## Introduction

The conversion of nearly half of the world’s ice-free land area to agricultural areas1 has contributed to three of humanity’s most pressing environmental challenges2,3: (i) agriculture is a major source of anthropogenic greenhouse gas emissions4,5,6, largely from the release of carbon stored in natural vegetation and soils7,8; (ii) agriculture is the main driver of habitat loss, the greatest threat to terrestrial biodiversity9,10,11,12; and (iii) agriculture is responsible for about 70% of global freshwater consumption13,14, leading to shortages of potable water in many arid parts of the world15,16. Rising global demands for animal products17 reduce hopes that the benefits of societal dietary shifts to decrease the environmental footprints of food production2,3,18 can be fully realised in the near future. Yield increases through more resource-efficient practices, technological advancements, and genetically enhanced crop varieties are promising2,3,19; however, a growing human population and increasing per-capita consumption20,21 threaten to offset the potential of these developments without complementary measures.

Ecosystem restoration has been identified as a key strategy for achieving large-scale carbon sequestration and reducing pressures on terrestrial biodiversity22,23,24. Indeed, carbon stocks and biodiversity lost from land conversion can often rapidly approach pre-disturbance levels when agriculturally degraded areas are allowed to regenerate25,26,27,28,29,30 (Supplementary Note 1). However, if total food production levels are to remain constant, the restoration of land currently used for agriculture will require production to be intensified or spatially expanded elsewhere. Whilst previous studies have identified priority areas for ecological restoration22,23,24, it is less clear how agricultural production should be spatially redistributed to maximise long-term environmental benefits without compromising food security. In addition to carbon and biodiversity gains, optimally relocating croplands could also substantially reduce the water footprint of agriculture if new areas were established where sufficient rainfall obviates the need for irrigation31. Importantly, relocating agricultural areas may not only represent an environmental opportunity, but may become a necessity for maintaining global food security as changing precipitation and snowmelt patterns are threatening crop water supply32,33 whilst shifting temperature regimes are reducing productivity34,35,36 across large parts of the world.

Here we determined the optimal distributions of global croplands that minimise carbon and biodiversity footprints whilst obviating the need for systematic irrigation, under current and future climatic conditions. We used global maps of the current growing areas of 25 major crops37 (see the “Methods” section), which between them account for 77% of croplands worldwide. For each crop we assessed the carbon impact associated with cultivation in an area as the difference between natural and crop-specific local carbon stocks in vegetation and soils8 (see the “Methods” section). Similarly, biodiversity impacts were estimated as the difference between local biodiversity under natural vegetation and under cropland38. For our main analysis, we measured local biodiversity in terms of range rarity, given by the sum of the inverse natural range sizes of locally occurring species (see the “Methods” section), a metric advocated as particularly meaningful for conservation planning39, given the strong relationship between species’ range sizes and their vulnerability to extinction40,41. The same methods allowed us to predict the potential carbon and biodiversity impacts of crop production in locations that are currently not cultivated (see the “Methods” section). We then combined these impact estimates with a global dataset of agro-ecologically attainable yields, available for the same 25 crops, across both currently cultivated and uncultivated areas, and for current and projected future climatic conditions42. We used potential yield estimates for three alternative management scenarios, representing the range from traditional, subsistence-based organic farming systems to advanced, fully mechanised production with high-yielding crop varieties and optimum fertiliser and pesticide application42 (see the “Methods” section). All estimates were derived assuming only rainfed water supply42; thus, any configuration of croplands based on them represents a scenario in which no systematic irrigation is required. Using these potential yields, we considered all possible spatial distributions of rainfed croplands for which the total global production of each individual crop was the same as at present (see the “Methods” section). In this step, the area assumed to be potentially available for agriculture in a grid cell was defined as the area not currently covered by water bodies, land unsuitable due to soil and terrain constraints, urban areas and infrastructure, crops not included in our analysis, pasture lands, and protected areas (see the “Methods” section). Finally, among all such distributions of croplands, we identified those for which global carbon and biodiversity impacts were minimal. On the 20 arc-minute (0.33°) grid used here, this required solving a ~1-million-dimensional linear optimisation problem (see the “Methods” section).

## Results and discussion

### Optimal transnational relocation with high-input crop management

The optimal distribution of croplands determined here depends on how carbon and biodiversity are weighted relative to each other in the impact minimisation, and we consider this trade-off later in our analysis; the following results are based on an optimal weighting between carbon and biodiversity impacts designed to minimise trade-offs (see the “Methods” section). We first consider the scenario of high-input crop management on relocated croplands, and examine the effects of less intensive farming practices later on. For this scenario, we estimate that a complete optimisation of the spatial distribution of croplands would simultaneously reduce the current carbon and biodiversity impacts of global crop production by 71% and 87%, respectively, whilst eliminating the need for irrigation altogether (Fig. 1). The total worldwide area used for agriculture in the optimised scenario would be less than half (48%) of the current area. The amount of carbon sequestered in vegetation and soils would be equivalent to 20 years of the current annual net increase of atmospheric CO2 of 5.1 Pg carbon per year43. Pressures on terrestrial species would be drastically lower than they are today given the major role of agricultural habitat destruction for global biodiversity loss10. In particular, optimally sited croplands overlap with only 0.2% of areas classified as tropical forest biomes44, representing a reduction of 98% in the tropical forest area that is currently being used for the crops in our analysis. Particularly pronounced spatial clusters of optimal cropping locations include growing areas of barley, cotton, rapeseed, soybean, sunflower, and wheat around the corn belt in the Midwestern USA; of cotton, maize, soybean, millet, and rice along a longitudinal band south of the Sahel zone in Sub-Saharan Africa; of maize, rice, and soybean in northeast Argentina and neighbouring regions; and of rapeseed and soybean in northeast China (Supplementary Movie 1), driven by high potential rainfed yields combined with relatively low environmental impacts in these areas (Supplementary Movie 2, Supplementary Fig. 1a–c).

