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Regional-scale trade-offs among beef production, emissions and land use impacts: A cattle diet composition perspective

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R. Wang<sup>a</sup>, L. Puillet<sup>b</sup>, C. Pinsard<sup>a</sup>, P. Lescoat<sup>c</sup>,F. Accatino<sup>a</sup>

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<sup>a</sup> INRAE, AgroParisTech, Université Paris-Saclay, UMR Science Action Développement - Activités Produits Territoires (SADAPT) 22 place de l'Agronomie, 91120 Palaiseau, France

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<sup>b</sup> INRAE, AgroParisTech, Université Paris-Saclay, UMR Modélisation Systémique Appliquée aux Ruminants (MoSAR) 22 place de l'Agronomie, 91120, Palaiseau, France

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<sup>c</sup> INRAE, AgroParisTech, Université Paris-Saclay, UMR Science Action Développement - Activités Produits Territoires (SADAPT) 22 place de l'Agronomie, 91120 Palaiseau, France

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Corresponding author: Francesco Accatino. Email: francesco.accatino@inrae.fr

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Abstract

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CONTEXT. Although playing a role in global food security, beef production systems cause concerns due to pressure on land for feed production and greenhouse gas emissions.

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OBJECTIVE. We aimed at quantifying the trade-offs associated with different beef cattle diet compositions, considering beef meat production, greenhouse gas emissions, and land use impacts. In addition, we evaluated the influence of dry periods and grazing improvement for trade-off mitigation.

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METHODS. We developed a model linking beef cattle diet composition to land use impact indicators (feed import requirements and feed-food competition indicators), beef production (proxied by total weight gain [WG]), and animal emissions in a year.
We applied the model to the grassland-based beef cattle region of Bourbonnais, France, with a three-step analysis: (i) we explored the model outputs over a joint range of cereal and grass intake; (ii) we investigated the sensitivity of each feed type intake on the outputs; (iii) we simulated scenarios representing situations affecting cattle diet, *dry seasons* (-20% average crop and grass yields, grazing time, cattle growth rate and less cattle grass intake compensated by an equivalent increase of other feed types), *grazing improvement* (increasing grass yield by 20% and its digestibility and gross energy content by 5%) and *mixed* (combining the previous scenarios).

## RESULTS AND CONCLUSIONS.
Analysis (i) showed that more digestible diets conciliate production with emission reduction; however, they also cause undesired feed imports and feed-food competition. Analysis (ii) showed that, although present in the diet in relatively small quantities, oil protein crops as feed have high impact on model variables and outputs. In analysis (iii), compared to *baseline*, *dry seasons* decreases slightly in WG and emissions but increases feed-food competition (human-edible feed +149g/kg WG) with extra feed importations; *Grazing improvement* increases WG (+6.02%) and decreases emissions (-3.03%), human-edible feed per WG (-37g/kg WG) and food-competing land per WG (-5.7×10⁻⁵ ha/kg WG) with no additional impact on feed imports; *mixed* scenario, increases total WG (+1.22%); decreases emissions (-3.25%) with less feed-food competition and less importation than *baseline* scenario.

## SIGNIFICANCE.
Beef cattle diet composition linked to land-use based management practices, is an effective tool to handle the trade-offs at the regional scale. Improving pasture quality alleviates the trade-offs by increasing production, reducing emission,
feed-food competition and feed imports. Improving resilience of grasslands to droughts alleviates the negative impacts of dietary changes during dry periods.

**Keywords:** Livestock weight gain, Feed-food competition, Digestibility, Grazing, Emissions

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## 1. Introduction

Cattle beef production contributes to a number of Sustainable Development Goals (Mehrabi et al., 2020) playing a crucial role in nutrition security (Lee et al., 2021) and generating employment. However, due to the increasing world demand for animal-sourced food, the area required to produce animal feed puts considerable pressure on agricultural land use (Davis et al., 2015; Govoni et al., 2023). Furthermore, the environmental impacts of cattle systems attracted the attention of multiple stakeholders and scientists (Gerber et al., 2015). In particular, beef contributes to about 23% of the world's meat production while contributing to over 60% of the total greenhouse gas emissions of the livestock sector, with about 60% of them being from enteric methane (see the FAO, 2023 estimation with the GLEAM model). In terms of land use, beef production uses over 60% of the world's agricultural land, mainly for pasture grazing and feed production (Greenwood, 2021). The reliance on both concentrate feed and extensive land use for pasture raises the question of feed-food competition given that the plant biomass used for concentrates may also be human-edible and the land used for pasture may be used to some extent for food production (Mottet et al., 2017). Nowadays, it is challenging—yet fundamental—for beef cattle systems not only to contribute to human food security but also minimize impacts on land use and greenhouse gas emissions. For this reason, understanding
and quantifying the trade-offs among food production, emissions and land use is
paramount (Davis et al., 2015). 74 75

