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  • View in gallery

    Caloric yield per acre and Nr use per human-edible calorie of animal- and plant-based foods. The range spanned by the MAD’s animal-based portion is shown in red, with the most likely value enclosed by the open square. The 43 plant-based items (solid circles) are divided into three categories: high Nr users (blue); low yielding low Nr users (magenta); and high yielding low Nr users (black). Names of items falling into each category are shown on the right. The green cross shows weighted means ± weighted mean deviations, ∑iciyi/∑ici ± ∑ici|yiy|/∑ici and ∑iciNri/∑ici ± ∑ici|NriNr|∑ici,/∑ici., where i = [1, 43] is the plant item index and ci is the weighting variable, the item’s caloric contribution to the MAD. The top right presents [in units of 106 kcal (acre × yr)−1 and g Nr (100 kcal)−1] the means and ranges (minimum/maximum for the three groups and standard deviation for the whole set; in dark green).

  • View in gallery

    Some composition statistics of the 1500 MC 3750-kcal daily diets derived by simultaneous Nr and land or no minimization [minimizing xTc or not in Equation (4), thick/left and thin/right, respectively, for each shown item]. Tick marks (diamonds) display percentiles 2.5, 50, and 97.5 (means). Shown are (a) masses of the leading individual items (items whose masses repeatedly dominate the daily diet), (b) the diet’s total mass, and (c) the protein and fat contents. Garlic is shown in (a), despite its small characteristic chosen mass because if the particularly low bounds applicable only to garlic were lifted, it would have dominated nearly all daily diets that feature it. Although (a) shows only major items, (b) and (c) are based on the full daily diets.

  • View in gallery

    Land and Nr performance of realistic annual plant-based diets. Each personal annual diet is displayed as a dot. There are 1000 gray (black) dots corresponding to diets whose environmental costs are explicitly minimized (not minimized): that is, for which xTc [Equation (4)] is (is not) minimized while choosing the diet’s composition. The nonuniform tick mark values show the various central values. Note that, although the cost vector used for minimization is c [Equations (3) and (4)], the costs reported here are based on the dimensional costs cNr and cland. The top-left bar shows the corresponding range (and best estimate in open square) for the animal-based portion of the MAD. The horizontal axis is reported in two units, with the top axis reporting 1/10 of the reciprocal of the bottom axis’ values.

  • View in gallery

    Comparison of land and Nr requirements of various personal annual diets. Four diet types are considered: (bottom left) purely plant-based diets and (top right) mixed ones, each considered either with or without resource minimization [minimizing xTc of Equation (4)]. The nonuniform tick mark values show the various central values (the Nr means of the minimized/unconstrained diet within each diet types are very close, so their combined means are shown by the vertical tick marks). Each dot is an annual personal diet with 365 × 3750 kcal. The plant-based diets are those shown in Figure 3, reexpressed in the shown units. The mixed diets comprise 1045 animal-based (2705 plant-based) kcal day−1 (28% and 72%). The animal-based portion of mixed diets is assumed to be produced with the land efficiency shown in Figure 3, 0.8 × 106 kcal (acre × yr)−1, and Nr efficiency randomly chosen from the [84, 129] lb Nr (acre × yr)−1 interval. The requirements of the plant-based portion of each of the mixed diets are ∼0.72 of those of a randomly chosen purely plant-based annual diet. See text for further details.

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Land Use and Reactive Nitrogen Discharge: Effects of Dietary Choices

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  • 1 Physics Department, Bard College, Annandale-on-Hudson, New York
  • 2 Department of Geophysics, The University of Chicago, Chicago, Illinois
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Abstract

Modern agriculture alters natural biological and geophysical processes, with magnitudes proportional to its spatial extent. Cultivation is also the main cause of artificially enhanced reactive nitrogen (Nr) availability in natural ecosystems. Sustainable food production should thus minimize Nr use while maximizing human-destined caloric output per acre. The authors demonstrate that it is possible to design realistic, nutritionally sound plant-based diets that require a quarter to a half of the Nr and a quarter to a third of the land the mean American diet’s animal-based portion does. Broad application of these findings (e.g., by incorporating environmental considerations into official dietary recommendations) would reduce food production’s environmental impacts dramatically.

