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

TL;DR

This paper introduces a state-space universal dynamic equations framework that combines ecological theory with neural networks to model and predict complex nonlinear ecological dynamics, including chaos and regime shifts, while accounting for uncertainty.

Contribution

It develops a novel state-space approach integrating universal differential equations with uncertainty modeling, enhancing ecological dynamic predictions.

Findings

Successfully recovered nonlinear biological interactions from data.

Achieved best forecasting on chaotic and oscillating time series.

Demonstrated applicability on simulated and empirical datasets.

Abstract

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 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 being achieved 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.