Small-scale integrated farming systems can abate continental-scale nutrient leakage

Beef is the most resource intensive of all commonly used food items. Disproportionate synthetic fertilizer use during beef production propels a vigorous one-way factory-to-ocean nutrient flux, which alternative agriculture models strive to rectify by enhancing in-farm biogeochemical cycling. Livestock, especially cattle, are central to these models, which advocates describe as the context most likely to overcome beef’s environmental liabilities. Yet the dietary potential of such models is currently poorly known. Here, I thus ask whether nitrogen-sparing agriculture (NSA) can offer a viable alternative to the current US food system. Focusing on the most common eutrophication-causing element, N, I devise a specific model of mixed-use NSA comprising numerous small farms producing human plant-based food and forage, the latter feeding a core intensive beef operation that forgoes synthetic fertilizer and relies only on locally produced manure and N fixers. Assuming the model is deployed throughout the high-quality, precipitation-rich US cropland (delimiting approximately 100 million ha, less than half of today’s agricultural land use) and neglecting potential macroeconomic obstacles to wide deployment, I find that NSA could produce a diverse, high-quality nationwide diet distinctly better than today’s mean US diet. The model also permits 70%–80% of today’s beef consumption, raises today’s protein delivery by 5%–40%, and averts approximately 60% of today’s fertilizer use and approximately 10% of today’s total greenhouse gas emissions. As defined here, NSA is thus potentially a viable, scalable environmentally superior alternative to the current US food system, but only when combined with the commitment to substantially enhance our reliance on plant food.

size n m . More broadly, it plays a key role in the system's overall nitrogen cycling efficiency and productivity, as discussed in later sections. 27 The ρ v,f factors denote nitrogen retention rates. They represent the fact that nitrogen 28 inputs (right hand sides of Eqs. S1 and S2) are imperfectly retained, because some 29 fraction-(1 − ρ v ) and (1 − ρ f ) for the vegetal and forage subunits respectively-is lost by 30 leaching into the environment as solutes in surface or shallow below surface flows [1]. While As written earliier, γ appears as a state variable. In fact, there is a straiightforward way to 41 obtain a single optimal value for γ. 42 To show this, let's derive an expression for the productivity 43 P := A v y v + ηn m (S4) of the system as a function of γ. P sums the system's two key outputs, vegetal food and 44 beef, where η ≈ 10 − 12 kg edible beef N the full herd produces annually per mother cow. 45 We assemble the building blocks for P by first recasting the equation for y v to incorporate The latter equation becomes Substituting this into the y v equation finally yields 49 A . (S8) The first of two additive terms in P, the above takes note of the impact of γ on vegetal 50 productivity by addressing both the rise of y v with rising γ and the corresponding decline in 51 manure supply due to declining y f with rising γ.

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The second P term, addressing beef supply, is and thus all the way to γ = 1 which is thus the optimal value.

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With the optimal γ = 1, the governing equations reduce to n m = βA f y f (S14) in the vegetal subunit, a distinct disadvantage that explains the optimality of γ = 1 despite 67 the fact that the dominant N source, symbiotic fixation, is more often than not larger in the 68 forage subunit (i.e., f f > f v ).

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B Solution strategy and approach 70 We will still need to manipulate Eq. S15 a bit to make it practically useable for the current 71 situation. The following introduction of the general solution strategy will explain why and 72 how.

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First, we choose specific A f,v -the vegetal and forage areas in a single unit farm-and thus where A t is the total area of the envisioned unit farm. 84 We solve the system in a Monte Carlo framework in which specific realizations of 85 {d, f v,f , α, β} are randomly drawn from corresponding distributions derived from robust 86 observations of lower and upper bounds of these paramters. Because α and β depend on 87 cattle diet, we consider three such diets (see Table A) whose quality ranges widely enough to 88 collectively fully bracket the range of diets that can be plausibly expected to actually 89 characterize a realistic deployment of the envisioned scenarios.

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With the above paramteres determined or specified for a given realization, the solution 91 sequence for a given Monte Carlo realization is as follows.    to see why this impact is small; the full input is (Eq. S15), whose manure representing second term is roughly the first term times 1 (because d is uniform and the ranges of f v and f f are quite similar).

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To leading order, therefore, the nitrogen input into the vegetal plot is d + f v .

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7. Use Eq. S15 to obtain the full nitrogen input into the vegetal subunit,    Table B.  All steps above that have not yet been described unambiguously are described in subsequent 125 sections.

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Overall, we consider 61 plant items whose full nutritional and environmental information we The same, albeit following a different logical path, holds for the beef based part of the diet.

