Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.

All Change Research on early warning signals for critical transitions in complex systems such as ecosystems, climate, and global finance systems recently has been gathering pace. At the same time, studies on complex networks are starting to reveal which architecture may cause systems to be vulnerable to systemic collapse. Scheffer et al. (p. 344 ) review how previously isolated lines of work can be connected, conclude that many critical transitions (such as escape from the poverty trap) can have positive outcomes, and highlight how the new approaches to sensing fragility can help to detect both risks and opportunities for desired change.

It has been suggested that tropical forest and savanna could represent alternative stable states, implying critical transitions at tipping points in response to altered climate or other drivers. So far, evidence for this idea has remained elusive, and integrated climate models assume smooth vegetation responses. We analyzed data on the distribution of tree cover in Africa, Australia, and South America to reveal strong evidence for the existence of three distinct attractors: forest, savanna, and a treeless state. Empirical reconstruction of the basins of attraction indicates that the resilience of the states varies in a universal way with precipitation. These results allow the identification of regions where forest or savanna may most easily tip into an alternative state, and they pave the way to a new generation of coupled climate models.

Coral reefs support immense biodiversity and provide important ecosystem services to many millions of people. Yet reefs are degrading rapidly in response to numerous anthropogenic drivers. In the coming centuries, reefs will run the gauntlet of climate change, and rising temperatures will transform them into new configurations, unlike anything observed previously by humans. Returning reefs to past configurations is no longer an option. Instead, the global challenge is to steer reefs through the Anthropocene era in a way that maintains their biological functions. Successful navigation of this transition will require radical changes in the science, management and governance of coral reefs.

Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called ‘early warning signals’, and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.