Forests cover about 41 million km2 — about 30% of the land surface. They play a fundamental role in the global carbon cycle, absorbing about 33% of anthropogenic carbon emissions, and are considered a key element for mitigating future climate change6. In addition, forests provide a series of ecosystem services that contribute to societal well-being, such as regulation of water flows, protection of soils and conservation of biodiversity7. Unfortunately, forest ecosystems are increasingly endangered by numerous disturbances, including natural agents (for example, fires, wind storms and pathogens) and anthropogenic pressures2. The persistence and functionality of these ecosystems are highly dependent on their resilience, defined as the ability to withstand and recover from environmental perturbations3,4,5. Low-resilience forests are more sensitive to anomalies in external drivers and are potentially more exposed to abrupt and possibly irreversible shifts (for example, regime shifts)8. This is particularly critical in view of the ongoing intensification of disturbance regimes that could affect the provision of key ecosystem services in the near future9,10,11. At the same time, forest-based mitigation strategies that rely on sustained carbon sinks and stocks are becoming crucial to achieve the most ambitious climate targets. In this context, it is increasingly important to investigate the vulnerability of forest carbon stocks and fluxes to external perturbations. However, little is known about how forest resilience has been evolving in response to global environmental change. Understanding the underlying mechanisms of forest resilience and its recent dynamics is therefore of paramount importance to develop sound conservation and management plans.

Theoretical studies have demonstrated that as systems approach a tipping point (that is, a threshold when a self-sustained runaway change starts), they lose resilience, so that small continuous external perturbations can shift the system into an alternative configuration12. It has been proposed that such a loss of resilience can be detected from the increased temporal autocorrelation (TAC) in the state of the system, reflecting a decline in recovery rates due to the critical slowing down (CSD) of system processes that occur at thresholds3,4,5 (Supplementary Methods 1–3 and Supplementary Figs. 1 and 2). In such a framework, resilience is defined as the capacity of ecosystems to withstand perturbations and avoid state shifts, and not as the recovery to the initial state after a state change is induced by a major event. The reduction in resilience can be caused by impaired physiological functions that make the ecosystem unstable or at least more vulnerable to regime shifts under perturbations (for example, in terms of productivity, leaf area index or species composition)12,13,14. This property was leveraged in previous studies to assess spatial patterns of static forest resilience15,16,17,18. However, application of this method at large scales in a dynamic context is challenging owing to the limited time series of observations, the presence of dominant seasonal frequencies in variations of both ecosystem responses and forcing signals, variations in autocorrelation of the forcing signals and the presence of stochastic noise4. So farthese challenges have limited the study of the temporal evolution of forest resilience in real systems19,20,21 and led to the substantial lack of global-scale assessments. In this respect, the expanding availability of temporally consistent Earth observations over multiple decades is now offering new opportunities to monitor time-varying forest resilience at regional to global scales.

Here we estimate CSD from time series of satellite-based vegetation indices to investigate the space–time variation in forest resilience that has occurred over the past two decades at the global scale. Specifically, we retrieved the 1-lag TAC as a CSD indicator related to resilience3,4,5 from satellite-based retrievals of the kernel normalized difference vegetation index (kNDVI) derived for the 2000–2020 period at the global scale at 0.05° spatial resolution from the Moderate Resolution Imaging Spectroradiometer sensor. kNDVI has recently been proposed as a robust proxy for ecosystem productivity22, and is therefore used in this study as a suitable metric to represent the state of forest ecosystems.

Trends and drivers of forest resilience

We initially explored the average TAC at the pixel level from the whole kNDVI time series (2000–2020; hereafter referred to as long-term TAC). This signal, by integrating the interplay between forest and climate, reflects the slowness of the forest–climate system resulting from the interplay of environmental drivers that affect plant growth and of the ecosystem capacity to recover from perturbations. A random forest (RF) regression model23 was then developed to identify the emergent relationships between long-term TAC (response variable) and a suite of forest and climate metrics (environmental predictors; Methods and Extended Data Table 1). Results show that global forests are characterized by a considerable spatial variability in long-term TAC (Extended Data Fig. 1) largely explained by local environmental conditions (R2 = 0.87; Extended Data Fig. 2 and Supplementary Discussion 1). To detect the resilience signal of the forest system and explore itstemporal dynamics in response to changing environmental conditions, we analysed the temporal evolution of TAC computed on kNDVI with 3-year rolling windows over the observational period. Factorial simulations of the previously developed RF model were performed to disentangle the contribution of the environmental factors and filter out the confounding signals originating from the TAC of climate drivers (details in Methods). This resulted in a time series of annual TAC and its temporal trend (δTAC) was used as an indicator of CSD to detect changes in forest resilience over time.

