Silicate chemical weathering disrupts the global patterns of phosphorus limitation

Abstract

Global change is accelerating the chemical weathering of silicate rocks and the associated phosphorus release. However, the effects of phosphorus release on the global patterns of plant phosphorus limitation remain unclear. Here, we show that approximately 47% of the exposed areas in global silicate rocks are subject to phosphorus limitation of vegetation growth, as estimated using the ratio of leaf nitrogen to phosphorus resorption efficiency. Phosphorus-limited areas are projected to expand markedly with global warming, and the proportion may reach 54 − 59% according to two model scenarios (the shared socioeconomic pathways SSP2-4.5 and SSP5-8.5). Nevertheless, phosphorus release from accelerated chemical weathering of silicate rocks mitigates this limitation, with a relative contribution of approximately 15.5%. This work highlights the implications of accelerated chemical weathering of silicate rocks and its resulting phosphorus release for the global patterns of phosphorus limitation, providing a scientific foundation for phosphorus management strategies.

Introduction

Chemical weathering of terrestrial silicate rocks not only deplete atmospheric CO₂ to produce inorganic carbon sinks^1,2 but also releases organic carbon oxidation CO₂ and primary macronutrients that encourage tree growth and regeneration, e.g., phosphorus (P)^3,4. The release of P via silicate chemical weathering has a limiting effect on vegetation growth and its productivity in the past and future, which in turn has important implications for the terrestrial carbon balance^5,6.

The global average release of P associated with the chemical weathering of terrestrial rocks driven by climate change ranges from 0.8 to 1.2 Tg P yr⁻¹, with an approximate increase of 12 ± 4% from 1850 to 2005^7,8. The effective P released into the soil solution by the chemical weathering of rocks enhances the photosynthetic capacity of vegetation by engaging in energy transfer and physiological metabolic processes, which in turn enables vegetation to absorb more atmospheric CO₂ to generate organic carbon sinks⁹. Vegetation promotes the weathering of silicate rocks through the effect of root splitting or secretion of organic acids by root systems and associated mycorrhizal fungi, thus releasing more effective P and increasing the bioavailability of P¹⁰. In addition, critical nutrient limitation of net primary productivity (NPP) governs major processes in terrestrial ecosystems such as carbon exchange capacity, ecosystem biodiversity, and water quality¹¹. Numerous studies have established P as a key constraint on vegetation growth¹², with recent evidence showing its limitation on global photosynthesis has surpassed that of nitrogen (N) over the past four decades¹³. Vegetation growth responses to climate change and CO₂ fertilization are becoming increasingly restricted by the effective P of soil solution, especially in tropical forests^14,15. Moreover, the effects of multiple factors, such as anthropogenic fossil fuels, synthetic nitrogen fertilizers, and the cultivation of legumes, have added more N inputs to the Earth’s surface, which have led to changes in the ratio of N and P concentrations in plant leaves, and thus the growth of terrestrial vegetation may be more severely P limited than N limited¹⁶. In addition, based on the stoichiometric endostasis hypothesis and the law of the minimum limiting factor, a theoretical framework for indicating N and P limitations using the ratio of the leaf N and P resorption efficiency has been proposed on the ecosystem-scale¹⁷. A high-resolution static spatial distribution of the limitations of N and P in global terrestrial ecosystems has been mapped by Du et al. ¹⁷, and the estimate of the proportion of land surface area affected by the limitation of P (~43%) appears to be generally higher than that affected by the limitation of N (~18%). Moreover, a significant portion of ecosystems stand close to the nutrient limitation threshold for vegetation growth¹⁸. This highlights the centrality of nutrient availability, particularly efficient P cycling and absorption, for sustaining ecosystem productivity and enhancing carbon capture under elevated CO₂ levels¹⁹.

Furthermore, it is noteworthy that P limitations on vegetation growth in terrestrial environments typically do not exhibit a static nature and might shift dynamically in response to anthropogenic disturbances²⁰. Therefore, future changes in vegetation productivity largely hinge on the responses of plant root uptake by the parent rock and soil P availability to global environmental change. The effects of P release associated with the chemical weathering of silicate rocks on the global dynamic patterns of the P limitation of vegetation growth urgently need to be systematically studied²¹. Deciphering the mechanisms underpinning the spatio-temporal variability of the P limitation associated with the chemical weathering of silicate rocks and its impact on vegetation productivity poses a challenge, and this knowledge remains critical to accurately predicting the effects of ongoing anthropogenic disturbances on terrestrial nutrient biogeochemistry.

Here, we investigated the response of the P limitation of global vegetation growth to the release of P associated with the chemical weathering of silicate rocks during 1950–2100 using field observation-constrained experimental site databases for hydro-chemistry and the resorption efficiencies of N and P, long time series of the Sixth International Coupled Model Intercomparison Project (CMIP6) data, and multiple sets of NPP products (Supplementary Table 1). We simulated and analyzed the magnitude and the spatial patterns of global P release fluxes (FP) from the chemical weathering of silicate rocks using a phosphorus release flux model, and further revealed the spatial patterns and variation trends of P limitation of vegetation growth from 1950 to 2100 by the ratio of the leaf N and P resorption efficiency. Based on these FP simulations, we quantified the contribution of the release of P associated with the chemical weathering of silicate rocks to the global patterns of the P limitation for vegetation growth. The results demonstrated that the release of P associated with the chemical weathering of silicate rocks with global warming alleviates the P limitation of vegetation growth.

Results and discussion

Global magnitude of phosphorus release

The dissolved silica in terrestrial rivers provides vital information about the weathering processes and rates^22,23. We projected the global fluxes of dissolved silica (F_DSi) from 1950 to 2100 based on compiled data for global river dissolved SiO₂ concentration sites (n = 12,409) (Supplementary Fig. 1). For the spatial simulation of F_DSi, we employed six distinct machine learning models for training, namely the Random Forest Model (RF), Conditional Inference Trees (Ctree), Generalized Boosted Regression Model (GBM), Support Vector Machines model (SVM), Back Propagation Neural Network Model (BP), and Categorical Boosting Model (CatBoost). We evaluated the accuracy of the F_DSi simulation obtained from these machine learning models using three key metrics, i.e., the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of Determination (R²) (Supplementary Fig. 2). Eventually, we identified the random forest model with the most robust performance as the preferred F_DSi prediction model (Supplementary Methods). During the present period from 1950 to 2014, the silicate rock exposure areas record a mean F_DSi of approximately 2.52 ± 0.77 t SiO₂ km⁻² yr⁻¹. We analyzed the results of the F_DSi simulation by comparing them with the compiled observations of river hydro-chemistry (n = 12,409). The simulated F_DSi correlates significantly with the observed data at the 0.05 level (Fig. 1), verifying the reliability of the simulated F_DSi.

Fig. 1: Spatial distribution and comparison of the simulated global dissolved silica fluxes (F_DSi) in the present period.

a Spatial distribution of simulated F_DSi. b Comparison of simulated F_DSi with observed F_DSi with observed F_DSi from supply-limited regions (SL) and kinetic-limited regions (KL). The black line represents the 1:1 line. The base map for all maps in this study is derived from the Standard Map Service of the Ministry of Natural Resources of China (review drawing number: GS(2016)1665).

