Global stability and tipping point prediction in a coral–algae model using landscape–flux theory

Abstract. Coral reef ecosystems are remarkable for their biodiversity and ecological significance, exhibiting the capacity to exist in different stable configurations with possible abrupt shifts between these alternative stable states. This study applies landscape–flux theory to analyze how these complex systems behave when subjected to random environmental disturbances. We use this theory to formulate and investigate several early warning indicators of ecosystem transitions in a well-known coral reef model. We studied a number of specific indicators, including the average flux (the driving force when the system is out of equilibrium), the entropy production rate (EPR), the non-equilibrium free energy, and the time irreversibility of the cross-correlation functions. These indicators demonstrate a distinctive advantage when compared to classical indicators based on the phenomenon of critical slowing down; they exhibit turning points midway between two bifurcations, enabling them to forecast transitions in both directions substantially earlier than conventional methods. In contrast, early warning indicators based on the critical slowing down (CSD) phenomenon typically only become apparent when the system approaches the actual bifurcation or tipping point(s). Our findings offer improved tools for anticipating critical transitions in coral reef and other at-risk ecosystems, with the potential to enhance conservation and management strategies.