Global land use implications of dietary trends

Global food security and agricultural land management represent two urgent and intimately related challenges that humans must face. We quantify the changes in the global agricultural land footprint if the world were to adhere to the dietary guidelines put forth by the United States Department of Agriculture (USDA), while accounting for the land use change incurred by import/export required to meet those guidelines. We analyze data at country, continental, and global levels. USDA guidelines are viewed as an improvement on the current land-intensive diet of the average American, but despite this our results show that global adherence to the guidelines would require 1 gigahectare of additional land—roughly the size of Canada—under current agricultural practice. The results also show a strong divide between Eastern and Western hemispheres, with many Western hemisphere countries showing net land sparing under a USDA guideline diet, while many Eastern hemisphere countries show net land use increase under a USDA guideline diet. We conclude that national dietary guidelines should be developed using not just health but also global land use and equity as criteria. Because global lands are a limited resource, national dietary guidelines also need to be coordinated internationally, in much the same way greenhouse gas emissions are increasingly coordinated.

We aim to extend the traditional definition of crop yield to apply to livestock products. In the context of crops, if p is the quantity produced, and a is the area of land used to produce the quantity p, then yield y is defined as In the remainder of this section we use the following labels: i denotes an animal product (e.g. cattle meat, milk, etc.), j denotes an animal meat product (e.g. cattle meat), k denotes a non-meat animal product (i.e. milk, eggs), and l denotes a crop (e.g. maize, oats, etc.).

Production
The FAO reports annual data for country, sub-continent, continent, and global-level production of various livestock products. Let us denote this quantity by p i where i labels a given animal product (e.g. cattle meat).

Adjusting production for import and export of live animals
At any scale smaller than the global one (e.g. country-level), the concept of production can be defined in several ways. For example, we may define production simply as p i ; that is, the quantity reported to have been produced in a given country. But consider production of cattle meat for a moment. In some cases it may be useful to regard exports of live cattle as contributing to a country's actual beef production. After all, the country used land to produce the cattle that was exported and so should be considered in the calculation of yield. If we let N (E) j denote the number of live animals exported of the type that produce a meat product j, and we let m j denote the average carcass weight, then we can define an adjusted meat production p (E) j to be On the other hand, suppose a given country imports a number N (I) j of animals that are slaughtered for meat. Then we should subtract this meat from the country's overall production because they did not use their own land to produce it. That is, we define another adjusted production p (IE) j to be This definition assumes that all imported animals are slaughtered for meat within the year in which the trade is reported.
Adjusting production for culling of dairy/egg animals Finally, there are cases when we would like to exclude meat produced from the culling of dairy or egg animals. If we denote culling rate by r k of dairy or egg animals labeled by k (e.g. dairy cattle) but of the same type that produce a meat product j (e.g. meat cattle), then the adjusted production p (IEC) j : where N k is the number of producing dairy or egg animals in a given year. This definition of production is useful when determining the amount of feed required to produce a given quantity of meat since the feed given to these culled animals was primarily used for milk or egg production.
The methods we used to estimate r k is differ for dairy and egg animals. Let us define the following quantities: N (t) is the stock of live animals (e.g. cattle) reported by a given country for the year t; I (t) and E (t) are the number of imported and exported live animals respectively; D (t) =N (t) +I (t) -E (t) is the number of domestic live animals; S (t) is the number of animals slaughtered for meat; P (t) is the number of animals producing milk or eggs.

Culling rate for dairy animals
The lifespan of typical dairy animals (e.g. cows) is greater than one year, which is the time resolution of the FAO data. For cattle, the number of animals not slaughtered is D (t) -S (t) . Thus, we estimate the number of cattle derived from cattle births from the previous year is The number of animals born into the dairy sector is assumed to be in the same proportion as the number of dairy animals relative to the domestic animal population. That is, the number of new dairy animals is given by Thus, the number of dairy animals in a given year that were present in the previous year is given by Finally, this implies that the number of dairy animals culled in a given year is given by so the culling rate is To check the validity of this method we can use the United States as an example. Our method gives average cull rate of 0.35 for U.S. dairy cattle, which is in excellent agreement with the value of 0.36 reported by the USDA 1 . Also, as the slaughter of cattle is forbidden in many states in India, we should expect a low culling rate there 2 . We find an average culling rate for dairy cattle in India of about 0.04.

Culling rate for egg-laying animals
The method to estimate the culling rate of egg-laying animals (e.g. hens) differs from that for dairy animals because, although the lifespan of egg-laying animals is typically longer than one year, that of a meat bird is typically much less than a year. In this case, we define the cumulative stock to be the sum of the number of animals slaughtered and the following year's stock: Then the number of new births in a given year is and number of animals born into the egg sector is Then the number of egg-laying animals in a given year that remain from the previous year is Finally, this implies that the number of egg-laying animals culled in a given year is given by so the cull rate is Again, we can check the method's results against what might be expected from known practices in the United States. There, and in much of the developed world, egg-laying hens are typically slaughtered at less than two years of age 3 . Thus, if we assume uniform age distribution, we expect a culling rate greater than 0.5 but less than one. For the U.S. we find an average culling rate for egg-laying hens of about 0.8. Moreover, we find a smaller culling rate in developing countries, where replacement hens may be less available and/or not economically viable.

