C-LLAMA v1.0: a traceable model for food, agriculture and land-use

We present C-LLAMA 1.0 (Country-level Land Availability Model for Agriculture), a statistical-empirical model of the global food and agriculture system. Based on the FALAFEL (Flux Assessment of Linked Agricultural Food production, Energy potentials & Land-use change) model, C-LLAMA aims to address the need for an open and transparent approach to 10 modelling the sensitivity of future agricultural land-use to drivers such as diet, crop yields and food-system efficiency. CLLAMA uses publicly available FAOSTAT data to make linear projections of diet, food system and agricultural efficiencies, and land-use at a national level, aiming to capture aspects of food systems in both developing and developed nations. In this paper we describe the structure and processes within the model and perform sensitivity analyses of key components.

Table 1 lists all the modules responsible for model processes in C-LLAMA, grouped into model sections. There is some overlap between the model-processes; the sections and model-process modules listed here are not necessarily in the order that they 65 appear in C-LLAMA, some sections are re-visited at later stages of the model. The first section of the model produces a food supply at a national level, disaggregated into calories and commodities.
The model operates across five continents: Africa, the Americas, Asia, Europe and Oceania, C-LLAMA then splits these into further subcontinental regions (for example, the Americas are split into N. America, S. America, Central America and the Caribbean), most of which contain several countries or states. The model is structured into the following four spatial 70 aggregations: global, continent, region, and country, aligning with the United Nations Statistics Division (UNSD), with each model process operating at one of these levels.
https://doi.org/10.5194/gmd-2021-169 Preprint. Discussion started: 13 July 2021 c Author(s) 2021. CC BY 4.0 License. as a default but any population projection data can be applied. The population data is interpolated linearly to produce a yearly population trajectory to 2050.

Food supply
We define food supply for a given country to be the mean number of kilocalories used per capita per day in a given year. This includes any post-production food waste; some food reaches consumers but is never eaten, either commercially or as domestic 105 waste. The proportion of food wasted in this way is as high as 30% in most developed countries (Alexander et al., 2017).
FAOSTAT food balance sheets contain food supply data disaggregated into different food commodities (Food and Agriculture Organization of the United Nations, 1997). C-LLAMA uses this data to produce a projected food demand for each country.
First, the generous goal of an ample westernised diet for everyone is set: an assumed 2500 kcal food intake per day per capita, with an additional 28% wasted, giving an idealised food supply of 3200 kcal (Kearney, 2010;Alexander et al., 2017;Parfitt et 110 al., 2010). A linear projection is made for each country from their current food supply to the idealised food supply in a given year, using the following equation: where is the food supply in year , target is the idealised food supply per capita, 0 is the mean of the most recent five years of historical food supply data. 0 and target are the starting year of the projection and the chosen year to reach the idealised 115 food supply, set at 2100 by default. Values of target beyond 2050 mean that the idealised food supply is not reached during the modelled time period.
Secondly, a linear regression is used to make a projection for the calorie supply from each of the food groups animal products, vegetal products, and aquatic products. Regression lines with a p-value greater than 0.05 are discounted (this threshold value can be changed), instead fixing the projection at the mean value of the most recent five years of data. These projections are 120 then converted into fractions. The proportion of food supply ( ) made up by group in year , is given by where and are the gradient and intercept of the regression line for that group and is the set of groups: animal, vegetal and aquatic products.
Third, the same process is applied to individual food commodities within the three food groups. Key food commodities are 125 represented individually, for example wheat, maize and rice in the vegetal product group, and bovine meat and poultry meat in the animal product group. Other commodities are represented in groups, for example 'cereals -other' contains all cereals that are not singled out as key commodities, while the 'luxuries' group contains all tea, coffee, and alcohol. Aquatic products are not the focus of the model as they have minimal to no land requirements during their production; thus they are placed in a single group. Hence, in C-LLAMA, aquatic products simply offset some of the calorific demand from the other food groups. 130 Where possible, C-LLAMA uses vegetal product groups defined in FAOSTAT data. A full list of food commodities and https://doi.org/10.5194/gmd-2021-169 Preprint. Discussion started: 13 July 2021 c Author(s) 2021. CC BY 4.0 License. groupings can be found in Appendix A. The commodities within a group are then converted into ratios, so the proportional calorific contribution of commodity to its umbrella food group in year is where and are the gradient and intercept respectively of the regression line for that commodity and is the set of 135 commodities within the group, for example if is wheat then would be all vegetal products. The structure of the projected food supply is then as follows: the total calorie projection is apportioned to each of the food groups by their projected ratios, which are in turn apportioned to the projected commodity ratios. Hence by combining equations 1, 2 and 3, the number of calories contributed to the mean daily food supply per capita by commodity (of group ) is where all symbols have their previously defined meanings. This approach facilitates the tuning of dietary scenarios by modifying the growth rate of the animal product group or dairy commodities to simulate increases in vegetarianism or veganism.