Previous studies highlight the importance of crop-livestock integration beyond the farm level (Martin et al., 2016) and the role of livestock in circular economy (van Zanten et al., 2019). Indeed, integration of crops and livestock brings benefits such as improved soil fertility and the possibility to consume feed with low opportunity costs. This view highlights the importance of focusing on the regional scale (from municipality to NUTS 3 (Nomenclature Unit for Territorial Statistics 3) and promoting policies and management strategies that take into account, at the same time, land use and livestock (Muscat et al., 2021). However, it is important to understand quantitatively and qualitatively the trade-off involved in the integrated crop-livestock system. Multiple objectives, often conflicting, arise, such as production and the minimization of feed-food competition, greenhouse gas emission, and feed imports (van Selm et al., 2024). 76 77 78 79 80 81 82 83 84 85 86 87

Cattle diet, in terms of quantity of dry matter intake and composition, is a key in crop-
livestock system management, because it impacts at the same time on productivity,
animal emissions, and land use. For cattle, this is more evident than in other
livestock species, as cattle systems are based on a wider range of feed intakes
ranging in Europe from pure grassland-based systems to landless grain-based
fattening systems (Greenwood et al., 2021). More digestible dietary components
reduce animal emissions and increase beef production (Cantalapiedra-Hijar et al.,
2018). At the same time, some feed items require agricultural land that might be
allocated to food production (Muscat et al., 2020) and in many cases need to be
imported, impacting land use in other regions or countries. In addition, two
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considerations about cattle diet and its impacts can be made. First, climatic events can cause temporary modification to cattle diet and therefore its impacts. For example, heat can lead to reduced crop and forage production and quality (Nettier et al., 2010). Second, management practices can mitigate negative impacts of diets; for example, grazing improvement can make grassland primary production more digestible for ruminants (Morais et al., 2018).

Modelling is a useful tool for exploring trade-offs from the perspective of diet quantity and composition and their impacts on production, emissions, and land use. Many studies in the field of animal nutrition developed models to predict beef cattle production depending on dietary composition (e.g., Faverdin et al., 2011; Huuskonen et al., 2013). Specifically, cattle-production responses to energy and protein intake have been widely investigated at the animal scale. To estimate emissions, models have been developed based on diet characteristics such as gross energy intake, digestibility and nitrogen content (IPCC, 2019; Eugène et al., 2019; Moraes et al., 2014). Additionally, several studies have explored strategies for mitigating emissions while maintaining animal production through the management of cattle diet (Cardoso et al., 2016; Grainger and Beauchemin, 2011). However, most studies regarding beef cattle production and emissions focused on a small scale (from animal to farm) or country level, without taking into account the region. In addition, to the best of our knowledge, no models explicitly quantified the trade-offs between production, emissions and land use affected by cattle diet.

In this study we consider the regional-scale perspective and, with a modelling approach, we analyze the effect of cattle diet at the same time on livestock performance (production and greenhouse gas emissions), and land use (feed-food
competition and import needs), considering also the possible consequences of
dietary variations imposed by external events or management strategies. At best of
our knowledge such a model-based analysis was not done before in the literature
and follows the track paved by previous studies about crop-livestock integration and
circularity, exploring the trade-offs involved and related to how diet links cattle
performance to land use impacts: Puillet et al. (2014) suggested including land use
and diet factors in emissions assessments of cattle production at different spatial
levels; Pinsard et al. (2021) linked feed availability in the region to livestock
management. In particular, we focus on the French region of Bocage Bourbonnais.
France is the highest beef producer in Europe (Hocquette et al., 2018) and the study
region is contained in the Charolais area which highlight contributes to the French
beef production (Veysset et al., 2015), is mostly grassland-based by also has some
crop systems allowing for cattle dietary diversification.