Results show a widespread and significant increase in TAC, and thus a temporal decline in resilience, in tropical, temperate and arid regions (1.63 × 10−3, 1.43 × 10−3 and 1.26 × 10−3 yr−1, respectively). By contrast, boreal forests show divergent local patterns with an average increasing trend in resilience (−1.54 × 10−3 yr−1; Fig. 1a,b and Extended Data Table 2) prominently associated with a decline in TAC occurring in Eastern Canada and European Russia. We further explored the temporal changes in resilience, by comparing the average TAC of kNDVI computed over two independent temporal windows (2000–2010 and 2011–2020; Methods). We found a statistically significant increase over time at the global scale (53% of the globe experiences a positive relative change; Fig. 2c). However, the global signal is limited by the compensation of contrasting patterns across different climate regions. In fact, the statistically significant increase of TAC in tropical, arid and temperate forests (56–63% of land with positive relative change) is partially offset by an opposite trend occurring in boreal forests (56% of land with negative relative change). The patterns deriving from the comparison of the two independent decades are consistent with the trajectories of δTAC (Fig. 1a,b and Extended Data Fig. 3), confirming the validity of the finding. These emerging signals suggest worrying trajectories for the resilience of much of global forests. The signals are particularly robust because they are based on a single sensor (the Moderate Resolution Imaging Spectroradiometer) and a vegetation index (kNDVI) that showed enhanced correlation with primary productivity and reduced noise and stability issues compared to other classical indices22 (Methods). Extensive sensitivity analyses further support the robustness of these emerging temporal drifts (Methods, Supplementary Discussion 2 and Extended Data Figs. 46).

Fig. 1: Temporal variations of forest resilience and its key drivers.
figure 1

a, Spatial map of the temporal trend of TAC (δTAC). Positive δTAC values (for example, tropical forests) suggest a reduction in recovery rates and thus a decline in resilience, and vice versa for negative δTAC values (for example, boreal forests). The values are averaged over a 1° × 1° moving window for visual purposes. b, δTAC as in a binned as a function of climatological temperature and precipitation. The black dots indicate bins with average values that are statistically different from zero (two-sided Student’s t-test; P value ≤ 0.05). c, Frequency distribution of the differences in TAC computed for two independent temporal windows (2011–2020 minus 2000–2010) and shown separately for different climate regions. The numbers refer to the percentage of the observations lower and greater than zero; the asterisks indicate distributions with averages that are statistically different from zero (two-sided Student’s t-test; P value ≤ 0.05). The thin vertical line in each plot shows the distribution average. d, The cover fraction corresponding to each climate region and colour code reported in c and shown over the latitudinal gradient. e, The zonal average of the trend in TAC (δTAC) as determined by the three drivers (X) at 5° latitudinal resolution and the corresponding 95% confidence interval shown as a coloured line and shaded band, respectively. The colours reflect the three different driver categories: forest density, background climate and climate variability.

Fig. 2: Effect of forest management on forest resilience and interplay with GPP.
figure 2

a, Frequency distributions of long-term TAC(2000–2020) for managed forests (MF) and intact forests (IF) located in a similar background climate. The coloured numbers report the respective averages, the top labels refer to the mean of the differences (diff.) in long-term TAC between managed and intact forests, and the asterisk indicates distributions that are statistically different (two-sided Student’s t-test; P value ≤ 0.05). b, The same as for a but for δTAC; the coloured numbers refer to the percentage of the observations lower and greater than zero (on the left and right of 0 on the x-axis, respectively). c, The same as for b but for the temporal correlation between annual GPP and TAC, denoted as ρ(GPP,TAC). d, A spatial map of ρ(GPP,TAC). e, ρ(GPP,TAC) binned as a function of climatological precipitation and temperature. The black dots indicate bins with average values that are statistically different from zero (two-sided Student’s t-test; P value ≤ 0.05). f, A spatial map of the areas, with different colours for the four combinations of positive/negative δGPP and δTAC. The cover fractions of each of the four classes for managed and intact forests are reported in stacked bars.

Looking at the marginal contribution of the drivers of δTAC, we found that the widespread vegetation greening that occurred in recent decades (Extended Data Fig. 2c and Extended Data Fig. 7a), probably driven by CO2 fertilization and climate change24, had a positive effect on global resilience, most prominently in cold and temperate climates (Fig. 1d,e, forest density). However, the concurrent intensifications of water limitations and extreme climate events, particularly severe in tropical, arid and temperate regions (Extended Data Fig. 2d,e and Extended Data Fig. 7c–j) have offset the benefits of CO2 fertilization and greening (Fig. 1d,e; |\(\delta \text{TAC}\)| due to changes in background climate and climate variability > |\(\delta \text{TAC}\)| due to changes in forest density). This ultimately resulted in a net loss in forest resilience in these biomes (Fig. 1a–c). The increasing forest vulnerability to natural disturbances and the increased tree mortality throughout much of the Americas and in Europe over recent decades provide independent evidence of ongoing decline of forest resilience25,26. The above-mentioned climate-related pressures have occurred in boreal forests as well, but their severity probably could not compensate the gain associated with the positive effect of CO2 fertilization and a warmer climate in most areas of this temperature-limited biome (Fig. 1d,e). However, the pattern observed at the high latitudes could eventually change in response to the expected decline in water availability due to the interplay between global warming and anticipated phenology27. In fact, recent observational studies suggest that global forests are switching from a period dominated by the positive effects of CO2 fertilization to a period characterized by the progressive saturation of the positive effects of fertilization on carbon sinks and the rise of negative impacts of climate change28,29.