* Corresponding author address: Gidon Eshel, Physics Department, Bard College, Annandale-on-Hudson, NY 12504–5000. geshel@bard.edu

Abstract

Modern agriculture alters natural biological and geophysical processes, with magnitudes proportional to its spatial extent. Cultivation is also the main cause of artificially enhanced reactive nitrogen (Nr) availability in natural ecosystems. Sustainable food production should thus minimize Nr use while maximizing human-destined caloric output per acre. The authors demonstrate that it is possible to design realistic, nutritionally sound plant-based diets that require a quarter to a half of the Nr and a quarter to a third of the land the mean American diet’s animal-based portion does. Broad application of these findings (e.g., by incorporating environmental considerations into official dietary recommendations) would reduce food production’s environmental impacts dramatically.

* Corresponding author address: Gidon Eshel, Physics Department, Bard College, Annandale-on-Hudson, NY 12504–5000. geshel@bard.edu

1. Introduction

Modern food production is environmentally costly (Galloway et al. 2003; Galloway et al. 2008; Gruber and Galloway 2008), depriving wildlife of needed habitats (Gibbs et al. 2009; Flynn et al. 2009) and compromising what is left. Farming alters surface heat (A. K. Betts et al. 2007; R. A. Betts et al. 2007) and momentum (Thom 1975) budgets, disrupts soil flora (Steenwerth et al. 2005; Wu et al. 2007), and changes local hydrology (Gordon et al. 2008), with magnitudes proportional to spatial extent. Of prime additional concern is excess bioavailable (reactive) nitrogen (Nr; Galloway et al. 2003; Galloway et al. 2008), mostly because of fertilization (Carpenter et al. 1998; Socolow 1999). It promotes greenhouse gas emissions (Bouwman et al. 2002; Robertson et al. 2002); land surface, estuarine, and coastal ocean eutrophication (Seitzinger and Sanders 1997; Jordan and Weller 1996; Diaz and Rosenberg 2008); and harmful algal blooms (Paerl 1997). Prudent food production must therefore minimize Nr use (and thus discharge; Bergström and Brink 1986) while maximizing land’s human-destined caloric output. Nr use per human-edible calorie, the quotient of per acre Nr use and human-edible caloric yield, combines the two optimizations and is the relevant performance metric of food production systems in this context. Because Nr and land-use minimizations are coupled, their combined benefits may exceed the sum of the benefits of either one alone.

Realizing the requisite optimizations will likely require both legislative means (Eshel 2010) and suitable personal dietary choices, which are our focus here. For either legislative or personal choices, simultaneous optimization is challenging, as optimizing different variables may result in different, even opposing, recommended diets. The main novel contribution of this paper is a simple method for guiding dietary choices. Employing the method to minimize Nr use while maximizing caloric yield, we demonstrate that the animal-based portion of the mean American diet (MAD) requires 2–4 times more Nr and 3.2–3.8 times more land than plant-based diets. To our knowledge, ours is the first quantification of these two related performance metrics. Even individually, we know of no previous effort to minimize Nr use by dietary choices, and, although the general notion that plant-based diets are land efficient is not new, we found no previous quantitative comparison of land demands of plant- and animal-based diets.

2. Approach

2.1. Plant-based versus animal-based food

The central observation that motivates our approach to the land–Nr dual minimization is the wide disparity in caloric efficiency and fertilizer use between animal- and plant-based diets. We consider the caloric yield per acre and Nr use per human-edible calorie of 43 plant-based foods (Figure 1) for which U.S. mean Nr and land-use data exist (U.S. Department of Agriculture 2008a; U.S. Department of Agriculture 2008b; U.S. Department of Agriculture 2008c; U.S. Department of Agriculture 2008d; U.S. Department of Agriculture 2008e; U.S. Department of Agriculture 2009a). Collectively, these plant staples account for 1849 kcal per person per day or 63% of the plant-based part of the MAD (United Nations 2008a).

