Recovering complex ecological dynamics from time series using state-space universal dynamic equations

Ecological systems often exhibit complex nonlinear dynamics like oscillations, chaos, and regime shifts. Universal dynamic equations have shown promise in modeling complex dynamics by combining known functional forms with neural networks that represent unknown relationships. 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 by combining universal difference and differential equations with a state-space modeling framework, accounting for uncertainty. We tested this framework on three 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 innovative approach leveraging both ecological theory and data-driven machine learning offers a promising new way to make accurate and useful predictions of ecosystem change. State-space universal dynamic equations can recover nonlinear biological interactions that produce complex behaviors, including chaos and regime shifts, offering a novel way for accurate predictions of ecosystem dynamics.