We addressed the trade-offs related to beef cattle diet at the regional scale,
answering to the following research questions: (i) how does cattle diet composition
(proportions and quantities of feed types) affect a set of outputs (production,
emissions, feed import requirements, feed-food competition indicators)? (ii) how are
outcomes affected by external events or management strategies? We first developed
a model for beef cattle linking diet to weight gain, emissions and land use. We
explored the trade-offs among outputs caused by different proportions of grass and
cereals intake in the diet and conducted a sensitivity analysis to rank the contribution
of each feed type to each output. Finally, we simulated scenarios involving external
events affecting diet composition (*dry seasons*) and management strategies aimed at
mitigating trade-offs (*grazing improvement*).
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## 2. Material and methods

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### 2.1 General model description

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The model operates on a unique one-year time step at the scale of small agricultural region (SAR), which, in the French system, is an administrative spatial entity with agronomic homogeneity and average area of 76,800 hectares (Accatino et al., 2019; Pinsard and Accatino, 2023). As depicted in Fig. 1, the starting point of the model is the quantity and composition of beef cattle diet, represented as an array of quantities of six feed types (Fig. 1A). Its main properties (total dry matter (DM) intake, average digestibility, gross energy content and nitrogen content) are determined by the plant production in the SAR (Fig. 1B) and serve as inputs for three sub-models that calculate, at the SAR level, (i) agricultural land use impact indicators (i.e., feed import needs and feed-food competition), (ii) cattle WG (iii) emissions from enteric fermentation and manure management. In this model, we only focus on beef cattle categories, keeping the other livestock species (and dairy cattle) as constant. We only consider the on-farm emissions for beef cattle, including methane and nitrogen emissions.
<figure><img src="image_1.png" /><figcaption>**Fig. 1.** General description of the model. Each sub-panel refers to a part of the model; thicker arrows refer to aggregation over model entities. Panel A: elements composing the diet for each beef cattle category; Panel B: elements composing the plant productions from different land uses in the region. Panel C: agricultural land use impact sub-model, leading to feed import demand and the feed-food competition indicators. Panel D: body growth sub-model applied to each beef cattle category; the sub-model has a daily time step and the final indicator, total weight gain, is obtained by aggregating over one year. Panel E: Emissions calculated for each beef cattle category; the final indicator corresponds to aggregation over all beef cattle categories.</figcaption></figure>

The agricultural land use impact sub-model (Fig. 1C) calculates and compares the total feed demands of beef cattle with the calculated available feed produced in the SAR, in order to quantify the necessity for external feed imports and feed-food competition (section 2.3). The body growth sub-model (Fig. 1D) starts from individual
diet intake, composition and animal numbers to calculate weight gain, considered as a proxy of beef production. The model adopts a metabolism approach based on energy partitioning across biological functions upscaled at the regional level (section 2.4). The emissions sub-model (Fig. 1E) calculates emissions of all beef cattle categories in the SAR from enteric fermentation using average diet digestibility, gross energy content and nitrogen content (section 2.5). In this methodological section we provide the general model structure and only the formulaic expression for the calculation of the final indicators (sections 2.3, 2.4, 2.5); however, all the terms with their definitions, units, values or related equations and sources are detailed in the Supplementary Table S1.

## 2.2 Conceptualization of beef cattle diet and agricultural production

It is necessary to formalize beef cattle diet, agricultural production, and the computation of the three main elements which are inputs to the subsequent sub-models: dietary intake, diet average digestibility, gross energy content and nitrogen content. The model considers a set of beef cattle categories *k*, characterized by a population size ($N_k^*$ [livestock unit (LU)] or $N_k$[head]) and a duration of stay in the category (see Supplementary Table S1 and S7). We considered six feed types: cereals, co-products, oil-protein crops, oilseed meals, forage and grass. Co-products are derived from the industrial processing of cereal crops. Oilseed meals provide energy, proteins and fiber to animals and are obtained through a series of oilseed processing. Forage includes fodder and silage. We assumed that grass is sourced from permanent grassland that is inherently unsuitable for conversion to cropland. Each category *k* is assigned a nominal quantity $u_{j,k}^*$, obtained from data and corresponding to the feed arriving at the farm ([kg DM/head/day]) of each feed type *j*.
(Fig. 1A). The nominal quantity for each feed type is then corrected into effective quantity $u_{j,k,t}$ ([kg DM/head/day]) which corresponds to the effective intake. This occurs because we account for losses within the farm (i.e., feed losses in the farm during storage and distribution of feed) and physiological limits of the animals (i.e., gut capacity). Details about the calculation of effective intake are given in Supplementary Material 3.