Furthermore, the mean value of the F_DSi in North America approximately reaches 2.10 ± 0.64 t SiO₂ km⁻² yr⁻¹, ranging between the mean F_DSi values estimated in previous related studies (1.8−2.46 t SiO₂ km⁻² yr⁻¹)²⁴. Compared to the existing global average of approximately 3.3 t SiO₂ km⁻² yr⁻¹ for silicate and non-silicate F_DSi²⁵, the F_DSi we calculated in the exposed areas of silicate rocks remains relatively low. The reason lies predominantly in the comprehensive effects of differences in observation databases, computational approaches, and lithology data categorization. Our findings indicate that the high values of F_DSi notably concentrate in tropical regions, where the moist and rainy climate facilitates enhanced chemical weathering of rocks, thereby contributing to an elevated F_DSi concentration. In contrast, the arid and water-scarce desert regions exhibit the opposite characteristics. As indicated by the relative importance of the various variables evaluated using two critical indicators (%IncMSE and IncNodePurity) (Supplementary Fig. 3), runoff (q) ranks highest in relative importance. Related studies also indicate that runoff, lithology, and slope act as the first order controls of F_DSi^26,27.

Based on the above simulation of F_DSi, the existing simulation of chemical weathering cation fluxes²⁸, and average relative proportions of P content across various silicate rock types (Supplementary Fig. 4; Supplementary Table 2), we then deduced the magnitude of phosphorus release in silicate rock exposure areas. Moreover, we developed high-resolution global spatial datasets of the FP in the silicate rock exposure areas from 1950 to 2100 (Fig. 2; Supplementary Fig. 5). Among them, from 1950 to 2014, the silicate rock exposure areas recorded an average value of FP at 11.02 ± 2.83 kg P km⁻² yr⁻¹, which falls within the range of FP associated with the chemical weathering of terrestrial rocks. As reported in existing studies, this range typically stretches from 8.53 to 23.1 kg P km⁻² yr^−17,8,29. The total flux of the release of P in the silicate rock exposure areas reaches 0.72 ± 0.19 Tg P yr⁻¹, and it also falls within the global total flux range of FP, which typically ranges from 0.8 to 21.08 Tg P yr⁻¹. Extrapolated from the global average of soil P³⁰, the average flux of FP accounts for approximately 2.90% of the total soil P and 36.42% of the secondary mineral P. According to the latest statistical database provided by the Food and Agriculture Organization of the United Nations (FAO) (https://www.fao.org), the total use of P fertilization in 2022 amounted to about 41.85 Tg P₂O₅, i.e., approximately 9.14 Tg P. Therefore, our calculations indicate that the total flux of P release associated with the chemical weathering of silicate rocks in the present period accounts for about 6% of the total use of P fertilizer in 2022.

Fig. 2: Distribution patterns and average annual trends of phosphorus release fluxes (FP) associated with the chemical weathering of silicate rocks in the present period.

a Spatial distribution of FP at the present period (1950−2014). b Latitudinal distribution of FP. c Average annual trends of FP at the present period. This trend represents the average annual change in FP related to the chemical weathering of silicate rocks from 1950 to 2014 (10⁻² kg P km⁻² yr⁻¹). d Test statistic (Z-score) for the trend of FP. Base map as in Fig. 1.

Regarding the latitudinal distribution of FP, P release peaks concentrate primarily near the equator (15°N to 15°S), with additional clusters between 50°N and 70°N and between 40°S and 55°S. In these latitudinal zones, higher values of P release are concentrated in humid and semi-humid areas. Analysis of the distribution patterns concerning the major effects of these factors revealed that water availability and lithology mainly constrained the distribution patterns. In the Yenisei River Basin in northern Asia, the combination of increased runoff, a more evenly distributed precipitation pattern, and the extensive exposure of basalt rocks in the northern part of the basin contributes to a higher chemical weathering potential within the basin. As well, the basalt itself possesses a higher P content, with a median concentration of 920 ppm for P based on the measured soil P (0−50 cm) and the data of the parent material P of 62 sites³¹, so the chemical weathering process accompanies the release of higher P relative to other regions³².

Patterns of phosphorus release

Overall, the total FP increases from 0.72 ± 0.19 Tg P yr⁻¹ in the 1950s to 0.86 ± 0.22 Tg P yr⁻¹ at the end of the 21^st century, representing a total increase of approximately 20%. In particular, from 2015 to 2100, the release of P is expected to increase by ~11.22%, surpassing the 7.62% increase simulated from 1950 to 2014 by 1.5 times. The 12 ± 4% increase in the P release flux from 1850 to 2005, as reported by Goll et al.⁸, roughly compares with the proportional increase in the release of P estimated in this work for the future period. This indicates that the P release flux associated with the chemical weathering of silicate rocks continuously increased from 1850 to the end of the 21st century. Meanwhile, the increasing trend in future P release from 2015 to 2100 aligns with the latest evidence on acceleration of P weathering under warm climates³³.

Although significant differences exist in the fluxes and total fluxes of the release of P associated with the chemical weathering of different types of silicate rocks in the present period, the variation trends are not evident for most of the individual types of silicate rock under the four shared socioeconomic pathways (SSPs) in the present and future (Supplementary Fig. 6). Comparatively, the FP linked with the chemical weathering exhibits greater prominence in Intermediate plutonic rocks (PI) and Basic plutonic rocks (PB), mainly owing to their higher relative proportions of phosphorus. In addition, based on the Sen’s slope and Mann-Kendall trend tests³⁴, we revealed that the spatial variability of the FP trends under different future scenarios from 2015 to 2100 (Fig. 3). The release of P associated with the chemical weathering of silicate rocks in the future period will increase at an average annual rate of 4.90 × 10⁻³ kg P km⁻² yr⁻¹. The increasing trend of the FP shows most pronounced under the SSP3-7.0 scenario, ~6.51 × 10⁻³ kg P km⁻² yr⁻¹, mainly owing to the land use and resource development patterns in this scenario differ from those in other scenarios. The regions with significant FP increases mainly distribute across the Amazon Basin region in South America, the eastern and northern regions of Asia, and the northeastern regions of North America.

Fig. 3: Average annual trends in phosphorus release fluxes (FP) associated with the chemical weathering of silicate rocks under different scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5) during the future period (2015−2100).

a Trend under SSP1-2.6 scenario. b Trend under SSP2-4.5 scenario. c Trend under SSP3-7.0 scenario. d Trend under SSP5-8.5 scenario. These trends represent the average annual change in FP (10⁻² kg P km⁻² yr⁻¹). Regions marked with black dots exhibit a statistically significant trend (Mann-Kendall test, (P-Value < 0.05). Base map as in Fig. 1.

