Nutrient delivery

Figure 1 (main) presents the 16 nutritional attributes whose delivery changes due to the meat to plant shifts exceed 25% of the approximate delivery by the full MAD (with further details in the Methods section).

Figure 1 Key nutritional (main) and environmental (insets b–e) consequences of replacing all meat (blue) and beef only (red) in the mean American diet (MAD) with protein conserving nutritionally sound plant based alternative diets. Panel a presents mean ± 1 standard deviation nutrient deliveries by the 500 MC plant replacement diets (bar lengths and whiskers) for all nutritional attributes whose two delivery differences from the respective replaced meat both exceed 25% of the corresponding delivery by the truncated mean American diet (tMAD, the nutrient delivery by all 73 plant and animal food items we consider, more formally defined in the Methods section). Alternating gray shading helps distinguish individual attributes. Insets (b–e) show use of land and reactive nitrogen (Nr), greenhouse gas emissions, and irrigation needs by the meat diets and their plant based replacement (with color convention shown by legend). The percent of total per capita dietary use of the resource (associated with the truncated MAD) to which values correspond are indicated numerically. Full size image

Of these 16 leading nutritional additions (note that all 16 changes are positive), all save vitamin B 12 —of which the replaced meats are a solid source while the plant diets deliver none—are nutritionally protective and desirable22,23. Increasing consumption of them, which is expected to accompany the putative shift to the plant based replacement diets under the assumption of consumption = production, is thus expected to improve public health. The lost B 12 delivery represents a well-known24 and potentially serious25 limitation of plant based diets, which fortunately can be readily alleviated by supplementation26. In terms of individual nutrient delivery, replacing all meat or beef with the proposed plant alternatives devised here is thus mostly advantageous22,27.

Resource use consequences

The expected direct daily per capita resource use consequences of the dietary shifts are presented in Fig. 1b–e and fall into two categories. The first comprises considerable reductions in the need for cropland, Nr, and GHG emission, amounting to saving 35–50% of the total dietary use of the resources. Conversely, the replacement plant based diets require additional irrigation that amounts to 5–15% of total current dietary water needs.

Next, in Fig. 2 we estimate national level consequences of a hypothetical adaptation of the meat-to-plant dietary shifts by the full U.S. population as the direct impacts per person committing to the dietary shift (Fig. 1e) times 327 million Americans. This rests on several key assumptions ranging in robustness. First, we assume sparing of pastureland used for beef grazing, not reallocation to other modes of food production. This is robust, as while vanishing beef consumption obviates grazing, most range and other extensive grazing lands are ill suited for crop production28.

Figure 2 Absolute (a–d) and relative (e) changes in national resource use associated with a hypothetical full population deployment of the considered all meat or beef only replacements (left and right bars of each metric respectively in a–d). Since the shown values are savings, positive ones mean savings and negative ones mean increased usage (see arrows on left of a and right of d). Panel e shows the changes as percent of the annual national total and dietary (associated with producing the truncated MAD) using the shown colors. White tick marks are 5% apart. Replacing all meat with plant based alternatives, e.g., will save about 34% and 24% of the current national dietary and total land use (2 rightmost land bars in e). Full size image

Second, we assume reallocation of high quality cropland currently used for feed production to production of the plant items that dominate the solution replacement diets with unchanged national mean yields. While surely not inevitable, this is consistent with evidence offered by current geographical variability and historical precedent for agronomic suitability of cropland to diverse crops. For example, the key protein source in the replacement diets, soy, is grown29 in widely diverse geographies from cool, continental North Dakota to maritime hot and humid North Carolina, with optimal location around Iowa. These States’ respective 2017 mean annual soybean yields29 were 35, 40 and 57 bu ac−1, about −29%, −19% and +16% above the 2017 national mean, 49.3 bu ac−1. The respective 1980 values were29 17, 18 and 39 bu ac−1, about −34%, −32% and +45% above the 1980 national mean, 26.5 bu ac−1. Thus as the national mean rises with time due to improved cultivars and agricultural practices, geographical variability regresses to the mean, with yields in suboptimal states slowly approaching the rising national mean while optimal states enjoying decreasing edge with time. That is, technical adaptation erodes the importance of geographically variable suitability for particular crops.

The key shortcoming of the above approach to estimating national level resource savings is that it does not, and cannot, address a full restructuring of the U.S. food system in response to the shifting food demands. Addressing this restructuring requires a full agro-economic model of the U.S. food system, which is well beyond the scope of this paper. It is thus fair to consider the estimated national level resource saving we report here as an upper bound on actual expected savings.

