Here, we provide a top-down method for understanding the demographic changes and resource constraints for a nationwide shift towards entirely grass-fed. Specifically we ask: (1) How many more exclusively grass-fed cattle would be required to produce the same amount of finished beef that is currently consumed? (2) How much exclusively grass-fed beef can the existing pasture resource support? To answer these questions we use a simple demographic model of US beef cattle. We then use this model to predict population changes necessary for pasture-finishing systems to keep pace with modern beef production rates and improve estimates of the amount of entirely pasture-raised beef that our present-day pastureland resources can support. We end with a discussion of sustainability metrics that warrant further study, as well as shifts in demand that would be required to keep exclusively grass-fed cattle production within biophysical limits.

To model future shifts to exclusively grass-fed beef, the size, lifespan, and weight gain of the present US beef cattle herd must be well understood. Multiple resources and studies have published global and national estimates of beef cattle populations [ 15 – 17 ], but national mean growth rates and residence times have not previously been reported. Grass-finished cattle have lower average daily weight gain (ADG) and finished weights than their grain-finished counterparts, because cattle eating grass have less efficient feed conversion ratios (FCR). This information has been widely reflected in localized studies about grass-finishing operations [ 18 ], but no study to date has calculated the consequences for scaling grass-finished operations up to the national level. A recent study found that current pastureland can support 35% of our present day beef output [ 19 ]. However, their model assumed a single aggregated FCR across all stages of rearing and finishing and did not model changes in ADG or finishing weight. These recent findings must be updated to adequately reflect differing feed requirements primarily in the finishing stage of production.

Because beef is the most land-demanding agricultural product in the US and the world, some have explored restricting cattle feed to pasturelands that are non-competitive with human food production [ 11 ]. Currently, 'grass-finished' beef accounts for less than 1% of the current US supply [ 12 ]. Imports of grass-finished beef to the US from Australia far outweigh the domestic US grass-finished beef supply [ 13 ]. Rapid growth in the grass-fed beef market of 20%–35% per year is leading suppliers to consider shifting domestic production to grass-finished beef [ 12 ]. Prior studies have considered market and infrastructure barriers to scaling grass-fed beef production [ 14 ]. However, biological and physical limits may inhibit the expansion of US grass-finished beef, including additional land for increased pasture and forage feed requirements.

While cattle are evolved to eat a diet primarily of grass and other forages not edible to humans, cattle are fattened in the final stages of their lives, or 'finished', on a diet of primarily grain in feedlots. The feedlot system has been the focus of concerns and investigations regarding food safety [ 7 ], environmental externalities [ 8 ], and animal welfare [ 9 ]. Feedlot systems rely on a high throughput of intensively grown crops, require frequent antibiotic and growth hormone usage, are located in regions where cattle are prone to heat exhaustion [ 9 ], and do not permit cattle to perform activities that conform with their natural instincts (i.e. grazing on open pasture). Furthermore, high volumes of manure and intensive manure management create odors which may result in human health consequences for agricultural workers and nearby residents [ 10 ] and undesirable aesthetic conditions. However, due to grain feed's higher nutrient density relative to grass, it requires significantly less land and generates less methane per unit of meat produced [ 3 , 6 ]. Large shifts in cattle herd management following macro-level consumer trends must therefore be quantified in light of environmental tradeoffs.

Beef cattle represent an important component of the US economy, totaling over $67bn in sales from more than 32 million cattle slaughtered in 2016 [ 1 ], with over three million cattle's worth of meat exported each year [ 2 ]. However, beef cattle have recently received focus as an inefficient means of procuring protein, resulting in greater feed and water costs and higher greenhouse gas emissions per unit of protein than other forms of meat or plant-based protein [ 3 – 6 ].

where F pasture is the national total pastureland-produced grass: 99 million metric tons (MMT) DM per year based on 2012 estimates [ 5 ] and used by Eshel et al [ 19 ]. The sum of n cow-calf(grassfed) and n finishing(grassfed) is the total cattle population required to sustain present-day beef output, while FR is the average daily feed requirement for grass-fed cattle, aggregated for the entire herd, in lbs DM head −1 day −1 . To calculate FR, we used National Research Council (NRC) nutrition requirements [ 23 ]. Fact sheets from the Oklahoma State Extension provide summary tables of NRC-derived feed requirements in lbs DM day −1 for typical US cow-calf subpopulations (including weaning calves, lactating and gestating cows, bulls, heifer replacements, and stocker cattle, but not finishing cattle) and rations [ 24 ]. We referenced these lookup tables using mean US cattle weights from EPA for each subpopulation to find their respective FR, then calculated the aggregate US cow-calf herd mean FR weighted by EPA subpopulation totals, excluding cattle finishing on grass. For grass-finishing cattle, we assumed similar feed requirements as larger stocker cattle, who are presently fed pasture and roughages, and we assumed a mean weight of 918 lbs, the linear mean of their starting placement weight w placement = 720 lbs and ending slaughter weight w slaughter(grassfed) = 1115 lbs. The resulting aggregated grass-fed cattle FR was 21.8 lbs head −1 day −1 . The denominator of equation 9 represents the total feed needs for the entire future grass-fed herd.

