Parameter estimation and identifiability analysis of stability and tipping points in potentially bistable ecosystems

Ecological regime shifts are potentially a common property of ecosystems, describing transitions between alternative stable states that can represent healthy or unhealthy conditions under the same environmental drivers. Once a tipping point, defined as a critical threshold separating alternative stable states, is crossed, the system may degrade and recovery can be difficult, making early detection essential for effective ecosystem management. Predicting these tipping points requires models that exhibit bistability, representing systems that can exist in two alternative stable states under identical environmental conditions. A key question is whether standard ecological monitoring data can be used to identify bistability and accurately estimate tipping points. Using the Carpenter model of lake eutrophication, which expresses bistability between clear and polluted water states, we generate synthetic data under known stability regimes. Profile likelihood analysis is then applied to assess parameter identifiability and detect system stability and tipping points. Our results show that standard monitoring data do not always provide sufficient information to distinguish bistable from stable regimes. Importantly, bistability and tipping points become practically identifiable only when data are collected very close to the tipping point.