Introduction

The accumulation of carbon dioxide (CO2) in the atmosphere due to fossil fuel burning has increased global gross primary production (GPP) and decreased the isotopic composition of atmospheric CO₂ (δ13CO2) – the ratio of the heavier (13C) to the lighter (12C) stable carbon isotope of atmospheric CO2 – over the past century, a phenomenon known as the Suess effect1. While changes in GPP can influence carbon isotope discrimination (Δ¹³C) during photosynthesis, the relationship is not strictly linear and depends on environmental and physiological conditions2, which means shifts in plant productivity may affect δ¹³CO₂ in complex ways. Atmospheric measurements show that δ13CO2, expressed as the normalized ratio of ¹³C to ¹²C compared to a standard, has declined by 0.027‰ per year over the period from 1978 to 20143,4. However, the observed δ13CO2 decrease is apparently smaller than expected when accounting for land and ocean carbon cycling and uptake in a simple calibrated model, which predicts a decline of about 0.032‰ per year3. To explain this shortfall, Δ13C of the terrestrial biosphere should have increased by 0.014 ± 0.007‰ per ppm of CO2 increase3. Whether a Δ13C change of this magnitude is consistent with actual terrestrial carbon fluxes remains uncertain.

Global Δ13C estimates from long-term tree-ring measurements do not show the increase in the Δ13C of C3 plants postulated by ref. 3. Although the Δ13C of C3 plants as recorded by tree rings has been variable across sites (increasing, decreasing, or unchanging2,5,6), globally it has remained roughly constant2. It is possible that post-photosynthetic fractionation processes2,7 and intrinsic age-related changes in tree development over their lifespan, such as tree height8,9 could affect inferences of long-term Δ13C trends from tree rings. However, these effects are not well understood or quantified. No alternative source of data for C3 plants are currently available. The mean residence time of C4 plant-derived carbon in the biosphere is generally shorter than that of C3 plant-derived carbon10,11 and there is no direct evidence of changes in Δ13C of C4 plants. Since atmospheric measurements reflect large-scale changes in vegetation dynamics while in situ measurements only record ecophysiological adjustments from the ecosystems studied, it is challenging to reconcile measurements on the ground with estimates from the atmosphere. Current models linking carbon fluxes and stocks between land and the atmosphere are complex, making comparison difficult. Simple modeling approaches are needed to determine recent changes in global GPP and associated Δ13C, and to disentangle the contribution from C3 and C4 plants to the observed atmospheric trends.

The global distribution of C3 and C4 plants reflects their divergent responses to climate as well as human activities via cropping and land management11,12. C3 plants include cool-climate grasses, most shrubs, and nearly all trees13, while C4 plants generally dominate in warm-climate grasslands and savannas. C4 plants possess a unique set of adaptations making them more competitive than C3 plants in warm, arid, and high-light environments14,15, primarily via reduced rates of photorespiration. In contrast, C3 photosynthesis is stimulated at high atmospheric CO2 concentrations. This is known as the CO2 fertilization effect and confers an advantage over C4 photosynthesis under elevated CO216.

Variations in Δ13C are closely related to environmentally driven changes in the stomatal limitation of photosynthesis, expressed as the ratio of leaf-internal to ambient partial pressures of CO2. Δ13C also depends on the pathway of carbon assimilation. Isotopic fractionation during the diffusion of CO2 through the stomata primarily influences Δ13C in C4 plants, while fractionation during Rubisco carboxylation has a stronger imprint on Δ13C in C3 plants, resulting in C3 plants being depleted in 13C compared to C4 plants17,18,19. Knowledge of the different isotopic signatures of C3 and C4 photosynthetic pathways and of their relative coverage across the globe can be used to estimate average δ13C across terrestrial environments, and so global Δ13C.

Several models of the distribution of C3 and C4 plants have been proposed. By far the most widely used C4 distribution map in ecophysiological research and land-surface modeling is the one developed by ref. 20 based on an approach published in ref. 11—see for example,21,22,23,24. However, this map is static, implying constancy over time. More recent work has considered the differential responses of C3 and C4 plants to recent environmental changes, based on an optimality model12. The derived map12 indicates that the global fraction of C4 plants has decreased over 2001–2019 due to a decrease in the natural abundance of C4 grasses with elevated CO2, even as the area of C4 crops increased. Such a shift would impact trends in global GPP and Δ13C. Reference 2 suggested that the lower-than-expected decrease in global δ13CO2 observed in atmospheric measurements (attenuation of the Suess effect)3 might be explained by changes in the abundance and distribution of C3 and C4 plants. In contrast, ref. 3 suggested that any change in C3/C4 distribution would have a negligible impact on atmospheric δ13CO2, given the higher carbon turnover rate in C4 than C3 plants—implying a dominant control on atmospheric δ13CO2 by C3 photosynthesis.

