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Sevenfold variation in global feeding capacity depends on diets, land use and nitrogen management


Harvested food carries a fraction of the nitrogen applied through fertilization; the remainder is typically lost into the environment, impairing planetary sustainability. Using a global agriculture model that integrates key drivers of food production and nitrogen cycling, we simulated upper bounds to global feeding capacity—and associated nitrogen pollution—as a function of nitrogen limitation under organic and industrial fertilization regimes. We found that the current agricultural area could feed ~8–20 billion people under unconstrained industrial fertilization and ca. 3–14 billion under organic fertilization. These ranges are inversely correlated with animal proteins in human diets, and are a function of feed–food competition, grassland-to-cropland allocation and—in the case of organic fertilization—nitrogen use efficiency. Improved nitrogen use efficiency is required to bring nitrogen pollution within planetary sustainability limits and is also essential in narrowing down food productivity gaps between organic and industrial fertilization regimes.

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Fig. 1: Food yield modelling.
Fig. 2: Yfood, Globalpop and rloss in the five global food production boundaries B1–B5 and over the benchmark period 1961–2013.
Fig. 3: NUEtot in global agriculture.
Fig. 4: Average non-compounding growth rates required in key variables of global food production and N cycling to feed, by 2050, 10 billion people while staying within planetary sustainability thresholds.

Data availability

The bulk of input data used in the analysis are derived from the statistics of the United Nations Food and Agriculture Organization (FAO), available at: The N content coefficients of primary crops are taken from ref. 58 and the N content coefficients of food supply are from FAOSTAT food balance sheets34. Data on crop yield gaps are taken from ref. 27. Other data sources are specified in the Methods. Source data are provided with this paper.

Code availability

The code developed in the study is available from the corresponding author upon reasonable request.


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The work was developed with funding from the research programme Emergence Ville de Paris Convention 2015 DDEES 165. The authors would like to thank T. Gregor for valuable stylistic remarks on a previous version of the manuscript.

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Authors and Affiliations



Both authors conceived and designed the study, analysed and interpreted the data, defined the Methods, developed the ALPHA model, discussed the ideas and results, and wrote and revised the paper.

Corresponding authors

Correspondence to Petros Chatzimpiros or Souhil Harchaoui.

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Nature Food thanks Longlong Xia and Gilles Billen for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Flow diagram of the modeling system.

Nitrogen (N) flows are indicated in absolute terms (in bold, that is kgN·yr−1) and per unit land (in light, that is kgN·ha−1·yr−1). τ and (1-τ) are respectively the share of grassland and cropland in total agricultural land. Food production (Nfood) is total primary production extracted from grassland (Ngrass) and cropland (Ncrop), plus crop residues used for feed (Nresidues), plus livestock production (Nlivestock) minus total feed (Nfeed). Nfood is human-edible biomass and is the sum of food supply (\({{{\mathrm{N}}}}_{{{{\mathrm{food}}}}}^{{{{\mathrm{supply}}}}}\)), seed, loss and other uses. Nfood and \({{{\mathrm{N}}}}_{{{{\mathrm{food}}}}}^{{{{\mathrm{supply}}}}}\) per unit agricultural land (ha) are respectively the food yield (Yfood) and unitary food supply \(\left( {{{{\mathrm{Y}}}}_{{{{\mathrm{food}}}}}^{{{{\mathrm{supply}}}}}} \right)\). αcrops and αresidues are respectively the shares of Ncrop and crop residues production used for feed. Total N input (Ntot in the equations – not illustrated) is the sum of N input to cropland and grassland from biological nitrogen fixation (BNF), industrial N fertilizers (Nind), atmospheric deposition (Natm) and potential N return to agriculture (Nbiowaste_return) from human waste management. Nbiowaste_return is a fraction (ρ) of \({{{\mathrm{N}}}}_{{{{\mathrm{food}}}}}^{{{{\mathrm{supply}}}}}\). Total N input divides into Nfood and N loss. Total system N use efficiency (NUEtot) is the ratio of Nfood to total N input. NUEtot integrates N use efficiency in cropland (NUEcrop) and grassland (NUEgrass), livestock proteins conversion efficiency (NCE), the fraction of N excretion voided on grassland (γ) and the share of manure N recovered to cropland (β).

Extended Data Fig. 2 Food yield drivers over the benchmark period (1961–2013).

Data are from ref. 1. a. Crop yield (Ycrop) b. Share of crops used for feed (αcrops). c. Share of crop residues used for feed (αresidues) including uncertainty between constant share of 30% and decreasing share from 75 to 30% over the period (see Methods) d. Grass yield (Ygrass) and uncertainty according to the value of αresidues e. Livestock nitrogen conversion efficiency (NCE) f. share of grassland in total agricultural land (τ).

Source data

Extended Data Fig. 3 Feed and livestock production over the benchmark period.

a.Total feed (TgN·yr−1) and breakdown among crops, grass and crop residues over the benchmark period (1961–2013) b. Current (2013) total livestock production (TgN·yr−1). Total feed and the amount delivered from crops are derived from FAOSTAT (ref. 33) as described in Methods. The sum of grass and residues is calculated as the difference between total feed and feed from crops. The relative contribution of grass and crop residues is approximated considering a range for crop residues used for feed from 70 to 30% (see Extended Data Fig. 2c, d and Methods). Livestock production is derived from FAOSTAT (ref. 1) for year 2013 and split into ruminants meat, dairy and monogastric production. Monogastrics are exclusively grain-fed, but feed of ruminants (dairy and beef) also includes crops.