Forest management and resilience

The results shown thus far have focused on the role of natural drivers in modulating spatial and temporal variations in forest resilience. However, anthropogenic disturbances, such as forest management and land use change, have the potential to influence the ability of forest ecosystems to recover from perturbations by directly affecting tree species, age distribution, cover density, rooting depth and primary productivity1,30,31 (Extended Data Fig. 2c and Extended Data Fig. 7a,b). To factor out such effects, we analysed long-term TAC and δTAC for managed and intact forests under similar background climate (Methods and Extended Data Fig. 8). Intact forests have considerably lower long-term TAC (that is, higher forest resilience) than managed forests (0.13 and 0.21, respectively; Fig. 2a). This finding reinforces the expectation that intact forests have a higher capacity to withstand external perturbations thanks to their typically higher structural complexity and species richness32,33. Independent observational evidence emphasizes the contribution of human pressures in the decline of forest resilience over recent decades1,26,30,34. Interestingly, in terms of temporal trends (δTAC), managed and intact forests do not present significant differences and show comparable fractions of forests experiencing positive trends (72% and 66%, respectively, Fig. 2b) and hence decreasing resilience. This is an important finding because it suggests that the average level of forest resilience in a given climate is heavily affected by forest management, whereas its ongoing temporal variations (Fig. 1a,b) are controlled by large-scale climate signals. The observed global trends, therefore, plausibly reflect the effective climate-induced changes in the capacity of forests to withstand external perturbations.

Resilience and primary productivity

Regardless of the forest type, changes in forest resilience may trigger variations in gross primary productivity (GPP) and vice versa, based on a mutual causal link. Understanding the interplay between these two variables is crucial given the role of GPP in the global carbon cycle35. We explored this by analysing the correlation of satellite-based GPP retrievals36 and TAC at the annual scale (short-term interplay) and comparing the trends in GPP and TAC (long-term interplay; Methods). In the short term, intact forests show a lower correlation between GPP and TAC than managed forests (Fig. 2c), probably because resilience is on average higher in intact ecosystems (Fig. 2a) and therefore probably less critical for productivity. Such bi-directional interactions translate into a negative correlation between GPP and TAC, with a closer link in dry and cold climates, probably reflecting the potential amplification of the two-way interplay in these regions (Fig. 2d,e). In the long term, about 70% of both managed and intact forests are experiencing a positive trend in GPP at present, but in 50% of these areas (about 36% in absolute terms), this occurs in combination with a positive trend in TAC (Fig. 2f, dark red patterns). This implies that a considerable fraction of forest area is increasing primary productivity while also experiencing a declining resilience, therefore leading to an expanding but more vulnerable forest sink. The widespread observations of rising tree mortality2, as well as observations of the growing terrestrial carbon sink37, confirm the co-occurrence of such antagonistic processes in response to global change2.

Early signals of abrupt forest decline

As a loss of forest resilience increases the sensitivity to external perturbations14, we explored the potential of δTAC to work as an early-warning signal of abrupt forest decline (theoretical framework described in Supplementary Methods 1 and 2). To exclude the effect of land management (for example, apparent abrupt declines (ADs) driven by forest harvest), we limited the analysis to global intact forests, with a focus on tropical and boreal regions that together cover about 97% of the investigated domain (Extended Data Fig. 8). ADs are defined here as sudden changes in the state of the forest ecosystem and detected, for a range of severities, as negative anomalies of 1 to 6 times the standard deviation (σ) of mean growing-season kNDVI with respect to the reference undisturbed mean in the time series. In this analysis, we quantify whether declining trends in resilience (that is, increases of δTAC) are associated with a consequent abrupt shift in the system, regardless of the disturbance type (details in Methods).

At the global level, intact forests have a probability of AD conditional on δTAC greater than 0.5 (Fig. 3a). This signal is statistically significant and increases with the severity of AD, suggesting that the progressive deterioration of ecosystem states, as tracked by the decline of resilience, has probably contributed to the upsurge of negative anomalies in forest dynamics. The emerging relation is mainly driven by boreal forests, particularly those in central Russia and western Canada, where there is an emergent, localized decline in forest resilience (Fig. 1a). Such patterns may indicate that in these zones the AD is following the drifting towards a critical resilience threshold, which is probably triggered by the changes in environmental drivers occurring at the northernmost latitudes38. Insect outbreaks, which are typically favoured by water stress39, may represent one of the main disturbances that have ultimately caused such ADs in the ecosystem state40,41. On the contrary, ADs in tropical forests are not statistically associated with high δTAC values (Fig. 3a). In these regions, fast and strong disturbance events, such as fires42 or droughts43, may induce an AD independently of long-term increasing trends in CSD (refs. 3,4; here represented by δTAC). The above-mentionedhypotheses are also consistent with the dominant climate drivers of δTAC in boreal and tropical regions (background climate and climate variability, respectively, Fig. 1d,e) and further supported by several independent pieces of evidence (for example, refs. 26,30,44,45).

