Empirical evidence for recent global shifts in vegetation resilience

Abstract

The character and health of ecosystems worldwide is tightly coupled to changes in Earth’s climate. Theory suggests that ecosystem resilience—the ability of ecosystems to resist and recover from external shocks such as droughts and fires—can be inferred from their natural variability. Here, we quantify vegetation resilience globally with complementary metrics based on two independent long-term satellite records. We first empirically confirm that the recovery rates from large perturbations can be closely approximated from internal vegetation variability across vegetation types and climate zones. On the basis of this empirical relationship, we quantify vegetation resilience continuously and globally from 1992 to 2017. Long-term vegetation resilience trends are spatially heterogeneous, with overall increasing resilience in the tropics and decreasing resilience at higher latitudes. Shorter-term trends, however, reveal a marked shift towards a global decline in vegetation resilience since the early 2000s, particularly in the equatorial rainforest belt.

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Articles
https://doi.org/10.1038/s41558-022-01352-2
1Institute of Geosciences, Universität Potsdam, Potsdam, Germany. 2Potsdam Institute for Climate Impact Research, Potsdam, Germany. 3Earth System
Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany. 4Department of Mathematics and Global Systems
Institute, University of Exeter, Exeter, UK. ✉e-mail: tasmith@uni-potsdam.de
Natural ecosystems are severely threatened by climate change
and biodiversity loss; the Amazon, African and southeast
Asian rainforests are key examples that have attracted sub-
stantial recent attention1–3. These tropical vegetation systems have
been inferred to exhibit multistability for broad ranges of mean
annual precipitation4,5; within the same precipitation ranges, both
the rainforest state and an alternative savannah state are simultane-
ously stable. This implies that, even absent long-term changes in
local or regional precipitation, transitions from the current rainfor-
est state to the savannah state are possible and may be triggered by
external perturbations such as droughts, forest fires and deforesta-
tion6. Although ecosystem transitions in tropical rainforests have
received widespread attention, the risk of transitions to alternative
ecosystem states appears to be a global characteristic that extends
to high-latitude7,8 and dryland ecosystems9. Given that ecosystem
transitions could turn net carbon sinks into carbon sources3 and the
tremendous potential of vegetation to reduce atmospheric carbon
dioxide concentrations10, the mitigation of anthropogenic climate
change and the maintenance of global biodiversity are strongly
dependent on the resilience of vegetation systems worldwide.
Ecosystem resilience is typically defined as the capacity to resist
and recover from external disturbances11–13. Unfortunately, this
definition only allows for the empirical measurement of resilience
either in controlled experiments (by applying an artificial distur-
bance) or by waiting for occurrences of large external disturbances
to natural vegetation systems. Due to the scarcity of suitably strong
external perturbations, it is difficult to quantify the resilience of
natural ecosystems at a global scale, and in particular to investigate
resilience changes over time.
Theoretically, the fluctuation–dissipation theorem (FDT) from
statistical mechanics14–17 suggests that for specific classes of systems,
the response to external perturbations can be expressed in terms of
the characteristics of natural fluctuations around the equilibrium
state. In other words, the FDT states that the rate at which a system
will return to equilibrium following an external disturbance can be
determined from its internal natural fluctuations. The tremendous
practical value of the FDT comes from the fact that, if it can be
shown to hold for a given system, the response to external perturba-
tions can be predicted on the basis of the internal variability of the
system in question. Evidence that the FDT holds has been revealed
in several real-world systems17, ranging from financial market
data18,19 to atmospheric and climate dynamics20,21.
Several studies have suggested that the lag-one autocorrelation
(AC1)—a measure of how strongly correlated neighbouring time
spans of a given time series are—and variance of a system can be
used as measures of vegetation resilience1,22–27. The variability of
natural fluctuations can be estimated in terms of the variance22,27,28,
while the strength of the system’s memory can be measured using
the AC11,23–25,28. Low-dimensional dynamical system frameworks
and designed experiments justify this choice by showing that vari-
ance and AC1 increase as the system approaches a critical thresh-
old beyond which a bifurcation-induced transition—a jump to an
alternative stable state—occurs, which is interpreted as a loss of
resilience29,30. The increase in AC1 together with a corresponding
increase in variance have been termed early-warning signals for
critical transitions; the underlying change in dynamics is referred to
as ‘critical slowing down’22,28. It has been shown that early-warning
signals can be identified before abrupt climate transitions evidenced
in palaeoclimate records31–33 as well as in ecosystem28 and climate34,35
model simulations. However, although the AC1 and variance have
been used to quantify the stability or resilience of different systems,
their actual suitability as measures of ecosystem, and in particular
vegetation, resilience has not been confirmed outside of controlled
and model-based experiments36,37, and in particular not based on
empirical evidence.
In this article, we use empirical remotely sensed vegetation data
to test for the correspondence between theoretical vegetation resil-
ience—AC1 and variance—and the rates of recovery from perturba-
tions. We first use large perturbations to derive empirical recovery
rates for diverse landscapes, vegetation types and climate zones using
two independent vegetation datasets based on optical (advanced
very-high-resolution radiometer (AVHRR) normalized difference
Empirical evidence for recent global shifts in
vegetation resilience
Taylor Smith 1 ✉ , Dominik Traxl 2 and Niklas Boers 2,3,4
The character and health of ecosystems worldwide is tightly coupled to changes in Earth’s climate. Theory suggests that eco-
system resilience—the ability of ecosystems to resist and recover from external shocks such as droughts and fires—can be
inferred from their natural variability. Here, we quantify vegetation resilience globally with complementary metrics based on
two independent long-term satellite records. We first empirically confirm that the recovery rates from large perturbations
can be closely approximated from internal vegetation variability across vegetation types and climate zones. On the basis of
this empirical relationship, we quantify vegetation resilience continuously and globally from 1992 to 2017. Long-term vegeta-
tion resilience trends are spatially heterogeneous, with overall increasing resilience in the tropics and decreasing resilience at
higher latitudes. Shorter-term trends, however, reveal a marked shift towards a global decline in vegetation resilience since the
early 2000s, particularly in the equatorial rainforest belt.