The estimated proportion of cattle that could be raised in the United States on pastureland grass resources relative to the present-day population has been previously calculated as 35% [ 19 ]. The conversion was calculated as the proportion of the present-day total cattle feed on a dry matter (DM) basis consisting of grass from pastureland. However, because less than 1% of cattle are finished on grass, this conversion rate did not appropriately account for the increased energy density, feed efficiency, and maximum fattening rate for finishing cattle on concentrates relative to grass-finished cattle.

where n finishing(grassfed) is the number of cattle finishing on grass, averaged over the year, required to sustain present-day beef production rates. Lastly, we assume that the number of cow-calf herd cattle must increase proportionally to the new rate of placement on grass-finishing operations.

where ADG grassfed = 1.4 lbs day −1 is the average daily weight gain of cattle finishing on grass, w slaughter(grassfed) = 1115 lbs is the mean slaughter weight of grass-finished cattle, and w placed = 720 lbs is the mean placement weight which we assume does not change from the present-day system. The longer residence time means that more cattle must reside within finishing operations, assuming steady-state:

Cattle finished on pasture reach a smaller maximum weight of approximately 1115 lbs [ 22 ]. In order to produce the same annual quantity of beef, the rate of cattle shipped to slaughter, hence the rate of cattle graduating to finishing from their cow-calf herds in a new equilibrium grass-fed system, must increase in proportion to the new lower slaughter weight.

To independently corroborate feedlot residence times, the daily weight gain implied by our mean residence time was calculated and compared to literature estimates. The resulting live slaughter weight of feedlot cattle was subtracted from their mean placement weight derived from 2012 USDA surveys to obtain daily feedlot weight gain representing the national average. Feedlot weight gain was then divided by mean feedlot residence time to obtain mean weight gain per day on feedlots, which was compared with literature values of 2.7 to 3.3 lbs day −1 [ 20 ].

where τ feedlot is mean residence time in days, n feedlot is the number of cattle on feedlots averaged over the full year in 2012, and r placement is the 2012 yearly rate of placements of cattle on feedlots in units of head per year.

To obtain the mean residence time of cattle on feedlots, the 2012 national yearly mean feedlot population was divided by the 2012 yearly rate of cattle feedlot placements, which we assume is approximately in steady-state and approximately equivalent to 2013 yearly slaughter rates. We then multiply the yearly mean residence time by 366 days to obtain residence time.

This number may be biased slightly low because 9% of cattle slaughtered in these facilities are culled stocker heifers and steers. Nonetheless, the resulting weight, w slaughter = 1386 lbs, is our best estimate for the national average live weight of grain-finished cattle from feedlots.

We used the 2012 national annual cattle population reported by the EPA in their Annual Emissions Inventory [ 20 ], which were derived from point-in-time cattle censuses conducted by USDA. All beef cattle that were not in feedlots were classified as cow-calf herd cattle, and include calves, dry and lactating cows, bulls, heifer replacements for dairy cows, and stocker cattle. Mean slaughter weight of cattle from feedlots were calculated using 2012 survey feedlot placement numbers, 2013 survey slaughter rates, and 2013 mean dressed weight at slaughter from the USDA NASS [ 21 ]. The mean weight of steers and heifers slaughtered in federally inspected commercial slaughterhouses was reported in dressed weight (carcass weight minus blood and internal organs). The dressed weight of commercially slaughtered finished heifers and steers was norMalized by the slaughtered number of each of these subpopulations then divided by 0.604, the ratio of live weight to dressed weight for all slaughtered cattle in aggregate, in order to obtain a live weight for feedlot cattle at slaughter.

Cattle on feedlots at any given time represent a fraction of the total US cattle population. Cattle are placed on feedlots only after reaching maturity so that their skeletal development and immune systems can support the high rate of fattening they are subjected to on feedlots. Additionally, the low fecundity rate of cows relative to other farmed animals, of roughly one calf per year, means that many additional cows and bulls are needed to produce calves that replace the slaughtered population. The large population of breeding cattle and their calves are herein referred to as the cow-calf beef herd. Within this population, we include stocker cattle, which are more mature than calves but have not yet been placed on feedlots. Beef cattle that have matured and been placed onto feedlots are referred to as feedlot cattle. Dairy cattle are almost an entirely different herd in the United States, and we distinguish them separately from the beef cattle that are the subject of our analysis.

