Resilience indicator for ecosystems subject to high risk of irreversible degradation: a probabilistic method based on Bayesian inference

Ecosystem degradation is usually abrupt and unexpected shifts in ecosystem states that cannot be easily reversed. Some ecosystems might be subject to high risks of irreversible degradation (RID) because of strong undesirable resilience. In this study, we propose a probabilistic method to quantify RID by measuring the probability of the recovering threshold being unattainable under real world scenarios. Bayesian inference was used for parameter estimations and the posteriors were used to calculate the threshold for recovery and thereby the probability of it being unattainable, i.e., RID. We applied this method to lake eutrophication as an example. Our case study supported our hypothesis that ecosystems could be subject to high RID, as shown by the lake having a RID of 72% at the whole lake level. Spatial heterogeneity of RID was significant and certain regions were more susceptible to irreversible degradation, whereas others had higher chances of recovery. This spatial heterogeneity provides opportunities for mitigation because targeting regions with lower RID is more effective. We also found that pulse disturbances and ecosystem-based solutions had positive influences on lowering the RID. Pulse disturbances had the most significant influence on regions with higher RID, while ecosystem-based solutions performed best for regions with moderate RID, reducing RID to almost 0. Our method provides a practical framework to identify sensitive regions for conservation as well as opportunities for mitigation, which is applicable to a wide range of ecosystems. Our findings highlighted the worst scenario of irreversible degradation by providing a quantitative measure of the risk, thus raising further requirements and challenges for sustainability.