### Optimal national relocation with high-input crop management

Moving agricultural production, and thus labour and capital, across national borders poses political and socio-economic challenges that may be difficult to resolve in the near future. We therefore repeated our analysis whilst requiring that, in the optimised scenario, the total production of each crop in each country remain identical to the one at present (see the “Methods” section). Assuming high-input crop management on relocated sites, we estimate that if each country independently optimised its distribution of croplands, the resulting worldwide carbon and biodiversity impacts would be 59% and 77% lower than they are currently (Fig. 1). The vast majority of production, corresponding to 99.4% of global croplands, could be nationally relocated so that rainfall provides sufficient water supply; however, some countries produce crops for which natural agro-ecological conditions within their borders are not suitable, and thus some irrigation or greenhouse cultivation remains needed to maintain the current national production levels of each crop (see the “Methods” section).

### Optimal cropland distribution under future climate scenarios

The optimal global distribution of growing areas providing the same total production of each crop as at present based on current climatic conditions is to a substantial degree similar for climatic conditions at the end of the century, irrespective of the specific climate change scenario. 73%, 73%, 70%, and 63% of the optimal areas for RCP 2.6, 4.5, 6.0, and 8.5 climate in 2071–2100 (Fig. 2a–d), respectively, overlap with those associated with the current climate in Fig. 1c. In particular, the four aforementioned major spatial clusters largely remain in place; though, parts the band south of the Sahel zone become somewhat less suitable under increased warming, whilst optimal sites in Argentina expand. Some smaller areas emerge as optimal locations as the result of climate change, including parts near the northwest American coast and east of the Ural Mountains in Russia (Fig. 2). Overall, our analysis suggests that if the global demand for the crops considered here does not decrease below current levels in the coming decades, then croplands established in optimal locations now would largely remain optimally sited in the future. The lack of suitable long-term projections of future global crop production levels (which are either too short-term45 or not specific enough46) prevents us from determining the optimal distributions of croplands for specific future scenarios of global food production; however, given an anticipated continued growth of the global population, total production levels of major crops are predicted to increase at least over the next decade45. In principle, large-scale dietary shifts could lead to a decrease in the future demand for some of the crops considered here, in which case some areas identified in our analysis may no longer represent optimal cropping locations; however, whilst such shifts could in theory generate nutritional and environmental benefits3,47,48,49, recent trends and future projections dampen expectations about a swift implementation46,50.

### Partial relocation of production and lower-input crop management

Thus far, we have considered the scenario in which all crop production is optimally relocated and in which newly established croplands are managed according to best practice. How do the potential environmental benefits of crop relocation change if these assumptions are altered? Across crops, the environmental impacts attributed to the production of one unit of produce vary greatly across current growing areas: half of the global carbon and biodiversity impact attributed to each crop is currently caused on areas accounting for only 23% and 5% of the crop’s total production, respectively (Supplementary Fig. 2). This suggests that prioritising the relocation of production away from these areas–where potential carbon stocks and biodiversity are high and yields are low–could generate particularly large environmental benefits. We repeated our analysis of the optimal distribution of croplands across and within national borders, but assumed that only a certain proportion of the current total production of each crop is being moved, beginning with current croplands where local impacts are highest in relation to local production (see the “Methods” section). As before, yields on newly established areas assume only rainfall water supply. For high-input management on new croplands, optimally relocating only around 15% of the production of each crop across borders, or around 25% within borders, could already generate around half of the potential carbon and biodiversity benefits previously estimated for a complete redistribution of areas (Fig. 3a, b). Even relocating the least agro-environmentally efficient areas accounting for as little as 5% of production to optimal locations could produce considerable environmental gains (Fig. 3a, b).

Potential impact reductions estimated under the assumption of high-input crop management on newly established croplands are necessarily higher than for less intensive farming practices, given the higher land requirements in the latter case. An important aspect in the context of lower-input crop management on new sites is that relocation beyond a certain proportion of production can increase environmental impacts, rather than reduce them. This occurs when crop production is moved from existing areas, on which yields are high as the result of intensive farming, to locations where crops are managed less intensively; this step may require an additional area that is so large that it offsets the environmental benefits of the new site. For medium- and low-input crop management, respectively, on newly established croplands, we estimate the threshold beyond which transnational or national relocation is no longer beneficial in terms of reducing carbon and biodiversity impacts at around 75% and 20–30% of production (Fig. 3c–f). At these levels, and assuming medium-input management on new croplands, current carbon and biodiversity impacts of global crop production would be simultaneously reduced by an estimated 54% and 80%, respectively, for an optimal relocation across national borders (Fig. 3c, black marker), and by 35% and 63%, respectively, for an optimal relocation within countries (Fig. 3d, black marker). For low-input management on new areas, carbon and biodiversity impacts, respectively, would be reduced by 27% and 65% for transnational relocation (Fig. 3e, black marker), and by 8% and 37% for national relocation (Fig. 3f, black marker). These results reaffirm that closing yield gaps is important for reducing the environmental footprint of agriculture2,3,18,19,20,51,52; at the same time, even for less intensive farming practices, carbon and biodiversity impacts on optimally distributed growing areas are substantially lower than they are at present (Fig. 3c–f), demonstrating that substantial benefits could be achieved by cropland relocation alone. This is particularly relevant given that implementing high-input crop management can be difficult, due to short-term marginal economic returns of mechanising production, using high-yielding crop varieties, and improving fertiliser and pesticide or due to local socio-economic, political, or infrastructural constraints53. Governmental and intergovernmental efforts to support farmers in sustainably intensifying production are key for realising the environmental benefits associated with closing agricultural yield gaps54.