Agricultural industrialisation parameter 145
There is significant variation in food-system efficiency, both at different stages and between developed and developing food systems. To reflect this in C-LLAMA, a parameter was developed to assign areas an appropriate degree of efficiency at each stage of the food system and in the model processes. The requirements of the system are the following: 1. Allow the food system efficiency of states to improve as the model progresses. 2. Limit improvement to a realistic maximum. 150 3. Be representative of most real-world cases. Outliers are inevitable but significant contributors of food demand or food production to the global food system should be captured well.
A highly developed nation in which the majority of farming practices are heavily industrialised with high levels of efficiency should have a score of greater than 1.0 whilst a less developed country in which the majority of people are fed through subsistence farming should score lower than 0.5. A metric such as GDP per capita is not suitable, because a state with extreme 155 income equality could score highly when in actuality the majority of inhabitants rely on subsistence agriculture. Other metrics such as irrigation, fertiliser use and agricultural machinery density were all considered. However, each of these metrics can be skewed by climate, crop types and traditional practices. As such these are also not always reflective of the relative agricultural efficiency of an area.
A parameter was developed based on the yearly mean of daily food energy consumption per capita. This is a self-moderating 160 quantity: unlike GDP there is a maximum realistic value that this can take regardless of economic disparity, so the mean cannot be skewed by extreme cases. The equation for the agricultural industrialisation parameter for a country in year is where is the country's total food supply in year and target is the idealised food supply defined in section 4.1. Using the ratio of food supply to an idealised food supply generates values in the approximate range 0.5 to 1.2. The values 0.5 and 0.7 165 scale the metric to produce values for in the range 0.0 and 1.0.
This parameter is then projected forward with a simple linear projection to 2050 for use in the model processes. In the very few cases where the projection prescribes a decline in industrialisation, the parameter is halted at the most recent historic value.
In the majority of cases this parameter reasonably depicts the position of a country along a scale between complete subsistence agriculture to complete agricultural industrialisation. However, due to the complexity of the real-world food system, there are 170 a small number of expected outliers, notably Japan and the Republic of South Korea, both of which score in the range 0.4 to 0.6, much lower than expected given their level of industrialisation. This can be explained by a combination of two factors: a slightly lower post-production food waste of around 15% (Liu et al., 2016) and typically a lower daily calorific intake than other similarly industrialised nations; a result of cultural and dietary trends (Tsugane and Sawada, 2014).
The parameter is used in the model processes to inform processes relating to agricultural efficiency, including food energy 175 losses at three stages: harvest, distribution, and post-production losses. Minimum and maximum values are chosen for each, representing either the totally subsistence or total industrialised case, and the metric is used to scale the value for a country between the two. The equation for a factor is: where is the value of the agricultural industrialisation parameter for the country in given year and sub and ind are the 180 subsistence or industrialisation boundaries of the factor respectively. The upper and lower boundaries for each of these parameters can be modified as a means of scenario adjustment. The behaviour of the boundaries as the model progresses can also be modified; they can be fixed at the initial values, or an overall efficiency increase can be prescribed, in which case the limits will also change over time.