With these stipulations in mind, these calculations yield two sets (for the all meat or beef only replacements), each comprising four resource use changes corresponding to the four considered resources. For example, we find (Fig. 2a–d) that replacing U.S. beef with plant alternatives stands to save annually approximately 29 (28, 30) million cropland ha, 3 (3.0, 3.1) billion kg Nr, 280 (276, 283) billion kg CO 2e , and −3 (−5, −3) billion m3, with parenthetical values denoting ± one standard deviation about the mean.

To test the plausibility of the above estimates, we use a recent independent estimate30 of 48.4 kg CO 2e (kg boneless edible beef)−1. About 15% of these emissions occur post farm gate (their Table 2). Consistency with our emission data thus requires reducing this to 85%, which yields about 41 kg CO 2e (kg farm gate beef)−1. Multiplying this by the 8.1 billion kg annual national beef consumption (which is the annual equivalent of the ≈70 g d−1 daily per capita beef consumption introduced earlier times 327 million Americans) yields 333 billion kg CO 2e y−1 emissions due to beef production. Subtracting the 55 billion kg CO 2e y−1 emissions required for producing the plant replacement diet yields 278 billion kg CO 2e y−1 difference, within 1% of our 280 billion kg CO 2e y−1 estimate. The two estimates thus agree closely.

The full set of expected national resource changes is shown in Fig. 2. Because meat production accounts for 5–10% of the total national GHG emissions and fresh water use, the reduced GHG savings and added water consumption shown in Fig. 1d,e translate to national level consumption changes (after accounting for the resource needs of the replacement plant diets) of only −5 and +3% of the respective total national resource uses. Conversely, because feeding livestock requires 36 and 21% of the national cropland31 and reactive nitrogen application5,20, the dietary shifts offer considerable savings of these resources, ≈10–20% of the respective current total national use of these resources.

Diet composition, nutrient delivery, and share of resource use

In daily per capita mass, tofu, soybeans, peanuts, and lentils dominate the all meat replacement, while green peas, lentils, asparagus, and spinach dominate the beef only replacement (Fig. S1a,b, which present the eight most dominant plant items in the mean replacement diets calculated over the 500 Monte Carlo realizations). Because these lists partly reflect the list of plant items we use and the upper mass bounds we impose (see Methods), they are unlikely to be the globally optimal plant replacements to the two meat masses and types (that is, more nutritious or environmentally sound alternatives may exist using items not included here). They also take no note of tastes, cuisines or palates, and may thus prove suboptimally deployable. Together, these two limitations of the presented solutions suggest that similarly (or more) environmentally and nutritionally desirable plant (or mixed) diets which better suit specific tastes and culinary preferences may exist.

Fig. S1c,d show the resources these leading items use, uniquely rearranged in descending order of importance for each of the four resources. (For the beef replacement, only four contributions are shown because those of the remaining items to the total resource uses are trivial.) There is some correspondence between items dominating by both mass and resource use (compare panel a and panels c in Fig. S1). Similarly, green peas, which dominate the mass of the beef replacement, claim substantial amounts of the 3 resources save land (Fig. S1d 1,4 ). But exceptions to these expectations abound in individual burdens (e.g., the contribution of tofu to water needs of the all meat replacement). Similar but differently ordered information is recast in Fig. 3 to more finely resolve the composition of and overall resource use by the diets. The figure shows only items that dominate the mean resource use by the 500 randomized plant based diets replacing all meat (panel b–e) or beef alone (panels f–i). Once chosen based on their contribution to total resource use by the diet, we rank items by mass contributions (in g person−1 d−1, horizontal axes), with contributions to total resource use shown cumulatively along the vertical dimension. The items are identified in panel a, along with their contributions to the diets’ respective overall protein contents. In panels b–i, high resource users per g (e.g., water use by peanuts in the all meat replacement or Nr use by asparagus in the beef replacement) form tall rectangles, while low resource users per g (e.g., all resource use by soy) form flat, wide rectangles. While sharing some items (e.g., lentils or green peas), the two mean replacement diets also differ. These differences stem from nutritional differences between beef alone and the weighted mean of all meats, which enter the problem as the imposed bounds (the elements of b(a) and b(b) used in the respective optimizations, as explained in the Methods section).

