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Site descriptionThe experiment was conducted at the Beef Cattle Research Center of the Institute of Animal Science/APTA/SAA, Sertãozinho, São Paulo, Brazil (21°08′16″ S e 47°59′25″ W, average altitude 548 m), during two consecutive years. The climate in this region is Aw according to the Köppen’s classification, characterized as humid tropical, with a rainy season during summer and drought during winter. The meteorological data is reported in Fig. 1. The soil in the experimental area is classified as an Oxisol42. Before the experiment, soil samples were collected for chemical characterization (Table 4), which was performed following the methodology described in Van Raij et al.43. Samples were collected in 18 experimental paddocks, at the depths of 0- to 10- and 10- to 20-cm layers, from 10 distinct sampling points in each paddock, in order to create one composite sample per unit, totaling 36 samples analyzed.Figure 1Meteorological data during the study period, obtained from the meteorological station located at Centro de Pesquisa de Bovinos de Corte, Instituto de Zootecnia/Agência Paulista de Tecnologia dos Agronegócios (APTA)/Secretaria de Agricultura e Abastecimento de São Paulo (SAA), Sertãozinho, São Paulo, Brazil.Full size imageTable 4 Chemical attributes of the soil in the experimental area, before installing the experiment (November 2015).Full size tableThe nitrogen total (Nt) content was determined by the micro-Kjeldahl method44, and the soil nitrogen stocks (SN) were calculated using the following equation below, according to Veldkamp et al.45.$${text{SN }}left[ {{text{Mg ha}}^{ – 1} {text{ at a given depth}}} right], = ,({text{concentration }} times {text{ BD}}, times ,{1}/{1}0),$$ where concentration refers to the Nt concentration at a given depth (g kg−1), BD is the bulk density at a certain depth (average 1.24 kg dm−3), and 1 is the layer thickness (cm).Description of treatments and managementsThe experiment was carried out in a 16-ha area, divided into 18 paddocks of 0.89 ha each (Fig. 2), organized in a randomized blocks design with three replicates and six treatments, namely conventional crop system with grain maize production (CROP), conventional livestock system with beef cattle production in pasture using Marandu grass (LS), and four ICLS for the production of intercropped maize grain with beef cattle pasture. All production systems were sowed in December 2015, under a no-tillage system. The fertilization recommendations in the systems were based on the recommendation presented in the Boletim 10046.Figure 2Localization and representation of the area of the experiment carried out in the study. Google Earth version Pro was used to construct the map (http://www.google.com/earth/index.html).Full size imageIn the CROP system, the maize Pioneer P2830H was cultivated, sowed in a spacing of 75 cm and sowing density of 70 thousand plants. Applications of 32 kg ha−1 of nitrogen (urea), 112 kg ha−1 of P2O5 (single superphosphate) and 64 kg ha−1 of KCl (potassium chloride) were performed. Complementarily, a topdressing fertilization was made using 80 kg ha−1 of nitrogen (urea) and 80 kg ha−1 of KCl. Sowing was carried out for two consecutive years (December 2015 and 2016), providing two harvests of maize grains (May 2016 and 2017), and between one harvest and the other, the soil remained in fallow without any cover crop. The total amount of fertilizer applied in two years was 224 kg ha−1 of nitrogen (urea), 224 kg ha−1 of P2O5 (single superphosphate) and 288 kg ha−1 of KCl (potassium chloride).For the LS treatment, Urochloa brizantha (Hoechst. ex A. Rich) R.D. Webster cv. Marandu (syn. Brachiaria brizantha cv. Marandu) was sowed in a spacing of 37.5 cm, with a density of 5 kg ha−1 of seeds (76% of crop value) for the pasture assemblage. Marandu grass seeds were mixed with the planting fertilizer, applying 32 kg ha−1 of nitrogen (urea), 112 kg ha−1 of P2O5 (as single superphosphate) and 64 kg ha−1 of KCl. Applications of 40 kg ha−1 of nitrogen, 10 kg ha−1 of P2O5 and 40 kg ha−1 of KCl were also performed as topdressing fertilization in October 2016 and March 2017. 90 days after sowing, the pasture was ready to be grazed (March 2016). Three grazing periods were carried out in continuous stocking systems, with the first period between March and April 2016, the second period between August and October 2016 and the third between November 2016 and December 2017. The total amount for 2 years was 112 kg ha−1 of nitrogen (urea), 132 kg ha−1 of P2O5 (single superphosphate) and 144 kg ha−1 of KCl (potassium chloride).The same cultivar, spacing, sowing density and fertilization rates described in the CROP treatment were used in all ICLS, as well as the same density of Marandu grass seeds and topdressing fertilization adopted in the pasture of the LS treatment. The total amount for two years was 192 kg ha−1 of nitrogen (urea), 132 kg ha−1 of P2O5 (single superphosphate) and 224 kg ha−1 of KCl (potassium chloride). In ICLS-1, Marandu grass was sowed in lines simultaneously with maize, while in ICLS-2, the sowing was also simultaneous, but the application of an under-dose of 200 mL of the herbicide Nicosulfuron was used, 20 days after seedlings emergence. In the ICLS-3, Marandu grass seeds were sown the time of topdressing fertilization of maize, thus the grass seeds were mixed with the fertilizer, and sowing was carried out in the interlines of maize, using a minimum cultivator. In ICLS-4, the sowing of Marandu grass was performed simultaneously with maize, but the grass seeds were sowed in both rows and inter-rows of maize, resulting in a spacing of 37.5 cm. In this treatment, the application of 200 mL of the herbicide Nicosulfuron was adopted, 20 days after seedlings emergence.In all ICLS treatments, maize harvest was carried out in May 2016. Ninety days after harvesting the plants, the pastures were ready to be grazed. Therefore, two grazing periods were made in continuous stocking, being the first period between August and October 2016 and the second period between November 2016 and December 2017. The method for animal stocking in treatments LS and ICLS was continuous with a stocking rate (put and take) being defined according to Mott47. Caracu beef cattle with 14 months of age were used at the beginning of the experiment, with an average body weight of 335 ± 30 kg.Estimations of the nutrient balance (NB) and nutrient use efficiency (NUE)In this study, the inputs and outputs of N were assessed at the farm level48,49. The NB was calculated by the equation below19,45,50.