Inefficiency in the food system 185
In C-LLAMA, losses in the food system are grouped in four ways: losses at the harvest stage, losses in the processing stage, distribution losses and post-production losses.
Losses at the harvest stage occur before any processing or distribution and are either non-recoverable or recoverable. Causes of non-recoverable losses include insect and animal pests, weeds, and disease. Developing regions see greater losses during production than developed regions due to the availability of disease and pest prevention measures (Oerke and Dehne, 2004;190 Savary et al., 2012). Losses due to these factors are accounted for in crop-yield data so no loss factor is applied at this stage.
The methodology for handling recoverable harvest losses: 'harvest residues', is more complicated since these are crop dependant. Not all harvested material is edible for humans, for example the husks and casings or `chaff' produced when harvesting grains. The formalisation of this concept is the harvest index, defined as the ratio of the mass of useful product to the mass of above ground biomass (Singh and Stoskopf, 1971). Despite being an inefficiency in the food system, many waste 195 products produced at the harvest stage can be used for other purposes to reduce this inefficiency. Chaff for example, while https://doi.org/10.5194/gmd-2021-169 Preprint. Discussion started: 13 July 2021 c Author(s) 2021. CC BY 4.0 License.
inedible to humans, is suitable feed for most livestock. Harvest residue indices and harvest residue recovery rates are used to inform a ratio of produced residue to recovered residue (Wirsenius et al., 2010;Krausmann et al., 2008). Tables of harvest residue indices and recovery rates can be found in appendix A.
Processing losses occur as the raw crops are processed to a form suitable for their intended purposes, for example the removal 200 of kernels from olives. Some of these losses are potentially recoverable for use as animal feed, bioenergy feedstock or in other industries (Van Dyk et al, 2013). Fodder crops generally incur less loss than crops destined for human consumption at the processing stage as they require little to no processing (Kitinoja, 2013;Gustavsson and Cederberg, 2011).
Distribution losses are incurred through transportation or storage. This stage is a major contributor to food system inefficiency in developing countries; due to poor road infrastructure, pests and lack of suitable refrigeration or other storage, losses at this 205 stage can be as high as 50% and as low as 5% in developing and developed areas respectively (Parfitt et al., 2010;Lipinski et al., 2013).
Post-production food waste refers to food lost at the consumer level, including food thrown away after purchase in the home, or in commercial environments such as restaurants. Unlike most other food system loss factors, the heaviest post-production losses are seen in the developed world (Parfitt et al., 2010;Stancu et al, 2016). 210

Production
Following the application of the loss factors determined in the food system efficiency section to the food supply projections described in section 4.1, each country is left with a food energy requirement for each food commodity, , calculated using the 215 following equation: where is the energy demand from a country for commodity , is a loss factor and is the set of processing, distribution, and post-processing losses. is the calorific contribution to the country food supply from commodity , described in section 4.1. The food energy lost due to efficiency loss factors is retained for potential re-use as livestock feed. Food demand is then 220 summed globally for each key commodity or commodity group is, so the global production requirement for the commodity where is the food energy demand for commodity from a country , and is the set of all countries. proportions of production for each crop commodity are calculated using the most recent five years of production data then allocated accordingly. For example, the USA was responsible for 42% of global wheat production between 2012 and 2017, thus 42% of all wheat production in C-LLAMA is allocated to the USA. Following this process, each nation is left with a production allocation for each key commodity and commodity group, the equation for which is where is the allocated production energy of commodity in the country , is the mean of the most recent five years of historical production mass of commodity in country and is the set of all countries.