Figure 3 Key resource using items in the plant based all meat (b–e) and beef (f–i) replacement diets, ranked by mass contributions (horizontal axes). Nr ≡ reactive nitrogen fertilizer; GHG ≡ greenhouse gas emissions. Panel a: protein contributions of leading item to the right of the item legend identifier, with the upper (lower) bar corresponding to the all meat (beef only) replacements. Panels b-i: items’ mass and resource use contributions by the plant based replacement diets. Rectangles’ horizontal extents show items’ masses, with vertical extents showing corresponding resource uses. For example, contributing ≈29 g cap.−1 d−1, spinach is prominent (4th by mass) in the beef replacement diet. Yet because it is not a top land user, it is thus absent from panel f. Standard deviations calculated in both dimensions over the 500 Monte Carlo diets are given by the white L shape near the lower-left corners of sufficiently large rectangles. Total resource demands of the plant based replacement diets as percentage of the corresponding demands of the replaced meat(s) are at the top of each panel, e.g., the mean all meat replacement plant diet uses 30 ± 2% of the cropland beef, poultry and pork currently jointly use (panel b). Full size image

To analyze this issue and better understand the composition of the replacement plant based diets, we identify inequality constraints that shape the solutions particularly strongly using the criteria described in the Methods section. For both beef and all meat replacements, constraints governing total mass and energy (associated with upper bounds), and monounsaturated fatty acid, vitamins D, B 3,6,12 , zinc, choline and selenium (associated with a lower bounds) prove critical.

Supplies of these critical nutrients are least likely to remain within desirable bounds following the considered meat-to-plant dietary shifts. Identifying such nutrients is thus an essential element in successfully, safely deploying animal-to-plant dietary shifts, to which the methodology introduced here is a powerful aid. It offers a practical message to those seeking plant based alternatives to meat in their diet: if increased caloric intake is undesired (because of weight, environmental or other concerns), supplies of protective monounsaturated fatty acids, Zn, Se, choline, and vitamins B 3 , 12 are least likely to be adequately delivered by plant based alternative diets, and thus require special attention. Note, however, that while these nutrients are unlikely to be adequately supplied spontaneously (with no deliberate efforts) while minimizing resource use without increasing caloric intake, some relaxation of the minimization is enough to fully meet those requirements, as is clearly shown by the fact that each one of the 500 Monte Carlo (see Methods) diets fully meets the needs for most of these nutrients (but not B 12 ) while also conforming with all other constraints (e.g., without appreciably increasing caloric intake relative to the lost calories in the forgone meat(s)). Ingesting enough of these nutrients thus requires deliberate efforts, but is eminently tractable.

It is also important to note that while the critical constraints are important to the composition of the solution diets Figs 1 and 3 present, they are not these diets’ sole final arbiters, for two reasons. First, the problem is high dimensional and features mostly inequalities, which together endow the solutions with considerable indeterminacy and flexibility. Second, if a solution exists (i.e., if a randomized problem proves feasible), the cost function also impacts the mass choices. To illuminate the tension between satisfying the nutritional constraints and resource use minimization in determining the solutions, we devise an index of suitability of plant items for satisfying the nutritional constraints, \({F}_{i}=\sum _{r}{\sigma }_{r}({a}_{ir}-{\bar{a}}_{r})/{s}_{r}\) The sum is over all constraints, and the sign parameter σ r = 1 for lower bound constraints and −1 for upper bound ones. The parenthetical term is the deviation of a ir , the element of the nutritional composition coefficient matrix A (see Methods) corresponding to plant item i and nutrient r, from \({\bar{a}}_{r}\), the mean of the rth row (the mean content of nutrient r of all plant items considered). This deviation is then normalized and nondimensionalized by s r , the standard deviation of r content over all plant items. The logic behind the index is that obvious candidates for inclusion in the diet are plant items that are unusually rich in desirable nutrients (with lower bounds and σ r = 1) but largely devoid of capped critical nutrients (with upper bounds and σ r = −1). While no plant item is ideal, some—whose dimensionless F i index is unusually high—are close. For such items, the \({a}_{ir}-{\bar{a}}_{r}\) terms are unusually positive for σ r = 1 constraints, and unusually negative when σ r = −1, both contributing to positive accumulation of the F i sum, whose high positive values signify high compatibility of the item’s nutritional composition with the inequality nutritional constraints.

To show the suitability index in action for the all meat replacement, in Fig. 4 the items in the mean beef replacement diet are arranged in descending mass order as the solid curve at the zero environmental cost plane shows. For each item, the figure shows two additional attributes: the combined environmental cost as height against the vertical axis, and the dimensionless suitability index as a color evaluated against the color bar on the right. While noisy, the plot reveals three regimes. The high mass items are quite compatible with the inequalities and environmentally cheap. On the other (low mass) extreme (on the right) are plant items that are environmentally costly and less compatible with the inequalities. In between these two endmembers are plants whose environmental costs and nutritional compatibility are intermediate. For both replacements, this is quantified in Table 1.