We found that not all of the areas with higher values of the release of P exhibit a continuous increase in the release of P. For example, the average annual release of P shows a non-significant increasing trend from 1950 to 2014 in global silicate rock exposure areas (Fig. 2c, d). However, the release of P in the Amazon basin area shows a non-significant decreasing trend. This represents an average annual reduction of about 4.43 × 10⁻³ kg P km⁻² yr⁻¹ in the P release flux associated with silicate rocks in the Amazon basin area from 1950 to 2014. It closely relates to the decrease in precipitation (0.43 mm yr⁻¹) in the Amazon basin, with a decrease in runoff of 0.49 mm yr⁻¹ in the present period. This aligns with the results of a previous study that suggested that changes in precipitation resulting from the feedback with deforestation dominate the runoff response³⁵. In contrast, the continental areas close to the Arctic Ocean display diverse trends of increased P release, driven by regional warming and glacial melting during this period³⁶, which in turn accelerates the flux of silicate chemical weathering and augments the amount of the release of P associated with the chemical weathering of silicate rocks.

Patterns of the phosphorus limitation

The release of P associated with the chemical weathering of silicate rocks mentioned above has a non-negligible significance for terrestrial vegetation growth. Along with the continuous release of P from the chemical weathering into terrestrial ecosystems, the dynamic patterns of the P limitation of vegetation growth need to be further clarified. Here, we mapped the dynamics map of the N and P limitations over a long time series (1950−2100) in global silicate rock exposure areas based on a database of the leaf N and P resorption efficiency and the random forest algorithm³⁷. We considered the main factors, such as climate change, soil properties, and vegetation changes, that mainly affect the limitations of N and P on vegetation growth³⁸. By comparing the analysis and validation of the different products of Net Primary Productivity (NPP) (Integrated Biosphere Simulator (IBIS) NPP, Boreal Ecosystem Productivity Simulator (BEPS) NPP, and Global Land Surface Satellite (GLASS) NPP) with observational data and Moderate Resolution Imaging Spectroradiometer (MODIS) NPP, we finally chose the IBIS-NPP (Supplementary Figs. 7–9).

We found that the P-limited areas of vegetation growth in silicate rock exposure areas account for about 47% in the present period (Fig. 4a), predominantly within the middle and low-latitude regions. The N-limited areas account for approximately 35%, primarily distributed in high-latitude and cold low-latitude regions such as the Qinghai-Tibet Plateau. Available evidence also suggests that vegetation growth in the Tibetan alpine permafrost region as N-limited³⁹. The remaining 18% constitute the regions with N and P co-limitation, mainly distributed in mid-latitudes. Although the N limitation occurs in approximately one-third of the global regions, the distribution extent of the P limitation proves larger, with the former being about 1.33 times more extensive than the latter. These results align more closely with the proportion of global P-limited areas (43%), N-limited areas (39%), and N and P co-limited areas (18%) estimated from existing simulations¹⁷. Furthermore, we validated the reliability of the constructed model by cross-validating the observed and simulated values (Supplementary Fig. 10). Overall, the spatial patterns of the ratios of the N and P resorption efficiency (NRE_dom/PRE_dom) reveal significant variability in the spatial patterns of the N and P limitations, mainly affected by climate change, soil, and vegetation variables. Existing studies also show that RE_dom/PRE_dom decreases with increasing mean annual temperature and mean annual precipitation, and increases with increasing latitude⁴⁰.

Fig. 4: Global spatial patterns and trends of the phosphorus limitation in silicate rock exposure areas.

a Spatial patterns of the ratios of nitrogen and phosphorus resorption efficiency (NRE_dom/PRE_dom) in leaves of dominant species in the present period (1950−2014). Blue indicates the phosphorus limitation regions, gray refers to co-limitation regions of nitrogen and phosphorus, and red represents the nitrogen limitation regions. The inset shows the spatial proportions of the phosphorus limitation (PL), nitrogen and phosphorus co-limitation (NPL), and nitrogen limitation (NL). b The average annual trend (slope) of NRE_dom/PRE_dom from 1950 to 2014 (10⁻²). The inset shows the proportion (%) of the area occupied by the silicate rock exposure areas by the distribution of trends in different colors. c, d represent the first decade of transition in the P-limited regions in the silicate rock exposure areas from 1950 to 2100 (SSP2-4.5 and SSP5-8.5), respectively. They represent the average change in the spatial extent of phosphorus-limited regions on an interdecadal scale from 1950 to 2100. The insets show the time series of proportional variation of the area of the phosphorus limitation in the silicate rock exposure areas. Base map as in Fig. 1.

In addition, we found that the interannual variations in the global P-limited pattern show a non-significant decreasing trend from 1950 to 2014 (Fig. 4b). In N-limited areas, the average value of NRE_dom/PRE_dom approximately reaches 1.15 in the present period, while in the P-limited areas, it approximately reaches 0.82. Around 8.51% of the N-limited areas exhibit a significant decrease in the NRE_dom/PRE_dom value, with major concentrations in northern North America, northern Asia, and Qinghai-Tibet Plateau (Supplementary Fig. 11). When this value drops below 1, it indicates an increasing P limitation on vegetation growth. Conversely, ~22.63% of the P-limited areas, primarily concentrated in South America, Africa, Southeast Asia, and eastern Australia, show a significant increase in the NRE_dom/PRE_dom value. This suggests a greater likelihood of N limitation when the NRE_dom/PRE_dom value exceeds 1. Overall, the extent of regions undergoing a significant increase in P limitation approximately reaches 2.59 times greater than the extent of areas experiencing a significant decrease in N limitation. Nevertheless, the magnitude of the NRE_dom/PRE_dom trend for the areas experiencing a significant decline in the N limitation approximately amounts to 3.94 times greater than the magnitude of the trend (Sen’s slope) for areas witnessing a significant increasing trend in the P limitation. Consequently, the NRE_dom/PRE_dom mainly features a decreasing trend in the exposed areas with global silicate rocks.

It is noteworthy that the NRE_dom/PRE_dom shows no significant change in more than half of the global silicate regions based on the Mann–Kendall test, approximately 55.43%, and these regions tend to be more limited by both N and P. This also indicates that future global P limitation patterns will exhibit continuous dynamic changes and significant spatial heterogeneity and will be primarily affected by the combined effect of multiple environmental factors³⁹, as well as the interactions between N and P⁴¹. The spatial and temporal trends of the NRE_dom/PRE_dom may be co-controlled by the availability of N and P. The availability of N depends on biological N fixation and N mineralization under the effect of climate change⁴², while the availability of P depends largely on the soil parent material formed by the weathering of rocks^31,43.

Furthermore, to accurately simulate the spatial patterns of global P limitation in silicate rock exposure areas under various future scenarios, we took 10 years as a transfer time interval to reveal the transfer mechanism behind the initial occurrence of P limitation within the SSP2-4.5 and SSP5-8.5 scenarios, respectively. Among them, in the SSP2-4.5 scenario, the proportion of the areas with global P limitation in silicate rock exposure areas will climb from approximately 46% to 54%, expanding its reach to higher latitudes and alpine regions. Meanwhile, the magnitude of the change in the P limitation significantly increases under the SSP5-8.5 scenario compared to the SSP2-4.5 scenario. And the fraction of the area limited by P in silicate rock exposure areas is expected to increase from about 46% to 59% under this scenario (Fig. 4c, d). Overall, under both two scenarios, the extent of the P-limited areas for vegetation growth will significantly expand northward after 2015, and an annual expansion of the P-limited area by an average 7.58 × 10⁴km² from 1950 to 2100. This may be attributed to global warming, which is expected to increase the rates of biological nitrogen fixation and nitrogen mineralization, and the consequent increase in phosphorus demand and uptake by vegetation at mid- to high-latitudes, leading to the P limitation⁴².