Crop yield
A large proportion of yield variation can be explained by climate variability, with the remainder being a result of farming practices and industrialisation Ray et al., 2015). C-LLAMA takes largely the same approach as 235 FALAFEL; historical yields for each crop and group are projected linearly to 2050, but this is done for each country. Yield has the potential for large transient variation on a year by year basis, often a result of climate events, pests or management (Frieler et al., 2017;Ray et al., 2015). Consequently, there is the possibility of yields increasing at an unrealistically high rate through this kind of projection. To address this, in C-LLAMA yields are capped at the historical maximum value for a region, preventing any region from exceeding an observed value whilst allowing each country within a region to catch up to a localised 240 observed maximum. Linear projections with a p-value greater than 0.05 (this threshold can be changed) or a decreasing yield are discarded. In either of these cases, the mean yield from the previous ten years of data is used instead.
For all key crops the raw yield data, in tonnes per hectare per year, was used to make the projection. In the case of grouped crops, the groups yield was calculated by taking mean of all crops contained in the group, weighted by national production mass. The group 'sugar crop' consists almost entirely of sugar beet since sugar cane is represented as an individual crop. For 245 palm oil, vegetable oils and other oil crops, an effective oil yield was calculated for each using their respective oil factors which can be found in the FAOSTAT database (Food and Agriculture Organization of the United Nations, 1997).

Livestock
Animal product demand is the highest contributor to agricultural land demand and greenhouse gas emissions globally and as such livestock are a crucial component of the C-LLAMA model (Van Zanten et al., 2018;Pikaar et al., 2018). As with vegetal 250 food commodities, livestock commodities are partially grouped, with major commodities: bovine meat, pig meat, mutton/goat meat and poultry meat remaining separate. The remaining meat products contribute comparably little to the global demand for animal products and are grouped into an 'other meat' category. Eggs, dairy and fish are each in their own groups. For each country, an animal commodity demand is produced per year in the diet and food supply section of the model. As is well established, livestock are inherently less resource efficient than vegetal products as a means of providing calories for human consumption. The feed consumed by livestock does not go directly to become fresh animal product, instead much of it supports the survival of the animal. This is commonly quantified as a feed conversion ratio (FCR) or livestock conversion efficiency (LCE), expressed as the quantity of feed energy or mass to fresh animal product mass or equivalent energy. This number varies drastically between animal product types: bovine meat has an energy FCR of approximately 3%, whereas poultry meat is much higher at 21% (Shepon et al., 2016). Note that these FCRs are produced from data acquired in the USA. Currently the values 260 used in C-LLAMA are taken from FALAFEL; a cohesive energy-equivalent FCR dataset was not found at a regional or country level. FCRs certainly do vary regionally, largely due to the different role of livestock in different food systems. A cow in a subsistence agriculture environment is more likely to be allowed to live to substantial age, providing dairy and driving machinery. This contrasts with a cow in industrialised agriculture, where it might be reared solely for meat and slaughtered in early adulthood (Wirsenius et al., 2010). A proportion of livestock feed demand is met through forage ( forage ) and the 265 remainder is met through feed and residues ( non-forage ). The proportion of demand met with fodder and residues (z) is calculated using the agricultural industrialisation parameter to assign a value between the subsistence case and the industrialised case, using the same method as in Eq. (6). The quantity of feed demand energy from non-forage for animal product in country where FCR is the livestock dependant feed conversion ratio and is the production allocation. The extreme cases for each animal product are centred around the FALAFEL numbers, with the developing limit being 20% lower and the developed limit being 20% higher. The proportion also varies dependant on the animal product, for example chickens and pigs typically obtain a higher proportion of their food energy from feed than ruminants (Tufarelli et al., 2018). An individual animal will likely be fed through a combination of forage and feed, but for the purpose of the model the assumption is made that the land footprint 275 of non-forage comes only from the land required for fodder crops. This approach is coarse compared with modelling livestock as entities with individual mixed feed demands, however the feed energy requirements are comparable.