Carbon and biodiversity impact reductions associated with cropland relocation are disproportionally high in relation to the change in total cropland area (Supplementary Fig. 4). For high-input crop management (Supplementary Fig. 4a), this demonstrates that the estimated benefits are not merely a consequence of the decrease in total area due to higher yields. This fact becomes even clearer in the case of low-input management, where considerable impact reductions can be achieved despite an increase in total cropland area caused by low yields on newly established areas (Supplementary Fig. 4c).

### Trade-off between carbon and biodiversity impact reduction

The trade-off between reducing carbon versus biodiversity impacts is very small, as shown by the high convexity of the lines representing sets of simultaneously achievable carbon and biodiversity impact reductions in Fig. 3. Optimising the distribution of croplands for each of the two impact measures independently allows for reduction potentials of up to 73% and 94%, respectively, in the case of a transnational relocation of areas, and up to 61% and 81%, respectively, in the case of national relocation, assuming high-input management on new croplands (Fig. 3a, b, end points of dark blue lines). These reductions are only slightly higher than those obtained simultaneously for the scenario of an optimal weighting considered hitherto (Fig. 3a, b, black markers). Results are similar for low- and medium-input crop management (Fig. 3c–f).

### Sensitivity to biodiversity metric

The strong relationship between species’ range sizes and their vulnerability to extinction40,41 makes range rarity a particularly relevant biodiversity metric for conservation39; however, like any indicator, it captures only certain aspects of biological diversity55. To assess the effect of using an alternative metric, we repeated our analysis in Fig. 1, but measured biodiversity in terms of species richness (Methods). We estimated that for a globally optimised distribution of croplands and high-input rainfed yields, carbon and species richness impacts of crop production would be 70% and 77% lower, respectively, than they are at present, whilst reductions of 60% and 67%, respectively, could be achieved by an optimal relocation within national borders (Supplementary Fig. 5). The locations of optimal cropping sites in these scenarios are overall similar to those identified based on range rarity, with 69% and 86% of optimal areas for across- and within-border relocation, respectively, overlapping with the respective areas in Fig. 1c, d. In particular, in the case of transnational relocation, optimal areas overlap in the Midwestern US corn belt, northeast Argentina, northeast China, and north of the Black Sea, though, the longitudinal band south of the Sahel zone is no longer optimal in terms of species richness (Supplementary Fig. 5b), due to the relatively high number of (generally not small-ranged) species in this area (Supplementary Fig. 1c, d). The slightly lower potentials for reducing biodiversity impacts, compared to our results based on range rarity, are due to the more uniform spatial distribution of species richness compared to that of range rarity (Supplementary Fig. 1c, d).

### Carbon payback times after crop relocation

The restoration of carbon stocks and biodiversity on abandoned agricultural areas is a long-term process, whereas the environmental impacts of relocating crop production to currently uncultivated optimal locations would be quasi-instantaneous. How long would it take for these new impacts to be offset by the gradual regeneration of abandoned areas? Assuming conservative estimates of the carbon recovery trajectory on agriculturally degraded land (see the “Methods” section) and high-input management on new croplands, we estimated that the net carbon impact of optimally relocating all current crop production within national borders would break even within a decade, and in less than half of that time for relocation across borders (Supplementary Fig. 6). For the optimal relocation of smaller shares of production that are currently located in areas with the highest restoration potentials (see the “Methods” section), break-even points would be reached disproportionally sooner (Supplementary Fig. 6) as the result of the unequal distribution of impacts and production across current areas (Supplementary Fig. 2). These short time scales again illustrate the considerable difference between current and minimum achievable carbon impacts. We did not attempt to estimate break-even timings for biodiversity, given the lack of recovery estimates with suitable spatial coverage.