Here we propose a new C3/C4 distribution model based on the well validated, optimality-based P model25,26,27 to test refs. 2, 3 hypotheses (hereafter denoted as Lavergne2022 and Keeling2017, respectively) and to determine whether changes in C3 and C4 plant distributions could explain the observed decrease in atmospheric δ13CO2 over the period from 1982 to 2016 (see workflow in Supplementary Fig. 1). We compiled a large global dataset of stable carbon isotope measurements from leaves28 and soils29 to evaluate model predictions of photosynthetic Δ13C in C3 and C4 plants and C3/C4 fractions, respectively. δ13Csoil is a good indicator of local changes in the abundance of C3 and C4 plants because of the contrasting isotopic signatures of the two photosynthetic pathways. We estimated recent changes in the abundance and distribution of C3 and C4 plants, GPP and Δ13C in response to environmental changes and compared them with those based on the C4 distribution maps of ref. 20 and ref. 12 (hereafter denoted as Still2009 and Luo2014, respectively). We performed an attribution analysis to determine the relative contributions of environmental drivers to the changes in the fraction of C4 plants, GPP, and Δ13C. Finally, we used a simple carbon-cycle box model30,31 to determine whether changes in C3 and C4 biomass, weighted by their relative fractions and carbon turnover times, could explain the magnitude of the observed decrease in atmospheric δ13CO2.

Results

The skill of the model to predict Δ13C for C3 and C4 plants was good with coefficients of determination (R2) averaging 0.50, 0.23 and 0.92, respectively for C3, C4 and total (C3 and C4) plants (Fig. 1a). However, the model underestimated the leaf-derived variability of Δ13C (standard deviation = 1.56‰ versus 2.63‰ for C3 plants, and 0.60‰ versus 1.32‰ for C4 plants, respectively for model and observations). The model reproduced 58% of the variability of the global soil isotopic δ13Csoil records (R2 = 0.58; Fig. 1b), an improvement over the simulations using the C4 maps of Still2009 and Luo 2024 (R2 = 0.32 and 0.37, respectively; Fig. 1c, d).

Fig. 1: Predictive skill of the model to reproduce leaf and soil stable carbon isotope data.
figure 1

a Comparison between predicted and observed Δ13C for C3 (purple) and C4 (brown) plants with associated coefficients of determination (R2). The R2 for all (C3 + C4) plants is shown in black. Comparison between predicted and observed δ13Csoil for b our C3/C4 competition map, c the global C4 map of Still2009, and d Luo2024, with associated coefficients of determination (R2).

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The predicted fraction of C4 plants (F4) was large in hot and dry regions including subtropical Africa, the southern part of North America, northeastern Brazil and northern Australia, but low in cold and temperate regions (Fig. 2a). Similar patterns of spatial variation were shown in Still2009 and Luo2024 (Fig. 2b, c), but were more pronounced in Still2009 than in the other two maps. Predicted F4 tended to decrease over the period studied in most regions with F4 > 5% (Fig. 3a), but to increase slightly in southern equatorial regions (0–20°S) in central Eurasia and high latitudes of North America (Fig. 3b). The predicted F4 decrease was greater than in Luo2024 over their common 2001–2016 period (Fig. 3b, c). Luo2024 showed increases in F4 in more regions than in our map (Fig. 3c). Globally, according to our model, F4 decreased from 14.1 to 10.3% for natural grasslands but increased from 1.7 to 2.0% for crops between 1982 and 2016. This resulted in a decrease of global F4 (considering both natural grasslands and crops) from 15.8 to 12.2% over the same period (Fig. 4a), and from 13.6 to 12.2%. Global F4 was 13.8% in Still2009 but decreased over 2001–2016 from 12.5 to 12.3% in Luo2024 (Fig. 4b). F4 decreased by 0.001% yr−1 (p < 0.001) in our analysis, but at a slower rate for Luo2024 (<0.001% yr−1, p < 0.01). The global average F4 over the common 2001–2016 period was 12.7% using our model, similar to Luo2024 (12.5%).

Fig. 2: Predicted fraction of C4 plants across the globe over 2001–2016.
figure 2

Model predictions using our simple C3/C4 approach, including both natural grasslands and croplands (a). Global C4 distribution maps from Still2009 (b) and Luo2024 (c).

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Fig. 3: Temporal trend in the global fraction of C4 plants (F4, in yr-1).
figure 3

Trend in F4 from our C3/C4 map over 1982–2016 (a) and 2001–2016 (b). Trend in F4 from Luo over 2001–2016 (c).

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Fig. 4: Global changes in the fraction of C4 plants, GPP and Δ13C over 1982–2016.
figure 4

Fraction of C4 plants (F4) from our model for (a) natural grasslands (green), crops (orange) and both natural grasses and crops (violet) and (b) total F4 compared to that from Still2009 (brown) and Luo2024 (light pink). GPP weighted by the fraction of C3/C4 plants (in PgC yr−1) for natural grasslands (green), crops (orange) and both natural grasses and crops (violet) in C3 (c) and C4 (d) plants and (e) for all plants (including C3 and C4 plants; Eq. 3c) using our maps and those. Δ13C weighted by the fraction of C3/C4 plants (in ‰) for natural grasslands (green), crops (orange) and both natural grasses and crops (violet) in C3 (f) and C4 (g) plants and (h) for all plants (including C3 and C4 plants; Eq. 4) using our map, Still2009 and Luo2024. The light shade is the uncertainty calculated as the 95% confidence interval of the simulated mean (a, b, f, g, h) or sum (c–e) plus the sum of uncertainties from the input data (assumed to be ±2% of the global average values). The uncertainty range of the C4 cropland area derived from LUHv2-2019 (orange) is assumed to be ±10% of the global average values following Luo.

