A Unified Data-Driven Framework for Ecological Dynamics: Derivation and Cross-System Validation

Traditional ecological models are often constrained by pre-defined theoretical structures that may not capture the full complexity of real-world systems. This paper presents a purely data-driven approach to derivea unified ecological dynamical equation from large-scale, heterogeneous datasets. We employed Sparse Identification of Nonlinear Dynamics (SINDy) on 12 distinct public datasets encompassing terrestrial, aquatic, and microbial ecosystems. The identified parsimonious core equation, 1Xi dXidt =αi−βiXi+ j̸=iγijXj + kδikEk, encapsulates intrinsic growth (αi), density-dependence (βi), species interactions (γij), and environmental forcing (δik). This unified model was rigorously validated on 10 additional independent datasets, achievingan average predictive accuracy (R2) of 0.953±0.003, significantly outperforming traditional models such as Lotka-Volterra and Logistic growth models. This work demonstrates the power of data-driven methods to discover fundamental, cross-system ecological principles, offering a powerful new tool for ecological forecasting.