### Policy aspects of cropland relocation

How can the relocation of croplands, at small or large scales, be implemented in practice? A number of national and supranational set-aside schemes, aimed at retiring agricultural land for environmental benefits, can offer useful templates for how payments for ecosystem services can reduce current impacts in socio-economically sustainable ways56,57,58. As a case example, China’s Grain for Green programme, the world’s largest national scheme of payments for ecosystem services, achieved the regeneration of 15 million hectares of farmland to forests between 1999 and 2010, with overall positive economic outcomes for the 124 million people involved59. The programme generated substantial carbon and biodiversity benefits, despite being primarily aimed at reducing soil erosion59,60. It also facilitated an effective relocation of cropland from southern to northern China61. Designing incentives to encourage the abandonment and regeneration of the least agro-environmentally efficient areas will be crucial for achieving benefits most effectively. International climate funds can support countries lacking the financial means for payments to farmers in implementing durable set-aside schemes62. In addition, in many parts of the world, agricultural subsidies prevent the abandonment of agricultural land that would otherwise occur naturally63; reducing subsidies in areas with high potential carbon stocks and biodiversity therefore represents a particularly cost-efficient strategy for generating environmental benefits64. A number of financial, infrastructural, and policy measures, ranging from land-use zoning to strategic agronomic support and certification schemes54, can incentivise the establishment of new agricultural land in optimal target areas. Simultaneously, strong legal and policy frameworks65,66,67,68 are needed to ensure an effective protection of regenerating abandoned croplands, and promote active restoration to support the recovery process when necessary. Finally, it is crucial that such measures accommodate the social equity dimension of agricultural land abandonment and relocation69. Acknowledging that financial compensation cannot replace social and cultural assets, and that relocation of farmland must be consensual, needs to be a cornerstone of any programme design.

### Uncertainties

Uncertainties in our analysis are linked to those of the relevant input data, specifically the global maps of carbon and biodiversity impacts and actual and potential yields; though, the lack of uncertainty estimates for these datasets does not allow us to formally quantify uncertainties in our analysis. Country- and crop-specific data used to generate global maps of observed yields and harvested areas used here differ in quality; however, the derived maps have been curated and validated extensively based on independent regional and national datasets and local expert opinion37. Estimates of potential crop yields are constrained by the availability and quality of climatic, ecological, and agricultural data required to calibrate yield models; spatially heterogeneous information on global soil properties in particular has been noted as a relevant limitation42. However, the derived estimates have undergone extensive ground-truthing based on local statistical records across the world42. Potential natural carbon stocks, used here to assess carbon impacts, were derived based on established methodologies that achieves robustness by providing estimates that are generally specific to a given combination of ecosystem, climate, and geographical region, and which may therefore underrepresent finer spatial heterogeneities8. Expert species range maps, used to estimate biodiversity impacts, are not without uncertainties and inaccuracies70,71; however, they allow for a consistent and transparent estimation of the effects of agricultural land conversion on natural biodiversity on currently cultivated and uncultivated areas worldwide that would not be trivial for alternative approaches to achieve38,72.

### Future perspectives

Considering rainfed potential yields has allowed us to identify cropland distributions that obviate the need for systematic irrigation; however, in several parts of the world, local water resources are at present73, or will be in future74, abundant enough to allow for sustainable irrigation, which can substantially increase yields53. This highlights the need for potential yield estimates assuming irrigation-based water supply, which are currently not available to the same extent as the rainfed yields used here42. Such estimates, combined with crop water use models31, would allow for a rigorous assessment of the three-way trade-offs between carbon, biodiversity, and water impacts.

We examined three different crop management scenarios at the global scale; in reality, farming intensity and yield gap closure are highly spatially heterogeneous53, depending on local socio-economic conditions. Estimates of the likely yield levels of crops in locations where they are currently not grown, given the specific current or projected future local circumstances, would be valuable for determining optimal relocation strategies in local contexts.

Here we did not attempt to also optimise the spatial distribution of global pastures (but assumed these to be unavailable for new cropland), due to a lack of appropriate maps of potential grass growth and the higher complexity of livestock compared to crop production processes. However, their immense size suggests tremendous potential for reducing environmental impacts through optimal relocation, which deserve examining. In this context of animal-based products, as well as that of crops, it will be highly informative to explore the potential benefit of a combined strategy of dietary shifts and spatial optimisation of agricultural areas, in which environmental impacts are minimised not whilst maintaining the global production levels of individual crops, as done here, but whilst meeting an appropriate production of nutrients.

## Conclusions

Spatial reallocation of agricultural production has tremendous potential for reducing the environmental impacts of global food production. Importantly, cropland relocation need not be implemented at full scale in order to generate substantial benefits; even a redistribution of small parts of production, across smaller spatial scales, and without fully optimised management on new sites, would have considerable positive effects. Whilst the political and socio-economic challenges associated with this strategy are undeniable, a range of proven policy measures are available for facilitating relevant steps in a sustainable manner. Their implementation will be crucial for realising the environmental potential of moving agricultural areas, providing gains that are badly needed if we are to reverse the ongoing degradation of global climate, biodiversity, and water under an ever-increasing demand for food.

## Methods

We use the notation in Table 1.

### Current crop production and areas, Pi(x), Hi(x)

We used 5-arc-minute maps of the fresh-weight production Pi(x) (Mg year−1) and cropping area Hi(x) (ha) of 25 major crops (Table 2) in the year 201037. These represent the most recent spatially explicit and crop-specific global data75. Separate maps were available for irrigated and rainfed croplands, allowing us to estimate the worldwide proportion of irrigated areas as 21% of all croplands.

