Cascading effects of regime shifts The potential for regime shifts and critical transitions in ecological and Earth systems, particularly in a changing climate, has received considerable attention. However, the possibility of interactions between such shifts is poorly understood. Rocha et al. used network analysis to explore whether critical transitions in ecosystems can be coupled with each other, even when far apart (see the Perspective by Scheffer and van Nes). They report different types of potential cascading effects, including domino effects and hidden feedbacks, that can be prevalent in different systems. Such cascading effects can couple the dynamics of regime shifts in distant places, which suggests that the interactions between transitions should be borne in mind in future forecasts. Science, this issue p. 1379; see also p. 1357

Abstract Regime shifts are large, abrupt, and persistent critical transitions in the function and structure of ecosystems. Yet, it is unknown how these transitions will interact, whether the occurrence of one will increase the likelihood of another or simply correlate at distant places. We explored two types of cascading effects: Domino effects create one-way dependencies, whereas hidden feedbacks produce two-way interactions. We compare them with the control case of driver sharing, which can induce correlations. Using 30 regime shifts described as networks, we show that 45% of regime shift pairwise combinations present at least one plausible structural interdependence. The likelihood of cascading effects depends on cross-scale interactions but differs for each type. Management of regime shifts should account for potential connections.

Regime shifts occur across a wide range of social-ecological systems (1–3). They are difficult to predict and reverse (4, 5) and often produce sustained shifts in the availability of ecosystems services (6). When a system undergoes a regime shift, it moves from one set of self-reinforcing processes and structures to another (2, 7–9). Changes in a key variable (for example, temperature in coral reefs) often make a system more susceptible to shifting regimes when exposed to shock events (such as hurricanes) or the action of external drivers (such as fishing) (10). More than 30 different regime shifts in social-ecological systems have been documented (3), and similar nonlinear dynamics are seen across societies, finance, language, neurological diseases, and climate (11, 12). As humans increase their pressure on the planet, regime shifts are likely to occur more often and more severely (13–15).

An emergent challenge for science and practice is that regime shifts can potentially lead to subsequent regime shifts. We define a regime shift as cascading when its occurrence may affect the occurrence of another regime shift. A variety of causal pathways connecting regime shifts have been identified (table S1). For example, eutrophication is often reported as a regime shift preceding hypoxia or dead zones in coastal areas (16). Similarly, hypoxic events have been reported to affect the resilience of coral reefs to warming and other stressors in the tropics (17). If, why, and how a regime shift somewhere in the world could affect the occurrence of another regime shift remain largely open questions and a key frontier of research (18, 19).

Research on regime shifts is often confined to well-defined branches of science, reflecting empirical, theoretical (20), or predictive approaches (10, 21). These approaches require a deep knowledge of the causal structure of the system or a high quality of spatiotemporal data. Hence, research on regime shifts has generally focused on the analysis of individual types of regime shifts rather than potential interactions across systems. We took another approach and instead explored potential cascading effects among a large set of regime shifts. We investigated two types of interconnections: domino effects and hidden feedbacks. Domino effects occur when the feedback processes of one regime shift affect the drivers of another regime shift, creating a one-way dependency (10, 19, 22). A feedback mechanism is a self-amplifying or -dampening process characterized by a pathway of causal processes that return to its origin, creating a cycle. Two-way interactions arise when two regime shifts combine to generate new feedbacks that cannot be identified in the separated regime shifts (18, 22) and, if strong enough, can amplify or dampen the coupled dynamics. We call them “hidden feedbacks” because they only show when two regime shift networks are combined. We contrast these cascading effects, in which the occurrence of a regime shift gives rise to subsequent regime shifts, with the potentially multiplying albeit different effect of two regime shifts being caused by common drivers. Driver sharing is likely to increase correlation in time or space among regime shifts but not necessarily interdependence (13, 19).

