergence. In contrast, scenarios using only log transformation and MICE imputation retained a higher number of features, leading to slightly increased training times despite using the same model.

The analysis of fractal dimensions before and after model prediction, as shown in Figure 5, provides insights into how well each machine learning model preserved the spatial and structural complexity of the input data. A smaller decline in fractal dimension suggests that the model better maintained the intrinsic patterns present in the data. CatBoost yielded the smallest percentage change in all three dimensions, particularly in the structural domain, indicating that its predictions were more consistent with the natural heterogeneity of the input features. In contrast, LightGBM and XGBoost showed slightly larger reductions in both spatial dimensions, suggesting a higher degree of smoothing or simplification in their outputs.

5.2. Discussing the Results of the Synthetic Data

A synthetic data quality score of 91% was achieved, indicating a strong correspondence between the original dataset and the generated synthetic data. Figure 6 displays a heatmap for the training data and the synthetic data, as well as a heatmap for the calculated difference in correlation values, to facilitate the comparison of field correlations. Preserving the integrity of field correlations can be crucial if the synthetic data is meant to be used for statistical analysis or machine learning.

In the synthetic dataset experiments, the predictive performance was slightly higher than that obtained using the original dataset, with an increase of approximately 2% in the R² values. The Random Forest and gradient boosting models achieved the best performance, consistent with the trends observed in the original dataset. Linear regression-based models showed comparatively lower R² values, although their performance remained slightly higher than that obtained with the real dataset.

The marginal 2% improvement in R² observed when training on the synthetic dataset under the same cross-validation setting is consistent with the smoother distributional properties inherent to generatively modeled data, where noise and outliers from real-world measurement error are reduced. This does not necessarily indicate superior generalization but, rather, reflects the statistical regularization effect introduced during the data synthesis process.

According to Table 15, the decision tree and the neural network were the only models where we could detect a change in the R-squared value, which increased by 1% when changing the geospatial column across the four datasets. When using Geo-class 3, R-squared = 0.967; using Geo-class 4, R-square = 0.9840; using Geo-class 6, R-squared = 0.9692.

5.3. Comparison of Previous Models

Unlike previous studies that relied primarily on combinations of linear regression models [6,37], where features containing more than 25% missing values were removed during preprocessing, the approach adopted in this study preserves these features by applying MICE and mode imputation techniques. This strategy allows the models to retain more ecological information while handling missing data more effectively.

In [37], combinations of regression models were evaluated and achieved R² and RMSE values of approximately 0.59 and 0.39, respectively. Similarly, [6] applied several gradient boosting models, achieving maximum performance values of approximately R² = 0.69 and RMSE = 0.31. That study also explored the Mixed-Effects Random Forest (MERF) model, which achieved slightly improved performance, with R² values close to 0.70 and RMSE around 0.30.

In contrast, the models developed in the present study achieved substantially higher predictive performance. The gradient boosting models, combined with the proposed preprocessing framework and k-fold cross-validation strategy, achieved an R² value of approximately 0.96 and an RMSE of 0.09. Furthermore, when trained on the generated synthetic dataset produced using the Gretel AI Navigator model, the models achieved R² values close to 0.98 and RMSE values around 0.02, demonstrating the potential of synthetic data augmentation for improving ecological prediction performance.

5.4. Implications of Findings

The use of MICE (Multiple Imputation by Chained Equations) for data preprocessing in this study underscores its effectiveness in handling missing data in ecological research. By preserving the statistical relationships within the dataset, MICE ensured a high-quality, bias-minimized dataset for model training. Compared to simpler imputation methods, MICE was better equipped to handle the multivariate complexity of ecological data, enabling more reliable predictions of annual litterfall weight. Its adaptability and efficiency make it a valuable preprocessing technique for similar datasets, particularly those with missing or incomplete information.

The superior performance of gradient boosting models in predicting annual litterfall weight highlights their ability to capture nonlinear relationships and complex interactions among variables. These models provided high predictive accuracy while offering insights into feature importance, shedding light on the environmental factors most critical to litterfall production. Their resilience to noise and flexibility make them particularly well suited for ecological applications, where data can often be noisy or incomplete. This reinforces their value as a preferred choice for predictive tasks in ecological and environmental research.

Together, the combination of MICE for preprocessing and gradient boosting models for prediction offers a robust framework for tackling complex ecological problems. This methodology not only enhances decision-making in areas such as forest management and carbon cycling but also serves as a benchmark for future research. While highly effective, careful attention should be given to preprocessing quality and model interpretability, so as to ensure that the findings are both accurate and actionable. These approaches pave the way for scalable, automated systems to support sustainable ecological management.