Average digestibility, gross energy content and nitrogen content of diet are calculated starting from the agricultural production in the region, assuming that, in a SAR characterized by crops and livestock, beef cattle diet is largely based on locally produced feed. Data about composition of imported feed from outside the region were not available, nor was available the information about the specific origin. Therefore we assumed that the imported feed has a composition similar to the local (in France a large fraction of animal feed is produced within the country and the feed imported from abroad mostly is density protein feed, which account for a small proportion).

We conceptualized a SAR as characterized by a set of land uses (allocated to either cropland or grassland). Each land use corresponds to a plant (crop or grass) $n$, which is characterized by agricultural surface ($S_n$ [ha]), annual yield in fresh matter ($Y_n$ [tons/ha]) and a conversion coefficient from wet matter to dry matter ($\tau_n$ [%]). Plant productions are then assigned to feed items and finally to the available feed types). The zoom in Fig. 2 shows more in detail that the harvested plant products are distributed among different feed items, or to non-feed uses (food, industry, biomass). To give an example, for soft wheat a fraction is used as grain feed, another fraction is used as feed in form of co-product (e.g., wheat bran). The coefficient $\alpha_{n,i}$ represents
the fraction (ranging between 0 and 1) of harvested dry matter of crop/grass $n$
converted into feed $i$. Once the plant $n$ contributing to each feed item $i$ is known, it is
possible to calculate the feed item quantity $q_i$.

Each feed item $i$ is characterized by a digestibility $\delta_i$, a gross energy content $\varepsilon_i$ and
a nitrogen content $v_i$. These parameters are aggregated at the feed type level,
weight-averaging or summing over the feed items contained in each feed type,
obtaining the average digestibility $\overline{d_j}$, gross energy content $\overline{e_j}$ and nitrogen content
$\overline{\eta_j}$, respectively, of feed type $j$. In turn, these two latter values are aggregated
(summed or weight-averaged) at the diet level, obtaining the average digestibility $\overline{D_k}$,
the total gross energy content $GE_k$ and total nitrogen content $\Pi_{k,t}$ of the diet of
category $k$. All the equations used for aggregating quantities from plant production to
feed types and diet are provided in Supplementary Table S1.

<figure><img src="image_2.png" /></figure>
Fig. 2 Calculation of feed imports in the region. The upper left-hand gray rectangle (labelled “feed availability”) represents the procedure for calculating feed type availabilities in the region. Crop/grassland areas produce a certain amount of harvest, which is partitioned to feed items or other uses (see the zoom rectangle). Feed items are then grouped into feed types. The upper right-hand gray rectangle (labelled “feed demand”) represents the procedure for calculating feed type demands in the region. Each livestock category has a certain demand per head of each feed type. Demands of each feed types are obtained by summing the requirements for each livestock category. Imports are obtained by comparing availability and requirement at the regional scale.

## 2.3 Agricultural land-use impact sub-model

The purpose of the agricultural land use impact sub-model is to determine feed imports and feed-food competition indicators. Higher feed imports suggest that the local land might not be sufficient to produce enough feed to meet the demand of livestock, leading to increased pressure on land and emissions elsewhere to produce the feed (Khatun, 2012). Understanding feed-food competition helps uncover the dynamic interplay between food crop production and feed production (Mottet et al., 2017; Muscat et al., 2020).

### 2.3.1 Calculation of feed import needs

The formula for the calculation of feed imports $Q_j^I$ for each feed type j is

$$Q_j^I = \max\{0, Q_j^{D,b} + Q_j^{D,s} - Q_j^A\} \quad (1)$$

where $Q_j^A$ is the total dry matter available for feed type j and $Q_j^{DR,b}$ and $Q_j^{DR,s}$ are the total dry matter demand of feed type j for beef cattle and other livestock species/categories, respectively. In this study, our focus is on beef cattle's diet; nonetheless, we consider the presence of other livestock species and incorporate
their consumption data into our analysis (considering the nominal consumption aggregated at the species level, without going into the detail of sub-categories and keeping it constant). The total dry matter of feed imported $Q^I$ is obtained by summing the dry matter of all the imported feed items. In order to calculate the feed imports (Eq. (1)), the agricultural land-use sub-model calculates the availability $Q_j^A$ and the demand $Q_j^D$ for each feed type (Fig. 2). Feed demand is aggregated from the demand per head of each feed type to the regional level (right-hand rectangle in Fig. 2, labelled “feed demand”). The operator max in Eq. (1) indicates that the import needs exist only if $Q_j^{D,b} + Q_j^{D,s} > Q_j^A$, i.e., if the demand exceed the feed available produced in the region.