Hypotheses of cascading effects In analyzing individual regime shifts, bifurcation theory often treats drivers as slow variables, which assumes that their change is relatively slower than changes in variables that describe the state of the system (1, 2, 11, 12, 23, 24). Applying the same logic to pairs of regime shifts, we first expect that domino effects will be dominated by connections from regime shifts occurring at larger spatial scales and slower temporal dynamics than regime shifts receiving the connection (25, 26). Second, hidden feedbacks are expected to occur when scales match in space and time because for a new feedback to emerge, regime shifts need to be somewhat aligned in the scale at which their process operates. Third, regime shifts occurring in similar ecosystem types or land uses will be subject to relatively similar sets of drivers, and thus, we expect driver sharing to be context-specific (13, 19). We tested the three hypotheses by analyzing regime shifts as networks of drivers and feedback processes. These directed signed graphs allowed us to explore driver co-occurrence, directional pathways, and emergent feedback cycles of coupled regime shift networks (27). The empirical basis for our investigation draws from the regime shifts database (figs. S1 and S2) (3), which offers syntheses of more than 30 types of regime shifts, and >300 case studies based on literature review of >1000 scientific papers. The database describes regime shifts in terms of their alternative regimes, drivers, feedback mechanisms, impacts on ecosystem services, and management options. It provides a set of 75 categorical variables about impacts, scales, and evidence types used to test our expectations (27). The database consistently encodes regime shifts into causal diagrams as a graphical summary of the drivers and underlying feedbacks of each regime shift (fig. S1). Causal diagrams for each regime shift were converted into a network by creating the adjacency matrix A, where A i,j is 1 if there is a connection or 0 if not (27). A link between two nodes in these networks means that there is at least one scientific paper reviewed in the database providing some evidence for a causal relationship (3, 13). Three response variables matrices were created by merging pairs of regime shift networks (Fig. 1): (i) For driver sharing, it is the number of common drivers; (ii) for domino effects, it is the number of directed pathways that connect two regime shifts; and (iii) for hidden feedbacks, it is the number of new cycles that emerge when joining two regime shift networks (27). We tested the hypotheses using exponential random graph models (27). In this framework, our research question can be rephrased as “What is the likelihood of a link between regime shifts in the response variable matrix, and what features change this likelihood?” As explanatory variables, we used the regime shift database categorical variables, focusing on how similar two regime shifts are and whether the similarity increases the likelihood of having a link on the response variable matrices (27). The specification for the model follows a Poisson reference distribution (28), given that the response variables contain weighted links of count data—how many domino effects, hidden feedbacks, or shared drivers link pairs of regime shifts. Fig. 1 Method scheme. Pairs of regime shift causal networks were merged to create a response variable matrix that accounted for drivers shared, domino effects, or hidden feedbacks. In all examples, two minimal regime shifts are depicted as causal diagrams, drivers are red, and variables belonging to feedbacks are purple. For driver sharing, the joint network is simplified as a two-mode network that allows us to study the co-occurrence of drivers (in red) across regime shifts (in blue). Driver a is shared by regime shifts 1 and 2, but driver b is not. The response variable matrix counts the number of drivers shared by all pairwise combinations of regime shifts. For domino effects, two regime shift networks are joined together, where driver c in regime shift 2 is also part of a feedback process in regime shift 1, creating a one-way dependency (orange link) between the two regime shifts. The response variable matrix counts all the one-way causal pathways between pairwise combinations of regime shifts. For hidden feedbacks, two minimal regime shifts, when joined together, give rise to a new unidentified feedback (orange circular pathway). The response variable matrix counts all hidden feedbacks that arise when merging pairwise combinations of regime shifts. The 30 causal networks used and the labeled matrices of the resulting response variables are shown in figs. S1 and S3.