To compare the above land and Nr efficiencies to those of animal-based diets, we calculate next the efficiency of the MAD’s animal-based portion. In the 2003 gross (nonloss adjusted) MAD (United Nations 2008a), animal-based items contributed 1045 kcal per person per day. With the corresponding U.S. population, ∼292 × 106, this amounts to ∼1.12 × 1014 kcal yr−1 nationally. To feed the animals that yielded those calories, the United States needed ∼1.4 × 108 acres (Table 1 and references therein) for feed production. The gross national land-use efficiency of the MAD’s animal-based portion is therefore lanimal ≈ 0.80 million kcal (acre × yr)−1.

The Nr intensity of land supporting the animal-based portion of the mean American diet can be estimated by considering the caloric yield of the principal animal feed crops in conjunction with their fertilization requirements (Table 2). As this calculation demonstrates, the best estimate of Nr intensity of land supporting the animal-based portion of the mean American diet is ∼107 lb Nr (acre × yr)−1, with the true value certainly falling between 84 and 129 lb Nr (acre × yr)−1.

The MAD’s land and Nr efficiency estimates (the coordinates of red line in Figure 1) reflect the whole animal-based portion (comprising beef, pork, dairy, etc.). Land and Nr efficiencies of each one of the considered plant items exceed our estimates for those of the MAD’s animal-based portion. Even when considering the lower bound of Nr demands of the MAD’s animal-based portion, only cauliflower proves slightly less efficient. Because of this unambiguous disparity, we tackle the minimization problem by comparing various plant-based diets to the MAD’s animal-based portion. Some may object to this thrust on the grounds that the seemingly inexorable rise in meat consumption (e.g., Speedy 2003) is inevitable. We consider this discussion—firmly rooted in the social sciences and culinary arts—largely outside the scope of this paper. Here, we simply wish to quantify the environmental costs of various dietary choices, and we expect market forces, along with unbiased pricing of natural resources, to dictate the degree to which our findings will affect actual diets.

With the above efficiency disparities in mind, we thus devise hypothetical mixed plant-based diets from the 43 plant items (Figure 1), starting with daily diets and then combining those into annual ones, and compare the latter to the MAD’s animal-based portion and to alternative mixed diets.

2.2. Design of plant-based diets

2.2.1. Daily diets

For nutritional adequacy, we require daily diets to comprise 3750 kcal (as in the actual MAD) and, following customary dietary recommendations assuming average weight, at least 100 g protein and at most 110 g fat. Accounting for relative bulkiness of plant-based diets and the characteristic mass of the actual daily U.S. diet (United Nations 2008a), we also require each diet’s total mass not to exceed N (1550, 5) g, where N (μ, s) denotes a normal distribution with mean μ and variance s2. Put together, these requirements are
i1087-3562-14-21-1-e1
where M ≤ 43 is the number of food items the considered diet comprises; xi is the mass of food i; and ei, pi, and fi are its energy, protein, and fat content.
In practice, the system (1) of coupled inequalities is solved using linear programming, as described in the online supporting information section of Eshel (Eshel 2010; see online at http://pubs.acs.org). To use linear programming, Equation (1) is recast as
i1087-3562-14-21-1-e2
where the meaning of is made clear by comparing Equations (1) and (2) and the sought vector x holds the masses of the diet’s various food items, so that the elements of Ax are the diet’s total mass, energy, protein, and fat.

We use the basic template of Equation (2) to construct multiple nutritionally sound daily plant-based diets. To obtain robust statistics and to reflect variability due to seasonality, location, cost, and taste, we construct 1500 such diets, employing the following randomization [Monte Carlo (MC)] protocol. First, each diet comprises 18 items randomly chosen from the 43 items shown in Figure 1. The choice of 18 is somewhat arbitrary because individuals vary widely in terms of the typical number of food staples they consume on a given day. The choice is guided by balancing the number of combinations, 43 choose k drops rapidly with |k − 21|, and our informal self-assessment of the characteristic number of distinct food staples we use in appreciable masses on a given day, ∼15. The choice of 18 is roughly in the middle of the 15–21 range but close enough to 21 to permit a large number of combinations. We repeated some of the analyses reported here by choosing 16 or 20 daily items with very similar results. Second, in each of the 1500 daily diets, the permitted mass of each included item falls between N (60, 8) and N (150, 8) g. Diets containing garlic require special care because (due to garlic’s high energy, high protein, low fat content, and minimal land requirements) the minimization algorithm often chooses unrealistically high garlic amounts. We therefore set a reduced permissible range for garlic of N (5, 2) to N (30, 2). The choices of 1) the 18 participating items, 2) their permissible mass ranges, and 3) the total daily mass form a “skeletal diet.” A skeletal diet becomes specific and unique when the actual masses xi of its 18 items are chosen.

