Three aspects of this paper are novel relative to prior work. First, the study focuses at the scale of the conterminous U.S. To our knowledge, such an analysis of how dietary change might impact land use and carrying capacity has not been conducted at this scale. Second, the “Foodprint model” (described below) estimates land requirements for complete diets, accounting for three important interactions: the multiuse nature of certain grain and oilseed crops, the suitability of multiple land types to grazing, and the relationship between dairy production and beef production. Finally, the study explores how assumptions about the partitioning of agricultural land and the suitability of cropland for cultivated crops influences estimates of carrying capacity.

The purpose of this analysis is to compare the per capita land requirements and potential carrying capacity of the land base of the continental United States (U.S.) under a diverse set of dietary scenarios. We argue that assessing human carrying capacity (persons fed per unit land area) is essential for fully understanding current and potential productivity of a land base. Estimates of carrying capacity represent the productive output of many crops grown across a heterogeneous land base in a single indicator, the number of people fed. While trade will remain essential to national food security in many countries, the purpose behind the closed system approach was to conduct a complete accounting of all land needed to meet total food needs and, thus, calculate carrying capacity.

The second lesson is cautionary. While livestock production is the largest land user on Earth, simplistic thinking about dietary change must be avoided ( Herrero and Thornton, 2013 ). Reviews of life cycle assessments of livestock systems and protein products show, definitively, that land use per unit of protein is generally lower with plant than animal sources ( de Vries and de Boer, 2010 ; Nijdam et al., 2012 ). However, they also demonstrate a wide range among individual livestock products and among different systems producing the same livestock product. In addition to this variability in area of land required, the quality of land required differs as well. Modeling studies suggest that the largest fraction of land needs for ruminant animals are from forages and grazing lands ( Wirsenius et al., 2010 ; Peters et al., 2014 ), which are often grown on non-arable land. Thus, reducing the most land-intensive products in the diet does not necessarily equate to freeing up land for cultivation. Finally, the land needs for producing animals do not always follow linear patterns, and can change rapidly when supplies of residual forage ( Keyzer et al., 2005 ) or oilseed byproducts ( Elferink et al., 2008 ) have been exhausted. When it comes to interpreting the land impacts of dietary change, caution is warranted.

A variety of approaches, each with its own limitations, have been applied to determine how dietary choices influence land use. No single method is definitive. Economic models project future demands for food commodities and account for competing sectors ( van Tongeren et al. 2001 ), but may not adequately capture supply side constraints ( Heistermann et al., 2006 ). Life cycle assessments can allocate the environmental impact of individual foods, but the approach faces methodological challenges and data limitations to modeling complete diets ( Heller et al., 2013 ). A variety of bio-physical approaches exist to estimate the land requirements of food consumption patterns (see, for example, Gerbens-Leenes et al., 2002 ; Peters et al., 2007 ; Wirsenius et al., 2010 ), yet this field is sufficiently young that comparison of the merits of each approach has not yet been assessed. Hoekstra and Wiedmann (2014) posit that “cross-fertilization” among different environmental footprint approaches will ultimately lead to more consistent frameworks. In other words, a melding of the best parts of each approach will occur over time. In the meantime, it is perhaps best to focus on what has been learned from attempts to understand the relationship between diet and land use.

This line of thinking is not new. The equation I=PAT, conceived in the 1970s, proposes that environmental impact is a function of population, affluence, and technology ( Parris and Kates, 2003 ). Calls for considering the environmental impacts of food consumption through changes in diet were made decades ago both in popular ( Lappé, 1971 ) and academic literature ( Gussow and Clancy, 1986 ). However, for most of the 20th Century the predominant agricultural science paradigm focused on increasing yield and production efficiency, expanding in the 1980s and 1990s to include ecological impacts of farming but not focusing on food systems ( Welch and Graham, 1999 ). Likewise, nutritional sciences and dietary advice over most of the past century have been guided almost exclusively by evidence on the relationships among nutrients, foods, diets and human health ( King, 2007 ). If strategies for sustainability must address both food consumption and production, then analyses that link agriculture and nutrition are needed.

2. Materials and methods

2.1 Overview of the approach A biophysical simulation model (the U.S. Foodprint Model based on Peters et al., 2007) that represents the conterminous U.S. as a closed food system was designed to calculate the per capita land requirements of human diets and the potential population fed by the agricultural land base of the continental United States. To do this, three sets of calculations were performed (Fig. 1). The first set of calculations estimated the annual, per capita food needs of the population based on daily food intake, the individual food commodities that comprise each food group, the weight of a serving of food, losses and waste that occur across the food system, and the conversion of raw agricultural commodities into processed food commodities. The second set of calculations estimated the individual land area required for each agricultural commodity in the diet based on yield data for each component crop and the feed requirements of all livestock. The third set of calculations estimated the potential carrying capacity of U.S. agricultural land, accounting for the aggregate land requirements of a complete diet, the area of land available, and the suitability of land for different agricultural uses. At key points in these calculations, marked with an asterisk in the diagram, additional calculations were performed to account for interdependencies in the food system. A description of the primary calculations and data sources is described below, and additional detail is provided in the Supplementary material.