Source data

Extended Data Fig. 4 Global average crop yield (Ycrop), food yield (Yfood) and N loss rate (rloss) per unit total agricultural area in the organic boundary (B5) as a function of the share of grassland in total agricultural area (τ).

The calculation is done for current share of crops used for feed (αcrop) of 57% and 70% in the case of organic boundary (B5) with increased biological N fixation rate in cropland (\({{{\mathrm{r}}}}_{{{{\mathrm{BNF}}}}}^{{{{\mathrm{crop}}}}}\)), biological N fixation rate in grassland (\({{{\mathrm{r}}}}_{{{{\mathrm{BNF}}}}}^{{{{\mathrm{grass}}}}}\)) and biowaste N return to agriculture (ρ) combined. The vertical dotted line indicates current global τ. The change in slope corresponds to Ycrop equaling maximum Ycrop (full closure of organic crop yield gap). For Ycrop below maximum, Ycrop increases with τ (because N limitation per unit cropland decreases with τ), but Yfood slightly decreases. For maximum Ycrop, the decrease in Yfood as a function of τ is steeper. The curves highlight that Ycrop increases with αcrops due to higher manure production, and this increase depends on the share of manure N return to cropland (β). The higher the β, the faster the increase in Ycrop as a function of αcrops.

Source data

Extended Data Fig. 5 Total simulated N input (Ntot) per source in the five food production boundaries (B1 to B5).

B1-B3 are under industrial fertilization (Nind) and B4-B5 under organic fertilization. Ntot is the sum of N input to cropland and grassland. Ntot is calculated for: a. current share of crops used for feed (αcrops = 57%) b. αcrops = 70% and c. αcrops = 0%. Natm stands for atmospheric N deposition, BNF for biological N fixation, Nind for industrial fertilizers input and Nbiowaste_return for biowaste N return to agriculture via human waste management.

Source data

Extended Data Fig. 6 Livestock production (TgN·yr−1 and %) in global food production boundaries (B1-B5) as a function of the share of crops used for feed (αcrops).

a. Food production boundaries under industrial fertilization (B1-B3). b. Organic food production boundary with current N use efficiency (B4). c. Organic food production boundary with improved N use efficiency (B5). We distinguish between livestock production from grassland and residues (no feed competition) and livestock production from cropland (grain-fed livestock). Production from grassland and residues is dairy and ruminants meat, and production from cropland is undifferentiated between dairy and monogastrics production (pork, poultry and eggs). The red line divides ruminants’ production between meat and milk. The vertical dotted lines indicate the share of crops used for feed (αcrops) that corresponds to animal proteins content in healthy diet that is 26% (ref. 44, Supplementary Table 3). Note that in B4, the share of animal proteins always exceeds the recommendation in healthy diets due to low crop yields.

Source data

Extended Data Table 1 Summary table of model variables, abbreviations, and units
Extended Data Table 2 Summary table of model variables classified between input and output over the benchmark period, and global weighted average data in 1961 and 2013
Extended Data Table 3 Summary table of model variables classified between input and output in the five global food production boundaries (B1-B5), and data used in the simulations

Supplementary information

Supplementary Information

Supplementary Discussion, Supplementary Tables 1–5, Supplementary Figs. 1–15 and Supplementary References.

Reporting Summary

Source data

Source Data Fig. 1

Model data output of food yield (Yfood) and trade-off between the share of crops used for feed (αcrops), animal proteins in diets and the share of grassland in total agricultural area (τ).

Source Data Fig. 2

Model output data of food yield (Yfood), animal proteins in food supply (Shareanimal) and nitrogen loss rate (rloss) over the benchmark period and in the five global food production boundaries (B1–B5).

Source Data Fig. 3

Model output data of total nitrogen use efficiency (NUEtot) over the benchmark period and in the five global food production boundaries.

Source Data Fig. 4

Model output data of growth rates required in key variables to achieve global food production and sustainability challenges.

Source Data Extended Data Fig. 2

Model input data of the six food yield (Yfood) drivers over the benchmark period.

Source Data Extended Data Fig. 3

Model input data of total feed per feed source and livestock production over the benchmark period.

Source Data Extended Data Fig. 4

Model output data of crop yield (Ycrop), food yield (Yfood) and nitrogen loss rate (rloss) in the organic boundary (B5) as a function of the share of grassland in total agricultural area (τ).

Source Data Extended Data Fig. 5

Model output data of total nitrogen input (Ntot) in the five global food production boundaries (B1–B5).

Source Data Extended Data Fig. 6

Model output data of livestock production composition as a function of the share of crops used for feed (αcrops) in the five global food production boundaries (B1–B5).

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Chatzimpiros, P., Harchaoui, S. Sevenfold variation in global feeding capacity depends on diets, land use and nitrogen management. Nat Food 4, 372–383 (2023).

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