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vegetation index (NDVI), 1981–201538) and passive microwave
(vegetation optical depth (VOD), 1992–201739) data; these data mea-
sure changes in vegetation with different methods and thus provide
complementary information for our analysis. We then show that for
VOD, the empirically estimated recovery rates from large external
perturbations are indeed closely related to the continuously measur-
able response to small natural fluctuations, quantified here by AC1
and variance. We further show that the AC1 and variance of NDVI
are not well matched to empirically estimated recovery rates from
large disturbances and conclude that VOD is a more suitable basis
for measuring vegetation resilience. We emphasize that while both
AC1 and variance have previously been used to estimate vegetation
resilience1, their theoretically expected relationships with recovery
rates from perturbations, and thus with resilience, have yet to be
confirmed empirically for vegetation systems. Moreover, temporal
changes in AC1 and variance of remotely sensed vegetation indices,
as we investigate here, have rarely been studied40,41.
By comparing with the empirical rates of recovery from external
perturbations, we demonstrate using VOD that both AC1 and vari-
ance provide robust, empirically verified global resilience measures.
On the basis of this relationship, we further quantify global-scale
changes in vegetation resilience since 1992 and find coherent resil-
ience loss across land-cover types that has accelerated in the past
two decades.
Quantifying vegetation recovery from external
perturbations
Vegetation in the natural world is constantly subject to disturbances
that vary greatly in frequency and intensity. Many of these signals
are subtle, and identifying minor and short-term disturbances is
difficult. Large excursions from the typical vegetation state of an
ecosystem can, however, be identified by abrupt transitions in time
series of vegetation indices. The empirical local recovery rate can
then be estimated after each abrupt negative transition by fitting an
exponential function to the time series as it recovers towards its pre-
vious state (Fig. 1, see Methods for details).
Both VOD (Fig. 1) and NDVI (Extended Data Fig. 1) are sub-
ject to the same types of major external disturbances (for example,
droughts or fires) that can rapidly reduce both vegetation density
(VOD) and vegetation productivity or greenness (NDVI). It is
important to note that while both datasets measure vegetation, the
data do not describe the same vegetation parameters and hence do
not respond identically to external shocks; this can in some cases
mean that the number of detected transitions differs between the
two vegetation datasets over the same period. In addition, while
vegetation recovery is measurable in both data, the time frame of
those recoveries, and hence the fitted exponential function, can
be dramatically different for the same perturbation (Fig. 1 and
Extended Data Fig. 1). Further discussion of the limitations of the
disturbance detection procedure can be found in Methods.
Estimating resilience from intrinsic variability
We find globally well-distributed recovery rates from diverse exter-
nal shocks (Fig. 2 and Extended Data Fig. 2). Not all landscapes
have experienced rapid and drastic changes in vegetation over the
satellite measurement period; for such regions, it is impossible to
directly measure vegetation resilience in terms of recovery from an
external shock. Even in regions where perturbations are relatively
frequent, they are too sparsely distributed to allow for an estimation
of changes in the recovery rate, and thus resilience changes, through
time (Fig. 2a).
The FDT suggests that the rate of a system’s recovery from large
external perturbations is related to the variability (quantified by
variance22,27,28) and memory timescale (quantified by AC11,23–25,28) of
natural fluctuations around the equilibrium16. Theory predicts an
exponential relationship between the AC1 and the negative recovery
rate r, that is, AC1 = erΔt, and a power-law relationship between
the variance of the VOD time series x and the recovery rate r, that
is, 〈x2〉 = −σ2/2rΔt, where σ is the standard deviation of the driv-
ing noise, r < 0, and we set the time steps to Δt = 1 (see Methods
for details). For the set of locations where empirical recovery rates
can be estimated (Fig. 2a), both AC1 and variance can be derived
directly from the corresponding time series. For areas where it was
possible to empirically estimate the recovery rate from large per-
turbations (Fig. 2a), there is broad spatial agreement with the AC1
(Fig. 2b) and variance (Fig. 2c) estimates (see also zoomed-in maps,
Supplementary Figs. 1 and 2). Moreover, the two theoretical recov-
ery rate estimates themselves, which are available for all vegetated
grid cells, exhibit similar spatial distributions (compare Fig. 2b,c),
especially if the relative order of values is considered (see the rank
comparison in Supplementary Fig. 3). Note that the AC1-based esti-
mate for the recovery rate r mostly underestimates the recovery rate
(Fig. 2d), especially in parts of North America, central Europe and
Southern Africa, while the variance-based estimate for the recovery
rate mostly overestimates the recovery rate (Fig. 2e).
To more concisely compare the empirical (Fig. 2a) with the two
theoretical recovery estimates (Fig. 2b,c), we compare them on a
point-by-point basis (Fig. 3). For the VOD, the expected relation-
ships hold remarkably well; for NDVI, the link between empirical
and theoretical resilience metrics is much weaker (see Extended
Data Fig. 3).
When considering the AC1 and variance values directly as func-
tions of the recovery rates for all available grid cells together, the
theoretically expected relationships are overall corroborated by
the observational data, although differences between geographical
regions are neglected when investigating the relationship in this
way. As expected, some differences are therefore visible (compare
Fig. 2). We note that the correspondence between theoretical and
empirical estimates becomes substantially better if only recovery
rates from exponential fits with R2 > 0.5 are considered, compared
with recovery rates from all fits with R2 > 0.1 (Fig. 3). This indicates
that the poor exponential fits to the recovering time series after
transitions are a key reason for the differences between measure-
ment and theory and suggests in turn that the more reliable the
recovery rate estimate, the closer is the match between empirical
and theoretical estimates of the recovery rates. We also note that for
the variance, uncertainties in estimating the standard deviation of
the driving noise σ also probably play a role. Estimating the variance
from the empirically determined recovery rate via 〈x2〉 = −σ2/2rΔt
requires an estimate of σ. We calculate each individual σi and then
bin the resulting data points to obtain the orange curve in Fig. 3b,
while we use the globally averaged σ to obtain the black curve.
Global shifts in vegetation resilience
Rapid large-scale perturbations are not evenly distributed in space
and time (compare Fig. 2), which renders a reliable estimation of
temporal resilience changes in terms of empirical recovery rates
impossible. As justified by the relationship between recovery rates
and theoretical resilience metrics (compare Fig. 3), we instead cal-
culate resilience in terms of both the AC1 and variance in rolling
five-year windows over all vegetated areas (Fig. 4). In the follow-
ing, we define resilience loss (gain) if at least one of the two indica-
tors (AC1 or variance) shows a statistically significantly increasing
(decreasing) trend while the other indicator does not exhibit a sig-
nificant trend in the other direction (Fig. 4).