Fig. 3: Early-warning signals of ADs in intact forests.
figure 3

a, Probability of occurrence of AD conditional on the values of δTAC for different severities of AD (expressed as anomaly n-times local standard deviation below the local mean, σ) shown separately for three different climate regions. The asterisks indicate probabilities statistically different from 0.5 (two-sided Student’s t-test; P value ≤ 0.05). b, TAC retrieved in the year preceding the occurrence of an AD (TACAD) binned as a function of climatological precipitation and temperature. c, Tolerance to TACAD (the absolute increase in TAC that an ecosystem in equilibrium can tolerate before reaching critical conditions) across a gradient of aridity index. The circle and whiskers refer to the average value and its 95% confidence interval; colours refer to the corresponding TACAD. Each binned aridity index ranging from 0 to 500 mm °C−1 counts 10,868, 16,799, 728, 59 and 13 sampled pixels. d, Proximity to TACAD (proximity of present intact forests to their critical condition threshold) binned as a function of climatological precipitation and temperature. The black dots indicate bins with average values that are statistically different from zero (two-sided Student’s t-test; P value ≤ 0.05). Negative values of proximity to TACAD represent areas where the threshold resilience for AD (TACAD) has been already overpassed, and vice versa for positive values. e, Frequency distributions of proximity to TACAD shown separately for different climate regions and computed over the whole domain (blue) and over those areas experiencing a concomitant positive δTAC (red). The coloured numbers refer to the percentage of the frequency distribution lower and greater than zero (on the left and right of 0 on the x -axis, respectively) with respect to the whole domain.

Critical threshold mechanisms

To further explore the threshold mechanisms and the causality associated with ADs, we retrieved TAC for the year preceding the occurrence of an AD (hereafter referred to as observed TACAD)—and thus reflecting the threshold value of resilience before the AD of the ecosystem. For each AD event, we retrieved the corresponding ecosystem tolerance expressed as the difference between TACAD and its average TAC computed in pre-disturbance conditions (details in Methods). This metric reflects the absolute increase in TAC that an ecosystem in equilibrium can tolerate before reaching critical conditions of AD. We found that, despite the average slow recovery rates (Extended Data Fig. 1 and Supplementary Discussion 1), ecosystems frequently exposed to water limitations experience ADs at higher levels of TACAD (Fig. 3b), thanks to their higher tolerance compared to tropical–humid and cold–dry forests (Fig. 3c). These patterns are probably due to the long-term adaptation of tree species in arid regions that leads to structural and physiological adaptation to water limitations (for example, deeper rooting systems, resistance to cavitation and higher root/shoot ratio), whereas humid and cold biomes have a higher vulnerability to water shortage46,47.

To evaluate the proximity of present intact forests to their critical resilience threshold, we extrapolated in space the value of TACAD by the use of the RF regression algorithm and compared it with TAC retrieved for the year 2020. Proximity takes negative or zero values when TACAD has already been reached in 2020 and positive values when there are still margins before reaching the critical threshold (Methods). Results show that, at the end of our observational period, about 30% of global intact forests have already reached or overpassed their TACAD (Fig. 3d,e). More critically, about 23% experienced a concomitant increase in δTAC (Fig. 1a), therefore implying an ongoing reduction in ecosystem resilience to levels that are already close to an AD and, potentially, to a tipping point. We estimated that 3.32 Pg C of GPP is exposed to such critical conditions, prominently in tropical forests (93%), an amount about three times larger than the carbon losses due to deforestation in the Brazilian Amazon during the past ten years26. We point out that these critical conditions are not sufficient to determine a regime shift (Supplementary Methods 3). However, they represent a strong indication of the rising risks of an increased instability and vulnerability to hazards of forest biomes. This is particularly critical for tropical forests, where the observed recent decline of the carbon sink48,49 could by further exacerbated by the continuous and progressive deterioration of forest resilience and the parallel increase in tree mortality and turnover rate.