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Once n m is gotten (by solving Eq. S14), we use the herd structure (see section E and 156 Table B) to calculate the annual beef mass the A v ≈ 0.43 ha part of the operation yields. As  Let's symbolically summarize the above as follows. Let x ∈ R 62×1 be the mass output vector.

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For a given Monte Carlo realization, has 16 nonzero elements: 3 correspond to the 3 randomly selected nitrogen fixing plant items, 12 correspond to the 12 randomly selected other (non nitrogen fixing) plant items, and a final one-x b -corresponding to beef. The numerical values of these nonzero elements reflect the expected mass yield. For example, if one of the randomly selected plant items in a particular Monte Carlo realization is onion, the corresponding x element will be to garlic and j to dietary calories, and E ik is 1.1 g CO 2eq (g spinach) −1 when i corresponds 177 to spinach and k to greenhouse gas emissions.

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With x, N and E thus defined,  With this background, we proceed to parameterize ρ v,f as Michaelis-Menten-like processes,  The analytic form of ξ(N in ) is where the subscript v is suppressed with no added ambiguity, with the varying input in which the non-essential brackets hold and thus clearly identify the total productively 252 available nitrogen input into the vegetal subunit, the right hand side of Eq. S15.
v , ρ f respectively, where, e.g., ρ ±5%  ρ v,f , we study the sensitivity of the solution to uncertainty inherent in this parameterization.

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A reasonable metric for evaluating the sensitivity is total system productivity P (Eq. S11). 264 We thus repeat the full calculation nine times (3 forage qualities times 3 γ values, 0.7, 0.85 265 and the default optimal 1), exploring the system productivity under multiple perturbations 266 that simultaneously address both above potential limitations of the paramterization.  Reassuringly, the results of these calculations (Fig. E) show that the key model   With the above consideration, the included district span 105 million ha, which is the value 307 we use for national upscaling.  In the current setting, the herd size is determined by manure production, which depends not 310 only on the animal numbers and sizes already discussed but also on the composition of the 311 rations and the amounts actually consumed. We consider separately high, medium, and low  The main output beef stream is due to finishers, at an approximate rate of 0.7× (450-600) 331 kg live weight per year.

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Adding the above contributions, total annual live weight beef production is about 520-540 333 kg per cow. 334 We assume[19] live to hot carcass losses of 39% (i.e., we assume a dressing percentage of 61), 335 and subsequent losses of 49% [20], for a total supply chain mass retention of 30%, so that a 336 7.0 total annual intake by one mother cow and her accompanying animals kg dry matter feed 7500 7850 8100 kg crude feed protein 1370 1060 860 kg feed nitrogen 220 170 140 total beef production per one mother cow and her accompanying animals kg edible beef y −1 155 155 125 a ≈ (0.9 × 0.85 − 0.16)n m , slaughter at 600 kg or age of 2 y b first pregnancy begins on first day in which age ≥ 310 d and weight ≥ 400 kg kg of live weight yields 300 g of edible beef.

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Per one mother cow, the herd thus yields 120-160 kg of total edible beef cow −1 y −1 . Above, we use the original notation: MNO is an individual animal's manure (feces plus 394 urine) nitrogen output in g N d −1 , NI is ration's nitrogen intake in g d −1 , and TF is the 395 forage percentage in the diet, here 100. We estimate NI by dividing crude protein intake by   Figure F: Dependence of the model calculated protein availability on the assumed acrossthe-board yield penalty in the NSA system relative to today's conventional agriculture. The shown delivery statistics (mean and spread) are calculated over the three forage qualities and 250 Monte Carlo realizations. The spread whiskers span the 5th and 95th percentiles of the distributions, i.e., the core 90% of the distributions. Each bar comprises the plant contribution in green, with the beef contribution stacked over it in red. The fraction of plant protein in total protein delivery is shown numerically near the bars' bottoms, rising from left to right with declining vegetal yield penalty. The default yield penalty, 85% (the complement to the default 15% assumed yield penalty on which the main results are based), is highlighted in purple and with the "def." annotation. follows.

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Since this empirical αβ range falls well within our calculated range (Eq. S32), we accept the 432 α and β values given by Eqs. S30 and S31 respectively as suitably representative. Recall that in our model, there are two vegetal yield demotion factors. The first is the one 436 handled by ξ (section B2). The second is the across-the-board 15% demotion of today's 437 yields, to account for presumed lower efficiencies and yields in the envisioned NSA 438 agricultural model relative to the mostly conventional production it strives to replace. This assumed yield penalty is not based on any data, as the envision NSA system is novel and 440 hypothetical, and its performance not covered by verified data. A reasonable guide is offered 441 by organic agriculture, which is somewhat similar yet less stringent in terms of nutrient 442 cycling. However imperfect the comparison may be, the assumed 15% yield penalty is