Over the period 1992–2017, the spatial pattern of resilience trends
in terms of AC1 and variance is complex (Fig. 4a and Extended Data
Fig. 5) but follows consistent latitudinal patterns where equatorial
(for example, Amazon and Congo basins) and monsoon-driven (for
example, southeast Asia) areas show generally increasing resilience
(negative trends in both indicators), and high-latitude areas typi-
cally show decreasing resilience trends, especially for the Northern
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Hemisphere. The global picture for long-term resilience trends is
thus mixed; there is only a slight majority of grid cells with resil-
ience losses (54.2%) compared with the number of grid cells with
resilience gains (41.6%) over the whole period 1992–2017. The
given percentages refer to the set of grid cells that have at least one
statistically significant trend in either of the two indicators; the
unconfined class with significant yet opposing trends contributes
the remaining ~4%. When we restrict the analysis to the first half of
our study period (1992–2004), trends are again mixed, with increas-
ing resilience in the tropics and decreasing resilience at higher lati-
tudes (Fig. 4b); these trends are stronger for variance than for AC1
(Extended Data Fig. 5).
From the early 2000s onward, however, we observe a marked
increase in resilience loss in terms of both indicators (that is,
significantly positive trends in AC1 and variance; Fig. 4c and
Extended Data Figs. 5–7). We observe an increase from 28.2%
to 59.4% of pixels with resilience loss between the periods 1992–
2004 and 2004–2017; the percentage of pixels showing resilience
gains decreased from 37.9% to 33.8%. Areas with significant yet
opposing trends contribute the remaining 33.8% and 6.8%, respec-
tively; many regions with opposing significant trends until 2004
show coherent resilience loss in both indicators for the period
since 2000, 2002 or 2004 (Fig. 4c and Extended Data Fig. 7). Some
regions, such as the high northern latitudes, southern Africa and
parts of Australia, show consistent resilience losses throughout the
study period, which broadly agrees with previous findings based
on alternative resilience metrics and AVHRR NDVI data41. Many
regions, in particular the equatorial rainforest belt, have reversed
from gaining resilience (blue regions, 1992–2004) to losing resil-
ience (orange and red regions, 2000s onwards). Long-term (1992–
2017) trends thus conceal a strong reversal from gains to losses in
resilience in many regions.
When changes in AC1 and variance are aggregated by land
cover42, we infer that evergreen broadleaf forests show overall
lower AC1 and variance (higher resilience) than other land-cover
types (Extended Data Fig. 6); nevertheless, the global tendency is
towards aggregate decreases in resilience (in terms of AC1) across
all land-cover classes. These trends maintain a similar form if a
three-year or seven-year rolling window is used to calculate con-
tinuous changes in resilience (Extended Data Fig. 6). It should
be noted, however, that this approach conceals considerable spa-
tial trend variability (Extended Data Fig. 5) and will (although
60° N
a
b
c
30° N
30° S
VOD
Residual VOD
1.2
1.1
1.0
0.9
0.8
0.7
0.050
0.025
–0.025
–0.050
–0.075
–0.100
–0.125
–0.150
2008 2009 2010 2011
Date
2012 2013 2014 2015
Residual subset
Exp. fit exponent = –0.342
R
2
= 0.322
Exp. fit exponent = –0.407
R
2
= 0.435
0
1992 1996 2000 2004 2008 2012 2016
0.10
0.05
–0.05
–0.10
0
180° 120° W 60° W 60° E 120° E 180°
1.8
1.6
1.4
1.2
1.0
VOD
0.8
0.6
0.4
0.2
0°
0°
Raw VOD
Deseasoned and detrended VOD
Fig. 1 | Global vegetation data. a, Global long-term mean of VOD39 (1992–2017). b, VOD time series for a given location in the Brazilian Amazon (8.375°S,
50.875°W). Raw time series in black, with deseasoned and detrended time-series residual in blue (see Methods for details). c, Recovery of the exemplary
time series to the previous mean state after a rapid transition, with commensurate exponential fits. Rare large disturbances, such as those in 2007 and
2010, can be used to track the recovery of vegetation and assign a recovery rate using an exponential fit. See Extended Data Fig. 1 for a corresponding figure
based on the NDVI. Exp., exponential.
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Articles NaTurE CLimaTE CHaNgE
confined to single land-cover types) smooth over vast differences
in biomes worldwide; hence, these aggregated time series should be
carefully interpreted in the context of the global trend maps (Fig. 4
and Extended Data Fig. 5). Variance presents a more mixed picture
when aggregated by land-cover class, with losses of resilience being
expressed more strongly since the early 2000s (Extended Data Fig. 6).
Previous work proposed that AC1 will always increase towards a
critical transition, but variance can in some cases decrease27; the
two metrics are also not guaranteed to change at the same rate. This
is also to some degree expressed in our global trends (Extended
Data Fig. 5), where variance trends, particularly for the tropics, are
more strongly negative than for AC1 over both the whole period
180° 90° W 0° 90° E 180°
0°
–0.4 –0.2 0 0.2 0.4
Relative deviation of recovery rate (from AC1)
d
180° 90° W 0° 90° E 180°
–0.4 –0.2 0 0.2 0.4
Relative deviation of recovery rate (from variance)
e
180° 90° W 0° 90° E 180°
0°
–3 –2 –1
AC1-based recovery rate
b
180° 90° W 0° 90° E 180°
–0.6 –0.4 –0.2
Variance-based recovery rate
c
180° 120° W 60° W 0° 60° E 120° E 180°
0°
–1.2 –1.0 –0.8 –0.6 –0.4 –0.2
Empirically estimated recovery rate
a
60° S
60° N
Fig. 2 | Global distribution of recovery rates. a, Recovery rate (for well-determined exponential fits, R2>0.2) for VOD (n=11,538 perturbations for 10,620
unique locations). b, Theoretical estimate of the recovery rate computed via rAC1=log[AC1] (Methods) from the AC1 of the detrended and deseasoned
VOD time series at each location. c, Theoretical estimate of the recovery rate computed via rVar=σ2/(2〈x2〉) (Methods) from the variance 〈x2〉 of the
detrended and deseasoned VOD time series at each location. Bare earth, snow and anthropogenic land covers are excluded from the analysis42 (Methods).