Waste and residues as feed
In some situations, livestock can utilise waste from the agricultural system, processing losses, post-production food waste and harvest residues. For each livestock commodity a potential feed ratio for each of these waste streams is estimated: the maximum 280 proportion of each waste type that could contribute to the livestock diet (z). These ratios can be found in appendix A. Waste produced by processing, distribution and post-production are calculated at the country of consumption, while harvest residues are calculated at the crop production stage. Post-production waste is assumed to only be available to animals in the area in which it was produced and is informed by a post-production waste to feed factor ( post ), scaled by the agricultural industrialisation parameter using Eq. (6) between 40% and 5% for the subsistence and industrialised cases respectively. Note 285 that in the case of post-production waste the subsistence extreme is 'more efficient' than the industrialised case. The remaining total available waste energy is multiplied by an other waste to feed factor ( other ), again informed by the agricultural https://doi.org/10.5194/gmd-2021-169 Preprint. Discussion started: 13 July 2021 c Author(s) 2021. CC BY 4.0 License.
industrialisation parameter using Eq. (6), with the subsistence and industrialised limits being 15% and 40% respectively. These numbers are taken from the low and high efficiency scenarios in FALAFEL. Waste energy is 'fed' to livestock, up to the potential feed ratio limit, allocated by the potential feed ratios (z). The energy used is then subtracted from the livestock feed 290 energy demand, the remainder of which is accounted for with fodder crops. The remaining feed energy demand to be met through fodder crops ( ′) is where is the total feed energy demand, is the maximum portion of feed energy that livestock can obtain from waste 295 stream , is the available waste energy and is the waste to feed factor. C is the set of all livestock commodities and is the set of all waste streams: post-production, processing, and harvest residues. is post for post-production waste and other for all other waste streams.

Fodder
Following the reduction of livestock feed demand through waste to feed and foraging, the remaining feed energy demand is 300 met with fodder crops. The historical fodder mix, the ratio of each crop making up fodder in a country, is calculated using the most recent five years of 'feed' energy data in the FAOSTAT food balance sheets. The cereals contributing the most to the fodder mix globally are maize, wheat, sorghum, barley and rice. In addition, soybeans, potatoes, cassava, pulses and fruits also contribute in the top ten. Each of these products are represented individually while all other products used as feed are grouped as 'other feed'. Around 8% of the total feed mass each year comes from non-crop products. The majority of this 8% is milk 305 and the remainder is largely comprised of aquatic products such as fishmeal and aquatic plants, often added to livestock feed to supplement nutrition (Holman and Malau-Aduli, 2013;Oliveira Vieira et al., 2015). These products are removed from the fodder mix, as these products require minimal additional land. The remaining livestock feed demand is split according to the derived fodder mix, so the contribution to the total fodder requirement ( ) in country from fodder product is where is the five year mean of feed data for fodder product from the FAOSTAT food balance sheets, milk and aq are the feed data for milk products and aquatic products respectively, is the set of all fodder products. ′ is the fodder demand for livestock commodity , is the set of all livestock commodities. The global production requirement for fodder product is In the same way as crop production for food, the fodder crop production demand is allocated based on historical production of the fodder products. The production allocation ( ) for fodder product for country is https://doi.org/10.5194/gmd-2021-169 Preprint. Discussion started: 13 July 2021 c Author(s) 2021. CC BY 4.0 License.
where is the five year mean production mass for fodder product and is the set of all countries. In the case where the product has been considered as a food commodity and thus a yield and production allocation has already been calculated, the 320 additional production allocation for fodder is simply added to the nations existing production quota of the commodity for food.
In some cases, it is necessary to perform a yield projection in the same manner as described in section 4.3. Following this stage, each country has a production quota for each year for each commodity, used for food, animal feed, or both, along with a corresponding yield trajectory.

Crop land use
Combing national crop yield projections and production allocation produces a yearly land demand trajectory for each crop within a given country. Since the model objective is to explore sensitivities rather than absolute land-use values, land-use is projected from the most recent value in the FAOSTAT data. In the case that total land demand for crops is less than the previous year, the land difference between the years is put into a 'freed land' class. In FALAFEL this land is then used for either 330 afforestation or energy crops, while C-LLAMA does not currently process this further. In reality land use change is multidimensional; the abandonment of agricultural land varies greatly between areas and industrialisation levels, influenced by climate, land productivity, tradition and governance (Lambin and Meyfroidt, 2011;Lambin et al., 2003). C-LLAMA currently does not consider non-agricultural land use. Further development to include more complex handling of land-use is intended. 335

