The OLUM

The OLUM (Optimal Land Use Model)16 is a linear programming (LP) model that includes a suite of organic farming activities that take place in nine Robust Farm Types: specialist cropping, mixed arable and livestock, specialist dairy, lowland grazing livestock, Less Favoured Area (LFA) grazing livestock, pigs and poultry, and other. These cover the entire agricultural land-base in England and Wales. The Objective Function of the model, which is maximised subject to constraints on resource availabilities, is the sum of total crop and livestock production, expressed as ME. Although human diets also need proteins, fats and nutrients, energy requirements are deemed to be a primary driver of consumption and an inadequate food-energy intake is almost always accompanied by insufficient intake of nutrients37.

The basic formulation of the OLUM is

$$Z = \mathop {\sum}

olimits_{{ij} = 0}^{n} {C_{{ij}} \cdot x_{{ij}}\,{\mathrm{subject}}\,{\mathrm{to}}\,Rx_{{ij}} \le {\mathbf{b}},x_{{ij}} \ge 0},$$ (1)

where \(Z\) is the objective function to be maximised, C ij is the ME output (fresh weight per unit crop area or livestock number yr−1) of agricultural product i on soil × rain class j, x ij is a scalar for the agricultural activity (crop area or livestock number), Rx ij is a factor for the input and resource requirement associated with the agricultural activity, and b is a vector for resource endowment and input availability (e.g., land by soil and rainfall class, and available soil N). Human dietary change is not considered.

In each farm type, the set of crop and livestock production activities available are fixed, as evidence suggests that the dominant agricultural activity (e.g., dairy farming) will usually stay in place post conversion to organic management, due to existing farm infrastructure, farming knowledge and local conditions43. However, these activities can be individually expanded and contracted endogenously. The land areas under each farm type are fixed, reflecting the areal coverage of their conventional equivalents recorded in the June Survey of Agriculture in 201044. A number of logical constraints are applied in the model to reflect: the availability of land in the various soil/rainfall classes (next paragraph); maximum permissible area of crop groups (e.g., cereals, root crops) reflecting rotational constraints; and upper limits on the total output of each crop, set at 150% of the current supply, following an assumption that further increases could not be absorbed by the market. Rotational N availability limits are also imposed, as determined by crop and livestock-product offtake (from the land), N supply from various sources, such as biological fixation, imported feed and atmospheric deposition, as well as manure-N availability in each region. We assume balances of P and K are maintained by applying P and K minerals commonly used in organic systems. Livestock numbers and associated product output volumes are constrained by feed availability, as well as maximum and minimum stocking density constraints.

Heavy, medium, light and humose soil classes are defined with specified organic matter contents and pH values, and their spatial distribution across England and Wales in 5 km × 5 km grid squares were obtained from the National Soil Inventory (www.LandIS.org.uk). Four rainfall classes are defined based on 30-year Meteorological Office annual rainfall data: dry 539–635 mm, medium 636–723 mm, wet 724–823 mm and very wet 824–2500 mm. The total areas of each soil × rainfall combination were determined by identifying the dominant combination in each 5 km × 5 km grid square and allocating to that combination the sum of the areas of each square, less any non-agricultural area.

The OLUM produces a best estimate of production under fully organic agriculture in England and Wales, assuming that food production would be maximised. To ensure that the results are reasonable, outputs are compared to the real-world distribution of conventional production in 2010 derived from a range of industry sources (Supplementary Table 4), and to results from a previous study on the production impacts of a switch to organic farming in England and Wales15.

The Agri-LCA models

We assessed the environmental impacts of conversion to organic farming using the Cranfield Agri-LCA models for England and Wales3. Fossil energy use and emissions of CO 2 , CH 4 and N 2 O per tonne of each food commodity produced under given soil and management conditions are combined with official data on levels of production, to provide estimates of the total GHG impact of agriculture. Results from earlier emissions analyses generated by these models for the current mix of agricultural systems in England and Wales are used as a comparator against which to assess the organic conversion scenario. We adjust the following components of the Agri-LCA models to better reflect organic agriculture using data sources listed in Supplementary Table 4: first, crop and grassland yields; second, crop cultivation practices and manure/compost application rates; third, crop and grassland areas by soil and rainfall type; fourth, livestock productivity and mortality rates; and fifth, livestock diet compositions.