Our analysis reveals that in recent decades both intact and managed forests have experienced substantial changes in resilience controlled by large-scale climate signals. We found that tropical, temperate and arid forests underwent a decline in resilience probably related to the concomitant increase in water limitations and climate variability. On the contrary, benefits induced by climate warming and CO2 fertilization have outweighed such negative effects in much of the boreal biome, ultimately leading to an increase in forest resilience. The increasing fragility to external perturbations in combination with an enhancement in productivity for a considerable fraction of global forests (about 36%) confirms the co-occurrence of antagonistic processes driving photosynthesis and tree mortality in response to global change2. We estimate that about 23% of intact undisturbed forests have already reached their critical threshold for an AD and are experiencing a concomitant further degradation of resilience. Considering the expected transition from a CO2-fertilization-dominated period to a warming/drying-dominated period27,28,29, the observed negative trajectories of forest resilience suggest potential critical consequences for key ecosystem services, such as carbon sequestration. Therefore, it is becoming urgent to account for these trends in the design of effective forest-based mitigation strategies to avoid future unexpected negative events triggered by the increasing vulnerability of carbon stocks. In this regard, our global data-driven assessment shows that resilience thinking50 can be developed effectively in a science-based and solution-oriented framework to support the many challenges of forest management in times of rapid climatic changes.


Climate drivers

To explore the impact of climate on forest resilience (see the following sections), we used monthly averaged total precipitation, 2-m air temperature, evapotranspiration deficit and surface solar radiation downwards acquired from the ERA5-Land reanalysis product at 0.1° spatial resolution for the 2000–2020 period (!/home). Evapotranspiration deficit was quantified as the total precipitation minus evapotranspiration. In this study, we referred to climate regions as defined by the Köppen–Geiger world map of climate classification51 ( The original 31 climatic zones were merged into major zones and only those characterized by vegetation cover were included in our study (tropical, arid, temperate and boreal; Extended Data Fig. 8).

Vegetation dynamics

NDVI data acquired from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument aboard the Terra satellite was used to derive changes in global vegetation for the period 2000–2020. We used cloud-free spatial composites provided at 16-day temporal resolution and 0.05° spatial resolution (MOD13C1 Version 6; and retained only pixels with good and marginal overall quality. The MODIS-derived NDVI dataset represents a state-of-the-art product of vegetation state whose retrieval algorithm is constantly improved52, and being derived from a unique platform and sensor, it is temporally and spatially consistent. Vegetation dynamics were analysed in terms of kNDVI, a nonlinear generalization of the NDVI based on ref. 22 and derived as follows:

$$\text{kNDVI=}\tanh \left({\text{NDVI}}^{2}\right)$$

kNDVI has recently been proposed as a strong proxy for ecosystem productivity that shows high correlations with both plot level measurements of primary productivity and satellite retrievals of sun-induced fluorescence22. In addition, kNDVI has been documented to be more closely related to primary productivity, to be resistant to saturation, bias and complex phenological cycles, and to show enhanced robustness to noise and stability across spatial and temporal scales compared to alternative products (for example, NDVI and near-infrared reflectance of vegetation). For these reasons, it has been retained in this study as the preferred metric to describe the state of the forest ecosystem.

To obtain an accurate estimate of resilience indicators, vegetation time series need to be stationary without seasonal periodic patterns or long-term trends53. To this aim, vegetation anomalies were obtained from kNDVI data by first subtracting the multi-year 16-day sample mean and then removing linear trends from the resulting time series. Missing data, due for instance to snow cover affecting the retrieval of reflectance properties, have been gap-filled by climatological kNDVI values. The time series of kNDVI-based vegetation anomalies was used to derive resilience indicators and assess their spatial and temporal variations (see next sections).

Interannual changes in vegetation were assessed in terms of growing-season-averaged kNDVI. To this end, a climatological growing season that spanned months with at least 75% of days in the greenness phase was derived from the Vegetation Index and Phenology satellite-based product54 ( and acquired for the 2000–2016 period at 0.05° spatial resolution. In addition, forest cover (FC) fraction was derived from the annual land-cover maps of the European Space Agency’s Climate Change Initiative ( over the 2000–2018 period at 300-m spatial resolution. FC was retrieved by summing the fraction of broadleaved deciduous, broadleaved evergreen, needle leaf deciduous and needle leaf evergreen forest. FC was resampled to 0.05° to match the kNDVI spatial resolution.

Spatial patterns of slowness and its dependence on environmental factors

In this study, we quantified the resilience of forest ecosystems—their ability to recover from external perturbations—by the use of the 1-lag TAC (refs. 3,4,5). Such an indicator was initially computed on the whole time series of vegetation anomalies (2000–2020) for forest pixels with less than 50% missing data in the original NDVI and FC greater than 0.05 and referred to in the text as long-term TAC. This analysis was used to assess the spatial patterns of the forest slowness mediated by environmental factors that affect plant growth rates and capacity to recover from perturbations. The long-term TAC was explored both in the geographic and climate space (Extended Data Fig. 1). In the climate space, long-term TAC was binned in a 50 × 50 grid as a function of average annual precipitation and temperature, both computed over the 2000–2020 period, using the average as an aggregation metric weighted by the areal extents of each record. We retained only bins with at least 50 records.

