A tipping point for tipping points

Tipping points (TPs) – often understood as abrupt changes to a system – have become a popular framework for ecology and environmental science across spatial and temporal scales. The underlying, quantitative foundation of TP theory is built on mathematical models from catastrophe and predator–prey theories. Tipping points based on a cusp catastrophe model were critiqued early, but that history did not happen for TPs derived from predator–prey theory. Here we summarize both histories and resulting flaws in the understanding and application of TPs. Unfortunately, much of what has been written about TPs is derived from predator–prey theory and is not readily defended: multiple assumptions cannot apply; other problems exist; and evidence is weak or lacking. Fortunately, early critique led to a viable approach to evaluate TPs based on the cusp catastrophe model. We suggest TPs based on predator–prey theory be abandoned and many putative TPs be re‐assessed with modern tools based on the cusp catastrophe model and/or other potential approaches. Tipping points may then be useful to understand changing systems if other important problems (publication bias, lack of empirical evidence, stability concepts, scale) can also be surmounted. In the meantime, the science of TPs lags far behind the concept's popularity, and so TPs are not yet a solid foundation for environmental policies.