Results Regime shifts can be structurally interdependent (Fig. 2). The three response variables combined show that ~45% of the regime shift couplings analyzed present structural dependencies in the form of one-way interactions for the domino effect or two-way interactions for hidden feedbacks. Whereas ~5 and ~2% of the couplings present only domino effects and hidden feedbacks, respectively, ~28% of the pairwise combinations are linked through two different types of connections, and ~9% are linked by all three of them. Only for 19% of the pairwise combinations can we be certain with the current dataset that there are no cascading effects. However, the discovery of new drivers or feedback mechanisms underlying these dynamics could reduce this estimate. Fig. 2 Potential structural dependencies between regime shifts. (A) The three response variables combined show eight different possibilities in which regime shifts can interact through cascading effects. (B) Driver sharing is the most common type found. (C) Domino effects and hidden feedbacks alone or in combination account for ~45% of all regime shift couplings analyzed, implying structural dependence. Driver sharing is the most common type of connection found (Fig. 2). Regime shifts can correlate in time and space because of common drivers, but they do not necessarily become interdependent (13, 19)—that is, the occurrence of one does not affect the probability of the second occurring. Of all pairwise regime shift combinations, 36% were coupled only by driver sharing. The resulting matrix for driver sharing describes the co-occurrence patterns of 77 drivers across the 30 regime shifts analyzed. In our sample, aquatic regime shifts tend to have and share more drivers, although the driver sharing is not exclusively with other aquatic regime shifts (Figs. 3A and 4B). The highest driver co-occurrence was found between regime shifts in kelps, marine eutrophication, and the collapse of fisheries. Terrestrial and polar regime shifts tended to have fewer and more specific sets of drivers. Large-scale regime shifts in polar and subcontinental areas (such as monsoon weakening) have fewer drivers but are hotspots of sharing, typically including climate-related drivers. Drivers that co-occurred most frequently were related to food production, climate change, and urbanization, yet none of them is ubiquitous in our sample (Fig. 3B). Fig. 3 Patterns of cascading effects. (A, C, and E) Regime shifts are ranked according to their role in (A) driver sharing, (C) domino effect, and (E) hidden feedbacks. (B, D, and F) Key variables involved in cascading effects are shown for (B) driver sharing, (D) domino effects, and (F) hidden feedbacks. The distribution of drivers shared per regime shift (A) with respect to the number of drivers each one has (black points) shows that regime shifts in aquatic environments tend to have and share more drivers. WAIS, West Antarctica Ice Sheet collapse. Regime shifts that produce most domino effects (high outdegree) are Earth system tipping points, whereas the regime shifts that receive the most (high indegree) occur in aquatic and land-water interface (C); labels are plotted only for regime shifts in which the maximum number of domino effects (four) is found. Most variables associated with domino effects are related to climate and transport mechanisms (D). These variables are part of a feedback mechanism in one regime shift that are in turn drivers in another regime shift. Hidden feedbacks occur typically in terrestrial and Earth system regime shifts. The distribution of hidden feedbacks (E) is organized by higher to lower mean number of feedbacks. Boxplots are shown in log-scale after zero values have been removed. The variables most often involved in hidden feedbacks have high betweenness and closeness centralities (F) calculated on the network of all regime shifts in our sample (n = 30). These measures reveal the variables (labeled) that lie on most shorter pathways from all other variables in the network. Fig. 4 Cascading effects across scales. (A) Summary of the statistical results. Only models with the lower Akaike information criteria were included on the figure. The figure is complemented by tables S3 to S5, with alternative models fitted. (B to J) Circular plots showing the mixing matrices of cascading effects [driver sharing, (B), (E), and (H); domino effects, (C), (F), and (I); and hidden feedbacks, (D), (G), and (J)] according to ecosystem type [(B), (C), and (D)], spatial scales [(E), (F), and (G)], and temporal scales [(H), (I), and (J)]. In line with our expectations, regime shifts were more likely to share drivers when they occurred in similar land uses but not necessarily under the same ecosystem types ( ) (Fig. 4 and table S3). We did not expect cross-scale interactions in driver sharing, yet we found that driver sharing is more likely in dynamics that are faster in time (from weeks to years) and when spatial scales match. Regime shift impacts on ecosystem services and human well-being were related to driver sharing. We found that affecting similar regulating and provisioning services increases the likelihood of common drivers. Evidence of cross-scale interactions for domino effects was only found in time but not in space. As expected, regime shifts that produce domino effects have slow temporal dynamics and larger spacial scales. These regime shifts include Earth system–tipping elements such as monsoon weakening, thermohaline circulation collapse, and Greenland ice sheet collapse (Fig. 3C). On the other hand, regime shifts influenced by domino effects were often marine and occurred over shorter times and more localized spaces, including mangrove transitions, kelp transitions, and transitions from salt marshes to tidal flats. The statistical models support this observation for temporal scales (Fig. 4 and table S4), but we did not find evidence for spatial ones. Having domino effects was significantly associated with affecting similar regulating and provisioning services (P < 0.001), but the size of the effects are dwarfed by its rarity. The sparse response variable matrix (Fig. 1) and the negative coefficient on the sum term in the statistical models (table S4) show that domino effects are not common. When they do occur, it is only through a few pathways between regime shifts (maximum of four in our sample). Key variables involved in domino effects were related to climate, nutrients, and water transport (Fig. 3D). Hidden feedbacks were expected to arise when regime shift dynamics matched scales in space and time. The statistical analysis supports our hypothesis: Regime shifts that occur on the range of decades to centuries and at national scale are more likely to have hidden feedbacks (Fig. 4 and table S5). We found fewer hidden feedbacks than one would expect by chance, but when hidden feedbacks did occur, they tended to couple regime shifts through multiple feedbacks. Most hidden feedbacks in our sample occurred in terrestrial and Earth systems (Figs. 3E and 4). The regime shifts with higher numbers of connections (15 to 18 out of 30 possible) are thermohaline circulation, primary productivity of the Arctic Ocean, forest to savanna, monsoon weakening, and the Greenland ice sheet collapse. Key variables belonging to many hidden feedbacks were related to climate, fires, agriculture, and urbanization (Fig. 3F).

