An ecosystem may suddenly shift to a new state, characterized by a different structure, species composition and/or functioning. This phenomenon is referred to as a “catastrophic shift” in ecology. Such shifts to a degraded state (e.g. occurring in drylands) can lead to dramatic economic as well as ecological consequences. A catastrophic shift, according to the mathematician René Thom’s catastrophe theory, is an abrupt change in the state of a system, which suddenly shifts from one stable state to another stable state, separated by a tipping point. Catastrophic shifts are usually associated with hysteresis. Catastrophic shifts may either have positive consequences (shifts to the “healthy” state) or negative consequences (shifts to the “degraded” state) for the ecosystem functioning and related services. In physics catastrophic shifts are known as first-order phase transitions, and in mathematics they are subcritical bifurcations.