Livestock land use
As mentioned in section 4.4, the land requirements for livestock in C-LLAMA come entirely from their pasture area; the implication being that all fodder fed animals are under roof, while their foraging counterparts graze pasture. This is generally not the case for foraging pigs and chickens, so a pasture factor ( ) of 0.1 is applied to reduce their land footprint from that of cows and sheep (Tufarelli et al., 2018). 340 The land used for livestock pasture is calculated using an effective pasture yield. First, the historical energy obtained from pasture by livestock was estimated using a similar process to the method adopted in Haberl (2007); for each country, available feed is subtracted from a livestock feed demand, calculated using historical production energy and feed conversion ratios. This leaves animal food acquired through forage. Dividing this quantity by land-area used for pasture in a given year results in the historical effective pasture yieldanimal product energy produced per hectare of pasture. The historical effective pasture yield 345 ( ) for animal products in country is where pasture is the country's pasture land area, is the production mass of an animal product , FCR is the feed conversion ratio for the animal product and is the set of animal products. is the quantity of available feed product and is the set of all feed products. The historical trajectory is linearly projected to 2050, then combined with the production mass demand for 350 each livestock commodity. As with crop land-use, the trajectory is scaled to the most recent FAOSTAT value for each country.
Instead of scaling the land-use however, the effective pasture yield is scaled. The scaling is calibrated to an anchor scenario described in section 5 to address counter-intuitive model behaviour, discussed in appendix C. This method is coarse but offers a catch-all method of translating a production demand into land-area for every country in C-LLAMA.

Model output 355
C-LLAMA produces a land-use trajectory to 2050 for each food commodity and commodity group within a country, output as a comma separated variable file. Animal product land-use is aggregated as pasture, explained in section 4.4. All crops have individual land-use trajectories. An output with crops aggregated into either crops or specifically fodder crops is also produced.
Data from intermediate stages of the model such as food supply and crop yield projections is retained upon completion of the model run, but for the sake of storage space is stored in a serialised format using the 'pickle' library, part of the Python standard 360 library (Van Rossum and Drake Jr, 1995).

Anchor Scenario
C-LLAMA is based around an anchor scenario, in which all parameters take default values based on literature and projections from historical data are made to 2050. This scenario aims to be as close an approximation to the real world as possible in the framework of the model, with targets for efficiency and industrialisation being set at middle of road values. Table B1 in

Comparison with FALAFEL
The globally summed land-use output of the C-LLAMA anchor scenario can be compared with the land-use trajectory of an analogous business as usual scenario produced in FALAFEL. In the same way as C-LLAMA, the FALAFEL model allows prescribed increases in efficiencyfor example a forced reduction in animal product consumption. To produce the business 395 as usual scenario in FALAFEL, linear projections are made where they are available and all prescribed efficiency changes are turned off. For comparison, the land-use data from both models is grouped into pasture, food crops (for human consumption), and fodder crops. The resulting land-use for both modelled scenarios is shown in Fig. 6. The trajectory of both the FALAFEL scenario and the C-LLAMA anchor scenario reach just over 5 Gha by around 2050. The difference in starting food crop area is indistinguishable between the models, however a small amount of additional growth occurs by 2050 in C-LLAMA. C-400 LLAMA starts with a greater area of fodder crops but sees less growth by 2050 than in FALAFEL. The largest difference lies https://doi.org/10.5194/gmd-2021-169 Preprint. Discussion started: 13 July 2021 c Author(s) 2021. CC BY 4.0 License.
in pasture, with C-LLAMA starting at just over 3 Gha and FALAFEL starting at around 2.6 Gha, although both models have approximately 3.5 Gha of pasture by 2050. Figure 6. Aggregated global land-use for food production in the C-LLAMA anchor scenario and a 'business as usual' 405 (BAU) FALAFEL scenario. FALAFEL accounts for the production of some non-food crops, however they are excluded for this comparative figure.
A comparison of the global diet projections for both the C-LLAMA anchor scenario and the FALAFEL business as usual scenario is shown in Fig. 7. The difference between the two scenarios is slight; in C-LLAMA fish contributes slightly more to the average diet than in FALAFEL, with animal products in general also contributing slightly more by 2050.