Note the sparsity of grid cells where there have been abrupt shocks that can be exploited to estimate the recovery rate (a), as opposed to theoretical
measures (b,c) that can be computed for all grid cells with vegetation. Also note the similarity of the spatial patterns in b and c and their resemblance to
the spatial pattern shown in a as far as there are values for the recovery rate available. d,e, Relative deviation d of theoretical recovery rate estimated from
AC1 (d) and variance (e) (for example, d=(r−rAC1)/r). Clear patterns of over- and underestimation of recovery rate indicate that the theoretical framework
does not perform equally in all locations. See Extended Data Fig. 2 for a corresponding figure based on the NDVI.
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1992–2017 and the early period 1992–2004. Both AC1 and variance
trends, however, are majority positive for the recent period ~2000–
2017 (Fig. 4c and Extended Data Figs. 5–7).
Note that many regions where we observe strong vegetation
resilience loss are also fire prone (for example, Siberia, Canada and
western North America); increasing fire frequencies due to drier
conditions in these regions could explain some of the observed
recent vegetation resilience loss43. Increases in temperature, along-
side changes in precipitation and weather extremes, could also be
a potential driver of changing vegetation resilience; we emphasize,
however, that a detailed analysis of the different potential causes for
the inferred resilience loss (and in particular its acceleration during
the past two decades) is still lacking and is an important topic for
future research.
Discussion
Our results provide empirical evidence that both AC1 and variance
are directly related to vegetation resilience, defined as the recovery
rate from external perturbations. The AC1 and variance can hence
be used to estimate resilience in situations where controlled experi-
ments are not possible and external perturbations are rare. Our
findings, therefore, justify the usage of AC1 and variance as vegeta-
tion resilience metrics1,41,44 and provide an empirical basis for future
studies based on these theoretical resilience metrics. However, our
results also show that the resilience estimates derived from the com-
mon AC1 and variance metrics directly using theoretical relation-
ships may be slightly biased, and instead the modified empirical
relationships revealed in Fig. 3 should be used to translate AC1 and
variance into the recovery rate as a measure of resilience. On the
basis of the thus empirically confirmed relationship between AC1/
variance and vegetation resilience, we infer a heterogeneous spatial
pattern of resilience gains and losses; resilience losses in the high
northern latitudes are consistent since the early 1990s, but in the
tropics, we detect gains during the 1990s and pronounced resilience
losses since around the year 2000. While the directions of AC1 and
variance trends broadly agree (Fig. 4 and Extended Data Figs. 5–7),
there remains considerable spatial heterogeneity.
We find marked differences in our results when using the NDVI
instead of the VOD data. While we cannot say with complete cer-
tainty what drives this disparity, it is likely that differences in the
parameters measured by the satellites play a critical role. VOD is
primarily sensitive to vegetation density and, thus, will respond to
changes in both leafy and woody biomass39. NDVI, however, is sen-
sitive to ‘greenness’, which is often interpreted as vegetation produc-
tivity or chlorophyll content; it is well known that NDVI is a poor
estimator of biomass45. Recovery in NDVI after a disturbance can
thus be rapid, even if a completely new species mix accounts for the
post-disturbance vegetation growth (for example, forest replaced by
0.8
ab
cd
Binned medians Binned medians
Binned medians (R2 > 0.1)
Binned medians (R2 > 0.2)
Binned medians (R2 > 0.3)
Binned medians (R2 > 0.4)
Binned medians (R2 > 0.5)
Binned means Binned means
Mean theoretical variance
Power-law fit (R2 > 0.3)
–σr
2/2r
–σr
2/2r
er
er
Binned medians (R2 > 0.1)
Binned medians (R2 > 0.2)
Binned medians (R2 > 0.3)
Binned medians (R2 > 0.4)
Binned medians (R2 > 0.5)
Exponential fit (R2 > 0.3)
0.7
0.5
AC1
Variance
0.4
0.3
0.2
–1.2 –1.0 –0.8 –0.6
Recovery rate
–0.4 –0.2 0
–1.2 –1.0 –0.8 –0.6
Recovery rate
–0.4 –0.2 0
–1.2 –1.0 –0.8 –0.6
Recovery rate
–0.4 –0.2 0
–1.2 –1.0 –0.8 –0.6
Recovery rate
–0.4 –0.2 0
0.6
0.8
0.7
0.5
AC1
0.4
0.3
0.2
0.6
0.006
0.005
0.003
0.002
0.001
0
0.004
Variance
0.006
0.005
0.003
0.002
0.001
0
0.004
Fig. 3 | Empirical confirmation of recovery rates. Comparison between empirically measured recovery rates and theoretical resilience metrics calculated
over the five years preceding each transition, for VOD data39. a, AC1 versus recovery rates r from exponential fits to recovering time series with R2>0.3;
the magenta (blue) line shows binned medians (means), which are close to the exponential fit of the empirical relationship between recovery rate and
AC1 values (red line). Grey shading shows data interquartile range. The AC1 thus shows the expected exponential relationship with the recovery rate,
but quantitatively, some deviations from the theoretically expected AC1=er (black line) are apparent. b, Same as a but for the variance. The variance
indeed shows the expected power-law relationship with the recovery rate, but as for the AC1, there are some deviations from the theoretically expected
⟨x2
⟩=−
σ2
r/2r
relationship (black line), where we use the spatial mean of the driving noise σr. The mean variance and corresponding interquartile range
are also shown for the case where the individual σr values for each grid cell are used to compute the variance (orange line, with shaded interquartile range).
c, Binned medians of AC1 as a function of the empirically measured recovery rate r, for increasing thresholds on R2 of the exponential fit to the recovering
time series after abrupt transitions, as indicated in the legend. d, Same as c but for the variance. Note that the match between empirical and theoretical
estimates of the recovery rate improves the more restrictive the empirical estimation of the recovery rate is; low R2 variance medians in d plot on top of
each other until R2>0.3. Bare earth, snow and anthropogenic land covers are excluded from the analysis42 (Methods). See Extended Data Fig. 3 for a
corresponding figure based on the NDVI and Extended Data Fig. 4 for a corresponding figure using the whole time series to compute AC1 and variance
with VOD. See Supplementary Fig. 4 for alternative measures of theoretical variance based on different σ estimates.