### Agro-ecologically attainable yields $${\widehat{Y}}_{i}(x)$$

We used 5-arc-minute maps of the agro-ecologically attainable dry-weight yield (Mg ha −1 year−1) of the same 25 crops on worldwide potential growing areas (Supplementary Movie 3) from the GAEZ v4 model, which incorporates thermal, moisture, agro-climatic, soil, and terrain conditions42. These yield estimates were derived based on the assumption of rainfed water supply (i.e., without additional irrigation) and are available for current climatic conditions and, assuming a CO2 fertilisation effect, for four future (2071–2100 period) climate scenarios corresponding to representative concentration pathways (RCPs) 2.6, 4.5, 6.0, and 8.576 simulated by the HadGEM2-ES model77. Potential rainfed yield estimates for current climatic conditions were available for a low- and a high-input crop management level, representing, respectively, subsistence-based organic farming systems and advanced, fully mechanised production using high-yielding crop varieties and optimum fertiliser and pesticide application42. We additionally considered potential yields representing a medium-input management scenario, given by the mean of the relevant low- and high-input yields. Future potential yields were available only for the high-input management level. Thus, we considered a total of 175 (=25 × 3 present + 25 × 4 future) potential yield maps. Potential dry-weight yields were converted to fresh-weight yields, $${\widehat{Y}}_{i}(x)$$, using crop-specific conversion factors42,78.

Both current and future potential rainfed yields from GAEZ v4 were simulated based on daily weather data, and therefore account for short-term events such as frost days, heat waves, and wet and dry spells42. However, the estimates represent averages of annual yields across 30-year periods; thus, whilst the need for irrigation on cropping areas identified in our approach during particularly dry years may in principle be obviated by suitable storage of crop production79, in practice, ad hoc irrigation may be an economically desirable measure to maintain productivity during times of drought, which are projected to increase in different geographic regions due to climate change80,81.

### Carbon impact Ci(x)

Following an earlier approach8, the carbon impact of crop production, Ci(x), in a 5-arc-minute grid cell was estimated as the difference between the potential natural carbon stocks and the cropland-specific carbon stocks, each given by the sum of the relevant vegetation- and soil-specific carbon. The change in vegetation carbon stocks resulting from land conversion is given by the difference between carbon stored in the potential natural vegetation, available as a 5-arc-minute global map8 (Supplementary Fig. 1a), and carbon stored in the crops, for which we used available estimates8,78. Regarding soil, spatially explicit global estimates of soil organic carbon (SOC) changes from land cover change are not available. We therefore chose a simple approach, consistent with estimates across large spatial scales, rather than a complex spatially explicit model for which, given the limited empirical data, robust predictions across and beyond currently cultivated areas would be difficult to achieve. Following an earlier approach8, and supported by empirical meta-analyses82,83,84,85,86, we assumed that the conversion of natural habitat to cropland results in a 25% reduction of the potential natural SOC. For the latter, we used a 5-arc-minute global map of pre-agricultural SOC stocks7 (Supplementary Fig. 1b). Thus, the total local carbon impact (Mg C ha−1) of the production of crop i in the grid cell x was estimated as

$${C}_{i}(x)={{C}}_{{{{{{\rm{potential}}}}}}\,{{{{{\rm{vegetation}}}}}}}(x)+0.25\cdot {C}_{{{{{{\rm{potential}}}}}}\,{{{{{\rm{SOC}}}}}}}(x)-{C}_{{{{{{\rm{crop}}}}}}}(i)$$
(1)

where $${{C}}_{{{{{{\rm{potential}}}}}}\,{{{{{\rm{vegetation}}}}}}}(x)$$ and $${C}_{{{{{{\rm{potential}}}}}}\,{{{{{\rm{SOC}}}}}}}(x)$$ denote the potential natural carbon stocks in the vegetation and the soil in x, respectively, and $${C}_{{{{{{\rm{crop}}}}}}}(i)$$ denotes the carbon stocks of crop i (all in Mg C ha−1). By design, the approach allows us to estimate the carbon impact of the conversion of natural habitat to cropland regardless of whether an area is currently cultivated or not.

In our analysis, we did not consider greenhouse gas emissions from sources other than from land use change, including nitrous emissions from fertilised soils and methane emissions from rice paddies87. In contrast to the one-off land use change emissions considered here, those are ongoing emissions that incur continually in the production process. We would assume that the magnitude of these emissions in a scenario of redistribution of agricultural areas, in which the total production of each crop remains constant, is roughly similar to that associated with the current distribution of areas. We also did not consider emissions associated with transport; however, these have been shown to be small compared to other food chain emissions88 and poorly correlated with the distance travelled by agricultural products89.

### Biodiversity impact Bi(x)

Analogous to our approach for carbon, we estimated the biodiversity impact of crop production, Bi(x), in a 5-arc-minute grid cell as the difference between the local biodiversity associated with the natural habitat and that associated with cropland. For our main analysis, we quantified local biodiversity in terms of range rarity (given by the sum of inverse species range sizes; see below) of mammals, birds, and amphibians. Range rarity has been advocated as a biodiversity measure particularly relevant to conservation planning in general39,90,91,92,93 and the protection of endemic species in particular39. In a supplementary analysis, we additionally considered biodiversity in terms of species richness.

We used 5-arc-minute global maps of the range rarity and species richness of mammals, birds, and amphibians under potential natural vegetation (Supplementary Fig. 1c, d) and under cropland land cover94. The methodology used to generate these data38 combines species-specific extents of occurrence (spatial envelopes of species’ outermost geographic limits40) and habitat preferences (lists of land cover categories in which species can live95), both available for all mammals, birds, and amphibians96,97, with a global map of potential natural biomes44 in order to estimate which species would be present in a grid cell for natural habitat conditions. Incorporating information on species’ ability to live in croplands, included in the habitat preferences, allows for determining the species that would, and those that would not, tolerate a local conversion of natural habitat to cropland. The species richness impact of crop production in a grid cell is then obtained as the number of species estimated to be locally lost when natural habitat is converted to cropland. Instead of weighing all species equally, the range rarity impact in a grid cell is calculated as the sum of the inverse potential natural range sizes of the species locally lost when natural habitat is converted; thus, increased weight is attributed to range-restricted species, which tend to be at higher extinction risk40,41.