Effects on the phosphorus limitation

The sensitivity analysis of the main variables in relation to NRE_dom/PRE_dom reveals that as the mean annual temperature (MAT), mean annual precipitation (MAP), evapotranspiration (ET), nitrogen deposition (Ndep), or net primary productivity (NPP) increase, NRE_dom/PRE_dom will show a decreasing trend (Supplementary Fig. 12a, b, c, f, and i). The variations in NRE_dom/PRE_dom driven by MAT and MAP correspond to the results of other related studies^17,40. The increase in NRE_dom/PRE_dom may be attributed to the promotion of biological carbon sequestration and nitrogen mineralization processes in response to climate change, especially higher temperatures. The stimulation of vegetation NPP by high nitrogen deposition increases the demand and uptake of P by vegetation, ultimately reducing the availability of soil P^16,41.

However, the trend of NRE_dom/PRE_dom increases with runoff (q), soil moisture content (SMC), FP, or leaf area index (LAI), (Supplementary Fig. 12d, e, g, and h). Runoff shows the most significant effect, followed by FP. Increased NRE_dom/PRE_dom implies that increased runoff in response to climate warming accelerates rock chemical weathering-associated phosphorus release through enhanced water-rock interactions, which in turn increases the availability of soil P. Additionally, vegetative growth may accelerate rock weathering and release more effective P through root splitting effect or secretion of organic acids by root systems and associated mycorrhizal fungi¹⁰. In addition, climate change may induce a strong soil hydrological cycle, implying that increased runoff and availability of soil water may increase leaching or denitrification, resulting in greater loss of N relative to P, which in turn may lead to a decrease in soil N availability. Remarkably, global warming may also exacerbate soil drying⁴⁴. This in turn attenuates the rates of biological N fixation and N mineralization, and ultimately may also lead to increased N limitation.

Additionally, we employed an optimal fingerprint analysis to detect the relative contributions of the alterations in the ultimate P-limited region resulting from variations in the driving factors (Supplementary Fig. 13). We found that the MAT and NPP factors collectively account for the interannual decreasing trend in the NRE_dom/PRE_dom within the global silicate rock exposed regions, with contributions of ~9.80% (Supplementary Table 3). This suggests that the accompanying interannual changes in vegetation productivity may have generated greater P demand and uptake. Nevertheless, we identified that the remaining factors explained the interannual increasing trend of the NRE_dom/PRE_dom. Among these factors, the FP associated with the chemical weathering of silicate rocks plays the most substantial role, with a relative contribution of approximately 15.50%. This indicates that the release of P related to the chemical weathering of silicate rocks with global warming benefits mitigating the P limitation of vegetation growth. Therefore, the release of P associated with chemical weathering of silicate rocks proves essential to predict future vegetation productivity in response to climate warming and elevated atmospheric CO₂ concentrations^6,45.

We speculate that the extent of phosphorus limitations for vegetation growth will be compensated in the future, largely due to the accelerated phosphorus release associated with the chemical weathering of silicate rocks with climate warming. To clarify how the interannual trends in P limitation in the future get offset by continued silicate weathering fluxes, and exactly where the potential spatial extent of the offset occurs, we spatially overlaid regions with simultaneous changes (simultaneous increase or decrease) in the interannual trends of NRE_dom/PRE_dom driven by all factors and the interannual trends of NRE_dom/PRE_dom driven by the release of P (Fig. 5a). We found that the release of P associated with the chemical weathering of silicate rocks in more than half of the silicate rock exposure areas (63%) alleviates the P limitation levels of vegetation growth (Fig. 5d). Under the Köppen-Geiger climate classification⁴⁶, the proportion of the area distribution of the release of P linked to the chemical weathering of silicate rocks appears more prominent in the arid and cold zones compared to the tropics and warm zones, which could be related to the sizes of the distribution areas within the different climate zones. Furthermore, we compare the interannual variation trends of the NRE_dom/PRE_dom, driven by all factors, within the spatial regions with P limitation mitigation (Fig. 5b) with the interannual variation in the NRE_dom/PRE_dom for the release of P mitigation areas. We found that the ranges of the variations in the two largely agree, with the primary difference being the magnitude of the variation values. The probability density distributions of the areas where these two aspects overlap further confirm the mitigating effect of the release of P on the P limitation (Fig. 5c). This further supports the plausibility that future intensification of the release of P associated with chemical weathering of silicate rocks at temporal and spatial scales will alleviate phosphorus limitation of vegetation growth.

Fig. 5: Spatial distribution of phosphorus release to alleviate the phosphorus limitation of vegetation growth.

a Trends (Sen’s slope) of the ratios of leaf nitrogen and phosphorus resorption efficiency (NRE_dom/PRE_dom) driven by the phosphorus release associated with the chemical weathering of silicate rocks; b Trends (Sen’s slope) of NRE_dom/PRE_dom driven by all factors within the phosphorus release mitigation regions ((NRE_dom/PRE_dom)_m); c Probability density distribution of (a) and (b); d Proportion (%) of mitigation regions of the phosphorus release under the Köppen-Geiger climate types (Af (Tropical, rainforest), Am (Tropical, monsoon), Aw (Tropical, savannah), BWh (Arid, desert, hot), BWk (Arid, desert, cold), BSh (Arid, steppe, hot), BSk (Arid, steppe, cold), Cwa (Temperate, dry winter, hot summer), Cwb (Temperate, dry winter, warm summer), Cfa (Temperate, no dry season, hot summer), Cfb (Temperate, no dry season, warm summer), Dsc (Cold, dry summer, cold summer), Dwc (Cold, dry winter, cold summer), Dfb (Cold, no dry season, warm summer), Dfc (Cold, no dry season, cold summer), ETk (Polar, tundra), EF (Polar, frost)). The sub-climate types with an area proportion greater than 1% are labeled. The remaining unlabeled sub-climate types are less than 1%. Base map as in Fig. 1.

Uncertainties and prospects

To validate the precision of the global FP related to the chemical weathering of silicate rocks, we performed a comparative analysis with the findings of existing relevant studies^7,8 (Supplementary Table 4). Our findings demonstrate that the FP related to the chemical weathering of silicate rocks (11.02 ± 2.83 kg P km⁻² yr⁻¹) falls within the FP range from the chemical weathering of terrestrial rocks, as reported in existing studies, typically spanning from 8.53 to 23.1 kg P km⁻² yr⁻¹. It is noteworthy that the chemical weathering rate of carbonate rocks exceeds that of silicate rocks^47,48,49,50, potentially leading to the release of more phosphorus. In addition, the average FP value calculated in this work for silicate rock exposure areas slightly exceeds the calculation by Hartmann et al (7.35 kg km⁻² yr⁻¹), with a discrepancy of ~33%⁷. This difference can primarily be attributed to variations in the factors and modeling methods employed in the simulation of FP. Hartmann et al. employed a P release calculation method based on a multiple linear regression approach, effectively integrating factors such as lithology, runoff, temperature, and soil properties. The spatial data for FP, obtained through this method, represent multi-year averages. In contrast, we consider factors such as soil moisture content and leaf area index, among others, all of which have been proven to exert a substantial impact on the chemical weathering of rocks⁵¹, and feature significant spatial heterogeneity. Furthermore, in comparison to existing studies, our simulated FP data capture the long-term variations. This offers valuable insight and implications for making effective predictions regarding future trends in the release of P.