3.1. Present-day distributions and productivity of beef cattle

A simple box model of national cattle populations is presented in figure 1. The national beef cow-calf herd cattle population is almost five times larger than the population of cattle on feedlots. This imbalance of cattle populations in different stages of rearing before slaughter explains why in the US most cattle can be seen grazing on pastures, but almost all beef in the US comes from confined feedlot operations [12]. This apparent paradox is explained by the facts that (1) many more breeding cattle are needed to replace the feedlot population annually and (2) beef cattle spend only 41% of their 18 month-long lives on feedlots. We calculated a mean residence time of 223 days, or approximately 7.5 months, of cattle on feedlots. Mean placement weight was 720 lbs and mean slaughter weight was 1386 lbs. Over 223 days, this corresponds to 2.98 lbs per day on feedlots, which agrees with the literature reported values of 2.7 to 3.3 lbs per day. Assuming an approximate steady state, 22 million cattle are slaughtered at 1386 lbs to produce more than 12 billion lbs of beef from feedlot cattle. Additional slaughter from culled dairy cows, beef cows and bulls, replacement steers and heifers, and veal calves, totaling 10 million cattle annually, are not included in this analysis, as their meat either goes towards lower-quality beef products such as ground beef mixtures and pet food or is sold as specialty veal. Figure 1. Fluxes and populations of cattle in millions for the current US grain-finishing beef system in 2012. Download figure: Standard image High-resolution image Export PowerPoint slide

3.2. How many more cattle fed exclusively on grass would be required to produce as much beef as is currently consumed?

Replacing the 13 million cattle presently finished in feedlots is not as trivial as raising an equivalent number of cattle on pasture. Cattle on pasture fatten at slower rates than those on feedlots. What follows is an analysis of the necessary increases in residence times and population that are needed in order to produce the same quantity of high-quality beef, approximately 12 billion lbs, currently produced by the feedlot system. Cattle finishing on pasture fatten at a rate of approximately 1.4 lbs per day and reach a smaller maximum weight of approximately 1115 lbs [22]. Therefore, to gain the necessary slaughter weight, finishing cattle need to spend 281 days, more than 9 months, grazing on pasture (table 1), as well as eating hay and forage supplements outside of their respective regions' growing seasons. To produce the same amount of high-quality beef as the current feedlot system, grass-finishing cattle would need to be slaughtered at a rate of 27 million cattle per year instead of 22 million, with just as many required for placement onto finishing systems (table 2). Due to the slower fattening rate and longer residence time, this would require 21 million cattle instead of 13 million cattle residing in finishing systems on an annually averaged basis, an increase in 67% (figure 2, table 2). Figure 2. Fluxes and populations of cattle in millions for hypothetical future grass-finishing system. Estimate assumes that the annual slaughtered amount of high-quality beef is held constant from 2012 at approximately 14 billion lbs, that grass-finished cattle are slaughtered at 1115 lbs, and that cattle are fattened on grass at a rate of 1.4 lbs per day. The mean productivity of cow-calf herds remains constant, with total population changing in proportion to the increased placement and slaughter rate. Download figure: Standard image High-resolution image Export PowerPoint slide Table 1. Finishing and slaughter rate parameters for present-day conventional feedlot-finished cattle and future hypothetical grass-finishing cattle. ⁎Source: USDA NASS. ⁎⁎Source: Pelletier et al 2010 [22]. Residence time (τ) Average daily gain (ADG) Slaughter rate (r) Slaughter weight (w slaughter ) days lb head−1 day−1 head year−1 lbs Conventional 223 3.0 21 864 000⁎ 1386 Grass-fed 281 1.4⁎⁎ 27 185 000 1115⁎⁎ Increases in cattle population, placements, and slaughter rates are demonstrated in figure 2. The increased slaughtering and placement numbers would also require a 24% increase in the size of the national beef cow-calf herd, proportional to the increased annual grass-finishing placement rate, in order to provide additional cattle to stock the grass-finishing stage. Increases in both the cow-calf herd and the grass-finishing population together would result in a total increase to the US cattle population of an additional 23 million cattle, or 30% more than the current US beef cattle population as a whole (table 2). Supporting a larger grass-fed cattle population would involve environmental tradeoffs. Emissions of methane, a greenhouse gas with a large warming effect relative to carbon dioxide per molecule, come from beef cattle in the forms enteric fermentation and manure emissions. We calculated a 43% increase in methane from enteric fermentation (table 2), assuming that cattle finishing on grass had the same daily methane emissions as present-day stocker cattle, who have nearly identical ADG and are fed primarily on roughage. Modeling the nuanced differences to present-day stocker cattle's diet would be largely hypothetical and subject to large geographic variation. Additionally, manure methane emissions are proportionally small for present-day beef cattle, about 4% relative to enteric fermentation. Future manure methane would thus likely increase proportionally to the cattle population but would be smaller than the increase in enteric fermentation. Taken together, an exclusively grass-fed beef cattle herd would raise the United States' total methane emissions by approximately 8%. Changes in other environmental impacts such as nitrous oxide emissions and water pollution are more challenging to predict, and are discussed further in section 3.4. The precision of our present-day beef cattle demographic model (figure 1) is made possible by inputs from nationally-representative USDA censuses (equations 1–3). Equivalent sampling does not exist for exclusively grass-fed systems. Because of a high level of heterogeneity in ADG and slaughter weights among individual grass-finished operations, reflecting different climatic conditions, terrain, soil, physical cattle activity, and nuanced management decisions such as cultivated forages and rotational grazing regimens, our estimates for exclusively grass-fed beef cattle production in the US are meant to reflect an approximate and hypothetical scenario. Different estimates can be made by assuming different values for ADG and finished weights (table 1) in equations (4–7). We performed a simple sensitivity analysis and found that increasing ADG grassfed and w slaighter(grassfed) each by 10% led to a decrease in the total grass-fed population of 1.9% and 3.7% respectively. This suggests that future developments in nutritional science, animal genetics, pasture management, and forage quality may enable producers to achieve higher efficiency in pasture-based systems than the estimates in this analysis [25]. Table 2. Beef cattle population and enteric fermentation methane emissions (in millions of metric tons) of present-day conventional beef systems and future hypothetical exclusively grass-fed beef systems. ⁎Source: US EPA. Population Enteric fermentation methane Cow-calf finishing Total MMT CH 4 Conventional⁎ 63 493 000 13 328 000 76 821 000 4.76 Grass-fed 78 946 000 20 876 000 99 822 000 6.79