Crop yield, cultivation and manure application data are adjusted for 12 main crops: wheat, barley, rye, oats, potatoes, oilseed rape, sugar beet, beans and peas, cabbage, carrots, onions and forage maize. These cover 98% of the cultivated land in England and Wales44. All data sources used in this exercise are provided in Supplementary Table 4. Crop and grassland areas under each of 16 soil and rainfall classes are derived from the OLUM results. The crop areas, by each soil and rainfall class, are used in the Agri-LCA models to adjust N 2 O and CO 2 impacts to reflect organic management. The functional units used in the LCA are tonnes of marketed crop-product.

Organic animal production data for the Agri-LCA are drawn from a range of industry sources to define, by livestock type: daily live-weight gain, annual fat-corrected milk yield, and feed conversion ratios. Data are also input to the Agri-LCA on the composition of livestock diets, stocking rates per hectare and the proportion of livestock on upland and lowland. These values ensure that feed intake meets the ME demand of livestock. Nitrogen excretion from livestock is derived from mass balances. Compound feed composition data are also applied to determine embedded impacts of feed production overseas. Direct CH 4 emissions from livestock are calculated as a function of dry matter intake (scaled in proportion to the forage dry matter intake), live-weight and milk yields. The Agri-LCA livestock emissions estimates are based on six commodities: eggs, milk, sheep, beef, pig and poultry meat. Meat outputs are defined in terms of total dressed carcass weight (tonnes), eggs by weight (tonnes) and milk output as fat-corrected litres3.

System boundaries and allocation of environmental burdens

The downstream system boundary applied in the Agri-LCA modelling is the farm gate, i.e., only resources consumed during the production of inputs and on-farm-based processes are considered (i.e., ‘from cradle to farm gate’2). The GHG emissions associated with downstream activities—such as distribution, consumption and disposal of products produced on the farm—are not included. Some on-farm processing, such as grain drying, milk cooling and potato storage, are included in the total impact assessment, as these operations are considered to be part of the on-farm production process3. Where multiple products are derived from the same agricultural activity, such as grain and straw from cereals production, the GHG emissions from fossil energy use associated with the different components are allocated on the basis of relative economic value and by system expansion with regard to manure (i.e., the manufactured N fertiliser avoided is discounted from the environmental burdens associated with non-organic crops). Where economic allocation is used in the Agri-LCA, an organic price differential is applied. Emission factors are derived from IPCC 2006 estimates and total emissions of CH 4 and N 2 O converted to CO 2 equivalents using their 100-year Global Warming Potentials (GWPs). The time-dependency of the GWP values introduces some uncertainty, particularly for CH 4 which has a 20-year GWP more than twice its 100-year value. However, allowing for this would introduce undue complexity. The emissions associated with animal feed production are allocated to the livestock emission estimates, not those for crop production.

Imports and exports

The GHG emissions associated with producing imported food are allowed for in the Agri-LCA models. We assume that any shortfall in supply from organic agriculture is made up by increased imports of organically produced commodities from overseas. We use data from industry sources (Supplementary Table 5) to allocate imported product to the historic regions of origin of imports45. The GHG emissions associated with the transport of imports to England and Wales is determined by multiplying the total volume of imported products by GHG coefficients derived from Hess et al.45. Transport burdens for imported sugar and sheep meat are derived from Plassman et al.46 and Webb et al.23, respectively.

Where the OLUM generates crop and livestock production in excess of domestic demand, the surpluses are assumed to be exported and the GHG and fossil energy burdens associated with production of the exported commodities are subtracted from the total environmental burdens of organic agriculture. The same adjustment is made to the GHG estimates of exports for conventional agriculture (see data sources for export volumes in Supplementary Table 5). Where the OLUM reduces production below the level of domestic demand it is assumed that no exports occur, i.e., domestic consumption would take priority.