2.2 Scenarios of food consumption Ten distinct diet scenarios were analyzed in this study (Table 1). The scenarios focused solely on differences in food consumption patterns; parameters for food losses and waste, processing conversions, livestock feed needs, crop yields, land availability, and land suitability were held constant. The structure of the scenarios was designed to compare the land requirements and carrying capacity of nine isocaloric (equal caloric content) diets, eight of which are comparable in nutritional quality but which differ in terms of their protein sources. The tenth diet, representing current average food consumption, was included as a reference point. The relationship between the scenarios is described in more detail below. Group Description Name Symbol Key attributes Current consumption Based on USDA estimates of per capita loss-adjusted food availability. Baseline BAS Food intake equals loss-adjusted food availability for individual food commodities. Positive control POS As above, except intake of fats and sweeteners is reduced to make diet energy-balanced. Healthy diet, omnivorous Complies with 2010 Dietary Guidelines for Americans. Includes animal flesh. 100% healthy omnivorous OMNI 100 100% of person-meals follow an omnivorous healthy diet pattern. 80% healthy omnivorous OMNI 80 80% of person-meals follow an omnivorous healthy diet pattern and 20% follow a ovo-lacto vegetarian healthy diet pattern. 60% healthy omnivorous OMNI 60 60% of person-meals follow an omnivorous healthy diet pattern and 40% follow a ovo-lacto vegetarian healthy diet pattern. 40% healthy omnivorous OMNI 40 40% of person-meals follow an omnivorous healthy diet pattern and 60% follow a ovo-lacto vegetarian healthy diet pattern. 20% healthy omnivorous OMNI 20 20% of person-meals follow an omnivorous healthy diet pattern and 80% follow a ovo-lacto vegetarian healthy diet pattern. Healthy diet, vegetarian Complies with 2010 Dietary Guidelines for Americans. Excludes animal flesh. Ovolacto vegetarian OVO Includes both eggs and dairy products. Lacto vegetarian LAC Includes dairy products. Excludes eggs. Vegan VEG Excludes all livestock products. The reference diet (Baseline) reflects contemporary food consumption patterns based on loss-adjusted food availability data from 2006–2008 (USDA Economic Research Service, 2010). The first isocaloric diet is identical to the baseline for the major food groups, but contains fewer discretionary calories in the form of added fats and sweeteners to prevent energy intake from exceeding caloric needs (Positive control, POS). The eight remaining diet scenarios generally conform to the USDA food group recommendations published in the 2010 Dietary Guidelines for Americans (U.S. Department of Agriculture and U.S. Department of Health and Human Services, 2010), hereafter referred to as the dietary guidelines. Each diet includes the weighted average recommendation for the U.S. population, based on the age-gender distribution of the population and each cohort’s respective food group and caloric recommendations. The single exception is the dairy food group, which did not meet the recommended level in all diets. Dairy was selected because its recommendation is driven by dietary reference intakes for calcium, which can also be obtained from plant sources, fortified foods, or supplements, and all diets already contained adequate amounts of dietary protein. Five of the “Healthy Diet” scenarios contained meat, and three were vegetarian. The diets containing meat (omnivore diets) represent varying degrees of transition toward plant-based sources of protein. The 100% healthy omnivorous diet represents a situation in which all Americans follow the dietary guidelines, requiring a modest (13%) reduction in protein-rich foods but retaining the current preference for meat (red meat, poultry, and fish) as the primary protein sources. The next four diets represent a transition toward vegetarian eating patterns (80%, 60%, 40%, and 20% healthy omnivorous), in which a decreasing percentage of meals follow the healthy omnivorous diet and are replaced by meals following an ovolacto-vegetarian diet. Effectively meat is substituted with additional servings of eggs, nuts, pulses, and tofu. The final three scenarios represent distinct vegetarian diet patterns: ovo-lacto vegetarian (OVO), lacto vegetarian (LAC), and vegan (VEG). Within each of the