As in the case of carbon, the approach allows us to estimate the biodiversity impact of crop production in both currently cultivated and uncultivated areas.

### Land potentially available for agriculture, V(x)

We defined the area V(x) (ha) potentially available for crop production in a given grid cell x, as the area not currently covered by water bodies42, land unsuitable due to soil and terrain constraints42, built-up land (urban areas, infrastructure, roads)1, pasture lands1, crops not considered in our analysis37, or protected areas42 (Supplementary Fig. 1e). In the scenario of a partial relocation of crop production, in which a proportion of existing croplands is not moved, the relevant retained areas are additionally subtracted from the potentially available area, as described further below.

### Optimal transnational relocation

We first consider the scenario in which all current croplands are relocated across national borders based on current climate (Fig. 3a, dark blue line). For each crop i and each grid cell x, we determined the local (i.e., grid-cell-specific) area $${\widehat{H}}_{i}(x)$$ (ha) on which crop i is grown in cell x so that the total production of each crop i equals the current production and the environmental impact is minimal. Denoting by

$${\bar{P}}_{i}={\sum }_{x}{P}_{i}(x)$$
(2)

the current global production of crop i, any solution $${\widehat{H}}_{i}(x)$$ must satisfy the equality constraints

$${\sum }_{x}{\widehat{H}}_{i}(x)\cdot {\widehat{Y}}_{i}(x)={\bar{P}}_{{{{{{\rm{i}}}}}}}\,{{{{{\rm{for}}}}}}\quad{{{{{\rm{each}}}}}}\,{{{{{\rm{crop}}}}}}\,i$$
(3)

requiring the total production of each individual crop after relocation to be equal to the current one. A solution must also satisfy the inequality constraints

$${\sum }_{i}{\widehat{H}}_{i}(x)\le V(x)\,{{{{{\rm{for}}}}}}\quad{{{{{\rm{each}}}}}}\,{{{{{\rm{grid}}}}}}\,{{{{{\rm{cell}}}}}}\,x\,,$$
(4)

ensuring that the local sum of cropping areas is not larger than the locally available area V(x) (see above). Given these constraints, we can identify the global configuration of croplands that minimises the associated total carbon or biodiversity impact by minimising the objective function

$${\sum }_{x}{\widehat{H}}_{i}(x)\cdot {C}_{i}(x)\to \,{{\min }}\quad{{{{{\rm{or}}}}}}\quad{\sum }_{x}{\widehat{H}}_{i}(x)\cdot {B}_{i}(x)\to \,{{\min }}$$
(5)

respectively. More generally, we can minimise a combined carbon and biodiversity impact measure, and examine potential trade-offs between minimising each of the two impacts, by considering the weighted objective function

$${\sum }_{x}{\widehat{H}}_{i}(x)\cdot (\alpha \cdot {C}_{i}(x)+(1-\alpha )\cdot {B}_{i}(x))\to \,{{\min }}$$
(6)

where the weighting parameter α ranges between 0 and 1.

Considering all crops across all grid cells, we denote by

$$\bar{C}={\sum }_{i}{\sum }_{x}{H}_{i}(x)\cdot {C}_{i}(x)$$
(7)

the global carbon impact associated with the current distribution of croplands, and by

$$\hat{C}(\alpha )={\sum }_{i}{\sum }_{x}{\hat{H}}_{i}(x)\cdot {C}_{i}(x)$$
(8)

the global carbon impact associated with the optimal distribution $${\{{\widehat{H}}_{i}(x)\}}_{i,x}(={\{{\widehat{H}}_{i}^{\alpha }(x)\}}_{i,x})$$ of croplands for some carbon-biodiversity weighting $$\alpha \in [0,1]$$. The relative change between the current and the optimal carbon impact is then given by

$$\hat{c}(\alpha )=100 \% \cdot \frac{\hat{C}(\alpha )-\bar{C}}{\bar{C}}$$
(9)

Using analogous notation, the relative change between the current and the optimal global biodiversity impact across all crops and grid cells is given by

$$\widehat{b}(\alpha )=100 \% \cdot \frac{\widehat{B}(\alpha )-\bar{B}}{\bar{B}}$$
(10)

The dark blue line in Fig. 3a visualises $$\widehat{c}(\alpha )$$ and $$\widehat{b}(\alpha )$$ for the full range of carbon-biodiversity weightings $$\alpha \in [0,1]$$, each of which corresponds to a specific optimal distribution $${\{{\widehat{H}}_{i}(x)\}}_{i,x}$$ of croplands. We defined an optimal weighting $${\alpha }_{{{{{{\rm{opt}}}}}}}$$, meant to represent a scenario in which the trade-off between minimising the total carbon impact and minimising the total biodiversity impact is as small as possible. Such a weighting is necessarily subjective; here, we defined it as

$${\alpha }_{{{{{{\rm{opt}}}}}}}={{\arg }}\,{{{\min }}}_{\alpha \in [0,1]}\left|\begin{array}{ll}\frac{\frac{\partial {\hat{c}}(\alpha)} {\partial {\hat{b}}(\alpha)}}{\hat{c}(\alpha)} \cdot \frac{\frac{\partial {\hat{b}}(\alpha)} {\partial {\hat{c}}(\alpha)}}{\hat{b}(\alpha)}\end{array}\right|$$
(11)