To explore the potential drivers of long-term TAC, we developed an RF regression model23 and predicted the observed long-term TAC (response variable) based on a set of environmental features (predictors). The use of machine learning in general and of RF in particular, being nonparametric and nonlinear data-driven methods, does not require a priori assumptions about the functional form relating the key drivers and the response functions. The environmental variables include vegetation properties (FC and growing-season-averaged kNDVI) and climate variables (total precipitation, 2-m air temperature, evapotranspiration deficit and surface solar radiation downwards). Each of the climate variables was expressed in terms of average, coefficient of variation and 1-lag autocorrelation and resampled to 0.05° spatial resolution to match the spatial resolution of kNDVI. All environmental variables were computed annually and then averaged over time, except the autocorrelation that was computed directly for the whole period, analogously to the long-term TAC. This resulted in a set of 14 predictors representing the forest density, the background climate, the climate variability and its TAC in the observational period (Extended Data Table 1). The RF model was developed by splitting the observed long-term TAC into two separate samples: 60% of records were used for model calibration, and the remaining 40% were used to validate model performances in terms of coefficient of determination (R2), mean squared error and percentage bias (PBIAS). Each record refers to a 0.05° pixel. The RF implemented here uses 100 regression trees, whose depth and number of predictors to sample at each node were identified using Bayesian optimization. The general model formulation is as follows:

$$\text{TAC}\,=\,f\left(X\right)+{\varepsilon }_{{\rm{f}}}$$

in which f is the RF regression model, X are the environmental predictors and εf are the residuals. We found that the model explains 87% of the spatial variance (R2) of the observed long-term TAC with a mean squared error of 0.007 and an average overestimation of 0.058 (PBIAS; Extended Data Fig. 2a). By definition, machine learning methods are not based on the mechanistic representation of the phenomena and therefore cannot provide direct information on the underlying processes influencing the system response to drivers. However, some model-agnostic methods can be applied to gain insights into the outputs of RF models. Here we used variable importance metrics to quantify and rank how individual environmental factors influence TAC (Extended Data Fig. 2b). Furthermore, using partial dependence plots derived from the machine learning algorithm RF, we explored the ecosystem response function (TAC) across gradients of vegetation and climate features (Supplementary Discussion 1 and Extended Data Fig. 2c–f).

CSD indicators

To explore the temporal variation in forest resilience, we used CSD indicators, here quantified in terms of temporal changes in TAC retrieved for two consecutive and independent periods ranging from 2000 to 2010 and from 2011 to 2020, and assessed the significance of the change in the sampled mean aggregated for different climate regions through a two-sided t-test (Fig. 1c). This analysis was complemented by the computation of TAC on the annual scale over a 2-year lagged temporal window (3-year window size) to track the temporal changes in CSD. This resulted in a time series of TAC with an annual time step.

We point out that temporal dynamics of annual TAC are driven by two processes: the changes in the resilience of the system that affect the velocity of the recovery from external perturbations and the confounding effects of the changes in autocorrelation of the climate drivers (Xac) that directly affect the autocorrelation of NDVI. Given the specific goals of this study, we factored out the second process from the total TAC signal to avoid that an increasing autocorrelation in the drivers would affect our analysis and conclusions about the resilience and the potential increase in instability56. For this purpose, we disentangled the temporal changes in TAC due to variations in autocorrelation in the climate drivers (\({\rm{TAC}}| {X}_{{\rm{ac}}}\)) by adopting the space-for-time analogy and applied the RF model (f) at an annual time step (t) in a set of factorial simulations as follows:

$${\text{TAC}}^{t}\,{\rm{| }}\,{X}_{{\rm{ac}}}=f\left({X}^{t}\right)-f\left({X}_{-{\rm{ac}}}^{t},{X}_{{\rm{ac}}}^{2000}\right)$$

The first term on the right side of equation (3) is the RF model simulation obtained by accounting for the dynamics of all predictors, and the second term is the RF model simulation generated by considering all predictors dynamic except the factors of autocorrelation in climate that are kept constant to their first-year value (year 2000). For such runs, we used predictors computed on an annual scale over a 2-year lagged temporal window, consistently to the TAC time series. We found that the direct effects of autocorrelation in climate have led to a positive trend of TAC in dry zones (due to the increasing autocorrelation of the drivers in these regions) and to an opposite effect in temperate humid forests (Supplementary Fig. 3). To remove these confounding effects, the estimated term \({{\rm{TAC}}}^{t}| {X}_{{\rm{ac}}}\) is factored out from the TACt by subtraction to derive an enhanced estimate of annual resilience that is independent of autocorrelation in climate (Extended Data Fig. 3).

Long-term linear trends computed on the resulting enhanced TAC time series (δTAC) represent our reference CSD indicator used in this study to explore the changes in forest resilience. δTAC was quantified for each grid cell (Fig. 1a) and represented in the climate space following the methodology previously described (Fig. 1b). We then assessed the significance of the trends at bin level by applying a two-sided t-test for the sampled trend distributions within each bin. This significance test is independent from the structural temporal dependencies originating from the use of a 2-year lagged temporal window to compute the TAC time series.