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From 1982 to 2016, while the predicted gross primary production (GPP) per unit land area for C3 plants (GPPC3) increased across the globe, GPP for C4 plants (GPPC4) decreased in line with the F4 decrease (Supplementary Fig. 2a, b). Total GPP, including both C3 and C4 photosynthesis, increased almost everywhere, but decreased in South America around 30°S, in northwestern Australia and in Africa around 20°N and 20°S (Supplementary Fig. 2c). Globally, GPPC3 increased at a rate of 0.75 ± 0.06 PgC yr–2 and GPPC4 decreased by 0.28 ± 0.02 PgC yr–2 (Fig. 4c), resulting in an increase of total GPP (including C3 and C4 natural grasslands and crops) by 0.47 ± 0.05 PgC yr−2—equivalent to an increase of 16.5 ± 1.8 PgC yr–1—during 1982–2016 (Fig. 4d). These estimates differ from those obtained using the fixed C4 distribution map of Still2009, where GPP increased at a faster rate of 0.53 ± 0.06 PgC yr–2—equivalent to an increase of 18.6 ± 2.1 PgC—with GPPC3 and GPPC4 increasing by 0.48 ± 0.04 PgC yr–2 and 0.07 ± 0.02 PgC yr–2 respectively (Fig. 4d). Over the 2001–2016 period, the rate of increase in GPP was slightly lower using our map than that of Still2009 or Luo2024: 0.45 ± 0.11 compared to 0.46 ± 0.12 and 0.50 ± 0.13 PgC yr–2, respectively. The mean GPP was similar using our map and that of Luo2024 (Fig. 4d). The average contribution of C4 photosynthesis to global GPP over 2001–2016 was around 16.2% for natural grasslands, and 18.5, 18.6, and 17.5% for total C4 plants (including crops) based on our map and the Still2009 and Luo2024 maps, respectively.

Predicted Δ13C increased for C3 plants (Δ13CC3) but decreased for C4 plants (Δ13CC4) from 1982 to 2016 (Supplementary Fig. 3a, b), resulting in an increase of total Δ13C, including both C3 and C4 photosynthesis, almost everywhere (Supplementary Fig. 3c). Globally, when using a constant F4 from the Still2009 map, Δ13C increased by 0.005 ± 0.001‰ yr−1 for C3 plants over 1982–2016 (p < 0.001) equivalent to 0.003 ± 0.001‰ per ppm increase of CO2, while Δ13C for C4 plants stayed broadly constant, decreasing by <0.001‰ yr–1 (p < 0.001) equivalent to <0.001‰ ppm–1 (Fig. 4e), resulting in a total Δ13C (including both C3 and C4 plants) increase of 0.005 ± 0.001‰ yr–1 (Fig. 4f) equivalent to 0.003 ± 0.001‰ ppm–1. However, when considering the global decrease in F4 over 1982–2016 using our C4 map, Δ13C in C3 plants increased at a faster rate (0.018 ± 0.001‰ yr–1, equivalent to 0.010 ± 0.001‰ ppm–1, p < 0.001), while Δ13C in C4 plants decreased by 0.003 ± 0.001‰ yr–1, equivalent to 0.002 ± 0.001‰ ppm–1 (p < 0.001), leading to a total Δ13C increase of 0.017 ± 0.001‰ yr–1, equivalent to 0.010 ± 0.001‰ ppm–1 (p < 0.001). Over the common period 2001–2016, global Δ13C increased by 0.004 ± 0.002‰ yr–1, equivalent to 0.002 ± 0.001‰ ppm–1 (p < 0.01) using Luo2024, and 0.014 ± 0.005‰ yr−1, equivalent to 0.007 ± 0.001‰ ppm–1, using our map.

The decrease in global F4 was mainly driven by the increase in atmospheric CO2 concentration (ca), followed by increasing daytime air temperature (Tair) and, to a lesser extent, by increasing daytime vapor pressure deficit (VPD) and soil moisture (θ) (Fig. 5a, b). Compared to ca, Tair and VPD, which showed spatially more-or-less homogeneous impacts on F4, the θ contribution to F4 was heterogeneous across the globe (Supplementary Fig. 4), reflecting heterogeneity in hydroclimatic changes (Supplementary Fig. 5). As expected, rising ca was the major contributor of GPP increase for C3 plants, while rising Tair increased GPP in C4 plants (Fig. 5c–e). Tair was the most important driver of Δ13C for both C3 and C4 plants, followed by VPD. Δ13C in C3 plants increased most with higher Tair, followed by ca and to a lesser extent θ, but decreased with higher VPD (Fig. 5f, g). In contrast, the decrease in Δ13C for C4 plants was mainly driven by rising Tair, while the increase in VPD attenuated this decrease (Fig. 5f, h).