Each of the two factors on the right-hand side represents the relative rate of change in the reduction of one impact type with respect to the change in the reduction of the other one as α varies. Thus, αopt represents the weighting at which neither impact type can be further reduced by varying α without increasing the relative impact of the other by at least the same amount. Scenarios based on this optimal weighting are shown in Figs. 1,  2, and Supplementary Figs. 36, and are represented by the black markers in Fig. 3.

Our approach does not account for multiple cropping; i.e., part of a grid cell is not allocated to more than one crop, and the assumed annual yield is based on a single harvest. Allowing for multiple crops to be successively planted in the same location during a growing period would increase the dimensionality of the optimisation problem substantially. However, given that only 5% of current global rainfed areas are under multiple cropping98, this is likely not a strong limitation of our rainfed-based analysis. As a result of this approach, our results may even slightly underestimate local crop production potential and therefore global impact reduction potentials.

### Optimal national relocation

In the case of areas being relocated within national borders, the mathematical framework is identical with the exception that the sum over relevant grid cells x in Eqs. (2) and (4) is taken over the cells that define the given country of interest, instead of the whole world. In this way, the total production of each crop within each country for optimally distributed croplands is the same as for current areas. The optimisation problem is then solved independently for each country.

### Optimal partial relocation

When (either for national or transnational relocation) only a certain proportion $$\lambda \in [0,1]$$ of the production of each crop (of a country or the world) is being relocated rather than the total production, Eq. (3) changes to

$$\mathop{\sum}\limits_{x}{\widehat{H}}_{i}(x)\cdot {\widehat{Y}}_{i}(x)=\lambda \cdot {\bar{P}}_{i}\,{{{{{\rm{for}}}}}}\,{{{{{\rm{each}}}}}}\,{{{{{\rm{crop}}}}}}\,i\,.$$
(12)

In addition, the area potentially available for new croplands, V(x), (see above) is reduced by the area that remains occupied by current croplands accounting for the proportion $$(1-\lambda )$$ of production that is not being relocated. We denote by $${H}_{i}^{\lambda }(x)$$ the area that continues to be used for the production of crop i in grid cell x in the scenario where the proportion λ of the production is being optimally redistributed. In particular, $${H}_{i}^{0}(x)={H}_{i}(x)$$ and $${H}_{i}^{1}(x)=0$$ for all i and x. For a given carbon-biodiversity weighting $$\alpha \in [0,1]$$ in Eq. (6), $${H}_{i}^{\lambda }(x)$$ is calculated as follows. First, all grid cells in which crop i is currently grown are ordered according to their agro-environmental efficiency, i.e., the grid-cell-specific ratio between the environmental impact attributed to the production of the crop and the local production,

$${E}_{i}^{\alpha }(x)=\frac{{H}_{i}(x)\cdot (\alpha \cdot {C}_{i}(x)+(1-\alpha )\cdot {B}_{i}(x))}{{P}_{i}(x)}.$$
(13)

Let $${x}_{1}(={x}_{1}(i,\alpha ))$$ denote the index of the grid cell in which crop i is currently grow for which $${E}_{i}^{\alpha }$$ is smallest among all grid cells in which the crop is grown. Then let x2 be the index for which $${E}_{i}^{\alpha }$$ is second smallest (or equal to the smallest), and so on. Thus, the vector $$({x}_{1},{x}_{2},{x}_{3},\ldots )$$ contains all indices of grid cells where crop i is currently grown in descending order of agro-environmental efficiency. The area $${H}_{i}^{\lambda }({x}_{n})$$ retained in some grid cell $${x}_{n}$$ is then given by

$${H}_{i}^{\lambda }({x}_{n})=\left\{\begin{array}{ll}{H}_{i}({x}_{n}) & {{{{{\rm{if}}}}}}\;\mathop{\sum }\limits_{m=1}^{n}{P}_{i}({x}_{m})\le (1-\lambda )\cdot {\bar{P}}_{i}\\ 0\, & \hskip-7.5pc{{{{{\rm{else}}}}}}\end{array}\right.$$
(14)

Thus, cropping areas in a grid cell $${x}_{n}$$ are retained if they are amongst the most agro-environmentally efficient ones of crop i on which the combined production does not exceed $$(1-\lambda )\cdot {\bar{P}}_{i}$$ (which is not being relocated). Growing areas in the remaining, less agro-environmental efficient grid cells are abandoned and become potentially available for other relocated crops. Note that $${H}_{i}^{\lambda }$$ depends on the weighting α of carbon against biodiversity impacts. Finally, instead of Eq. (4), we have, in the case of the partial relocation of the proportion λ of the total production,

$$\mathop{\sum}\limits_{i}{\widehat{H}}_{i}(x)\le V(x)-{H}_{i}^{\lambda }(x)\quad{{{{{\rm{for}}}}}}\,{{{{{\rm{each}}}}}}\,{{{{{\rm{grid}}}}}}\,{{{{{\rm{cell}}}}}}\,x\,.$$
(15)