In making the final mass choices for individual plant items, each of the 1500 skeletal diets is used twice. In the first use, the mass of each of the 18 participating items is chosen from within the permissible ranges based only on meeting the mass, energy, protein, and fat content criteria, setting the land and Nr costs of all items to zero (see below). In the second use, those masses are chosen by linear programming minimization of Nr and land use that chooses the amounts of each of the 18 included items from within a randomly chosen combination of lower and upper bounds for each. Because linear programming can only minimize scalar cost functions, we minimize land and Nr use simultaneously by using the combined dimensionless cost vector:
i1087-3562-14-21-1-e3
In (3), the Nr costs cNr (in pounds of Nr per food gram), normalized by those costs’ (cNr elements’) standard deviation sNr, are added to the land costs cland (in acre × yr per food gram) normalized by their standard deviation sland. The normalization renders cNr and cland additive by nondimensionalizing them and roughly equalizes their role in setting a given food’s overall environmental cost because ‖cNr/sNr‖/‖cland/sland‖ ≈ 0.98. This near-unity ratio is specific to Nr and land but need not hold for other environmental variables. In the general case of this ratio deviating appreciably from unity, it will make sense to arbitrarily inflate the smaller of the two terms so as to achieve near unit ratio, permitting both variables approximately equal sway over the solution. Note that this procedure readily generalizes to more variables than two (Eshel 2010).
The formal minimization problem arising in the second use of each skeletal diet is therefore
i1087-3562-14-21-1-e4
Each MC realization yields1 a daily diet by choosing the masses (xi, 1 ≤ i ≤ 18) of 18 randomly chosen food staples. The mass choices are made within permitted ranges drawn randomly from the specified normal distributions. The random choices of items and their ranges represent realistic diets’ variability due to, for example, taste, activity, season, location, or food availability. The chosen food masses jointly minimize Nr and land requirements while meeting the nutritional criteria of Equation (1) so that daily diets are nutritionally adequate and environmentally optimal.

Table 3 gives the optimized and unconstrained compositions of a sample daily diet, whereas Figure 2 shows summary statistics of the daily diets. The diets are diverse (Figure 2a; lesser items not shown) and meet basic nutritional adequacy criteria (Figures 2b,c). They also clearly favor high energy density, low environmental impact items such as barley, oats, and rice, which most optimal diets include at the maximum mass allowed and which dominate such ancient cuisines as Chinese or Middle Eastern.

Note that, although the fat constraint is an inequality, ∑ifixi ≤ 110 g fat, most daily diets contain nearly or exactly the maximum fat mass allowed, 110 g (as can be inferred from the proximity of the fat content medians and means in Figure 2c to the bar tops, 110 g). This means that the fat mass constraint affects very strongly the diet composition so that, if the maximum permitted were increased, the extra allowed fat mass would have been nearly fully claimed in most cases, changing appreciably the diet’s composition. This is reflected in the randomly chosen sample diets in Table 3, whose top items are soy oil and peanuts. In light of our improved understanding of fat’s nutritional virtues and limitations (e.g., Willett 2005) and the refined view afforded by the breakdown into saturated and unsaturated fats (and finer distinctions within each group; Hunter et al. 2010), it may well be possible, indeed prudent, to relax the total fat mass constraint (or replace it with finer biochemical distinctions within lipids).

2.2.2. Annual diets

Next, we use the 1500 daily diets to construct 1000 annual diets whose environmental performance can be compared with that of the MAD’s animal-based portion. Because realistic diets vary daily, each annual diet is the sum of 365 daily diets randomly chosen from the 1500 calculated. Categorical, bulk statistics of the annual plant-based diets are given in Table 4. For each annual diet, we sum the land and Nr needs of the 365 daily diets using the items’ nutritional data (U.S. Department of Agriculture 2009b) and their land and Nr requirements (Figure 1). We thus obtain the annual diet’s overall land and Nr use, which we express in Figure 3 as 106 kcal and lb Nr (acre × yr)−1, respectively.