Discussion and conclusions Regime shifts are ubiquitous in nature, yet how they can interact has remained an unexplored question. Although this question is fundamental for scientists to forecast the dynamics of ecosystems, the answers are relevant for policymakers and managers because regime shifts can affect ecosystem services and human well-being and hence undermine the achievement of sustainable development goals. Domino effects and hidden feedbacks are often disregarded because research on regime shifts is divided by disciplines that focus on one system at a time. Consequently, data collection and hypothesis testing for coupled systems have largely remained unexplored (18, 19). Although few studies have investigated cascading effects by looking at temperature-driven tipping points in the climate systems (15, 25, 29), a growing body of literature has started to offer hypotheses on how different regime shifts can be interconnected (table S1). We have developed a network-based method that allows us to systematically identify potential cascading effects and differentiate whether a regime shift coupling is expected to create structural dependencies in the form of domino effects or hidden feedbacks (Fig. 2). Our findings align with previous results on the type of variables and processes that can couple regime shifts (table S1), highlighting the role of climate, agriculture, and transport mechanisms for nutrients and water (Fig. 3). Recent literature (table S1, references) reports potential linkages between eutrophication and hypoxia, hypoxia and coral transitions, shifts in coral reefs and mangrove transitions, or climate interactions. Other examples in the terrestrial realm report potential increase in Arctic warming from higher fire frequency in boreal forest or permafrost thawing. Regime shifts in the Arctic can affect any temperature-driven regime shift in and outside the Arctic (30), including the weakening of the thermohaline circulation. Moisture recycling is a key underlying feedback on the shift from forest to savanna or the Indian monsoon but also has the potential to couple ecosystems beyond the forest that depend on moisture recycling as an important water source. Changes in moisture recycling can affect mountain forests in the Andes, nutrient cycling in the ocean by affecting sea surface temperature, and therefore regime shifts in marine food webs or exacerbation of dry land–related regime shifts. Not all cascading effects reported in the literature and our results are expected to amplify each other. For example, it has been reported that climate-tipping points can regulate each other and reduce the probability of regime shifts in forests (29, 31). Guided by the practice of explaining and modeling single regime shifts as emergent dynamics from fast and slow processes (2, 8, 11, 20, 23–25), we hypothesized that cascading effects between regime shift couplings were determined by cross-scale interactions. For domino effects, we only found support of cross-scale interactions in time but not in space. For hidden feedbacks, we found evidence of matching in space and time. Together, these results show that the likelihood of regime shift coupling depends on cross-scale interactions but differs for each cascading effect type. Lack of evidence for interactions across spatial scales for domino effects suggests that stochastic and transient dynamics might be playing an important role in regime shifts (32) and their cascading effects. A major role of stochastic and transient dynamics in regime shift–couplings limits the applicability of early warning signals (10, 21) to predict cascading effects (25). Developing early warning signals for coupled regime shifts is therefore a research need. Synchronization of regime shifts in time or space is a subject of debate (19, 33–35). Temporal correlations—typically induced by driver sharing—can be broken by spatial heterogeneity (19), indicating that context matters for correlations to emerge. Spatial heterogeneity can smooth out critical transitions (36, 37). Yet, identifying common drivers is useful for designing management strategies that target bundles of drivers instead of well-studied variables independently, increasing the chances that managers will avoid