### 2.3.2 Calculation of feed-food competition indicators

Following Mottet et al (2017), we used two indicators for expressing feed-food competition in beef cattle production for a region. The first indicator $F^B$ is the human-edible biomass consumed by beef cattle over the weight gain (feed-food competition for biomass consumption):

$$F^B = \frac{\sum_j Q_j^{R,b} \times \omega_j^B \times 1000}{WG} \quad (2)$$

Where $Q_j^{R,b}$ is the amount of feed required by all beef cattle categories in the SAR, whereas $\omega_j^B$ is a coefficient equal to 0 if the feed type is not edible by humans, and is equal to 1 if it is edible by humans (it is the case for cereals and oil-protein crops).

The second indicator $F^L$ is the food-competing land over the weight gain of growing beef cattle (feed-food competition for land):
$$F^L = \frac{\sum_j A_j^R \times \omega_j^L}{WG} \qquad (3)$$

where, $A_j^R$ is the total area of the surface required to produced feed type j, in order to calculate it we use the average yield (see Supplementary Material S5). The coefficient $\omega_j^L$ is 1 if the crop is produced on land in competition for food production, and 0 otherwise. Following the study of Mottet et al (2017), we identified feed types that are grown on land also suitable for food crops: cereals, oil-protein crops, forage (grown on arable land), and soybean meals.

## 2.4 Body growth sub-model

The body growth sub-model calculates the annual cumulated WG of beef cattle as a proxy of production and as a function of the diet properties (DM intake, gross energy content, digestibility), with a metabolism approach based on energy balance and partitioning among biological functions. Our model normally has a yearly time step; however, because animal weight gain depends on the animal live weight itself, we decided to implement the model with a daily time step to have a finer and more accurate calculation, and then aggregate over time throughout the year. The total weight gain $WG_k$ for each category k cumulated over one year is given by:

$$WG_k = \sum_{t=1}^{t_k^G} DWG_{k,t} \qquad (4)$$

Where $DWG_{k,t}$ corresponds to the daily weight gain and $t_k^G$ corresponds to the growth duration within a year (corresponding to 365 days if the category has a permanence duration longer than one year, and to less otherwise (e.g., calves 7-12 months)). The
equation for $DWG_{k,t}$ was obtained by reversing the equation in IPCC (2019) to calculate the net energy for growth $NE_{k,t}^g$:

$$DWG_{k,t} = \left( \frac{NE_{k,t}^g}{22.02 \times \left( \frac{LW_{k,t-1}}{C_k^g \times TW_k} \right)^{0.75}} \right)^{0.9116} \quad (5)$$

Where $LW_{k,t-1}$ [kg] is the live body weight on the previous day, $TW_k$ [kg] is the empirical value of the targeted weight of beef cattle category $k$ at the end of the corresponding growth stage, and $C_k^g$ is the growth coefficient. We iterated this process of calculation over a corresponding duration $t_k^g$ in one year to determine each $DWG_{k,t}$: we added the $DWG_{k,t}$ to the weight at the end of the previous day $LW_{k,t-1}$ to get the live weight of the day $LW_{k,t}$.