Following an analogous approach described in equation (3), we disentangled the effect of the variation in forest density, background climate and climate variability on temporal changes in TAC (Fig. 1d,e). We recognize that other environmental factors not explicitly accounted for in our RF model could play a role in modulating the temporal variations in TAC. However, given the comprehensiveness of the suite of predictors used in equation (2) (Extended Data Table 1), it seems plausible that residuals mostly reflect the intrinsic forest resilience, the component intimately connected to the short-term responses of forests to perturbations, which is not directly related to climate variability. Forest ecosystem evolutionary processes could also play a role, but longer time series would be required to reliably capture these dynamics. Furthermore, abrupt declines (ADs) in the vegetation state and following recoveries, similarly to those potentially originating from forest disturbances (for example, wildfires and insect outbreaks), could influence the TAC changes. However, such occurrences, being distributed across the globe throughout the whole period, are expected to only marginally affect the resulting trend in TAC time series.

Sensitivity analysis

To assess the robustness of our results with respect to the modelling choices described above, we performed a series of sensitivity analyses for the difference in TAC retrieved for the two independent periods (2000–2010 and 2011–2020). To this aim, we tested their dependence on: the quality flag of the NDVI data used for the analyses (good, good and marginal); the gap-filling procedure tested on different periods (year and growing season); the inclusion or exclusion of forest areas affected by ADs; the threshold on the maximum percentage of missing NDVI data allowed at the pixel level (20%, 50% and 80%); the threshold on the minimum percentage of FC allowed at the pixel level (5%, 50% and 90%); and the pixel spatial resolution used for the analyses (0.05°, 0.25° and 1°). In addition, we tested the sensitivity of the trend in total TAC signal on the moving temporal window length used to calculate autocorrelation at lag 1. Results obtained for the different configurations were compared in terms of frequency distributions, separately for climate regions (Extended Data Fig. 4), and further explored in the climate space (Extended Data Figs. 5 and 6). Outcomes of the sensitivity analysis are discussed in Supplementary Discussion 2.

Interplay between GPP and CSD

Resilience and GPP interact with each other through mutual causal links. On one hand, a reduction in forest resilience makes the system more sensitive to perturbations with potential consequent losses in GPP (ref. 26). On the other hand, a reduction in GPP may lead to a decline in resilience according to the carbon starvation hypothesis, and may be associated with increasing hydraulic failure46. To explore the link between forest resilience and primary productivity, we quantified the correlation between TAC and GPP. Estimates of GPP were derived from the FluxCom Model Tree Ensemble for the 2001–2019 period at 8-daily temporal resolution and 0.0833° spatial resolution and generated using ecosystem GPP fluxes from the FLUXNET network and MODIS remote sensing data as predictor variables36 ( Annual maps of GPP were quantified and resampled to 0.05° to match the temporal and spatial resolution of TAC time series. The Spearman rank correlation (ρ) was then computed between annual GPP and TAC over a 1° spatial moving window to better sample the empirical distribution of the two variables (Fig. 2d). The significance of ρ(GPP,TAC) was assessed over the climate space separately for each bin (Fig. 2e), similarly to the approach used to test the significance of δTAC. Furthermore, we explored the relationships between the trend in GPP (δGPP) and the trend in TAC (δTAC) by clustering the globe according to the directions of the long-term trajectories of the above-mentioned variables (Fig. 2f).

Disentangling the impact of forest management

To characterize TAC on different forest types and disentangle the potential effects originating from forest management, results were separately analysed for intact forests and managed forests. Intact forests were considered those forest pixels constituting the Intact Forest Landscapes57 dataset ( Intact Forest Landscapes identifies the forest extents with no sign of significant human activity over the period 2000–2016 based on Landsat time series. The remaining forests pixels—not labelled as intact—were considered as managed forests (Extended Data Fig. 8). The resulting forest type map is consistent with those used for United Nations Framework Convention on Climate Change reporting58, although with more conservative estimates of intact forests in the boreal zone due to the masking based on FC and percentage of missing data applied in this study.

We analysed the differences in long-term TAC (computed for the whole 2000–2020 period) between managed and intact forests by masking out the potential effect of climate background. To this aim, we compared the climate spaces generated separately for managed and intact forests by extracting only those bins that are covered by both forest classes. The resulting distributions—one for each forest class—have the same sample size, and each pair of elements shares the same climate background. Potential confounding environmental effects on average recovery rates are, therefore, minimized. We then applied a two-sided t-test for analysing the significance of the difference in the sampled means (Fig. 2a). An analogous approach was used to test the differences in δTAC and ρ(GPP,TAC) between managed and intact forests (Fig. 2b,c).