several regime shifts under the influence of the same sets of drivers (13, 38). For example, management options for drivers such as sedimentation, nutrient leakage, and fishing can reduce the likelihood of regime shifts such as eutrophication and hypoxia in coastal brackish lagoons as well as coral transitions in adjacent coral reefs. Our results complement previous findings (table S1) by offering a wide spectrum of causal hypotheses about how regime shifts can be coupled. However, the limitations of our method need to be acknowledged. Regime shifts were represented as static networks, and the cascading effects were identified by matching two pieces of information: variable names and positions within the causal diagram. Therefore, the method identifies structural dependencies but cannot predict how the dynamics will unfold in space or time. For example, if a connection between mangrove collapse and coral transitions is found through protection against coastal erosion, geographical distance between the two systems or the direction of oceanic currents can change or even cancel out the coupling strength. In fact, coupling strength is expected to change from one place to another. Hence, our method identifies plausible connections between regime shifts, but identifying the conditions that change plausible to probable requires more detailed understanding of regime shift mechanisms. Empirical studies and modeling syntheses are required to translate our identification of possible mechanisms into context-sensitive forecasts. Dynamic models of these types of dynamics require careful assumptions about parameter values and the functional form of the system equations. Generalized modeling is a promising technique that does not require particular assumptions, allowing the researcher to reach more general conclusions based on stability properties of the system (39, 40). Another potential avenue for future research is looking at how transport mechanisms couple physically distant ecosystems—for example, through the moisture-recycling feedback (41) or international trade (18). A key lesson from our study is that regime shifts can be interconnected. Regime shifts should not be studied in isolation under the assumption that they are independent systems. Methods and data collection need to be further developed to account for the possibility of cascading effects. Our finding that ~45% of regime shift couplings can have structural dependence suggests that current approaches to environmental management and governance underestimate the likelihood of cascading effects. More attention should be paid to how Earth is social-ecologically connected (18), how those connections should be managed, and how to best prepare for regime shifts. Our research suggests that regional ecosystems can be transformed by ecosystem management far away and, conversely, can themselves drive the transformations of other distant ecosystems. Decisions made in one place can undermine the achievement of sustainable development goals in other places. For example, it has been shown that many Arctic regime shifts have the potential to affect non-Arctic ecosystems far away and the provision of their ecosystem services (30, 42, 43). It implies that whoever does make decisions on management is not necessarily the one who has to deal with the impacts. This issue is evident in governance of water-transport systems, whether run-off or atmospheric transport, but it is applicable to other dynamics that connect faraway ecosystems through other mechanisms, such as climate change, fire, nutrient inputs, or trade. Our results highlight variables that are key for domino effects and hidden feedbacks, such as climate, agriculture, transport of nutrients, and water. They are also good observables for monitoring early-warning indicators of the strengthening of regime shift coupling. How and when nonlinear change can be transmitted across space and time in the Earth system should be considered in assessments and management of future environmental change.

Supplementary Materials www.sciencemag.org/content/362/6421/1379/suppl/DC1 Materials and Methods Supplementary Text Figs. S1 to S5 Tables S1 to S5 References (44–78)

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