Sensitivity
Four key projections are made throughout the course of the model for each country. Diet and crop yields are projected directly 415 from the historical data, whereas the agricultural industrialisation parameter and effective pasture yield are internal values calculated from historical data, which are then projected. To explore the sensitivity of the final land-use output of C-LLAMA to these four projections, each was fixed at the mean value of their most recent five years and the land-use by 2050 compared with the anchor scenario. The results of this are shown in Fig. 8.  The impacts of each of these projections are within an order of magnitude of each other. Halting the projection of crop yields results in an increased agricultural land-use of just over 100 Mha from the anchor scenario. This is consistent with the current trend of increasing crop yields in most areas of the world: a result of improved access to irrigation, agrochemicals and 425 machinery (Iizumi et al., 2017;Ray et al., 2012). Suspending the projection of the agricultural industrialisation metric has the greatest impact on the total land-use with an increase of approximately 450 Mha. Suspending the agricultural industrialisation metric locks many countries in a state of lower efficiency, unable to meet the increasing food demand from the growing population. Halting changes in pasture yield leads to an increase in land-use of around 150 Mha. While the 'effective pasture yield' is not a real-world quantity, it aims to capture a wide range of factors that govern the output of grazed land. This quantity 430 is increasing in the majority of countries, the result of livestock intensification by transfer to more intensive pasture or a covered system (Thornton, 2010;Davis and D'Odorico, 2015). Stopping the projection of dietary trends reduces the final land-use by 50 Mha. Current global dietary trends are toward increased animal product consumption in developing countries and stagnation of animal product consumption in developed nations (Van Zanten et al., 2018;Tilman and Clark, 2014). Coupled with the prescribed trajectory toward an idealised diet, leading to an increase in calorific intake in the majority of countries, this explains 435 the decrease in land-use when suspending the projection of diet. Loss factors in C-LLAMA are dynamic, governed by the agricultural industrialisation metric. To explore the sensitivity of the model to loss factors every country was fixed at the lower and upper boundary values, equivalent to scoring every country at 0.0 or 1.0 respectively on the agricultural industrialisation metric. Figure 9 shows the results of this analysis. An increase in efficiency leads to a land-use reduction of approximately 900 Mha by 2050, and a decrease in efficiency leads to a drastic 440 increase of just under 3000 Mha by 2050. The present efficiency scenario is achieved by halting the agricultural industrialisation parameter, identical to the 'indust param' scenario in Fig. 8. The greater sensitivity to decreased efficiency is a result of the distribution of agricultural industrialisation scores: more countries score higher than 0.5 than lower, hence setting all countries to 0.0 is a greater 'shift' than setting all countries to 1.0. The magnitude of these changes is significantly larger than those seen in Fig. 8. 445

Limitations
The strength of C-LLAMA lies in its simplicity: it can be easily modified, adapted, and improved. However, there are limitations to the approach and two key areas for improvement have been identified. One area with scope for improvement is in the allocation of crop and livestock production described in section 4.3. The current method uses a snapshot of current production to distribute the projected production of a crop; this approach works for earlier projected years since interannual 455 changes to trade are relatively slow, being on similar timescales to changes in demand. However, long term changes to global trade are not captured, specifically those likely to arise from improved access to wealth and subsequent demand for luxury and animal products in developing countries. Improvements might include trade matrices for each food commodity, or projection of the commodity production allocation, which would allow dynamic trade representation without the need for any agent based or economically driven modelling. The other area with great potential for improvement is the representation of livestock and, 460 more broadly, land-use within the model. The current method for estimating land-use for crops and livestock is effective for exploring questions surrounding global-scale changes and scenario options. However, a land class system with productivity, land-use transitions, and associated carbon exchange would facilitate a more nuanced exploration of the drivers of land-use and their consequences, particularly in the case of livestock, forests, and grasslands.
Including the DRC, Libya, Sudan, Somalia, and Papua New Guinea would be beneficial as together they account for a 465 significant portion of the global land area (approximately 3%). Papua New Guinea and the DRC have humid, equatorial climates with highly productive land; excellent conditions for agricultural productivity (Kottek et al.;2006). While not included in the food balance data, they are present in other FAO data, so it may be possible to construct an approximate food balance dataset from their available FAO data and regional averages. Another approach would be to construct food balances using other data sources, however this approach would contravene the internal consistency of C-LLAMA. 470