Dividing production into pastoral and mixed/landless production
For ruminants, we used estimates of the quantity produced in both the pastoral and mixed/landless agricultural systems at the sub-continent level 4 . Using a quadratic interpolant on the relative production in these two systems, we divide the production p i of ruminant animal products into two parts: production in the pastoral system p (P) i , p (P,E) i , p (P,IE) i , p (P,IEC) i , and production in the mixed/landless system p (ML) In the event that production data is missing from the FAOSTAT for a given country and year, we estimate the production to be the same as that in either the next or previous year in which production data was reported. If no such data can be found, we assume that the production is zero.

Land area used for meat production
The land used to produce animal products is divided into two parts: pasture area and cropland used to produce feed.

Ruminant production and pasture area
Ruminant livestock such as cattle and sheep require pasture for their production. Data for the total pasture area A P used for agricultural production is provided in the FAOSTAT database at the country, sub-continent, continent and global levels. If no such data can be found, we assume that the pasture area is 69% (world average) of the country's agricultural area. To determine the pasture area required to produce a given product (e.g. cattle meat) in a given country, we first divided the pasture area into two parts: pasture area in the pastoral system, and pasture area in the mixed/landless system, denoted by A (P) and A (ML) respectively. This was done using a quadratic interpolant on estimates of grass land areas in these two agricultural systems in the corresponding sub-continent 4 .
Next, let us denote the stocks of animal i in livestock units by U i where i labels one of the following animals: meat cattle, dairy cattle, meat buffalo, dairy buffalo, horses, asses, mules, meat sheep, dairy sheep, meat goats, meat camels, dairy camels, and camelids 5 . The stocks of meat animals is defined to be the total number of animals minus the number of dairy or egg animals, where applicable. We further divided those stocks into parts found in the pastoral and mixed/landless systems, denoted by U (P) i and U (ML) i respectively. The latter was again done using a quadratic interpolant on estimates of the proportions of each livestock population that is in either production system in the corresponding sub-continent. The proportions were inferred from the production, carcass weight/production per animal, and off-take rates in each production system 4 . Then the area of pasture in the mixed/landless system assigned to an animal n is the total area of pasture in the mixed/landless system times the fraction of all livestock units represented by meat cattle. That is, the pasture area in the pastoral and mixed/landless system assigned to the production of an animal product i is given by

Cropland area used for feed
Ruminant livestock in the mixed/landless system as well as non-ruminant livestock, including pigs and chickens, consume feed. This feed can be composed of grasses (for ruminants), crop residues and food crops. The land required to produce the grasses used in ruminant feed is already accounted for in the pasture area. We regard the land used to produce the residue portion of feed to be zero since that land was primarily used for a different purpose (e.g. crop production). Thus, here we are interested in the area of cropland used to produce the proportion of feed represented by food crops.
Bouwman et al. give estimates of the feed conversion rate r (f) i at the sub-continent level for a given animal product labeled by i; that is, the number of units of feed (dry matter) required to produce one unit of the animal product 4 . They also give estimates of the proportion of feed f i represented by food crops for a given animal product. Using a quadratic interpolant on these data we can estimate the quantity of food crops required to produce a unit of the animal product by p (ML,IEC) i f i r (f) i . However, we do not use this value, which for the moment we will call the unnormalized feed quantity, for the feed quantity because we do not have a reliable way to convert dry matter to harvest weight, the latter of which is reported in the FAOSTAT database, and we could not find any data on the time dependence of feed composition 6 . Instead, for a given animal product i, we estimated the proportion p i of the total available feed quantity that is assigned to the production of that product to be the proportion of the total feed quantity represented by the animal product i. That is, For any given crop the quantity of that crop in a country's supply that is available for livestock feed is reported in the commodity balances of the FAOSTAT database. Let Q j denote the quantity of crop labeled by j assigned to feed. Data for the country's production P j , imports I j and exports E j of a crop j are given in the FAOSTAT database, which can be used to determine the country's self-sufficiency ratio s j for that crop, Then the quantity of that feed q ij that is assigned to the production of a given animal product i is given by The factor s j accounts for the fact that land is not required to produce feed that imported by a given country. Finally, the yield y j of crop j is given in the FAOSTAT database, so the area of cropland required to produce the amount of that crop that was produced domestically for feed that was used to produce the animal product i is given by In the event that there is insufficient data in the FAOSTAT database to complete the calculation for a given country and year, we estimate the area to be the same as that in either the next or previous year in which sufficient data was reported.

Yield
With the above definitions, calculating the yield y i of an animal product in the sense of production per hectare of land used is straightforward.
1) Africa dataset. Graphical representation of Africa showing the amount of land spared or required in total to meet the recommendations in the Dietary Guidelines for Americans 2010. The red depicts the amount of land spared or required domestically while the blue line combines domestic land and displaced land to depict a total amount of land spared overall. A negative surplus is to be interpreted as a deficit, meaning that the country would need more food from that group to follow the guidelines.