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a
180° 120° W 60° W 0° 60° E 120° E 180°
–60° S
0°
60° N
Both significantly
positive
b
180° 120° W 60° W 0° 60° E 120° E 180°
–60° S
0°
60° N
c
180° 120° W 60° W 0° 60° E 120° E 180°
–60° S
0°
60° N
Increasing resilience Decreasing resilience
6.1% 35.5% 4.3% 43.4% 10.8%
37.9% ~0.0% 33.8% ~0.0% 28.2%
8.3% 25.5% 6.8% 43.9% 15.5%
Both significantly
negative
One significantly
negative
Mixed significant
trends
One significantly
positive
Both significantly
positive
Both significantly
negative
One significantly
negative
Mixed significant
trends
One significantly
positive
Both significantly
positive
Both significantly
negative
One significantly
negative
Mixed significant
trends
One significantly
positive
Fig. 4 | Global resilience trends. a–c, Direction (+/–) of global resilience trends for AC1 and variance using VOD data39 for 1992–2017 (a), 1992–2004
(b) and 2004–2017 (c). Bare earth, snow and anthropogenic land covers are excluded from the analysis42 (white areas) (Methods). Linear trends are
calculated on the basis of five-year rolling-window AC1 and variance estimates; only trends with P<0.05 in either AC1 or variance are shown in colour
(see Methods for details on significance testing). Pixels with mixed significant trends (for example, AC1 positive, variance negative) are shown in grey. See
Supplementary Table 1 for raw pixel counts. See Extended Data Fig. 5 for global AC1 and variance trends for all three periods, and Supplementary Fig. 5 for
latitude-aggregated trends. Note the increases in the strength of resilience loss since the 2000s, especially in the tropics (Extended Data Figs. 5–7).
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grass). VOD, however, will remain suppressed until vegetation den-
sity (for example, leaves and stems) returns. It is thus likely that the
empirically derived recovery rates for NDVI contain much higher
levels of noise and that some recoveries to previous NDVI values
represent a transition to a new vegetation mix rather than a return
to the actual previous vegetation state. The relatively poor con-
straint on vegetation type provided by NDVI is a major barrier to its
use in assessing ecosystem state and stability; we therefore propose
to rather employ VOD data for such purposes.
A few potential caveats should be kept in mind when inter-
preting our results. (1) We do not have a strong constraint on the
type and cause of the vegetation perturbations used to calculate
recovery rates. Sufficient data on all types of disturbances, their
spatial extent and their magnitude do not exist; we thus rely on a
data-driven approach to estimate the timing and magnitude of a
given disturbance. We note, however, that since we determine the
empirical recovery rates using only parts of the time series follow-
ing an abrupt transition, we can estimate a recovery rate without
knowing what kind of event (for example, fire, drought) caused the
abrupt transition. (2) Possible spurious or missed time-series transi-
tions are carried forward into our analysis of the global relationship
between empirical and theoretical vegetation resilience; this prob-
ably accounts for some of the scatter seen in Fig. 3 (see Methods
for further details). (3) Some changes in variance and autocorrela-
tion are not necessarily related directly to vegetation resilience, for
example, in the case of time-lagged vegetation response to water
deficits46 that could modify the measured AC1. At the global scale
of our analysis, however, we posit that our empirical confirmation
of resilience metrics and long-term trends remain robust. (4) We are
limited by the mathematical framework to studying only systems
that return to the previous state and therefore probably miss many
important ecosystem transitions from which there has been no
recovery to the original state. Finally, (5) it is important to note that
we cannot say for certain whether the acceleration of resilience loss
observed in the past decades (Fig. 4) will continue into the future;
indeed, it is possible that global vegetation resilience is responding
to a (multi-)decadal climate variability mode (compare Extended
Data Fig. 6), which could in principle drive a global-scale reversal
towards renewed resilience gains. Theoretically, a critical transition
will occur when the AC1 reaches a value of one, corresponding to
a vanishing recovery rate; in practice, however, extrapolating AC1
trends into the future is not feasible. Our results are based on empir-
ical data and are thus not predictive; they show only how vegetation
resilience has changed in recent decades. We have also not assessed
changes in the magnitude or frequency of external disturbances (for
example, droughts47), which also play a key role in controlling global
vegetation health; a comparison between vegetation resilience and
contemporaneous changes in external disturbances would provide
key context for the attribution of observed resilience changes to
explicit drivers. Despite these caveats, our work represents the first
empirical confirmation of previously proposed vegetation resilience
metrics in terms of variance and AC1 and thus provides the basis for
further investigations.
Our study shows that the satellite-derived VOD data can be used
to establish a global empirical manifestation of t he FDT for vegetated
ecosystems. Vegetation resilience, defined as the capacity to recover
from external perturbations, can hence be approximated from the
characteristics of natural internal variability in terms of AC1 and
variance. On the basis of this correspondence, we identify a global
loss in vegetation resilience over the course of the past decades,
although the spatial pattern is heterogeneous and the inferred
resilience changes depend on climate zones. The spatial pattern is
complex for the full period for which reliable VOD data are avail-
able (1992–2017), with overall resilience gains in the tropical belts
and losses in the higher northern and southern latitudes. From the
2000s onwards, however, we find globally almost coherent resilience
loss; further work is required to constrain the causes of this loss and
especially to investigate whether the observed resilience losses can
be attributed to anthropogenic climate and land-use change. Our
results establish a firm basis for a global, satellite-driven monitoring
system of ecosystem resilience.
Online content
Any methods, additional references, Nature Research report-
ing summaries, source data, extended data, supplementary infor-
mation, acknowledgements, peer review information; details of
author contributions and competing interests; and statements of
data and code availability are available at https://doi.org/10.1038/
s41558-022-01352-2.