Fig. 5: Global averaged change in the impact of environmental drivers on F4, GPP, and Δ13C.
figure 5

Temporal changes of the impact of atmospheric CO2 concentrations (ca), daytime air temperature (Tair), vapor pressure deficit (VPD), and soil moisture (θ) on F4 (a), and GPP (c) and Δ13C (f) for C3 and C4 plants over 1982–2016. b, d, e, g, h Global average of the individual impacts over the last 5 years (2012–2016). In (a, c, f), the light shade represents the 95% confidence interval of the simulated mean.

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Running the simple carbon cycle box model, in its original version30, we were able to reproduce the results of ref. 3: a larger-than-observed decrease in atmospheric δ13CO2 when assuming a constant Δ13C (18‰), but consistent observed and predicted trends when using a varying Δ13C driven by increases in atmospheric CO2 (Fig. 6a). Assuming a constant F4, and with the simplifying assumption that box 1 of the model (with small biomass and fast turnover) represents C4 vegetation while boxes 2 and 3 (with intermediate to high biomass and intermediate to low turnover) include only C3 vegetation, we predicted a faster-than-observed decrease in atmospheric δ13CO2 (Fig. 6b). The difference between observations and predictions was greater when we assumed a constant Δ13C (equal to 6‰ for C4 plants and 18‰ for C3 plants) than when we let Δ13C vary annually using our global model outputs (difference between observed and predicted Δ13C of around 0.30 versus 0.16‰ in 2012–2016). When accounting for both varying Δ13C and F4, our predicted δ13CO2 values were closer to the observed trends, but they did not fully reproduce the magnitude of the decrease (the difference was around 0.08‰ over 2012–2016). Thus, by accounting for both changes in Δ13C and F4 and for differences in biomass and carbon turnover for C3 and C4 plants, the difference between observed and predicted trends in atmospheric δ13CO2 was only slightly reduced.

Fig. 6: Observed versus predicted δ13CO2 (‰) estimated from a simple carbon cycle model with three biosphere boxes.
figure 6

a Original model configuration predicting δ13CO2 with simple (blue) and CO2-driven (green) Δ13C as in ref. 3 and ref. 30—denoted Keeling2017 and Graven2020, respectively. b Model predictions when box 1 represents only C4 plants, while boxes 2 and 3 are populated only by C3 plants. In blue is the simulation when both Δ13C and F4 are constant. In green is the prediction when Δ13C is modeled as in Equations S11–S13 with constant F4 and F3. In brown is the simulation when Δ13C, F4, and F3 vary.

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Discussion

We estimated the global fraction of C4 plants (F4) based on a simple optimality modeling approach driven by climate reanalyses and remote sensing observations to quantify spatiotemporal changes in F4, gross primary production (GPP), and land carbon isotopic discrimination (Δ13C) over the period from 1982 to 2016. We also used a simple carbon-cycle box model to determine whether the observed magnitude of the decrease in global atmospheric δ13CO2 could be explained by recent changes in the global abundance and distribution of C3 and C4 plants, as suggested by Lavergne2022.

Spatiotemporal variations in predicted F 4 and differences among approaches

The spatial patterns of F4 predicted by our approach are quite similar to those from Still2009 and Luo2024 over the common period (2001–2016). However, Still2009 tends to overestimate F4 in sub-Saharan and southern Africa and northern Australia compared to our study and that of Luo2024—as also indicated by the higher predicted than observed δ13Csoil values found in Still2009 for these regions (Fig. 1c). C4 plants are important components of African savannas, grasslands, and shrubs32 and dominate grasslands in the subtropical northeast of Australia33,34, but they are probably not as overwhelmingly dominant in these regions as the Still2009 map suggests. Both our model and that of Luo2024 capture the relative abundance of C3 and C4 plants in this region. No soil isotope data were available in the dry northeast of Brazil (the Caatinga region) to evaluate the maps; however, the region is known to have a high diversity of both C3 and C4 plants35,36. The Still2009 estimate that more than 80% of Caatinga vegetation follows the C4 pathway is thus probably too high, and the co-dominance of C3 and C4 plants suggested by our map and Luo (F4 around 0.5–0.6) seems more realistic.

The Luo2024 map predicts that on average, from 2001 to 2016, C4 plants, including natural grasslands and crops, occupied around 12.5% of the global land surface (excluding deserts and ice-covered lands) and contributed 17.5% of global photosynthesis. These values are slightly lower than those given in the original article (17.5% and 19.5%, respectively) because we considered a larger global land area. Our model estimates are similar to those of Luo2024. We predict that the fraction of C4 plants is 12.7%, contributing 18.5% of global photosynthesis. The value is consistent with previous estimates (18–23%11,37,38) and higher than the ensemble mean of dynamic global vegetation models (14 ± 13%12). The predicted decrease in global F4 is greater using our map than using Luo2024, probably because we predicted a decrease in the fraction of C4 in more regions.