3. Results

Plant-based diets outperform the MAD’s animal-based portion (Figure 3). The minimized and unconstrained plant-based diets appear rather similar. This is mostly due to the wide ranges of the axes in Figure 3, which are needed to accommodate the MAD’s animal-based portion. In fact, the clouds of minimized and unconstrained diets are entirely nonoverlapping, and the mean minimized diet requires 85% of the land and 81% of the Nr that the mean unconstrained diet does. Although these differences are dwarfed by the differences between either of the plant-based diets and the MAD’s animal-based portion, an added 15%–20% efficiency is nontrivial.

An acre devoted to producing the MAD’s animal-based portion requires 2–4 times as much reactive nitrogen as plant-based diets, while delivering 26%–30% of the human-edible calories. That is, in terms of Nr and land use, which is centrally important environmental performance metrics, plant-based diets impact the physical environment significantly less than animal-based ones.

These results are perhaps more readily appreciated when the performance metrics are cast in terms of annual dietary needs of a person consuming a realistic “MAD like” diet comprising a total of 3750 kcal day−1, with 3750 − 1045 = 2705 of those derived from plants. This recast comparison is summarized in Figure 4, and its details are as follows.

Let α = 2705/3750 ≈ 0.72 denote the MAD’s plant-based caloric fraction and lk denote diet k’s land performance in kcal (acre × yr)−1 shown along the horizontal axis of Figure 3. The annual per capita land requirements of that plant-based diet is
i1087-3562-14-21-1-e5
acres, shown along the horizontal axis of Figure 4. Similarly, with fkplant denoting the Nr performance of the kth annual plant diet in lb Nr (acre × yr)−1, shown along the vertical axis of Figure 3, the Nr requirements per person per year of the kth plant-based diet is
i1087-3562-14-21-1-e6
lb Nr, shown along the vertical axis of Figure 4.
The kth mixed diet’s land performance, shown along the horizontal axis of Figure 4, is
i1087-3562-14-21-1-e7
acres, where lanimal ≈ 0.8 × 106 kcal (acre × yr)−1 is the previously calculated and defined mean land-use efficiency of the MAD’s animal-based portion. Because the Nr performance of the animal-based portion is a range rather than a single value, the kth mixed diet’s Nr performance, shown along the vertical axis of Figure 4, is
i1087-3562-14-21-1-e8
lb Nr, where Ui[84, 129] denotes random draws from the uniform distribution over the indicated closed interval.

The message of Figure 4 is simple: a person’s annual diet requires 1) 0.42–0.55 acres and 19 lb Nr on a plant diet or 2) 0.79–0.89 acres and 64 lb Nr on a mixed diet.

Plant-based diets thus require ∼29% of the Nr and 47%–70% of the land that mixed diets do (these values may be somewhat different for purely grazing cattle; however, because of the minuscule caloric contribution of this cattle, we leave this issue for future contributions).

These differences may have profound implications. The extreme case is that of the entire U.S. population (∼307 million in 2010) switching to a pure plant-based diet. Taking mean savings associated with this switch of 45 lb Nr and 0.36 acres per person, this shift amounts to saving 6.3 million metric tons of Nr and 109 million acres.

The Nr savings amount to 55% of the entire U.S. consumption, 11.5 million metric tons (in 2007, the last year for which data are available; IFADATA 2010; U.S. Department of Agriculture 2010), and are 525% of the mean annual Mississippi River Nr flux feeding the Gulf of Mexico dead zone, ∼1.2 million metric tons (Bianchi et al. 2009). Because fertilizer production causes greenhouse gas emissions (EPA 2010), the Nr savings are also associated with directly averted emissions. Although the exact conversion is somewhat uncertain, Snyder et al. (Snyder et al. 2009) offer a lower bound range of 2.6–3.2 kg CO2-eq (kg Nr)−1, which translates to averted emissions of 16–20 million metric tons CO2-eq, equivalent to the total emissions by 670 000–830 000 Americans. It should be noted that these averted emissions are a minor subset of the total annual emission savings associated with this hypothetical dietary change. These savings—1500 kg CO2-eq per person annually (Eshel and Martin 2006), roughly evenly split between direct energy related CO2 emissions and the combined methane and nitrous oxide emissions by manure management and enteric fermentation—amount nationally to roughly half a billion metric ton CO2-eq, or 7% of the nation’s total emissions.