Early-warning signals of abrupt forest declines

When forest ecosystems are subject to an extended and progressive degradation, the loss of resilience can lead to an AD (refs. 3,4,5). Such abrupt changes can trigger a regime shift (tipping point) depending on the capacity of the system to recover from the perturbations (Supplementary Methods 1 and 2). We investigated the potential of changes in TAC as early-warning signals of ADs in intact forests over the 2010–2020 period. To this aim, we quantified at the pixel level ADs as the events occurring on a certain year when the corresponding growing-season average kNDVI was more than n-times local standard deviation below the local mean. Local mean and standard deviation (σ) were computed over the 10-year antecedent temporal window (undisturbed) period and n varies between 1 and 6 with higher values reflecting more severe changes in the state of the system. For each pixel and for each fixed n value, we recorded only the first AD occurrence, thus imposing a univocal record for each abrupt change in the state of the system.

We then explored whether the retrieved ADs were statistically associated with antecedent high values of δTAC. To avoid confusion with the attribution of causality, for each AD that occurred at time t (over the 2010–2020 period), we derived the δTAC over the temporal window 2000 − (t − 1). The resulting trend in δTAC is therefore antecedent and independent of the changes in vegetation associated with the AD. Then, for each pixel with an AD at time t, we also extracted randomly one of the undisturbed (with no AD) adjacent pixels and retrieved δTAC over the same temporal window. This analysis produced two distributions of δTAC associated with pixels with and without ADs (AD and no AD, respectively). The two distributions have the same size and each pair of elements shares similar background climate. We calculated the probability of occurrence of AD conditional on the trend in δTAC (\({\rm{AD}}| \delta {\rm{TAC}}\)) as the frequency of ADs for which \(\delta {\rm{TAC}}\left(\mathrm{AD}\right)| > \delta {\rm{TAC}}\left(\mathrm{no\; AD}\right)\), and the significance of the difference in the two sampled means (AD and no AD) was evaluated through a two-sided t-test. Probability and significance were assessed for different climate regions and severity of ADs (Fig. 3a). High statistically significant probabilities suggest that the AD is following the drifting towards a critical resilience threshold plausibly associated with changes in environmental drivers.

We complemented the aforementioned analyses by retrieving the tolerance and proximity to AD, hereafter determined for a 3σ severity. We first quantified the TAC that proceeded the occurrence of an AD and followed a progressive loss of resilience as captured by positive δTAC. This value, hereafter referred to as abrupt decline temporal autocorrelation (TACAD), reflects the TAC threshold over which we observed an abrupt change in the forest state (Fig. 3b). The tolerance to AD was quantified as the difference between the local TACAD and the TAC value averaged over the 2000–2009 period to characterize the pre-disturbance conditions. The tolerance metric was explored across a gradient of aridity index59 (Fig. 3c).

TACAD can be directly retrieved only on those forest pixels that have already experienced an AD. As a considerable fraction of undisturbed forests could potentially be close to their critical TAC threshold, or even have already passed it, it is important to determine their TACAD. To this aim, we developed an RF regression model that expresses the TACAD as a function of the set X of environmental variables used in model f (equation (2)) but excluding the autocorrelation in climate drivers (Xreduced) already disentangled in the TAC signal. The general formulation is as follows:

$${{\rm{TAC}}}_{{\rm{AD}}}=g\left({X}_{\text{reduced}}\right)+{\varepsilon }_{{\rm{g}}}$$

in which g is the RF regression model, Xreduced are the environmental predictors and εg are the residuals. Implementation, calibration and validation of g follow the same rationale described before for the f model. We found that the RF model explains 50% of the variance (R2) of the observed TACAD, with a mean squared error of 0.019 and an average underestimation of 0.86 (PBIAS).

The RF model was then used to predict the TACAD over the whole domain of intact forests and served as input to quantify the proximity to AD of undisturbed forest pixels at the end of the observational period (year 2020). Here we defined the proximity metric as the difference between the value of TAC in 2020 and TACAD. Proximity takes negative or zero values when TACAD has already been reached (\({{{\rm{TAC}}}^{2020}\ge {\rm{TAC}}}_{{\rm{AD}}}\)) and positive values when there are still margins before reaching the critical threshold (\({{{\rm{TAC}}}^{2020} < {\rm{TAC}}}_{{\rm{AD}}}\)). Together \(\delta {\rm{TAC}} > 0\) and \({{{\rm{TAC}}}^{2020}\ge {\rm{TAC}}}_{{\rm{AD}}}\) therefore represent the most critical conditions, as they indicate that the critical resilience threshold for AD has already been reached and the ecosystem is continuing to lose its capacity to respond to external perturbations. We finally quantified the amount of GPP potentially exposed to such critical conditions by linearly extrapolating the GPP for the year 2020 (available GPP data stop in 2019) and overlaying it on the map of critical conditions (proximity to \({\rm{AD}} < 0\) and \(\delta {\rm{TAC}} > 0\)).

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this paper.