$${text{NB}}_{{text{N}}} = {text{ Input}}_{{text{N}}} {-}{text{ Output}}_{{text{N}}}$$As for the NUE, this parameter was evaluated as defined by the EU Nitrogen Expert Panel51, being calculated as the ratio between outputs and inputs of nitrogen.$${text{NUE}}_{{text{N}}} = , left[ {{text{Output}}_{{text{N}}} /{text{ Input}}_{{text{N}}} } right]$$where NB is the nutrient balance, N is nitrogen, Input is the N concentration in the mineral fertilizer (urea), Output is the nitrogen concentration in export (maize grain and animal tissue), and NUE is the use efficiency of the nutrient.The amount of N exported in maize grains, the grain production results (Table 2) were multiplied by the mean value of N, consulted in Crampton and Harris52.In order to estimate the amounts of nutrient exported by the animals in their tissues, the values of live weight gain were considered [kg ha-1 of live weight (PV)] (Table 2), as well as the nitrogen values of the tissue, according to the methodology proposed by Rasmussen et al.21. Those authors reported that for animals weighting less than 452 kg/PV, it represents 2.7%, while heavier animals have a 2.4% nitrogen content representation of their body weight.The inputs and outputs of N in each production system are represented in Figs. 3, 4 and 5. Biological N fixation, atmospheric deposition, denitrification, leaching, rainfall, and volatilization and absorption of ammonia were not considered in the calculation of NB.Figure 3Representation of inputs and outputs of nitrogen and organic residues generated in the crop system.Full size imageFigure 4Representation of inputs and outputs of nitrogen and organic residues generated in the livestock system.Full size imageFigure 5Representation of inputs and outputs of nitrogen and organic residues generated in the integrated systems.Full size imageData for animal tissue, animal excreta, and N concentration in grains were obtained from key manuscripts from the scientific literature in order to estimate the N balance.Calculation of nitrogen quantity and valuation of organic residuesThe amount of N in the organic residues was determined as a function of the system (Figs. 3, 4, 5). The residue considered in the CROP was the straw derived from maize, while for LS it was the litter deposited (LD) in the grass Marandu, and animal manure (feces and urine). The ICLS were considered as the straw, LD, and animal manure.The N concentration in straw and LD was determined following the methods of AOAC (1990). Straw was sampled immediately after maize grain harvest, using a 1-m2 frame in the field. The material was collected in two spots of the plot that were chosen randomly. All straw deposited on the soil was sampled, weighted and dried in an oven with air circulation (60 °C) until constant weight, for the determination of dry matter in kg of straw per hectare (Table 2). The LD in the pasture system (Table 2) was analyzed according to Rezende et al.53.In order to estimate the daily amount of excreta, we considered the stocking rate adopted in the experiment (Table 2) and the values proposed by Haynes and Williams54. 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Climate driversTo 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 (https://cds.climate.copernicus.eu/cdsapp#!/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 (http://koeppen-geiger.vu-wien.ac.at/present.htm). 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 dynamicsNDVI 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; https://lpdaac.usgs.gov/products/mod13c1v006/) 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:$$text{kNDVI=}tanh left({text{NDVI}}^{2}right)$$
(1)
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 (https://vip.arizona.edu/) 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 (https://www.esa-landcover-cci.org/)55 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 factorsIn 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:$$text{TAC},=,fleft(Xright)+{varepsilon }_{{rm{f}}}$$
(2)
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 indicatorsTo 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:$${text{TAC}}^{t},{rm{| }},{X}_{{rm{ac}}}=fleft({X}^{t}right)-fleft({X}_{-{rm{ac}}}^{t},{X}_{{rm{ac}}}^{2000}right)$$
(3)
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 analysisTo 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 CSDResilience 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 (http://www.fluxcom.org/). 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 managementTo 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 (https://intactforests.org/). 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 declinesWhen 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:$${{rm{TAC}}}_{{rm{AD}}}=gleft({X}_{text{reduced}}right)+{varepsilon }_{{rm{g}}}$$
(4)
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 summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this paper. More