### Solving the optimisation problem

All datasets needed in the optimisation (i.e., $$A(x)$$, $${P}_{i}(x)$$, $${H}_{i}(x)$$, $${C}_{i}(x)$$, $${B}_{i}(x)$$, $${\widehat{Y}}_{i}(x)$$, $$V(x)$$) are available at a 5 arc-minute (0.083°) resolution; however, computational constraints required us to upscale these to a 20-arc-minute grid (0.33°) spatial grid. At this resolution, Eq. (6) defines a 1.12 × 106-dimensional linear optimisation problem in the scenario of across-border relocation. The high dimensionality of the problem is in part due to the requirement in Eq. (3) that the individual production level of each crop is maintained. Requiring instead that, for example, only the total caloric production is maintained31,99 reduces Eq. (6) to a 1-dimensional problem. However, in such a scenario, the production of individual crops, and therefore of macro- and micronutrients, would generally be very different from current levels, implicitly assuming potentially drastic dietary shifts that may not be nutritionally or culturally realistic.

The optimisation problem in Eq. (6) was solved using the dual-simplex algorithm in the function linprog of the Matlab R2021b Optimization Toolbox100 for a termination tolerance on the dual feasibility of 10−7 and a feasibility tolerance for constraints of 10−4.

In the case of a transnational relocation of crop production, the algorithm always converged to the optimal solution, i.e., for all crop management levels, climate scenarios, and proportions of production that were being relocated. For the relocation within national borders, this was not always the case. This is because some countries produce small quantities of crops which, according to the GAEZ v4 potential yield estimates, could not be grown in the relevant quantities anywhere in the country under natural climatic conditions and for rainfed water supply; these crops likely require greenhouse cultivation or irrigation can therefore not be successfully relocated within our framework. Across all countries, this was the case for production occurring on 0.6% of all croplands. When this was the case for a certain country and crop, we excluded the crop from the optimisation routine, and a country’s total carbon and biodiversity impacts were calculated as the sum of the impacts of optimally relocated crops plus the current impacts of non-relocatable crops.

This issue is linked to why determining the optimal distribution of croplands within national borders is not a well-defined problem for future climatic conditions. Under current climatic conditions, if a crop cannot be relocated within our framework, then its current distribution offers a fall-back solution that provides the current production level and allows us to quantify environmental impacts. Different climatic conditions in the future mean that the production of a crop across current growing locations will not be the same as it is today, and therefore the fall-back solution available for the present is no longer available, so that a consistent quantification of the environmental impacts of a non-relocatable crop is not possible.

### Carbon and biodiversity recovery trajectories

Our analysis in Supplementary Fig. 6 requires spatially explicit estimates of the carbon recovery trajectory on abandoned croplands. Whilst carbon and biodiversity regeneration have been shown to follow certain general patterns, recovery is context-specific (Supplementary Note 1) in that, depending on local conditions, the regeneration in a specific location can take place at slower or faster speeds than would typically be the case in the broader ecoregion. Here, we assumed that these caveats can be accommodated by using conservative estimates of recovery times and by assuming that local factors will average out at the spatial resolution of our analysis. The carbon recovery times assumed here are based on ecosystem-specific estimates of the time required for abandoned agricultural areas to retain pre-disturbance carbon stocks82. Aiming for a conservative approach, we assumed carbon recovery times equal to at least three times these estimates, rounded up to the nearest quarter century (Table 3). Independent empirical estimates from specific sites and from meta-analyses are well within these time scales (Supplementary Note 1).

Applying the values in Table 3 to a global map of potential natural biomes44 provides a map of carbon recovery times. We assumed a square root-shaped carbon recovery trajectory across these regeneration periods101; similar trajectories, sometimes modelled by faster-converging exponential functions, have been identified in other studies25,27,30,102,103,104,105. Thus, the carbon stocks in an area of a grid cell x previously used to grow crop i were assumed to regenerate according to the function

$$\left\{\begin{array}{ll}{{C}}_{{{{{{\rm{agricultural}}}}}}}(x)+\sqrt{\frac{t}{{{T}}_{{{{{{\rm{carbon}}}}}}}(x)}}\cdot ({{C}}_{{{{{{\rm{potential}}}}}}}(x)-{{C}}_{{{{{{\rm{agricultural}}}}}}}(x)) & {{{{{\rm{if}}}}}}\,t \; < \; {{T}}_{{{{{{\rm{carbon}}}}}}}\\ \hskip14.7pc{{C}}_{{{{{{\rm{potential}}}}}}}(x) & {{{{{\rm{if}}}}}}\,t\ge {{T}}_{{{{{{\rm{carbon}}}}}}}\end{array}\right.$$
(16)

where, using the same notation as further above

$${{C}}_{{{{{{\rm{potential}}}}}}}(x) ={{C}}_{{{{{{\rm{potential}}}}}}\,{{{{{\rm{vegetation}}}}}}}(x)+{{C}}_{{{{{{\rm{potential}}}}}}\,{{{{{\rm{SOC}}}}}}}(x)\\ {{C}}_{{{{{{\rm{agricultural}}}}}}}(x) ={{C}}_{i}(x)+0.75\cdot {{C}}_{{{{{{\rm{potential}}}}}}\,{{{{{\rm{SOC}}}}}}}(x)$$
(17)

### Reporting summary

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