### 2.4.1 Calculation of the net energy for growth

In order to provide an explanation of the net energy for growth, it is important to give a context about the energetic terms involved in the metabolic model. Only a part of gross energy is used as digestible energy $DE_{k,t}$. Digestible energy is then partitioned between body growth ($DE_{k,t}^g$) and non-body-growth ($DE_{k,t}^{ng}$). The portion not lost in urine, gaseous emissions or heat produced during digestion constitutes the net energy for body growth ($NE_{k,t}^g = DE_{k,t}^g \times r_k^g$) and non-growth ($NE_{k,t}^{ng} = DE_{k,t}^{ng} \times r_k^{ng}$); $r_k^g$ [-] and $r_k^{ng}$ [-] are the ratios of digestible energy to net energy for growth and non-growth, respectively (see calculation in Supplementary Material S7). Net energy for non-growth use ($NE_{k,t}^{ng}$) is partitioned for different functions, i.e., maintenance ($NE_{k,t}^m$),
activity ($NE_{k,t}^a$), and, optionally, lactation ($NE_{k,t}^l$) and pregnancy ($NE_{k,t}^p$), depending on cattle category and physiological period: $NE_{k,t}^{ng} = NE_{k,t}^m + NE_{k,t}^a + NE_{k,t}^l + NE_{k,t}^p$. All these energetic terms are not necessarily active for all the categories along the whole year, specifically, $NE_{k,t}^l$ is only used by cows aged 3-4 years and $NE_k^p$ is used only by heifers aged 2-3 years and cows aged 3-4 years. Therefore, the equation for net energy allocated for body growth is (following IPCC, 2019):

$$NE_{k,t}^g = \left( DE_{k,t} - \frac{NE_{k,t}^m + NE_{k,t}^a + NE_{k,t}^l + NE_{k,t}^p}{r_k^{ng}} \right) \times r_k^g \quad (6)$$

The terms appearing in Equation 5 and 6 are described accurately in Supplementary Table S1. Equation (5) is iterated over a number $t_k^G$ of daily time steps; within this period, each energetic term $p$ (metabolism, activity, lactation, pregnancy) is activated over a number $t_k^p$ of days for category $k$.

## 2.5 Emissions sub-model

We followed the IPCC Tier 2 approach to assess emissions from enteric fermentation and manure management. Methane emissions from enteric fermentation are calculated starting from gross energy intake ($GE_{k,t}$) and a methane conversion factor $\phi_k$ [%] (i.e., the percentage of feed gross energy converted into methane during the process of enteric fermentation in the rumen). For methane conversion factor $\phi_k$, as recorded in the IPCC (2019) report, multiple sets of values for feed digestibility and methane conversion factor are available for different cattle categories. To estimate the correlation between feed digestibility $\bar{D}_k$ and methane conversion factor $\phi_k$ for
each category, we used the relevant data from IPCC (2019) report to plot the corresponding functions assuming $\phi_k$ as a decreasing linear function of $\overline{D_k}$ (see Supplementary Material 9). Methane emissions from manure management are calculated based on the estimation of the excretion rate of volatile solids (VS) and the proportion of VS that are converted to methane by different manure management systems, where VS is estimated by diet intake quantity $u_{j,k,t}$ and average digestibility $\overline{D_k}$. The nitrous oxides emissions includes both direct and indirect emissions arising from volatilization of ammonia, leaching and disposals of manure during the storage and treatment of manure. The emissions are calculated based on the fraction of the total ammoniacal nitrogen (TAN), which depends on the amount of nitrogen excreted by animals. They are determined by diet intake quantity $u_{j,k,t}$, diet nitrogen content $\overline{\Pi}_{k,t}$, average digestibility $\overline{D_k}$ and animal daily weight gain.

Total emissions are calculated by combining all the emissions above and converted to carbon dioxide equivalents.

## 2.6 Case study

As a case study, we selected the Bocage Bourbonnais SAR (hereafter Bourbonnais), which is located in the Massif Central region of France. Beef production from grassland-based extensive cattle rearing dominates the land use of the agricultural sector, followed by arable crops and sheep/goat breeding (Accatino et al., 2022). Table 1 provides guidance about the main data sources and where to find in the paper the values of different variables or parameters. Data about animal number for each category and crop yield for each plant originates from Ministère de l'Agriculture et de l'Alimentation (2022) based on 2016 Annual Agricultural Statistics at the department level. Animal numbers have been downscaled to SAR level. Crop yield
data at the SAR level is assumed to be equivalent to that of the department level.

Data about crop surface for each plant is from RPG (Registre parcellaire graphique) at thr SAR level for the year 2016 (IGN, 2016); ; data about feed intake comes from Therond et al. (2017); data about feed parameters comes from INRAE-CIRAD-AFZ (2022) and INRA et al., (2018); data for the body growth and emission sub-model comes from IPCC (2019). Table 1 gives an overview of the main information about feed types. The nominal feed intake is obtained from Therond et al. (2017) for beef cattle as whole and is distributed to beef cattle categories through LU coefficients $C_k^{LU}$.