Fossil energy use and GHG emissions associated with the production of oilseed rape, sugar beet, wheat and lamb from non-European countries are derived from Pelletier et al.47, Tzilivakis et al.48 and Webb et al.23. The environmental burdens associated with crop and livestock products sourced from Scotland, Northern Ireland and the rest of Europe are derived from the Agri-LCA, under the assumption that similar emissions and fossil energy use would occur in these systems3.

Soil carbon sequestration

We obtain an upper estimate of potential sequestration rates in organic systems based on rates of change of soil C measured in the National Soil Inventory (NSI) of England and Wales49, as follows. Kirk and Bellamy28 summarised the NSI results by fitting to the data the simple single-pool model

$$dC/dt = I - kC,$$ (2)

where C is the C content per unit land surface area, I is the rate of input from vegetation and other sources and k is a rate constant for decomposition. They fitted Eq. (2) to the data for each NSI land use class separately, omitting organic soils (which accounted for <5% of all the soils in the NSI) because their rates of change were less certain. The soil C content at steady state, when dC/dt = 0, is equal to I/k. Soils with C contents greater than the steady-state value lose C; those with C contents less than it sequester C.

We take the NSI class ‘rotational grass’ (i.e., grass that is sown and then tilled every few years as part of an arable rotation) to represent potential C contents under ideal organic management, and the class ‘arable’ to represent C contents under conventional arable management. The mean soil C contents were 43.2 (n = 552 sites) and 58.7 (n = 301 sites) Mg C ha−1 under arable and rotational grass, respectively, and the calculated steady-state C contents were 37.6 and 55.0 Mg C ha−1, respectively, indicating the rotational grass soils were on average close to steady state and their C contents therefore represent maximum potential sequestration levels. The values of I and k for rotational grass were 2.54 Mg C ha−1 yr−1 and 0.046 yr−1, respectively (equivalent to negative emissions of −9.3 and −0.17 Mg CO 2 ha−1 yr−1). Substituting these values and the mean arable C content in Eq. (2) gives for the mean rate of sequestration on conversion from arable to rotational grass ((2.54 − 0.046 × 43.2) + 0)/2 = 0.28 Mg C ha−1 yr−1 (or −1.03 Mg CO 2 ha−1 yr−1). After adjusting for the proportion of arable to arable plus rotational grass, the rate is 0.28 × 552/(552 + 301)=0.18 Mg C ha−1 yr−1 (or 0.66 Mg CO 2 ha−1 yr−1). We use this as the high C sequestration rate in Fig. 3. We assume sequestration rates in established swards of permanent pasture or rough grazing to be zero given that these sites will have already reached steady state.

For comparison, in a literature survey of experiments comparing conventional and organic farming, Gattinger et al.24 found sequestration rates between 0.07 and 0.45 Mg C ha−1. However, most of these comparisons involved very high rates of external organic matter inputs to the organic systems. The average inputs were four times those under conventional farming for the full dataset and two times for systems with inputs equivalent to those from one European Livestock Unit (ELU) ha−1 26. We calculate that quantities of farmyard manure would be only approximately 12% greater under organic farming, as a result of greater numbers of grazing livestock (Supplementary Table 3). We therefore consider Gattinger et al.’s upper and middle sequestration estimates to be unrepresentative and take as the moderate sequestration rate in Fig. 3 their lower value of 0.07 Mg C ha−1 yr−1.

Gains through C sequestration will be time-limited, because any given soil has a finite capacity to accumulate C and a new steady-state C content will be reached after a few years, when increased C inputs are matched by increased losses at the greater soil C content. Our estimated sequestration rates therefore only apply in the early-years following conversion to organic methods. Based on the NSI data, a new steady-state C content on conversion from arable to rotational grass would only be attained after (55.02 − 43.15)/0.28 = 42 years.

Additional emissions from overseas LUC and C sequestration

We estimate the additional overseas land area required for each of the food products listed in Fig. 1, produced organically, as follows. For crops, we use first, regional yield data from Eurostat, second, organic crop yields from the recent meta-analysis by de Ponti et al.32 and third, results of an LCA for milling wheat grown in Canada47. For livestock, we use first, regional yield data from Eurostat, second, results from the Agri-LCA3 and third, recent studies on the environmental burdens of imported lamb from New Zealand23,50. The additional land area is calculated from the total overseas area required less the amount required for imports in the conventional baseline (based on the values in Supplementary Table 6). The corresponding emissions are calculated as follows.