Figure 4 Analysis of the determinants of the beef replacement solution vector (the Supplementary Information offers the all meat counterpart to this plot). The plant items are arranged in descending order of mass prominence along the right horizontal axis (labeled “plant items arranged by mass in diet”), with the corresponding masses themselves shown along the left horizontal axis (labeled “mass in replacement diet, g d−1”). Individual food items are identified by the list of names on the z-axis that corresponds with descending order of mass (“plant items arranged by mass in diet”). The vertical bars show two attributes for each plant item. The bar heights show the combined nondimensional environmental cost (see Methods), with taller bars indicating higher resource use by the chosen mass of the item. To avoid parallax perception errors, white tickmarks show the rising environmental costs in increments of 0.05, and the full bars are projected in fainter colors on the back “wall” at mass = 30 g d−1. The bar colors, with a color scale shown on the right, show the relative compatibility of plant items with the critical constraints, with details in the subsection entitled Diet Composition, Nutrient Delivery, and share of Resource Use in the Results and Discussion section. The all-meat counterpart to this is given in the Supplementary Information file. Full size image

Table 1 Three statistics of three groups of items in the mean solutions to the two replacement problems considered. Full size table

Table 2 The 44 nutritional attributes addressed in the replacement calculations. “U”, “L” and “E” indicate attributes subject to upper bounds, lower bounds, and equality (only protein) respectively. Vit. = vitamin; FA = fatty acids; unsat. = unsaturated. Full size table

The table’s suitability columns show that compatibility with the constraints is the primary determinant of the solution composition for both replacements; leading terms are highly compatible with the constraints (as indicated by their high mean F i values), and trailing ones (rows 2 and 3) less so. This stems from the nontrivial challenges the replacements pose. The initial and decisive test for any linear programming problem is feasibility; not a specific combination of plant item masses, but confirmation that a combination of the considered items (here a different set for each Monte Carlo realization) can satisfy all nutritional constraints with individual item-specific masses below the imposed maxima. This primacy of compatibility explains the shown declining F i values down the rows. Once compatibility is established, the emergent null space (non-uniqueness of the solution) presents the opportunity to minimize environmental costs by considering the resource needs of individual plant item members of the feasible set. This explains the similar mean costs of items 1–10 and 11–20, because the dominance of all 20 is governed primarily by feasibility, and only secondarily by cost minimization. Indirectly, it also explains the higher environmental costs of the trailing third group, whose items are on average simultaneously less compatible with the constraints and more environmentally costly. Their representative masses reflect cost minimization in the presence of enforced diversity due to the randomized specified minimum masses (see Methods). This is readily demonstrated by fitting a model of the form c i = c 0 eαi (where c 0 is an optimizable parameter and, conformal with the Methods section, c i denotes the combined nondimensional environmental cost of food item i, α is a fit parameter, and items are arranged according to the corresponding items’ masses with mass i ≥ mass i+1 and i ∈ [21, 64]). These α s are positive for both the all meat and beef replacements, and significant at <0.008 and <0.030 respectively, showing that, as argued above, items’ environmental costs rise exponentially with their decreasing mass contributions. Critical inequality constraints, other more easily satisfied constraints, and item specific nutritional composition and resource use thus jointly determine the composition of each replacement diet and these diets’ statistics shown in Figs 1–3.

Returning briefly to Fig. 3, it also visualizes the disconnect between individual plant items’ chosen masses, fractional protein contributions, and resource use. For example, with ≈69 g person-1 d-1, soy and tofu jointly dominate the mean all meat replacement diet (first suitability group), delivering a full third of the total protein, yet account for about 12% of Nr and water needs, and <22% of the cropland needs. Similarly, lentils contribute the most protein to the beef replacing diet (about 3 g d-1 or 24%), but accounts for only 6% of this diet’s overall N fertilizer needs. Still in the beef replacement diet, by contrast, pumpkin delivers 6% of the mass but under 2% of the total protein while requiring ≈10% of the water and emissions (third suitability group).

These disconnects are not surprising—no obvious interdependence couples an item’s mass, protein delivery, and water or Nr needs per g—but are important because they highlight the potential for further resource savings by dietary choices beyond replacing meat achievable by favoring some plant items over others. The opposite side of this coin—the possibility of nutritionally or environmentally questionable plant based diets that nonetheless require considerable efforts to switch to—is equally important. Thus while the means of the plant and animal based categories differ markedly, the variability of individual items within each group renders the broad distinction—relatively desirable plant based food and relatively undesirable animal based group—an imperfect, and sometimes unhelpfully truncated approximation for the design of specific individual diets.