Although the fractal-inspired features were rooted in ecologically relevant scaling principles, they contributed only marginally to model performance. The limited improvement may be attributed to the relatively low structural complexity of the dataset and the existing capacity of ensemble models to capture nonlinear relationships. Nonetheless, this experiment underscores the feasibility of integrating fractal theory into ecological feature engineering and highlights potential avenues for future research involving more heterogeneous or multi-layered datasets.

The original dataset was effectively supplemented by the synthetic data produced through Gretel AI, enabling strong training of machine learning models. This method showcased its ability to address issues linked to restricted datasets by generating 5000 high-quality synthetic records, which is especially beneficial in ecological studies, where gathering data can be both time-consuming and resource-intensive.

The integration of synthetic data into the modeling process yielded a high predictive accuracy (91%), confirming the utility of the synthetic dataset in enhancing the performance of predictive models. This underscores the potential of synthetic data to bridge data gaps without compromising model reliability.

Beyond model performance improvements, the use of synthetic ecological data has important practical implications for environmental forecasting. Ecological datasets are often limited due to the high cost and time required for field measurements. Synthetic data generation provides a scalable approach for augmenting existing datasets while preserving their statistical structure. This enables machine learning models to be trained on larger and more diverse datasets, potentially improving their robustness and applicability in ecological monitoring and environmental prediction tasks.

5.5. Limitations

While the use of synthetic data enabled us to overcome sample size limitations and improve model training stability, it also introduces potential drawbacks. In particular, there is a potential risk that machine learning models may partially overfit to patterns present in the synthetic data distribution, rather than fully reflecting real-world ecological variability. Synthetic data may not fully capture all of the complex, real-world variability present in ecological systems, particularly when rare or extreme events are underrepresented in the original dataset. Additionally, although the Gretel Navigator model preserves statistical properties through advanced generative modeling, it does not guarantee the preservation of causal relationships. Therefore, predictions made using synthetic-augmented datasets should be interpreted with caution, especially when extrapolating to new regions or unseen environmental conditions.

Furthermore, the generalizability of the findings may be constrained by the specific ecological context represented in the dataset. Climatic, geographic, and species-specific characteristics associated with the study sites may limit the transferability of the trained models to other forest ecosystems or regions with different environmental conditions. Although cross-validation provides a robust estimate of model generalization within the available data, evaluating the proposed Hybrid Preprocessing and Augmented Boosting Framework (HPABF) on independent real-world datasets from different bioclimatic zones would further strengthen its external validity and broader applicability.

Moreover, although the proposed framework addresses data scarcity through synthetic data augmentation, the robustness of the approach under varying levels of real data availability was only partially evaluated in this study. A minimal data scarcity test was conducted to assess model performance when trained on reduced fractions of the original dataset (50%, 25%, and 10%), demonstrating that the models—particularly XGBoost—remain relatively robust. Future work could extend these experiments across all scenarios and incorporate synthetic augmentation under extremely low-data conditions to provide a more comprehensive evaluation of the HPABF’s effectiveness in ecological prediction tasks with limited field observations.

6. Conclusions

The findings of this study show that gradient boosting models demonstrated strong capability for modeling and predicting litterfall dynamics under limited data conditions, highlighting the advantages of a Hybrid Preprocessing and Augmented Boosting Framework (HPABF). The results highlight the importance of robust preprocessing strategies, particularly feature-preserving imputation and data transformation techniques, in improving predictive performance for ecological datasets with missing values.

To address data limitations, synthetic data generated using Gretel AI’s Navigator model was used to augment the dataset while preserving its statistical properties. This approach demonstrates the potential of synthetic data generation as a practical solution for ecological modeling tasks where data availability is limited.

In addition to predictive modeling, fractal dimension analysis provided a novel evaluation perspective by assessing the structural complexity of model outputs. The results suggest that fractal-based evaluation can complement traditional performance metrics such as R², RMSE, and MAE, offering additional insights into the structural consistency of ecological predictions.

The proposed framework demonstrates a scalable and transferable approach to ecological prediction, particularly valuable for data-scarce regions. Accurate litterfall predictions can inform forest management practices, including nutrient cycling assessment, carbon budgeting, and early detection of ecosystem stress. This study underscores the importance of integrating advanced machine learning, synthetic data, and fractal geometry to improve ecological modeling.

Future research should expand geographic coverage, refine fractal feature design, explore integration with feature selection techniques, and investigate the application of the proposed methodology to other environmental and spatial datasets to further enhance interpretability and model generalizability.