We assume that woodland would not be converted for food production as this would conflict with the principles of the International Federation of Organic Agriculture Movements (IFOAM)51. We calculate emissions from the conversion of grassland to crops from the area converted multiplied by LUC emission estimates specified by the British Standards Institute for a range of countries52. Considering that not all the LUC would be from grassland, we compare three ways of assessing the net emissions from overseas LUC and associated soil C sequestration, plus that of home production, as follows. First, High: all the additional land required is converted from grassland, with no net soil C sequestration at home or overseas. Second, Medium: 50% of the additional arable land is converted from grassland, with a moderate rate of C sequestration (0.07 Mg C ha−1 yr−1) at home and overseas. Third, Low: 25% of the additional arable land is converted from grassland, with a high rate of C sequestration (0.18 Mg C ha−1 yr−1) at home and overseas.

Following Searchinger et al.35, we also calculate the additional ‘carbon opportunity cost’ (COC) of using the land for agriculture as the quantity of C that could be sequestered annually if the average productive capacity of land used to produce 1 kg of each food product globally were instead devoted to regenerating forest. We calculate the total COC from Searchinger et al.’s35 COC factors per unit fresh weight of each food product (separating crops for human consumption from those used as animal feeds) multiplied by the additional fresh weight imports of each product required to offset home production shortfalls. This is in addition to the emissions calculated under the LUC and C sequestration scenarios (1)–(3) above. This ‘C gain’ method—as opposed to a ‘C loss’ method based on plant and soil C lost to date per unit food production—applies if it is only possible to increase C by re-establishing forests.

Uncertainty analysis

Estimates of uncertainty for each main commodity analysed were produced following the method of Wiltshire et al.53. Uncertainties were derived using Monte Carlo simulations with each domestically produced crop commodity given an uncertainty estimate of 10% (i.e., in a triangular distribution with upper and lower bounds at 10% of the mean) and each domestically produced livestock commodity at 15%. The emissions for crops and livestock were summed in separate Monte Carlo simulations to produce overall uncertainty estimates for each sector (as the standard deviation). These were increased by 15% for all imported commodities en bloc. Emissions from import transportation were assumed to have a standard deviation of 10% of the mean53, i.e., the coefficient of variation (CV) is 10%. The areas of land derived by the LP were assumed to have an error of 15%, which was applied to the whole solution, not per crop, given that all areas were derived from any individual solution. Error bars on production area per crop (or livestock commodity) are thus not shown.

The final emissions and uncertainty estimates for each production system were derived from the sum of emissions from domestically produced crops and livestock together with emissions from imported crop and livestock production, together with their transport emissions, based on supply chain data from Webb et al. (2013)23 and Williams et al. (2017)54. Estimates of the uncertainty from LUC were derived from Houghton55 and those from C sequestration from Kirk and Bellamy28 for the upper rate and from Gattinger et al.24 for the medium and lowest rates. These were implemented as the uncertainty being a proportion of the means that were applied to the LUC and C sequestration scenarios. These were established as having a CV of 17% for LUC55, which was increased for the carbon opportunity cost of Searchinger et al.35 by a factor of 1.5 to allow for the extra uncertainty of the method (i.e., CV of 26%). The uncertainty of the high level of C sequestration was 86 and 24% for lower levels.

The uncertainty estimates for the sum of crop and livestock commodities, transport and land use change emissions and sequestration are summarised in Supplementary Table 7. These were used as input values of uncertainties in the last stage to derive the overall uncertainties of each scenario. We tested the significance of differences in mean values, z, using Eq. (3)53

$$z = \frac{{\left| {m_A - m_B} \right|}}{{\sqrt {CV_A^2 \times m_A^2 + CV_B^2 \times m_B^2} }} \times 100,$$ (3)

where m A and m B are the means of systems A and B, respectively, and CV is the CV of each mean (expressed as whole numbers). The threshold for a significant difference at the 5% level was z ≥ 1.96.

Reporting summary

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