Spatiotemporal changes in GPP and Δ13C driven by F 4 and implications for atmospheric δ13CO2 variations

The predicted increase in annual total GPP considering both C3 and C4 photosynthesis (16.5 ± 1.8 PgC) from 1982 to 2016 falls within the range of recently published values21,39. The 31 ± 5% increase in GPP over 1900–2010 reconstructed from ice-core records of carbonyl sulfide40 implies that annual GPP may have increased by around 14 ± 5% (equivalent to 17.2 ± 1.5 PgC) over 1982–201621. Using a light-use efficiency model driven by remote sensing observations41, suggested an increase in the global GPP of 0.27 ± 0.02 Pg C yr–2 (or 9.5 ± 0.7 PgC yr−1, i.e., a 6.1% increase using as reference the mean 1982-1983 values of 115 Pg C yr−1) over the period from 1982 to 2015. The spatial distribution of GPP changes highlighted in Fig. S2c is also consistent with that predicted by ref. 21, i.e., an increase in GPP in regions where the CO2 effect on C3 photosynthesis is the largest contributor to the change in GPP39, such as tropical and European forests. It differs from ref. 41, who suggested a decrease in GPP in large parts of the tropics, but that study ignored the CO2 fertilization effect. Although net carbon uptake in parts of the Amazon rainforest has declined over the past three decades due to increased carbon losses from tree mortality42, recent estimates of global forest land changes suggest GPP increased in most forests over the past decade43, in line with our predictions.

When assuming a constant F4, predicted global Δ13C including both C3 and C4 plants increased by 0.003 ± 0.001‰ per ppm increase of CO2 over the 1982–2016 period, consistent with other estimates that ignored changes in the C3/C4 fraction2. However, when the global decrease in F4 over the study period is accounted for, global Δ13C increased by 0.010 ± 0.001‰ ppm–1 due to the increase in Δ13C of C3 plants (and also the slight decrease in Δ13C of C4 plants). Including crops into this analysis has a minimal effect on Δ13C and does not significantly change the magnitude of the global Δ13C trends.

Over their common period (2001–2016), the magnitude of global Δ13C increase predicted using our F4 map is larger than using Luo2024, despite their relative agreement in predicting global F4 and GPP increase over the recent years. The two maps agree from the late 2000s onwards. The difference could be due to an overestimation of the fraction of C3 plants (F3) across the globe in our map, exacerbating the increasing global Δ13C trend. We assumed that the sum of F3 and F4 in each land grid point (excluding deserts and snow/glacial lands) is always equal to 1, but this might be an overestimate, as some areas may be covered by other types of land surface.

Using the simple carbon cycle box model, we show that accounting for Δ13C variations alone—contrary to Keeling2017—cannot explain the observed reduction of the Suess effect in atmospheric δ13CO2. However, predicted global changes in the abundance and distribution of C3 and C4 plants only slightly reduce the differences between observations and predictions during 2012–2016. The combined effects of increasing global Δ13C and decreasing fraction of C4 plants reduce the difference from 0.30 to 0.08‰. Thus—contrary to Lavergne2022—our analysis cannot explain the full magnitude of the decrease in atmospheric δ13CO2, indicating a need to consider other drivers of the isotopic signature of atmospheric CO2. Uncertainties in biosphere processes—especially isotopic fractionation during post-photosynthetic pathways and soil respiration, and carbon residence times in soils—as well as ocean–atmosphere exchanges and fossil fuel emissions, can cause discrepancies between simulated and observed atmospheric δ13CO230,44.

Limitations of our analysis

The approach to C3/C4 distribution by Luo2024 is based on a model predicting influences of atmospheric CO2, water stress (soil moisture and vapor pressure deficit), and nitrogen availability on both C3 and C4 photosynthesis45. Our model is simpler; it assumes that the impacts of elevated CO2 and water stress are important only for C3 photosynthesis (Supplementary Figs. 11 and 12) and neglects nitrogen availability effects. Nonetheless, our attribution analysis suggests patterns of variability of F4 with elevated CO2 and water stress (Fig. 5) similar to those in Luo2024. Global F4 and GPP values predicted with our F4 model over the recent years are in line with those using the Luo2024 map over their common period (2001–2016). Finally, when comparing measured and predicted δ13Csoil, our simple model provides better predictions of δ13Csoil than Luo2024 (R2 = 0.58 versus 0.37), giving us confidence in our predictions.

We considered the photorespiratory effect on Δ13C trends for C3 plants, but not additional effects (notably the effect of mesophyll conductance), whose importance is debated. Keeling2017 suggested a contribution from the mesophyll conductance effect to the globally increasing Δ13C trends of 0.006 ± 0.003‰ per ppm increase of CO2, which would induce a higher Δ13C trend in C3 photosynthesis than predicted here: 0.009 ± 0.003‰ ppm−1 (as opposed to 0.003 ± 0.001‰ ppm−1) over 1982–2016. On the other hand, Lavergne2022 argued that the mesophyll effect could reduce Δ13C values and trends by around –0.001 ± 0.001‰ ppm−1, so the magnitude of the increase in Δ13C reported here would then be overestimated. This argument relied on the assumption that the ratio of stomatal to mesophyll conductance is independent of environmental factors, leading to an optimal ratio of the chloroplastic to ambient CO227. This is probably oversimplified; however, the controls of mesophyll conductance are not fully understood.