Applications
C-LLAMA takes a simple approach to modelling the drivers of land availability, offering transparency and adaptability where many other, more complex modelling approaches do not. Of the many drivers of future land-availability, the simplicity and traceability of the model make it well placed to explore the impacts of broad scale drivers such as changes in livestock production systems, crop yields, dietary trends and food system efficiency on the future of land available for food agriculture,  Table A2. Animal products and groups. In the case of these animal products, the 'individual' animal products represent a small group of products but are dominated by a single product. For example while bovine meat includes derivative products and buffalo, the majority of the bovine meat supply and consumption is formed of cattle meat. There are only two sets of grouped animal products: dairy and 'other meat'. Dairy is a significant contributor to global food supply and demand, but meat products not listed individually do not. Dairy includes milk, butter, ghee and cream. Products 490 such as cheese and yoghurt are also included in the data for milk.

Individual products
Grouped products Post-production waste to feed 0.40 0.05 Low and high efficiency scenarios in FALAFEL. (Powell, 2015) Other waste to feed 0.15 0.40

Appendix C
Counter-intuitive behaviour arises when setting the proportion of animals fed through fodder and residues (fed without forage -FWF) to extreme values. Decreasing the FWF factor (more animals are fed through pasture) leads to an increase in land-use 505 by 2050. This is expected, as pasture is typically far less land-efficient than housed animals fed through fodder and residues (Pikaar et al., 2018). However, this trend does not continue when the FWF is increased, instead an increased land-use is observed. The behaviour of the FWF prompted further investigation; the factor was scaled by a range of values between 0.5 and 1.5 to observe the behaviour around the default values (a scaling of 1.0), the global agricultural land-use values for which are shown in Fig. C1. 510 Inspection of the land-use for pasture, fodder and food crops revealed that food crop land-use was constant as expected since only animal product production methods are being varied. Fodder crop land-use also behaved as expectedincreasing with 515 FWF, as more fodder crops must be produced to meet the feed demand of animals not produced on pasture. However, pasture did not behave as expected, instead following the same trend as the global land-use, with an increased land-use when varying the FWF factor in either direction. The cause of this behaviour has been identified as the scaling method applied to pasture https://doi.org/10.5194/gmd-2021-169 Preprint. Discussion started: 13 July 2021 c Author(s) 2021. CC BY 4.0 License. land area. When the scaling is turned off, variations in the FWF factor lead to expected behaviour: global land use decreases as FWF increases. The effective pasture yield is calculated using the projected 2017 land-use value before any scaling is 520 applied. When FWF is increased the quantity of animal products produced on pasture decreases, including the 2017 value, however the historical pasture area remains unchanged. The result is an artificial decrease in effective pasture yield as FWF increases when the scaling is applied, as shown in Fig. C2. To resolve this and any similar anomalies arising from scaling methods, the effective pasture yield is now scaled based on the projection pasture area in the anchor scenario, regardless of the scenario parameters. This can introduce minor discrepancies in the early years of the projection when setting factors to a fixed value, but this is not the normal mode of operation for the model. This sensitivity test varied the FWF factor for the entire projection, including the starting values, where in normal 530 model operation any changes to this factor would be applied as a gradual deviation from the normal value. For example the scaling might vary from 1.0 in 2017 to 1.5 in 2050, as opposed to being 1.5 from the start as in this sensitivity analysis.