Unifying framework for quantifying regime shifts in complex ecosystems

Complex ecosystems exhibit more nonlinearity and stochasticity than the simple ones, rendering timely and accurate detection regime shifts in complex dynamic ecosystems a challenge. To resolve this dilemma, one of the most critical steps is to determine and quantify the equilibrium states reached by complex ecosystems under a given disturbance. This study utilizes the energy-transfer-network equilibrium model based on Nash-equilibrium theory and the maximum power principle to quantify and predict the equilibrium state of a complex ecosystem with multiple trophic levels. The model successfully simulated ecosystem energy transfer under equilibrium and quantified ecosystem state. The application of the model to monitor the aboveground biomass of a long-term dataset of un-grazed steppe achieved the description and prediction of the regime shift. This approach can possibly be used not only to find the equilibrium state for complex and simple ecosystems but also to remove the limitations of current methods to determine the attraction domain or stable points through statistical or difference equations in regime shift studies.