3.3. How much exclusively grass-fed beef can the existing pasture resource support?

We estimate that present-day pastureland grass resources can sustain only 27% (P = 0.27) of our current beef output. The amount of grass feed needed to sustain present-day beef production in an exclusively grass-fed system is 387 MMT DM year−1, a 37% increase in dry weight relative to present-day national total cattle feed of 283 MMT DM year−1 [5], which includes grain. Using the present-day total feed weight of 283 MMT DM year−1 reproduces the result of 35% (P = 0.35) from Eshel et al [19]. Therefore, it is apparent that Eshel et al assume a constant feed conversion ratio for beef across all feeds, i.e. that grass and grain are interchangeable for beef cattle growth. To the contrary, these two feed stocks have disparate feed efficiencies, produce different metabolic byproducts such as methane and manure, and allow cattle to fatten at different maximum rates [23]. We updated their results by calculating the increase in size of the beef cattle herd and increased feed needs for a larger exclusively grass-fed herd (equation 9), rather than simply dividing the dry weight of grass presently fed to cattle by the dry weight of all feeds presently feed to cattle. This estimate excludes grain, hay, silage, and other roughage grown on croplands as a potential feed source for exclusively pasture-raised cattle to match the definition of 'sustainable beef' used by Eshel et al and others [11, 19]. However, hay and silage from these lands provide a critical source of supplemental feed to pasture-raised cattle during dormant cold or dry seasons and pasture-based certifications schemes by third parties allow for supplemental forage feed during dormant seasons [26]. Adding the 126 MMT DM year−1 of roughage feed that are presently grown on croplands to F pasture brings the amount of grass-fed beef that pastures in the US could support to 61% (P = 0.61) of our current beef supply. Additionally, croplands currently utilized for grains fed to farmed animals could be substituted for alfalfa, a high-yielding forage crop. On more than 5 million highly-productive cropland hectares on which 38 MMT DM grain beef cattle is presently grown each year, we calculate that farmers could instead grow 34 MMT DM of alfalfa at present yields on high-productivity cropland (assuming 29% dry matter). Including these 'replaced' forages, the US land base could support up to 71% of the current US beef production exclusively grasses and forages. These forages, however, would necessarily be in competition with human food crops, a scenario that advocates for an exclusively grass-fed cattle future would likely hope to avoid. Research is still needed to assess yield gaps between present and potential future productivity of US pasturelands and roughage croplands. Statistical and processed-based modeling can assess underperforming areas [27], which could be optimized through better fertilizing, soil conditioning, and rotational management. Currently, less than 2% of all agricultural lands in the US undergo a rotation between cropland and pasture [28], though this type of management is known to increase forage productivity [29]. The required 30% increase in the overall cattle population must be accompanied by large increases in the productivity of existing pastures, on the order of 40%–370%, to avoid clearing additional native vegetation or competition with the human food supply.

3.4. Implications for sustainability and future research directions