Combining Ecological Theory with Data to Predict Nonlinear Ecosystem Dynamics

Ecosystems often exhibit complex nonlinear dynamics like oscillations, chaos, and regime shifts. Accurately representing these dynamics requires a flexible modeling framework that can learn nonlinear relationship from available data sets. Universal dynamic equations  (UDEs) have shown promise in modeling complex dynamics by combining functional forms to encode known biological mechanisms and constraints, with neural networks that learn unknown relationships from data. However, these methods do not yet accommodate the forms of uncertainty common to ecological datasets. To address this limitation, we developed State-Space Universal Dynamic Equations (SSUDEs) by combining universal differential equations with a state space modeling framework, accounting for uncertainty. We tested this framework on two simulated and two empirical case studies and found that this method can recover nonlinear biological interactions that produce complex behaviors including chaos and regime shifts. Their forecasting performance is context-dependent with the best performance on chaotic and oscillating time series. This new approach leveraging both ecological theory and data-driven machine learning offers a promising new way to make accurate and useful predictions of ecosystem change, such as we are observing in coral, intertidal and sea grass ecosystems.