Received: 30 August 2021; Accepted: 25 March 2022;
Published online: 28 April 2022
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Methods
Data preparation. We use two vegetation datasets in our analysis to provide a
holistic view of vegetation response to shocks and stresses. (1) VOD at 0.25° spatial
resolution; specically, we employ the Ku-band and use daily values for the
period 1992–201739. Note that we do not use the entire VOD data record (1987–)
as some pixels exhibit extreme discontinuities before 1992 (Extended Data
Fig. 6). We posit that this is due to the change from Special Sensor Microwave/
Imager satellite F08 to F11 in the VOD dataset39. While we observe these
discontinuities only in the tropics, we choose to discard all data before 1992 for
consistency; it should be noted, however, that our global-scale results are robust
whether we use 1987 or 1992 as our rst year of data (Extended Data Fig. 6).
(2) NDVI (from AVHRR) at 1/12° spatial and 15-day temporal resolution for
the period 1981–2015; specically, we use GIMMSv3g38. We further use the
moderate-resolution imaging spectroradiometer (MODIS) MCD12C1 land-cover
database (2014 annual composite, resampled via the mode of land covers in each
VOD/NDVI pixel)42 to break our analyses into distinct land-cover types (for
example, Extended Data Fig. 6).
To limit the impact of anthropogenic land use on our results, we further use
MODIS MCD12Q1 (500 m, annually 2001–2017) land-cover data to identify any
pixels that were at any point during the period 2001–2017 subject to human land
use (for example, urban, cropland). We then remove any NDVI/VOD pixels that
had one or more anthropogenic land-cover pixels (at least one 500 m pixel) in at
least one year between 2001 and 2017. This step helps to remove pixels that, for
example, were once logged and then returned to grasslands; those pixels would
not be classified as ‘anthropogenic’ for the entire period following the logging and
thus might introduce spurious results. While this does not completely eliminate
anthropogenic influence from our results (we do not have sufficient land-cover
data before the MODIS sensing period), it conservatively removes all 0.25°
(~25 × 25 km) regions where human use occurred. We thus cannot completely
rule out the influence of human-driven land-cover change on our results at the
global scale but have endeavoured to remove it to the furthest extent possible given
data limitations. As a final robustness check, we have also used the ref. 48 global
deforestation dataset to remove any pixels from our long-term trend data (Fig. 4)
that suffered forest loss (Supplementary Figs. 6 and 7); as this dataset also includes
non-anthropogenic forest loss—for example, due to natural fires—it serves as an
even more conservative land-cover removal step. Removing these additional
pixels does not substantially impact our reported long-term trend results or our
inferred conclusions.
Cloud cover and other data artefacts are removed from the NDVI data using
an upward-smoothing approach to gap filling49. VOD data are resampled to a
twice-monthly time step to match the temporal resolution of the NDVI data by
taking the median of each time window; this step ensures that divergent results
between the two vegetation datasets are not due to spatial or temporal sampling
differences. Using these cleaned and evenly sampled time series, we then deseason
and detrend the data using seasonal trend decomposition by loess (STL50–52). We
decompose the full-year signal using a period of 24 (one year at bi-monthly time
sampling) and an adaptive loess filter. We use a value of 47 for the trend smoother
(one point less than two years) and 25 for the low-pass filter (one point more than
one year), according to the rules of thumb originally presented by ref. 50 (see code
archive53 for details). We then maintain the residual (deseasoned and detrended)
time-series term for analysis.
Note that the VOD dataset is a multi-satellite composite, with variable overlap
between different input Ku-band datasets39. As multiple datasets are averaged in
different configurations throughout the VOD period, there is the potential for
changes in noise levels that could influence the computed AC1 and variance values
if the underlying signal (for example, vegetation) changes on a slower timescale
than the measurement noise. Stronger averaging associated with an increasing
number of satellites would lead to step-wise increases in AC1 and step-wise
decreases in variance.
For the period we consider, we do not see step changes in AC1 or variance as
would be expected if the noise level or character changed with the introduction
or removal of a new satellite; indeed, we see consistent resilience loss during
long periods of constant satellite configurations (for example, 2002–2009,
Extended Data Fig. 6). Furthermore, there are no contemporaneous jumps in the
variance, which would also be expected to change with shifts in data averaging. We
posit that the changes in AC1 and variance that we observe are highly unlikely to
be driven by data aggregation and are instead representative of a global change in
vegetation resilience.
Perturbation detection and recovery analysis. We use two methods to detect
perturbations in our residual time series: (1) a moving-average54 and (2) a linear-fit
approach55. For both methods, we use an 18-point (9 month) moving window
over our residual time series and calculate either the simple mean difference
between the first and second halves of our moving window (method 1) or a linear
trend over the moving window (method 2). We then smooth these resultant
derivative time series with a Savitzky–Golay filter (7 points, first order) to remove
high-frequency noise56. Finally, we isolate any derivative values above the 99th
percentile and label consecutive time steps as individual disturbance periods. We
then use the highest peak within each disturbance as the perturbation date. Note
that the results of our analysis are nearly identical whether we use method (1)
or method (2) to detect perturbations; thus, we present here only data based on
method (1). In our tests, a comparable set of disturbances was found using 12-,
24-, 36- and 72-point moving windows, which resulted in similar spatial (for
example, Fig. 2) and global (for example, Fig. 3) patterns; for simplicity, we present
only results using the 18-point moving window here.
As we use a percentile approach to delineate large perturbations, we will not
always capture each perturbation for a given time series; our detected perturbations
will be biased towards the largest excursion within each individual time series. We
acknowledge that not all events will be equally represented in both the VOD and
NDVI datasets; in the case where a much stronger response is engendered in one
dataset than the other, the percentile threshold may not identify the same event in
both time series. Furthermore, we will by construction detect some non-significant
perturbations, in particular for the case where a given time series does not experience
a strong disturbance. We thus impose the condition that the raw time series must
descend more than 0.01 to be considered a valid perturbation. While we do not
identify every perturbation over the entirety of both datasets, we generate a large and
diverse set of recovery rates that are well distributed in space and time. To ensure
that our estimated recovery rates represent a return to the previous state, and not a
transition to a new vegetation regime, we further apply the condition that the five
years of data before and after the disturbance must pass a two-sample Kolmogorov–
Smirnov test (P < 0.05). We choose five years as our baseline to minimize the impact
of long-term (for example, decadal) changes in vegetation state while maintaining
enough data on both sides of the transition for a robust comparison.