The 109 million acres land savings are roughly as large as the surface area of California (∼105 million acres). They can sustain 198–260 million additional plant-eating Americans (64%–85% of the 2010 U.S. population).

4. Conclusions

The clearly superior Nr and land environmental performance of plant-based diets versus animal-based diets reported above augments earlier results (Eshel and Martin 2006), in which greenhouse gas emissions were the environmental performance metric. That is, broadly defining the environmental footprint as minimizing greenhouse gas emissions, land use, and reactive nitrogen discharge does not result in intricate and possibly values-laden weighing of competing objectives, as is often the case in environmental discourse. Rather, all three deleterious effects of food production can be dramatically reduced by consuming less animal-based foods.

Gradually shifting human diet toward much heavier reliance on plants, which is also desirable for health reasons given recent decades’ advances in nutritional science (e.g., Willett 2005), must therefore be viewed as a central element in broader national and global food policies that emphasize renewed commitment to minimizing food disparities, hunger, and climate change.

Acknowledgments

We thank the chief editor Dr. Mahmood and two reviewers for their thoughtful, useful comments, which significantly improved the quality and clarity of this paper. GE thankfully acknowledges the generous support of the Jeffery Cook Charitable Trust and the Bard Faculty Research Fund.

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APPENDIX

The Feed Percentage of Soy

From the U.S. Department of Agriculture (USDA; U.S. Department of Agriculture 2009b),
i1087-3562-14-21-1-eqa1
Because
i1087-3562-14-21-1-eqa2
(U.S. Department of Agriculture 2009b), the caloric oil content of raw soybean is
i1087-3562-14-21-1-e9
The remainder of this appendix is based on 2000–03 U.S. data from FAOSTAT (United Nations 2008a; United Nations 2008b).
The U.S. mean soy consumption has been 503 kcal per person per day, virtually all as soybean oil. With a U.S. population of 286 287 325 and the above caloric oil fraction, this consumption requires
i1087-3562-14-21-1-e10
nationally. Given raw soy’s energy content, 4 460 000 kcal ton−1, this is equivalent to the need for
i1087-3562-14-21-1-e11
of soy for human consumption nationally. However, the U.S. actual mean soy production has been 73 878 645 ton yr−1. The fraction of total produced soy for feed is therefore
i1087-3562-14-21-1-e12
That is the soy feed fraction used in Table 1 (fifth column from the right).
Figure 1.
Figure 1.

Caloric yield per acre and Nr use per human-edible calorie of animal- and plant-based foods. The range spanned by the MAD’s animal-based portion is shown in red, with the most likely value enclosed by the open square. The 43 plant-based items (solid circles) are divided into three categories: high Nr users (blue); low yielding low Nr users (magenta); and high yielding low Nr users (black). Names of items falling into each category are shown on the right. The green cross shows weighted means ± weighted mean deviations, ∑iciyi/∑ici ± ∑ici|yiy|/∑ici and ∑iciNri/∑ici ± ∑ici|NriNr|∑ici,/∑ici., where i = [1, 43] is the plant item index and ci is the weighting variable, the item’s caloric contribution to the MAD. The top right presents [in units of 106 kcal (acre × yr)−1 and g Nr (100 kcal)−1] the means and ranges (minimum/maximum for the three groups and standard deviation for the whole set; in dark green).

Citation: Earth Interactions 14, 21; 10.1175/2010EI321.1

Figure 2.
Figure 2.