Finally, when we tested the simple carbon-cycle box model for its sensitivity to changes in the abundance of C3 and C4 plants on atmospheric δ13CO2, we only incorporated our global Δ13C estimates for C3 and C4 plants as model inputs, modulated by changes in their relative abundance, carbon use efficiency, and turnover. The standard biosphere carbon model embedded in the box model does not differentiate C3 and C4 photosynthesis and allows the sizes of all three land reservoirs to grow due to CO2 fertilization. Although we removed the CO2 fertilization effect from the first box (C4 photosynthesis), these simplifications of the drivers of C3 and C4 photosynthesis may have biased estimates of net primary production (NPP) and increased uncertainties in modeled carbon dynamics. We also made some assumptions regarding carbon turnover values for the different plant types examined, based on the published parameterization of the carbon cycle box model30. For instance, we assume that the carbon turnover for C4 herbaceous (box 1) is about 10 times lower than that of C3 herbaceous (box 2). Although there is ample evidence showing that the turnover time of C4-derived soil carbon is substantially shorter than that of C3-derived soil carbon46, carbon turnover may still vary across regions. The extent of these variations and potential underlying drivers are still not well constrained.

Regardless of the simplifications in our analysis, however, our results imply that neither of the tested hypotheses2,3 provide a comprehensive explanation for the observed trend in atmospheric δ13CO2. Recent shifts in global Δ13C and the abundance and distribution of C3/C4 plants can only partially explain the magnitude of the observed decrease in δ13CO2. Factors other than changes in species abundance and distribution must influence carbon isotope flux exchanges. Further analyses are needed to determine their nature and quantify their contribution to the Suess effect.

Methods

Modeling approach based on optimality principles

We used the P model25,26,27, a light-use efficiency model based on eco-evolutionary optimality principles, to simulate ecosystem gross primary production (GPP) and carbon isotope discrimination (Δ13C). We also developed a simple scheme based on the P model to predict the share of C4 plants in the total GPP (see Supplementary Note 1 for more details on the model and workflow in Supplementary Fig. 1). We converted the potential share of C4 plants in the total GPP to fraction of C4 plants (F4,pot) using the emergent constraint in ref. 12 as the share of C4 plants divided by 1.13.

Since the total fractions of C3 and C4 biomass consist of natural ecosystems (trees, grasses) and crops, we estimated the C4 fraction of natural ecosystems (F4,nat) by removing the fraction of human managed areas (C3 and C4 crops and urban areas) from F4,pot:

$${F}_{4,{nat}}={F}_{4,{pot}}-\left({F}_{3,{crops}}+{F}_{4,{crops}}\right){-F}_{{urban}}$$
(1)

We then calculated the total fraction of C4 and C3 plants (F4,tot and F3,tot) considering natural ecosystems (F4,nat and F3,nat) and crops (F4,crops and F3,crops) as:

$${F}_{4,{tot}}={F}_{4,{nat}}+{F}_{4,{crops}}$$
(2a)
$${F}_{3,{tot}}={1-F}_{4,{tot}}={F}_{3,{nat}}+{F}_{3,{crops}}$$
(2b)

We estimated C3, C4 and total (C3 + C4) GPP from their respective potential GPP (\({{GPP}}_{C3,{pot}}\) and \({{GPP}}_{C4,{pot}}\)) as:

$${{GPP}}_{C3}={{GPP}}_{C3,{pot}}{F}_{3,{tot}}$$
(3a)
$${{GPP}}_{C4}={{GPP}}_{C4,{pot}}{F}_{4,{tot}}$$
(3b)
$${{GPP}}_{{tot}}={{GPP}}_{C3}+{{GPP}}_{C4}$$
(3c)

We aggregated GPP for C3, C4, and all (C3 + C4) plants from each grid cell, weighted by grid-cell area for each prediction with each C4 map, and compared their respective temporal changes (GPP, in PgC yr−1).

We then estimated the land Δ13C assuming that the biosphere is composed of three terrestrial components (C4 herbaceous, C3 herbaceous and C3 woody) with different carbon turnover times (\({{{\rm{\tau }}}}\), year) and carbon use efficiencies (CUE, unitless; the ratio of net to gross primary productivity, NPP/GPP):

$${\Delta }^{13}C=\frac{{f}_{4,{herb}}\,{\Delta }_{4}\,{{{{\rm{\tau }}}}}_{4,{herb}}+{f}_{3,{herb}}\,{\Delta }_{3}{{{{\rm{\tau }}}}}_{3,{herb}}+{f}_{3,{woody}}\,{\Delta }_{3}{{{{\rm{\tau }}}}}_{3,{woody}}}{{{{{\rm{\tau }}}}}_{4,{herb}}+{{{{\rm{\tau }}}}}_{3,{herb}}+{{{{\rm{\tau }}}}}_{3,{woody}}}$$
(4)

with \({{{{\rm{\tau }}}}}_{4,{herb}},\,{{{{\rm{\tau }}}}}_{3,{herb}},{{{{\rm{\tau }}}}}_{3,{woody}}\) the carbon turnover times and f4,herb, f3,herb and f3,woody the fractions adjusted by CUE (CUE4,herb, CUE3,herb and CUE4,woody) for C4 herbaceous, C3 herbaceous and C3 woody plants respectively.

$${f}_{4,{herb}}={F}_{4,{tot},t0}-\left({F}_{4,{tot},t0}-{F}_{4,{tot}}\right){\,{CUE}}_{4,{herb}}$$
(4a)
$${f}_{3,{herb}}={F}_{3,{tot},t0}-\left({F}_{3,{tot},t0}-{F}_{3,{tot}}\right){\,{CUE}}_{3,{herb}}$$
(4b)
$${f}_{3,{woody}}={F}_{3,{tot},t0}-\left({F}_{3,{tot},t0}-{F}_{3,{tot}}\right)\,{{CUE}}_{3,{woody}}$$
(4c)

\({F}_{4,{tot},t0}\) and \({F}_{3,{tot},t0}\) are the fractions of C4 and C3 plants, respectively, at time t0 - the first year of the records (1982).