For each detected time-series perturbation, we then find the local minimum
of the residual time series with a two-month constraint to account for the fact
that disturbances are often detected before the residual time series reaches its
lowest point. We then take a period of five years after the local minimum and
fit an exponential function, capturing both the exponent r and the coefficient of
determination R2. To create the map for Fig. 2, if there is more than one transition
at a given pixel location, we use the average recovery rate of all transitions. For
Fig. 3, we maintain all recovery rates (for example, a single time series could
contribute more than one recovery rate). We note that most locations studied have
only one significant transition during the study period, and it is a relatively small
number that have two or more. The computed transition points and recovery rates
can be found in our data repository53.
Resilience estimation. Resilience is defined as the capacity to recover from
external perturbations11,12. Quantitatively, it can be determined in terms of the
recovery rate r after a perturbation to some value x0:
x(t)
≈
x0ert
where x(t) is the state of the system at time t after the perturbation. If r is negative,
the system will recover to its equilibrium state at rate ∣r∣. The characteristic
recovery time is given by ∣r∣−1. Note that for positive r, the initial perturbation
would instead be amplified, indicating that the system is not resilient. Empirically,
we estimate r for each perturbation in each residual NDVI and VOD time series as
described in the previous section.
The AC1, a measure of how strongly correlated neighbouring time spans of
a time series are, has been suggested as a measure for resilience1,23–25,57 and more
generally as an early-warning indicator for forthcoming critical transitions28,31.
Theoretically, this can be motivated from a linearization of the stochastic dynamics
around a given equilibrium point x*. For the fluctuations ¯
x
=
x
−
x∗
d
¯
x
dt
=κ¯
x+ση ,
which defines an Ornstein–Uhlenbeck process with linear damping rate κ < 0 and
white-noise forcing with standard deviation σ > 0. It can be shown that the variance
⟨
¯
x2⟩
and lag-n autocorrelation α(n) of the stochastic process obtained from a
discretization of the Ornstein–Uhlenbeck process into time steps Δt are given by58
⟨¯
x2⟩=
σ2
1−e2κΔt
≈−
σ2
2κΔt
and
α
(
n
)=
enκΔt.
If the stability of an equilibrium state gradually decreases, κ will approach zero
from below, and correspondingly, the variance
⟨
¯
x2⟩
will diverge to positive infinity
and the AC1 α(1) will increase towards + 1. These increases in the damping rate
κ, as well as the variance of the fluctuations
⟨
¯
x2⟩
and the AC1 α(1) can thus serve
as precursor signals for a forthcoming critical transition and, in relative terms, as
measures for stability or resilience changes.
The theoretical estimates for the recovery rates shown in Fig. 2b for AC1 and
in Fig. 2c for the variance are given in terms of the damping rate κ, obtained by
inverting the preceding equations. For the variance, an estimate of the driving
noise σr is also needed, which we obtain from
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Articles NaTurE CLimaTE CHaNgE
d
¯
x
dt
=r¯
x+σrη,
where we used the empirically estimated recovery rate r rather than the damping
rate κ on the right-hand side. Practically, we obtain very similar theoretical
expressions for the variance when computed using the σκ obtained when putting κ
instead of r into the preceding equation (Supplementary Fig. 4).
For an empirical confirmation of the FDT, we thus have to show that for the
observed vegetation data, an exponential relationship between the AC1 and the
recovery rate r, as well as a power-law (1/r) relationship between the variance and
the recovery rate r, hold. It is important to note that for the comparison between
empirical recovery rates and AC1 or variance, we consider only time series that
eventually return to their pre-disturbance state, implying that the residual time series
under study are, apart from infrequent large perturbations, approximately stationary.
Long-term trend estimation. To better understand temporal changes in vegetation
resilience, we calculate the AC1 and variance on moving windows (with a size of
3, 5 and 7 years) over each entire residual time series. Using these windowed AC1
and variance measurements, we calculate Kendall–Tau59 statistics to check for
increasing or decreasing trends. As our rolling-window data are by construction
serially correlated, we test for statistical significance based on a set of 10,000
phase-shuffled surrogates, which preserve the variance and autocorrelation function
of the original time series31–33. These phase surrogates are obtained by computing
the Fourier transform of the original time series, uniformly randomly shuffling their
phases and then applying an inverse Fourier transform to each of them. We then
calculate the probability that our measured AC1 Kendall–Tau trends are significant
using a threshold of P < 0.05. Finally, we discard six months of data at either end
of each time series before calculating trends, as the variance and autocorrelation of
the residual produced by the STL procedure are less reliable within one half of the
length of the seasonal decomposition window. The python codes to replicate our
trend estimation procedure can be found in our code repository53.
Data availability
The satellite data used in this study are publicly available38,39,42. The data used for
Figs. 2 and 3 are available via Zenodo: https://doi.org/10.5281/zenodo.5816934.
Code availability
The Python codes used in this study are available via Zenodo: https://doi.
org/10.5281/zenodo.5816934.
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Acknowledgements
The State of Brandenburg (Germany) through the Ministry of Science and Education
supported T.S. and D.T. for part of this study. T.S. also acknowledges support from the
BMBF ORYCS project. D.T. acknowledges funding from the ClimXtreme project of the
BMBF (German Federal Ministry of Education and Research) under grant 01LP1902J.
N.B. acknowledges funding by the Volkswagen foundation. This is TiPES contribution
no. 144; the TiPES (Tipping Points in the Earth System) project has received funding
from the European Union’s Horizon 2020 research and innovation programme under
grant agreement no. 820970.
Author contributions
N.B. conceived the study. All authors designed the study methodology. T.S. processed the
data and performed the numerical analysis with contributions from N.B. and D.T. All
authors interpreted the results. T.S. and N.B. wrote the manuscript with contributions
from D.T.
Funding
Open access funding provided by Universität Potsdam.
Competing interests
The authors declare no competing interests.
Additional information
Extended data is available for this paper at https://doi.org/10.1038/s41558-022-01352-2.
Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s41558-022-01352-2.
Correspondence and requests for materials should be addressed to Taylor Smith.
Peer review information Nature Climate Change thanks Ingrid van de Leemput
and the other, anonymous, reviewer(s) for their contribution to the peer review
of this work.