We have revealed the present and future dynamics patterns of the release of P related to the chemical weathering of silicate rocks and have identified spatial regions that mitigate the P limitation on vegetation growth. This not only contributes to meaningful insights into the understanding of global P limitation of vegetation growth and P biogeochemical cycling studies, but is also essential to achieve scientific P management as well as sustainable development. Nevertheless, it is crucial to acknowledge the remaining uncertainties in our study.

Firstly, our findings indicate that with global change, the chemical weathering of silicate rocks in tropical regions releases more P, which in turn contributes to alleviating the P limitation of vegetation growth. Nevertheless, we also recognized that in the tropics, the eventual release flux of P from rock weathering may be limited if the bedrock itself contains less P^31,41. In addition, the P limitations primarily affect the growth of individual tree species rather than the entire forest communities in tropical forests⁵². Moreover, our study has not yet considered the effects of effective P in ancient soils depleted by long-term higher weathering and leaching on vegetation P limitation. However, P depletion is not unique to all tropical soils. Some tropical soils are relatively young and P-rich⁵³. With some natural disturbances, such as volcanism, erosion, and uplift, etc., the supply of P in rocks can be rejuvenated, especially in highly weathered soil systems²¹. In the future, field investigations need to quantify ancient soil areas at various spatial scales.

Secondly, we focus on the release of P associated with the chemical weathering of silicate rocks, not yet considering the P deposition fraction from activities such as the use of P fertilization and biomass burning⁵⁴. Consequently, our findings may not be directly applicable to areas such as agricultural fields, cities, and glaciers¹⁷. Existing studies have used process models to simulate the effects of the P limitation on agricultural production under various future scenarios⁵⁵. Indeed, we must carry out moderate P addition to guarantee agricultural production and achieve sustainable development goals. In addition, existing studies indicate that mineral aerosols are the only source of the dry and wet deposition of atmospheric P, and they mainly originate from dust and fly ash from biomass, coal combustion and wildfires, with a total estimated global flux of about 3−4 Tg P per year³⁸. The P input enters terrestrial ecosystems and significantly contributes to terrestrial carbon sinks. For example, studies in central Africa have demonstrated that ecosystem productivity responds to increased changes in the P deposition to a degree comparable to the combined effects of increased atmospheric CO₂ and climate change⁵⁶. It is worth noting that irrational human activities and climate extremes may aggravate soil erosion, which may lead to increased loss of P in the affected areas⁵⁷. Moreover, the unidirectional movement of this P can cause the eutrophication of water bodies, which in turn can lead to serious ecological damage such as algae blooms, hypoxia and fish kills, deterioration of water quality, and ultimately loss of biodiversity and degradation of aquatic ecosystem services⁵⁸. In the future, more experiments on effective P addition to soils need to be conducted widely. Additionally, compiling more in-situ observations will be instrumental in providing the scientific foundation required for optimizing and validating P limitation models.

Thirdly, we analyzed the uncertainties arising from the results calculated in this work using Monte Carlo error propagation methods. By assuming an error of approximately 10% in the proportional relationship between the P content and the total content of major cations and dissolved SiO₂ in different silicate rock types⁵⁹, and substituting it and other simulated factors (FHCO₃⁻ and F_Dsi) into the Monte Carlo error propagation, the final error of the FP ~26%. In addition, although we excluded the area proportion of carbonates in part of the silicate rock exposure areas based on the existing studies (Supplementary Table 2), there might still be an effect of the chemical weathering of trace carbonate minerals⁶⁰. We performed a mixed test of chemical end members (precipitation, evaporite, silicate, and carbonate) using a classical inverse model based on hydro-chemistry observations from 75 silicate rock-dominated river basins (Supplementary Methods; Supplementary Fig. 14). Our findings indicate that the release of P from trace carbonate minerals may overestimate the FP linked with the chemical weathering of silicate rocks by about 42.72% (Supplementary Text). Regrettably, we neglect to take the effect of anthropogenic solutes into account when calculating the chemical weathering flux of silicate rocks, because of the lack of necessary field monitoring data. Moreover, the Na (and, to a lesser extent, Mg) in rivers can be partially attributed to salting practices on the road. During wintertime, the Na from road salt will far exceed the Na related to the chemical weathering of silicate rocks in many locations in the Northern Hemisphere⁶¹. Therefore, field investigations and indoor modelling with respect to the effects of anthropogenic solutes and trace carbonate minerals will play a more prominent role in the future.

Furthermore, the process of P accumulation on soil mineral surfaces, also known as adsorption, and the release of P via the desorption due to the presence of silicon need to be considered in future studies. The model for the P release calculation and the model for assessing the effective P limitation require further optimization. Moreover, rock weathering may lead to the release of not only P but also other nutrients, and/or heavy metals, all of which could have non-negligible impacts on terrestrial ecosystems. Therefore, the effects of the release of elements related to the chemical weathering of global terrestrial rocks on ecosystem productivity need to be considered in an integrated manner in the future.

In short, we reveal the global patterns of the P limitation that occur in response to the release of P related to chemical weathering of silicate rocks from 1950 to 2100, leveraging integrated field observation-constrained hydro-chemistry sites and a leaf N and P resorption efficiency database, long time series of CMIP6 ecohydrological data, and multiple sets of NPP products. We estimate the global FP from the release of P related to the chemical weathering of silicate rocks from 1950 to 2014 at 11.02 ± 2.83 kg P km⁻² yr⁻¹. This release primarily concentrates in humid and semi-humid regions, with water availability and lithology among the constraining factors. Our analysis based on the ratio of the leaf N and P resorption efficiency shows that about 47% of the global silicate rock exposure areas represent P-limited areas in the present period. According to our model scenarios, we expect this fraction to increase in the future. The release of P related to the chemical weathering of silicate rocks mitigates the level of the P limitation of vegetation growth. This release makes a relative contribution to this effect rate of approximately 15.50%. The additional phosphorus release associated with the chemical weathering of silicate rocks evolved in response to climate warming compensates for 15.50% of that P limitation. This not only contributes to meaningful insights into the understanding of global P limitation of vegetation growth and P biogeochemical cycling studies, but also proves essential for achieving scientific P management and sustainable development.