Table S1 presents a detailed classification of the beef cattle categories; Table S4 presents data for the harvested plant and feed items, including yield, cultivated area and feed characteristics. Table S5 presents the nominal total consumption of each feed type by the non-beef-cattle livestock categories. Table S7 contains all the parameters for all the growing beef cattle categories for the implementation of the body growth sub-model. These parameters refer to the Charolais breed, which is the most reared in Bourbonnais. All these values form the baseline scenario: some of these parameters are modified in the scenario section.

<table><caption>**Table 1.** Characteristics (nominal intake, average gross energy content and average digestibility) of each feed type and total feed availability in the baseline scenario in the Bocage Bourbonnais</caption><thead><tr><th>Feed type</th><th>Nominal intake [kg DM/LU/day]</th><th>Average gross energy content [MJ/kgDM]</th><th>Average digestibility[%]</th><th>Average nitrogen content [kgN /100kgDM]</th><th>Total feed availability [tons/year]</th></tr></thead><tbody><tr><td>Cereals</td><td>0.76</td><td>15.96</td><td>82.85</td><td>1.83</td><td>110 399</td></tr><tr><td>Coproducts</td><td>0.29</td><td>16.91</td><td>71.81</td><td>1.79</td><td>23 964</td></tr><tr><td>Oil protein</td><td>0.06</td><td>23.12</td><td>82.49</td><td>3.37</td><td>5 308</td></tr><tr><td>Oilseed</td><td>0.34</td><td>19.7</td><td>75.79</td><td>3.30</td><td>11 426</td></tr></tbody></table>
<table><thead><tr><th>meals</th><th></th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>Forage</td><td>5.99</td><td>17.30</td><td>68.36</td><td>1.66</td><td>328 496</td></tr><tr><td>Grass</td><td>7.24</td><td>16.80</td><td>68.40</td><td>1.26</td><td>485 289</td></tr></tbody></table>

## 2.7 Sensitivity analyses of cattle diet

Research question (i) regarded the role of diet composition on the trade-offs among production, emissions, and land use. We proceeded with two sensitivity analyses: the first considered only cereal and grass, two main feed types of cattle diets, distinguishing pasture-based and landless systems; the second considered all the feed types.

### 2.7.1 Sensitivity analysis on cereals and grass intake

To investigate the model's performance along a gradient from cereal-intensive to grass-intensive diet, we performed a sensitivity analysis over a range of values of grass dry matter intake and cereal dry matter intake. The range of cereals dry matter intake was set from 0.76 to 2.94 kg/LU/day. Simultaneously, the range of grass dry matter intake was set from 7.24 to 5.42 kg/LU/day. This range largely contains diets typical of the Bourbonnais regions and representative of Western Europe (according to Mottet et al. 2017) allowing an overall exploration of the parameter space. We run the model with 10000 combinations of these two dietary inputs randomly extracted from their respective ranges, keeping all the other feed item quantities and other parameters to their nominal values, and we interpolated the model outputs. Not all the explored combinations were realistic, however, this being a sensitivity analysis, the purpose was to visualize the trade-offs among the outputs.

### 2.7.2 Sensitivity analysis on all feed types
For a more complete analysis of the impact of each feed type, we performed a second sensitivity analysis varying systematically the cattle diet to explore the impact of each feed type on the model outputs. We explored all the possible combinations of the 6 feed types with 5 levels of values: nominal value, variations -0.02, +0.1, +0.22 and +0.34 tons/LU/year from the nominal value. We computed variance-based sensitivity indices (Pianosi et al., 2016) to rank the contributions of each feed type to the main model variables (gross energy, digestibility and nitrogen content of the diet) and outputs (WG, emissions, required feed imports and feed-food competition).

## 2.8 Simulated scenarios

The second research question regarded external events impacting diet composition or management strategies mitigating the impact of diet composition on the model outputs. We designed three scenarios (see parameter changes in Table 2): *dry season*, *grazing improvement*, and *mixed* (that combined the previous two). We also considered the *baseline* scenario, corresponding to unvaried parameters.