Reprints and permissions information is available at www.nature.com/reprints.
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Extended Data Fig. 1 | Global vegetation data. (a) Global long-term mean of normalized difference vegetation index (NDVI, 1981-2015). (b) Time series
for a given location (8.375∘ S, 50.875∘ W). Raw time series in black, with deseasoned and detrended time series residual in blue (see Methods for details).
(c) Recovery of the exemplary time series to the previous mean state after a rapid transition, with commensurate exponential fit. Rare large disturbances
can be used to track the recovery of vegetation and assign a recovery rate using an exponential fit.
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(a)
(b) (c)
Extended Data Fig. 2 | Global distribution of recovery rates. (a) Recovery rate (for well-determined exponential fits, R2>0.2) for Normalized Difference
Vegetatation Index (NDVI, n=256,807 perturbations for 227,079 unique locations). (b) Theoretical estimate of the recovery rate computed from the
AC1 of the detrended and deseasoned NDVI time series at each location (c) Theoretical estimate of the recovery rate computed from the variance of
the detrended and deseasoned NDVI time series at each location. Bare earth, snow, and anthropogenic landcovers have been excluded from the analysis
using MODIS landcover data. Note the sparsity of grid cells where there have been abrupt shocks that can be exploited to estimate the recovery rate (a),
as opposed to theoretical measures (b,c) which can be computed for all grid cells with vegetation. Also note the similarity of the spatial patterns in (b)
and (c), and their resemblance to the spatial pattern shown in (a) as far as there are values for the recovery rate available. Relative deviation of theoretical
recovery rate estimated from (d) AC1 and (e) variance.
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Extended Data Fig. 3 | Empirical confirmation of recovery rates. Comparison between measured recovery rates and theoretical resilience metrics for
NDVI data. (a) AC1 versus recovery rates r from exponential fits to recovering time series with R2>0.3; the magenta (blue) line shows binned medians
(means), which are close to the exponential fit of the empirical relationship between recovery rate and AC1 values (black line). Gray shading shows data
interquartile range. (b) Same as (a) but for the variance. The variance does not show the expected power-law relationship with the recovery rate; there are
substantial deviations from the theoretically expected
⟨x2
⟩=−
σ2
r/2r
relationship (black line), where we use the spatial mean of the driving noise σr. The
mean variance and corresponding interquartile range is also shown for the case where the individual σr values for each grid cell are used to compute the
variance (orange line, with shaded interquartile range). (c) Binned medians of AC1 as a function of the empirically measured recovery rate r, for increasing
thresholds on R2 of the exponential fit to the recovering time series after abrupt transitions, as indicated in the legend. (d) Same as (c) but for the variance.
Low R2 variance medians in (d) plot on top of each other until R2>0.3.
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Extended Data Fig. 4 | Empirical confirmation of recovery rates. Comparison between measured recovery rates and theoretical resilience metrics for
VOD data when using the entire time series to calculate theoretical resilience. (a) AC1 versus recovery rates r from exponential fits to recovering time
series with R2>0.3; the magenta (blue) line shows binned medians (means), which are close to the exponential fit of the empirical relationship between
recovery rate and AC1 values (black line). Gray shading shows data interquartile range. (b) Same as (a) but for the variance. The variance indeed shows
the expected power-law relationship with the recovery rate; there remain deviations from the theoretically expected
⟨x2⟩
=
−σ2
r/2r
relationship (black
line), where we use the spatial mean of the driving noise σr. The mean variance and corresponding interquartile range is also shown for the case where
the individual σr values for each grid cell are used to compute the variance (orange line, with shaded interquartile range). (c) Binned medians of AC1 as
a function of the empirically measured recovery rate r, for increasing thresholds on R2 of the exponential fit to the recovering time series after abrupt
transitions, as indicated in the legend. (d) Same as (c) but for the variance. Low R2 variance medians in (d) plot on top of each other until R2>0.3.
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−180° −120° −60° 0° 60° 120° 180°
−60°
0°
60°
−0.5 0.0 0.5
AC1 Trend 1992-2017
−180° −120° −60° 0° 60° 120° 180°
−60°
0°
60°
−0.5 0.0 0.5
AC1 Trend 2004-2017
(a)
(b)
(c)
(e)
−180° −120° −60° 0° 60° 120° 180°
−60°
0°
60°
−0.5 0.0 0.5
AC1 Trend 1992-2004
−180° −120° −60° 0° 60° 120° 180°
−60°
0°
60°
−0.5 0.0 0.5
Variance Trend 1992-2017
−180° −120° −60° 0° 60° 120° 180°
−60°
0°
60°
−0.5 0.0 0.5
Variance Trend 1992-2004
−180° −120° −60° 0° 60° 120° 180°
−60°
0°
60°
−0.5 0.0 0.5
Variance Trend 2004-2017
(d)
(f)
Extended Data Fig. 5 | Global resilience trends by metric. Statistically significant (p < 0.05) trends in vegetation optical depth (VOD) (a,c,e) AC1 and
(b,d,f) variance for the time periods (a,b) 1992–2017, (c,d) 1992–2004, and (e,f) 2004–2017.
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Extended Data Fig. 6 | Global resilience time series by land-cover. Rolling-window AC1 for different land cover types in vegetation optical depth (VOD)
data. Top row: three-year window, middle row: five-year window, bottom row: seven-year window. AC1 in left column and variance in right column.
Each line covers one land-cover type. 1992 shown as black dashed line, with light colors representing data potentially contaminated by discontinuities
before 1992. Note that only the broadleaf evergreen class shows a distinct drop before 1992. Globally coherent changes in resilience are visible across all
land-cover types and with different moving window sizes.
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Extended Data Fig. 7 | See next page for caption.
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Extended Data Fig. 7 | Global resilience trends. Direction (+/-) of global resilience trends (a: 2000-2017, b: 2002-2017, c: 2004-2017) for AC1 and
variance, using vegetation optical depth (VOD) data. Bare earth, snow, and anthropogenic land covers are excluded from the analysis (white areas, see
Methods). Linear trends are calculated based on five-year rolling window AC1 and variance estimates; only trends with p <0.05 in either AC1 or variance
are shown in color (see Methods for details on significance testing). Pixels with mixed significant trends (for example, AC1 positive, variance negative) are
shown in gray.
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