This study highlights the critical impact of the release of P related to the chemical weathering of silicate rocks on the evolving global patterns of the P limitation for vegetation growth. This is of  significance to future comprehensive investigations of nutrient and carbon cycles to help achieve carbon neutrality goals, and provides a scientific foundation for developing P management strategies. To this end, we have proposed the following four phosphorus management strategies, namely regionalized management, data-driven intelligent decision-making, climate-coordinated management and optimized land use. Specifically, we should focus on humid and semi-humid areas where phosphorus release remains relatively concentrated. We should adjust water flow according to water availability and rock properties to promote the chemical weathering of silicate rocks, thus facilitating the release of phosphorus and meeting the needs of vegetation growth. We ought to utilize multiple data to build models, predict and allocate phosphate fertilizers based on the trend of phosphorus limitation, and give priority to ensuring the supply of phosphate fertilizers for key vegetation. We must select suitable tree species for afforestation to promote carbon sequestration and ensure the sustainable utilization of phosphorus. It is necessary to protect the ecological environment in silicate rock exposure areas to stabilize the natural release of phosphorus. We should develop agricultural and forestry models with low phosphorus requirements or phosphorus-fixing capabilities, such as intercropping leguminous plants and food crops. We must avoid key areas of the phosphorus cycle in urban and industrial planning. However, it cannot be denied that when implementing phosphorus management strategies, we should further consider whether other elements released via rock weathering will have negative effects on the environment.

Methods

Data compilation and processing

We compiled hydrochemical data from field observations (Supplementary Fig. 1), sourced from the latest Global River Chemistry Database (GLORICH) and global river discharge database (GEMS-GLORI)^62,63. Specifically, these data include global river dissolved SiO₂ concentration data collected from a total of 12,409 stations, encompassing approximately 530,000 samples. We primarily utilize these data for predicting dissolved SiO₂ fluxes on a spatial grid scale. Meanwhile, we gathered major ion concentration data (Ca²⁺, Mg²⁺, Na⁺, K⁺, Cl^–, and HCO₃^–) from 319 river basins. These data are instrumental in conducting mixing tests with various chemical end-members. For predicting P limitations, we utilized the terrestrial plant leaf N and P resorption efficiency database (PRENP, version 1.0) (171 samples)¹⁷. In addition, we compiled multi-source eco-meteorological and hydrological data (Supplementary Table 1), including runoff (q), mean annual temperature (MAT), mean annual precipitation (MAP), evapotranspiration (ET), soil moisture content (SMC), nitrogen deposition (Ndep), leaf area index (LAI), multiple sets of NPP products (Integrated Biosphere Simulator (IBIS), Global Land Surface Satellite (GLASS), Boreal Ecosystem Productivity Simulator (BEPS), and Moderate Resolution Imaging Spectroradiometer (MODIS)), cation exchange capacity (CEC), clay content (Clay), soil pH, weathering cation fluxes (F_Cations), soil carbon dioxide partial pressure (pCO₂), physical erosion rate (ELU), new global lithological map database, Köppen-Geiger climate type, and soil type. To facilitate data processing and analysis, we applied the nearest neighbor interpolation method to match all geographically referenced datasets with a spatial resolution of 25 km.

Silicate chemical weathering flux

The estimates of phosphorus release fluxes often have a close correlation with those of chemical weathering fluxes in terrestrial silicate rock types^7,8. The flux of chemical weathering of silicate rocks, the most abundant type of terrestrial rocks, comprises the combined fluxes of major cations (2Ca²⁺+2Mg²⁺+Na⁺+K⁺), dissolved silica, and carbonate-driven CO₃ for a given river drainage outlet in theoretical conditions⁷. Numerous studies related to the chemical weathering of silicate rocks have been reported to date^50,64,65,66. The simplified chemical equations for the chemical weathering of carbonate-driven silicate rocks are as follows.

$$ {{{{\rm{Ca}}}}}_{x}{{{{\rm{Mg}}}}}_{(1-x)}{{{{\rm{Al}}}}}_{2}{{{{\rm{Si}}}}}_{2}{{{{\rm{O}}}}}_{8}+2{{{{\rm{H}}}}}_{2}{{{\rm{C}}}}{{{{\rm{O}}}}}_{3}+2{{{{\rm{H}}}}}_{2}{{{\rm{O}}}} \\ \quad \to x{{{{\rm{Ca}}}}}^{2+}+(1-x){{{{\rm{Mg}}}}}^{2+}+2{{{\rm{HC}}}}{{{{{\rm{O}}}}}_{3}}^{-}+2{{{\rm{Si}}}}{{{{\rm{O}}}}}_{2}+2{{{{\rm{Al}}}}}_{2}{({{{\rm{OH}}}})}_{3}$$

(1)

$$ {{{{\rm{Na}}}}}_{x}{{{{\rm{K}}}}}_{(1-x)}{{{\rm{Al}}}}{{{{\rm{Si}}}}}_{3}{{{{\rm{O}}}}}_{8}+{{{{\rm{H}}}}}_{2}{{{\rm{C}}}}{{{{\rm{O}}}}}_{3}+{{{{\rm{H}}}}}_{2}{{{\rm{O}}}} \\ \quad \to x{{{{\rm{Na}}}}}^{+}+(1-x){{{{\rm{K}}}}}^{+}+{{{\rm{HC}}}}{{{{{\rm{O}}}}}_{3}}^{-}+3{{{\rm{Si}}}}{{{{\rm{O}}}}}_{2}+{{{\rm{Al}}}}{({{{\rm{OH}}}})}_{3}$$

(2)

Here, relying on the principle of charge balance, we hypothesize that the flux of bicarbonate (FHCO₃⁻) resulting from the chemical weathering of silicate rocks would be approximately balanced by the flux of cations (F_Cations). It is worthy of note that the ratio of FHCO₃⁻ to F_Cations calculated from field observations data typically depends on the stoichiometric composition of weathered silicate rocks. In addition, it is essential to exclude cations contributed by dispersed trace carbonate minerals in silicate rock exposures when calculating the flux of cations^60,67. We conducted a mixed test of chemical end members (precipitation, evaporite, silicate, and carbonate) using a classical inverse model with Na-normalized mole ratios in various river basins (Supplementary Methods; Supplementary Table 5). Additionally, we explicitly quantified the proportion of total river cation concentrations (31.73–53.71%) driven by trace carbonate weathering in river basins dominated by silicate rocks.

Nevertheless, quantifying the effects of trace carbonate minerals on the chemical weathering of different types of silicate rocks at the global grid scale still faces challenges, primarily due to the lack of high-precision maps of trace carbonate mineral distributions and long time series hydrochemical field observations. Based on publicly available lithological database⁶⁸, combined with previous research on the proportions of carbonate and silicate⁶⁹, we excluded the area proportion of carbonates in part of the silicate rock exposure areas (Supplementary Table 2). Consequently, we calculate the chemical weathering fluxes of silicate rocks in this work as follows.

$${{{{\rm{F}}}}}_{{{{\rm{Cations}}}}+{{{\rm{SiO}}}}2}={{{{\rm{F}}}}}_{{{{\rm{Cations}}}}}+{{{{\rm{F}}}}}_{{{\rm{DSi}}}}$$

(3)

$${{{{\rm{F}}}}}_{{{{\rm{Cations}}}}}=(2[{{\mbox{Ca}}}^{2+}]\times {{{{\rm{M}}}}}_{{{{\rm{Ca}}}}}+2[{{\mbox{Mg}}}^{2+}]\times {{{{\rm{M}}}}}_{{{{\rm{Mg}}}}}+[{{\mbox{Na}}}^{+}]\times {{{{\rm{M}}}}}_{{{{\rm{Na}}}}}+[{{\mbox{K}}}^{+}]\times {{{{\rm{M}}}}}_{{{\rm{K}}}})\times q$$

