drivers but are hotspots of sharing, typically in-
cluding 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).
In line with our expectations, regime shifts
were more likely to share drivers when they
occurred in similar land uses but not neces-
sarily under the same ecosystem types (P≪ 0 :001)
(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 dy-
namics 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 pro-
visioning services increases the likelihood of
common drivers.
Evidence of cross-scale interactions for dom-
ino 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 circula-
tion collapse, and Greenland ice sheet collapse
(Fig. 3C). On the other hand, regime shifts in-
fluenced by domino effects were often marine
and occurred over shorter times and more local-
ized 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 neg-
ative coefficient on the sum term in the sta-
tistical models (table S4) show that domino
effects are not common. When they do occur,
it is only through a few pathways between re-gime 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 feed-
backs. Most hidden feedbacks in our sample
occurred in terrestrial and Earth systems (Figs.
3Eand4).Theregimeshiftswithhighernum-
bers of connections (15 to 18 out of 30 possible)
are thermohaline circulation, primary prod-
uctivity of the Arctic Ocean, forest to savanna,
monsoon weakening, and the Greenland ice
sheet collapse. Key variables belonging to manyRochaet al.,Science 362 , 1379–1383 (2018) 21 December 2018 3of5
Fig. 3. Patterns of cascading effects.(A,C,
andE) 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.
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