Δ4 and Δ3 are the carbon isotope discrimination of C4 and C3 plants, respectively (see Supplementary Note 1), calculated for each month (mth) and weighted by each month’s C3 and C4 GPP to obtain annual averages of Δ3 and Δ4:

$${\Delta }_{x,{yr}}=\sum\limits_{t}\frac{{\Delta }_{x,{mth}}\times {{GPP}}_{x,{mth}}}{{\sum }_{t}{{GPP}}_{x,{mth}}}$$
(5)

with x being the plant type (C3 or C4) selected.

On average, biomes dominated by C4 plants have both higher carbon turnover rates and lower biomass than those dominated by C3 plants46,47,48, so their relative contribution to land ∆13C is expected to be lower than that of C3 plants. \({{{\rm{\tau }}}}\) values estimated as the ratio of carbon stocks in vegetation and soils to NPP from TRENDYv12 model outputs49 vary strongly among models. For instance, global average \({{{\rm{\tau }}}}\) (median ± standard deviation) are 8.7 ± 11.2, 22.4 ± 34.2 and 15.3 ± 27.5 year for C4 grasses, 33.8 ± 33.3, 40.5 ± 81.1 and 534.3 ± 217.7 year for C3 grasses, and 561.6 ± 173.7, 616.0 ± 224.3, and 641.3 ± 181.2 year for C3 woody, respectively for CABLE-POP, CLASSIC, and ORCHIDEE models. Given the large uncertainties in these estimates and to ensure consistency with our whole approach, we use the same range of \({{{\rm{\tau }}}}\) values as in a carbon cycle box model parameterization when the CO2 fertilization effect is on for C3 plants30 (\({{{\rm{\tau }}}}\)4,herb = 2.4 ± 0.3 year, \({{{\rm{\tau }}}}\)3,herb = 24.4 ± 6.5 year, and \({{{\rm{\tau }}}}\)3,woody = 299.4 ± 144.5 year; see also Supplementary Table 1). These values are at the lower end of the estimates from the three TRENDYv12 models but are consistent with the relative differences in τ between C4 herbaceous, C3 herbaceous and C3 woody plants (very fast, intermediate, and slow, respectively).

Non-forest biomes, including grasslands, shrublands, and crops, tend to have higher CUE than forests (0.46  ±  0.11 versus 0.41  ±  0.11), except for C4 grass-dominated savanna ecosystems, which show a lower CUE (0.32  ±  0.12)50. However, the contribution of C3 and C4 plants in grasslands, shrublands, and crops, and their relative CUEs remain unclear. Here, we use the average CUE values reported in reference 46, assuming that C4 biomass is a mixture of grasslands, savanna ecosystems, and crops (0.41 ± 0.10), that C3 herbaceous biomass is a mixture of grasslands and crops only (0.46 ± 0.10), and that C3 woody biomass includes both forests and shrubland biomes (0.40 ± 0.10)46. We acknowledge the limitations of our approach, especially given that \({{{\rm{\tau }}}}\) and CUE may vary not only across plant functional types but also across environmental conditions, in particular temperatures50,51,52,53.

Optimality model configuration and simulation

We ran the P-model on a 0.5° resolution grid at a monthly timestep over the period 1982–2016, forced by monthly mean values of daytime air temperature (Tair, °C), daytime vapor pressure deficit (VPD, Pa), incident photosynthetic photon flux density (PPFD, mol m–2 month–1), the fraction of incident PPFD absorbed by foliage (fAPAR, dimensionless), the atmospheric partial pressure of CO2 (ca, Pa), root-zone volumetric soil moisture (\({{{\rm{\theta }}}}\), m3 m–3) and elevation (z, m). Monthly mean Tdaytime and VPD were calculated from minimum and maximum temperature and actual vapor pressure from the Climatic Research Unit (CRU) gridded time-series (CRU TS4.03) dataset54 to consider only the part of the day when photosynthesis occurs55. Monthly shortwave downwelling radiation (SWdown) was obtained from WATCH-Forcing-Data-ERA-Interim (WFDEI) data56 and used to calculate monthly PPFD. Supplementary Table 2 summarizes the data information and sources used in this study.

Monthly fAPAR data were derived from the Advanced Very High Resolution Radiometer (AVHRR) Global Inventory Modeling and Mapping Studies (GIMMS) fAPAR 3 g product57 gridded at 0.5° resolution. Since monthly ca varies spatially, we used the annual ca data (μmol mol–1) derived from ref. 58 and converted them into Pa using elevations derived from WATCH-WFDEI. Monthly \({{{\rm{\theta }}}}\) (m3 m–3) over a 1 m soil depth was calculated using a modified version of the SPLASH model59 driven by daily precipitation, Tair and SWdown from the WATCH-WFDEI dataset over 1979–2018. The model \({{{\rm{\theta }}}}\) outputs were derived from ref. 60.