(4)

$${{{{\rm{FHCO}}}}}_{3}^{-}=[{{{{\rm{HCO}}}}}_{3}^{-}]\times {{{{\rm{M}}}}}_{{{\rm{HCO}}}3}\times q$$

(5)

$${{{{\rm{F}}}}}_{{{\rm{DSi}}}}=[{{{{\rm{SiO}}}}}_{2}]\times {{{{\rm{M}}}}}_{{{{{\rm{SiO}}}}}_{2}}\times q$$

(6)

where F_cations+SiO2 (t km⁻² yr⁻¹) refers to the total solute flux of the chemical weathering of silicate rocks. F_Cations (t km⁻² yr⁻¹) denotes the mass flux of the chemical weathering cations. F_DSi (t km⁻² yr⁻¹) signifies the flux of dissolved SiO₂ (μmol L⁻¹), and q (mm yr⁻¹) refers to runoff. $[{{\mbox{Ca}}}^{2+}]$, $[{{{{\rm{Mg}}}}}^{2+}]$, $[{{\mbox{Na}}}^{+}],$, and $[{{{{\rm{K}}}}}^{+}]$(μmol L⁻¹) are the concentrations of cations attributed solely to the chemical weathering of silicate rocks. ${{{{\rm{M}}}}}_{{{{\rm{Ca}}}}},\,{{{{\rm{M}}}}}_{{{{\rm{Mg}}}}},\,{{{{\rm{M}}}}}_{{{{\rm{Na}}}}}$, and ${{{{\rm{M}}}}}_{{{{\rm{K}}}}}$ (g mol⁻¹) are the atomic weights of the elements. $[{{{{\rm{HCO}}}}}_{3}^{-}]$ and [SiO₂] (μmol L⁻¹) are the concentrations of bicarbonate and dissolved silica, with M_HCO3 and M_SiO2 (g mol⁻¹) being their respective molar masses. The units of concentration are converted from μmol L⁻¹ to mg L⁻¹ within the calculation of Eq. (4) by applying the respective molar weights. We derive FHCO₃⁻ from the accumulation of data from previous work²⁸.

Through a comparison of diverse machine learning models, we calculated dissolved SiO₂ fluxes (F_DSi) from 1950 to 2100 using a random forest regression model (see Supplementary Methods) (Supplementary Fig. 2)³⁷. In the process of calculation, we considered environmental factors closely related to dissolved SiO₂ fluxes as input variables for the model^{26,51,70,71,72,73}. Subsequently, we constructed the random forest regression model using observed data, with the regression tree parameters set at 1000. And we determined the final input variables by evaluating the accuracy of this model. We employed three key indicators, namely root mean square error (RMSE), mean absolute error (MAE), and Coefficient of Determination (R²), to assess the accuracy and robustness of the modeling model. Through this evaluation process, we selected q, MAT, MAP, ET, SMC, pCO₂, LAI, and ELU as the input variables for predicting the dissolved SiO₂ fluxes.

$${{{{\rm{F}}}}}_{{{{\rm{DSi}}}}}={{{\rm{Average}}}}\left({\sum }_{i}^{\mu }{h}_{i}({x}_{k}|({f}_{j}))\right)$$

(7)

wherein F_DSi refers to the ultimate prediction value of dissolved SiO₂ fluxes. Average (·) signifies the spatial average. h_i(·) represents the prediction outcome of the ith regression tree. µ refers to the number of regression trees, with a value of 1000. x_k | (f_j) refers to the samples composed of the input bootstrap samples (x_k) of the note (k) and the feature vectors (f_j) corresponding to the note. j refers to the number of feature vectors.

Furthermore, we performed cross-validation by assessing the correlation coefficient between observed and simulated values of F_DSi to verify the reliability of the model. We also evaluated the relative importance of these factors using two metrics: %lncMSE and IncNodePurity (Supplementary Fig. 3). %lncMSE quantifies the mean reduction in precision calculated based on out-of-bag (OOB) error rates, while IncNodePurity presents the average reduction value of non-purity of nodes.

Phosphorus release flux model

Apart from the silicate chemical weathering flux addressed above, there are still other crucial factors that need to be considered in estimating phosphorus release fluxes, such as the P content within various silicate rock types^7,74. According to existing studies, we hypothesized that the stoichiometry between the P content and the content of the major cations and dissolved SiO₂ in different silicate rock types maintains a relatively constant state^7,69. We mapped the spatial patterns for the relative proportion of P content in different silicate rock types (Supplementary Fig. 4a). These patterns consider the average relative proportions between the P content and the content of major cations and dissolved SiO₂ in global various silicate rock types^7,69. We compare the relative proportions of P content used in this study with those of North America from the Macrostrat database, which contains comprehensive, chronostratigraphic summaries of the age and properties of rocks for portions of the upper crust⁷⁴. Global erosion coupled to sedimentary P-enrichment forged a markedly P-rich crust at the dawn of the Phanerozoic, making the relative proportions of P content in North America overall higher than the global average (Supplementary Fig. 4b). Nevertheless, the relative proportions of the P content stay at the same level, especially for basic volcanic rocks and intermediate volcanic rocks. Due to the lack of data for portions of the upper crust on longer geologic time on a global scale, we considered a multi-year average of the relative proportion of P content in different silicate rock types.

Therefore, the calculation of P release fluxes (FP) related to the chemical weathering of silicate rocks on the grid scale is in the following equation.

$${{{\rm{FP}}}}={{{{\rm{b}}}}}_{{{{\rm{relative}}}}\; {{{\rm{P}}}}-{{{\rm{content}}}}} \times ({{{{\rm{F}}}}}_{{{{\rm{C}}}}{{{\rm{ations}}}}+{{{\rm{SiO}}}}2})$$

(8)

where, FP (kg P km⁻² yr⁻¹) refers to the P release fluxes related to the chemical weathering of silicate rocks. b_{relative P-content} (%) refers to relative ratios of the P content to major cations and dissolved SiO₂ (Cations+SiO₂) content in silicate rock exposure areas (Supplementary Fig. 4). F_Cations+SiO2 (t km⁻² yr⁻¹) refers to the flux of the chemical weathering of silicate rocks.

Nutrient limitation patterns

Fertilization experiments serve as the main methods available to measure N and P limitations^14,18,75,76, the ratio of leaf N and P method^12,77,78, and the ratio of leaf N and P resorption efficiency^17,40,79. We chose the N and P resorption efficiency ratio method suitable for assessing global N and P limitation patterns at the ecosystem scale, and the main expression relationships are as follows.

$$\frac{{{{\rm{NRE}}}}_{{{\rm{dom}}}}}{{{{\rm{PRE}}}}_{{{\rm{dom}}}}} < 1$$

(9)

$$\frac{{{{\rm{NRE}}}}_{{{\rm{dom}}}}}{{{{\rm{PRE}}}}_{{{\rm{dom}}}}} > 1$$

(10)

where NRE_dom and PRE_dom are the leaf N and P resorption efficiency of the dominant species, respectively. A ratio of NRE_dom to PRE_dom (NRE_dom/PRE_dom) less than 1 means that the regions are mainly P-limited, while the reverse indicates that the regions are mainly N-limited. In addition, there may also be regions where N and P are co-limited by the simulated error of the ratio of NRE_dom to PRE_dom as the magnitude of variation, with the range of the limitation centered on 1.