ten diet scenarios, foods were divided into five major groups (grains, vegetables, fruits, dairy, and protein-rich foods) and two discretionary categories (added fats and sweeteners). Vegetables were further divided into subgroups as done in the dietary guidelines. In addition, the dairy and fats groups were broken into subgroups. The dairy group distinguishes fluid products (e.g. milk and yogurt) from other products (e.g. cheese and ice cream) as a heuristic way to enable the scenarios to represent dietary guidelines to choose lower fat sources of dairy. Similarly, plant sources of added fats were separated into plant oils (which are generally encouraged) and animal sources (which are recommended only in moderation). Protein rich foods were reported individually and in subgroups of similar foods (e.g. dry beans, peas, and lentils) because the literature suggests that these foods vary significantly in terms of their individual land requirements. Daily intake of the major food groups, food subgroups, and protein foods for each of the ten diet scenarios are reported in Table 2. Food group Food subgroup Unit BAS POS OMNI 100 OMNI 80 OMNI 60 OMNI 40 OMNI 20 OVO LAC VEG Grains Whole and refined grains oz 7.66 7.66 7.01 7.01 7.01 7.01 7.01 7.01 7.01 7.01 Vegetables Total vegetables cups Dark green vegetables cups 0.16 0.16 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 Red and orange vegetables cups 0.30 0.30 0.82 0.82 0.82 0.82 0.82 0.82 0.82 0.82 Dry beans, lentils, and peas cups 0.11 0.11 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 Starchy vegetables cups 0.46 0.46 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 Other vegetables cups 0.53 0.53 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 Fruits All fruit cups 0.86 0.86 1.92 1.92 1.92 1.92 1.92 1.92 1.92 1.92 Dairy All dairy cups Cow’s milk products cups 1.68 1.68 1.68 1.77 1.85 1.94 2.02 2.11 2.25 0.00 Fluid milk and yogurt cups 0.68 0.68 1.43 1.50 1.58 1.65 1.72 1.79 1.92 0.00 Cheese and other dairy cups 1.00 1.00 0.25 0.26 0.28 0.29 0.30 0.31 0.34 0.00 Soy milk cups n/a n/a 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.89 Protein All protein foods meat oz equivalents 6.67 6.67 5.80 5.80 5.80 5.80 5.80 5.80 5.80 5.80 Dry beans, lentils, and peas meat oz equivalents n/a n/a 0.00 0.25 0.51 0.76 1.01 1.26 1.53 2.02 Nuts meat oz equivalents 0.77 0.77 0.67 0.91 1.16 1.40 1.65 1.89 2.29 2.29 Tofu meat oz equivalents n/a n/a 0.00 0.33 0.66 0.98 1.31 1.64 1.98 1.48 Beef meat oz equivalents 1.80 1.80 1.56 1.25 0.94 0.62 0.31 0.00 0.00 0.00 Pork meat oz equivalents 1.19 1.19 1.03 0.83 0.62 0.41 0.21 0.00 0.00 0.00 Chicken meat oz equivalents 1.51 1.51 1.31 1.05 0.79 0.53 0.26 0.00 0.00 0.00 Turkey meat oz equivalents 0.39 0.39 0.34 0.27 0.21 0.14 0.07 0.00 0.00 0.00 Eggs meat oz equivalents 0.53 0.53 0.46 0.57 0.68 0.79 0.89 1.00 0.00 0.00 Fish meat oz equivalents 0.48 0.48 0.42 0.33 0.25 0.17 0.08 0.00 0.00 0.00 Added fats Plant oils grams 64.46 28.03 28.03 28.03 28.03 28.03 28.03 28.03 28.03 28.03 Dairy fats grams 7.26 2.14 1.09 1.09 1.09 1.09 1.09 1.09 1.09 0.00 Animal fat (lard and tallow) grams allowed in diet 2.90 0.86 0.44 0.35 0.26 0.17 0.09 0.00 0.00 0.00 Sweeteners All sweeteners tsp 28.91 8.53 4.34 4.34 7.23 4.34 4.34 4.34 4.34 4.34 The macronutrient profiles of the ten diets differed in two important ways (Table 3). First, while the baseline diet represented current per capita energy intake, all other diets were balanced to meet the age-gender weighted average caloric requirements of the U.S. population, roughly 2,150 kcal person-1 day-1. Second, the nine isocaloric diets differed in terms of total protein, fat, and carbohydrate content. Diets with higher levels of animal-based foods contained higher levels of protein and fats, and less carbohydrate, than diets that were more plant-based. Scenario name Scenario symbol Total energy (kcal day-1) Protein (g day-1) Fat (g day-1) Carbohydrate (g day-1) Baseline BAS 2,844 92.1 119.8 363.1 Positive control POS 2,153 91.9 80.9 272.6 100% healthy omnivorous OMNI 100 2,153 88.7 73.0 296.8 80% healthy omnivorous OMNI 80 2,153 86.5 72.5 301.4 60% healthy omnivorous OMNI 60 2,153 84.2 72.0 306.1 40% healthy omnivorous OMNI 40 2,153 82.0 71.5 310.8 20% healthy omnivorous OMNI 20 2,153 78.9 71.0 315.4 Ovolacto-vegetarian OVO 2,153 77.5 70.5 320.1 Lacto-vegetarian LAC 2,154 75.7 69.7 325.6 Vegan VEG 2,154 74.0 65.8 336.2