Some composition statistics of the 1500 MC 3750-kcal daily diets derived by simultaneous Nr and land or no minimization [minimizing xTc or not in Equation (4), thick/left and thin/right, respectively, for each shown item]. Tick marks (diamonds) display percentiles 2.5, 50, and 97.5 (means). Shown are (a) masses of the leading individual items (items whose masses repeatedly dominate the daily diet), (b) the diet’s total mass, and (c) the protein and fat contents. Garlic is shown in (a), despite its small characteristic chosen mass because if the particularly low bounds applicable only to garlic were lifted, it would have dominated nearly all daily diets that feature it. Although (a) shows only major items, (b) and (c) are based on the full daily diets.

Citation: Earth Interactions 14, 21; 10.1175/2010EI321.1

Figure 3.
Figure 3.

Land and Nr performance of realistic annual plant-based diets. Each personal annual diet is displayed as a dot. There are 1000 gray (black) dots corresponding to diets whose environmental costs are explicitly minimized (not minimized): that is, for which xTc [Equation (4)] is (is not) minimized while choosing the diet’s composition. The nonuniform tick mark values show the various central values. Note that, although the cost vector used for minimization is c [Equations (3) and (4)], the costs reported here are based on the dimensional costs cNr and cland. The top-left bar shows the corresponding range (and best estimate in open square) for the animal-based portion of the MAD. The horizontal axis is reported in two units, with the top axis reporting 1/10 of the reciprocal of the bottom axis’ values.

Citation: Earth Interactions 14, 21; 10.1175/2010EI321.1

Figure 4.
Figure 4.

Comparison of land and Nr requirements of various personal annual diets. Four diet types are considered: (bottom left) purely plant-based diets and (top right) mixed ones, each considered either with or without resource minimization [minimizing xTc of Equation (4)]. The nonuniform tick mark values show the various central values (the Nr means of the minimized/unconstrained diet within each diet types are very close, so their combined means are shown by the vertical tick marks). Each dot is an annual personal diet with 365 × 3750 kcal. The plant-based diets are those shown in Figure 3, reexpressed in the shown units. The mixed diets comprise 1045 animal-based (2705 plant-based) kcal day−1 (28% and 72%). The animal-based portion of mixed diets is assumed to be produced with the land efficiency shown in Figure 3, 0.8 × 106 kcal (acre × yr)−1, and Nr efficiency randomly chosen from the [84, 129] lb Nr (acre × yr)−1 interval. The requirements of the plant-based portion of each of the mixed diets are ∼0.72 of those of a randomly chosen purely plant-based annual diet. See text for further details.

Citation: Earth Interactions 14, 21; 10.1175/2010EI321.1

Table 1.

The major feed crops’ needed acreage 2001–06 means. Feed percentages for corn, sorghum, barley, and oats are taken directly from data (U.S. Department of Agriculture 2008b), whereas that of wheat is based on using Tables 1 and 13 of the wheat yearbook (U.S. Department of Agriculture 2008c) simultaneously. Soybean feed percentage is derived from 2000–03 data (U.S. Department of Agriculture 2008d), as described in the appendix. We use calculated “needed” rather than actual acreage to account for export–import imbalances.

Table 1.
Table 2.

Nr application rates of the major feed crops (U.S. Department of Agriculture 2008a). Hay Nr application rates vary widely and are not currently recorded by the USDA. We therefore entertain the broad 100–200 lb Nr acre−1 yr−1 range, which spans (with comfortable margins) recommendations of USDA offices in major hay-producing states (Texas, California, Wisconsin, Kansas, and Missouri; e.g., Rayburn 2006; McKenzie 2005).

Table 2.
Table 3.

A randomly chosen daily diet constructed by solving Equation (4). The skeletal diet’s two compositions, both comprising exactly 3750 kcal and 110 g fat, are presented, with the right-hand diet land and Nr optimized and the left-hand diet unoptimized.

Table 3.
Table 4.

Bulk categorical caloric percent statistics of the annual diets. The left (right) four-column set corresponds to unconstrained (minimized) results [i.e., as in Figure 2, results obtain by not minimizing or minimizing xTc in Equation (4), respectively]. Minima, maxima, and means are derived from the 1000 annual diets. In dividing food items into the four categories, we use the popular view rather than the anatomical–botanical one (e.g., tomato is considered a vegetable). Corn oil is included in the oil category, not the grain category.

Table 4.
1

By employing linear programming, as described in technical details in the online supporting information section of Eshel (Eshel 2010).

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