Unlike the static patterns of the N and P limitations of existing studies¹⁷, we simulated patterns of the N and P limitations over a long time series using a random forest algorithm (see Supplementary Methods)³⁷. We chose a database based on simultaneously monitored leaf N and P resorption efficiencies of dominant species, while selecting factors such as climate change, soil properties, and vegetation changes that mainly affect the N and P limitations for vegetation growth^9,38,41,43, mainly including MAT, MAP, ET, q, SMC, soil pH, CEC, Clay, Ndep, FP, LAI, and NPP. We constructed a random forest regression model based on site observations of leaf N and P resorption efficiencies of the dominant species and the predictor variables chosen above, and predicted the ratio of NRE_dom to PRE_dom from 1950 to 2100 by constructing 1000 random trees.

In addition, we also cross-validated the observed and simulated values of the resorption efficiency ratios of N and P by correlation coefficient to verify the reliability of the model, and evaluated the relative importance of these factors using the %lncMSE metric (Supplementary Fig. 10). Ultimately, we unveiled the dynamic patterns of global N limitation, P limitation, and co-limitation of both using the ratios of N and P resorption efficiency mentioned above, along with their standard deviations. Specifically, the dynamic patterns of co-limitation center around 1 and range from the standard deviation of the simulated ratio of NRE_dom/PRE_dom. The remaining regions greater than 1 become N limitation regions, while the remaining areas less than 1 turn into P-limited regions.

Optimal fingerprint analysis

To detect the relative contributions of variations in the ratio of NRE_dom to PRE_dom driven by different affecting factors, we employed the optimal fingerprint analysis method, a variant of the regression-based technique of detection and attribution^80,81. This method bases its principle on the classical technique of generalised linear regression⁸². The standard approach to optimizing fingerprint identification assumes that the response pattern simulated by the model is perfectly known, i.e., not subject to sampling uncertainty. We applied optimal fingerprint analysis method to implement the relative contributions of variations of the ratio of NRE_dom to PRE_dom. The specific equation of the method in this study is as follows.

$$Y={\sum }_{i=1}^{n}{\beta }_{i}{x}_{i}+\varepsilon$$

(11)

where Y refers to the simulated patterns of the ratio of NRE_dom to PRE_dom. x refers to the affecting factors. i refers to MAT, MAP, ET, q, SMC, Ndep, FP, LAI, and NPP, respectively. β_i refers to the slopes driven by different affecting factors, and $\varepsilon$ refers to internal variability. In this work, $\varepsilon$ mainly refers to relatively stable variables such as soil pH, CEC, Clay, etc.

We assumed the mutual independence of these variables (MAT, MAP, ET, q, SMC, Ndep, FP, LAI, and NPP) and performed sensitivity analyses on each of them separately (see Supplementary Methods). Then, we calculated their relative contributions (Contribution_i) through the interannual variation trends of the ratios of NRE_dom to PRE_dom driven by different affecting factors. Based on the already constructed random forest model for simulating the ratio of NRE_dom to PRE_dom, we alter one variable each year from 1950 to 2014, while the remaining variables remain constant from the initial year. We re-simulated the ratios of NRE_dom to PRE_dom driven by nine variables (MAT, MAP, ET, q, SMC, Ndep, FP, LAI, and NPP), and calculated the Theil-Sen median trends, which reflect the average annual variation of the ratios of NRE_dom to PRE_dom (see Statistical methods). Meanwhile, residual variables refer to relatively stable variables such as soil pH, CEC, Clay, etc. The specific calculation formula of the relative contributions of the main variables affecting the ratio of NRE_dom to PRE_dom is as follows.

$${{\mbox{Contribution}}}_{i}=\frac{{{\beta }_{i}}^{2}}{{\sum }_{1}^{i}\,{{\beta }_{i}}^{2}}\times 100\%,\,(i={{\mathrm{1,2,3}}},\ldots,9)$$

(12)

where Contribution_i represents the relative contribution of an individual variable to the total interannual variation trend of the predicted ratio of NRE_dom to PRE_dom. Here, _i represents diverse factors including MAT, MAP, ET, q, SMC, Ndep, FP, LAI, or NPP. β_i refers to the interannual variation trend of the predicted ratio of NRE_dom to PRE_dom driven by a single variable that experiences changes from 1950 to 2014. Meanwhile, we hold the other variables constant at their values in the initial year (1950). We derive these trends through the Theil-Sen median trend analysis (see Statistical methods).

Statistical methods

We implemented the spatial trend analysis of disparate variables through the Theil-Sen median trend analysis method and the Mann-Kendall trend test (see Supplementary Methods). These two methods, as nonparametric tests, do not require the variable sample data to follow a specific distribution pattern, and their trends remain unaffected by outliers^34,83,84. Therefore, they can robustly estimate the trend or slope in the variable sample data. The methods are now widely used for dynamic characterization of variables at different regional scales⁸⁵. Specifically, we assumed that the global-scale phosphorus release fluxes of the time series and the ratio of NRE_dom to PRE_dom, as well as the different NPP products (IBIS-NPP, BEPS-NPP, and GLASS-NPP) exhibited evolutionary characteristics, and calculated the values of the Theil-Sen slopes, respectively. Meanwhile, we detected the level of statistical significance (P-Value < 0.05 and P-Value < 0.01) of the changing trends of various variables based on the Mann-Kendall test method. In addition, we employed Taylor diagrams⁸⁶ to test the matching degree of the three NPP (IBIS-NPP, BEPS-NPP, and GLASS-NPP) products matched with the observed data and combined with MODIS data to finally select IBIS-NPP data as an indicator to express vegetation productivity.

To effectively reveal the regional extent of the contributions of the release of P to the P limitation of vegetation growth using CMIP6 simulations and IBIS-NPP, we conducted independent analyses under two scenarios (SSP2-4.5 and SSP5-8.5) using the average of the first decade. Furthermore, the terrestrial P limitation patterns varied over time from 1950 to 2100. The equation for the proportional variation in the area of terrestrial vegetation growth limited by P is as follows.

$${\gamma }_{{{{\rm{PL}}}}}=\frac{{A}_{t}}{{A}_{1950{{{\rm{s}}}}}}\,\{t=1950{{{\rm{s}}}},1960{{{\rm{s}}}},\cdots,2090{{{\rm{s}}}}\}$$

(13)

where γ_PL is the proportional variation of area of terrestrial P limitation, and A represents the area of terrestrial P limitation. t stands for decade and divides into consecutive ten-year phases.

In addition, we ran the uncertainty propagation calculation using higher-order Taylor expansion and Monte Carlo simulation for 1,000,000 Monte Carlo simulations in the “propagate” package of R 4.4.0. This error propagation method with the covariance structure is widely used in the computation of uncertainty^87,88. Its model inputs include data for estimating the variation equations (such as F_DSi, F_Cations, b_{relative P-content}) as well as model parameter statistics (mean and standard deviation).

Reporting summary

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