Annual data on percentage tree cover, used to estimate the fraction of C4 plants (see Text S1), were derived from the NASA Making Earth System Data Records for Use in Research Environments (MEaSURES) Vegetation Continuous Fields (VCF) 5KYR v00161 for the 1982–2016 period. The years 1994 and 2000 are missing from this dataset. We interpolated tree cover for these years by averaging values from the previous and subsequent years (1993 and 1995, and 1999 and 2001, respectively).

We used the urban areas and C3 and C4 crop distribution estimates from the LUHv2-2019 dataset (https://daac.ornl.gov/VEGETATION/guides/LUH2_GCB2019.html). Data for the remote-sensing products given at 0.05° resolution were aggregated to 0.5° resolution using the mean of all the 0.05° grid cells within the 0.5° grid cell. Climate and remote sensing data were filtered with the MODIS Land Processes Distributed Active Archive Center (LP DAAC; https://www.earthdata.nasa.gov/data/catalog/lpcloud-mcd12q1-061) snowandice and barren_sparsely_vegetated maps to retain only vegetated regions free of snow and ice.

Optimality model evaluation and comparison

We evaluated the simulations of Δ13C for C3 and C4 plants using a compilation of leaf stable carbon isotope data28 that includes 3601 measurements for C3 plants and 531 measurements for C4 plants (see Supplementary Fig. 8a for site locations). Measured leaf δ13C were converted into leaf Δ13C using atmospheric δ13CO2 from ref. 62. We also evaluated the model predictions of the fraction of C4 plants (F4) over the 1982–2016 period using a new compilation of 2156 soil δ13C measurements derived from published sources specifically compiled for this study29 (see Supplementary Table 3 and Supplementary Fig. 8b for data information and locations). Predicted Δ13C values for C3 and C4 plants were converted to δ13C using atmospheric δ13CO2 from ref. 62. Since measured soil δ13C is an average of the stable carbon isotopic signature of soil organic matter accumulated over several years, we estimated soil δ13C from the model as the average of predicted δ13C for both C3 and C4 plants, weighted by their relative yearly fraction, over the entire period 1982–2016 to enable comparisons with the observations. We assumed that any additional isotopic fractionation within the soil is negligible over the study timeframe.

We compared the predictive skills of our approach with those from two independent, global C4 distribution maps. We used the map from ref. 20 available at https://daac.ornl.gov/cgi-bin/dsviewer.pl?ds_id=932 and the map recently developed by ref. 12 for the period 2001–2019 (https://zenodo.org/records/10516423)—referred to as Still2009 and Luo2024, respectively. Since these maps covered different regions of the world, we homogenized them to make them comparable. When grid points were set to “NA” but were on land (excluding deserts and snow/glacial lands), we assumed F4 = 0. As a result, the estimated F4 values derived from the maps may be slightly different from those reported in the respective publications. We predicted soil isotopic composition using each of the maps and compare them with the soil isotopic network. We also compared the mean and trends in total F4, GPP, and Δ13C derived from each of the maps.

We conducted additional simulations to quantify the contributions of ca, Tair, VPD and θ to F4, GPP and Δ13C changes. To do so, we ran the model for four different scenarios in which we used the input of ca, Tair, VPD and θ of the first year (1982), respectively, to simulate GPP over the whole period. We then used predicted GPP for the different scenarios to estimate F4 for each year. We calculated the difference between the original model simulations and those derived from each scenario to determine the relative contributions of ca, Tair, VPD and θ to F4, GPP, and Δ13C changes.

Simple carbon cycle model to estimate atmospheric δ13CO2

To account for differences in land ∆13C, biomass and carbon turnover between C3 and C4 plants, we estimated global average atmospheric δ13CO2 (‰) over 1982–2016 using the simple carbon cycle model from ref. 30, also used in ref. 3. The model simulates carbon cycling in atmospheric, oceanic, and biospheric reservoirs, and includes one atmospheric box, three biospheric boxes with different biomass and carbon turnover times, and a one-dimensional box diffusion ocean model with 43 ocean boxes. We conducted our historical simulations using the same initial model configuration and calibrated parameter ranges as in ref. 30. A few small changes were made to the model code: defining different Δ13C values for C3 and C4 plants that consider temporal changes in the fraction of C3 and C4 plants, and different carbon turnover (τ) and use efficiency (CUE) for the three biospheric boxes (see also Supplementary Note 1 for more information). We first ran the model in its standard mode, initially with a constant Δ13C (equal to 18‰) and then with a variable Δ13C based on CO2 changes as in ref. 3. We then tested the model using our global average annual model outputs for ∆13C and F4 by allowing box 1, with low biomass and rapid τ, to represent only C4 herbaceous, while boxes 2 and 3, with intermediate and high biomass and intermediate and slow τ, represent C3 herbaceous and woody, respectively. Since CO2 fertilization only impacts C3 photosynthesis, we assume it to be null for C4 photosynthesis (box 1).