<table><caption>**Table 2.** The parameters and variations of the scenarios</caption><thead><tr><th>Parameters</th><th>Dry seasons</th><th>Grazing improvement</th><th>Mixed</th></tr></thead><tbody><tr><td>Average yield</td><td>-20%</td><td>+20% only for grass</td><td>-20% for all crops (excluding grass)</td></tr><tr><td>Grazing time at pasture</td><td>-20%</td><td></td><td></td></tr><tr><td>Coefficient for growth</td><td>-20%</td><td></td><td>-20%</td></tr><tr><td>Nominal intake</td><td>u<sup>*</sup><sub>j=grass,k</sub> -20%, u<sup>*</sup><sub>j≠grass,k</sub> increases to same quantity as baseline</td><td></td><td></td></tr><tr><td>Digestibility of grass</td><td></td><td>+5%</td><td>+5%</td></tr><tr><td>Gross energy content of</td><td></td><td>+5%</td><td>+5%</td></tr></tbody></table>
416

417 **2.8.1 Dry seasons scenario**

418 During extended dry and hot periods, an array of repercussions emerges, impacting
419 phenology, plant yield, nutritional quality, and animal growth dynamics (Nettier et al.,
420 2010). Similar cases in the literature have shed light on instances where farmers
421 adjust their grazing routines and have to source feed from alternative regions due to
422 decreased crop and grass yields (Salmoral et al., 2020). We simulated the *dry*
423 season scenario in light of the context of decreased average yields across all plants,
424 with an average reduction of 20%. Because the present study is focused on cattle
425 dietary composition, we assume that farmers purchase feed from outside the farm
426 instead of destocking, which would introduce a confounding factor in results. As
427 grass becomes scarcer, possible farmers' responses involve implementing controlled
428 or restricted grazing to avoid overgrazing and preserve the available forage
429 (Salmoral et al., 2020; Accatino et al., 2022). This leads to less grazing time,
430 ultimately leading to decreased grass intake. We assumed that, as a countermeasure,
431 to achieve target weights, farmers opt for a resilience feed management strategy by
432 retaining all cattle while purchasing additional feed of other types (concentrates and
433 forage). Lower growth rate is simulated by lowering the growth coefficient $C_k^g$.
434 Reduced grass yield is simulated by reducing average yields $\bar{Y}_j$ by 20%. Grazing time
435 at pasture $t_k^{gr}$, intake of grass $u_{j=grass,k}^*$ are also reduced by 20% to simulate the
436 reduced pasture activity by cattle. Reduced grass intake is compensated by
437 increasing other feed type quantities $u_{j \neq grass,k}^*$ to obtain the same daily diet dry
438 matter intake as in the baseline.
439 **2.8.2 Grazing improvement scenario**

440 According to Cardoso et al. (2016), various practices, including fertilization, tillage,
441 the change of grass varieties, and the implementation of dynamic rotational grazing,
442 possess the potential to exert a dual influence on pastures. These practices can
443 affect not only the quantity, as measured by yield, but also the quality, encompassing
444 factors like digestibility and gross energy content, thus presenting valuable avenues
445 for enhancing overall pasture productivity. Therefore, grazing improvement was
446 simulated by increasing grass yield, digestibility and gross energy content. In the
447 context of pasture management in France, studies, such as those conducted by
448 Baumont et al. (2012), have explored the multifaceted impacts of variability in pasture
449 management on pasture yield and quality. With the evidence from the study by
450 Cardoso et al. (2016) and Baumont et al. (2012) that reformed pasture can increase
451 5%-20% of digestibility for beef cattle and 20% daily live weight gain, grazing
452 improvement was simulated by increasing grass yield $\overline{Y}_{j=grass}$ (+20%), digestibility
453 $\overline{d}_{j=grass,k}$ (+5%) and gross energy content $\overline{e}_{j=grass,k}$ (+5%).

454 **2.8.3 Mixed scenario**

455 The *mixed* scenario incorporated the concepts from the previous two scenarios,
456 representing cattle farming enduring a dry season within the framework of grazing
457 improvement. The reduction in yield of non-grass and lower growth rate caused by
458 dry seasons still exist. However, the improvement of grass yield thanks to grazing
459 improvement, serves as a counterbalance to the dry season-induced yield reduction.
460 Consequently, the availability of grass remains unaffected, facilitating continuous
461 pasture grazing for cattle. Therefore, grazing improvement was simulated by
reducing average yield of crops $\overline{Y_{j \neq grass}}$ (-20%) and coefficient for growth $C_k^g$ (-20%),
with increased digestibility $\overline{d_{j=grass,k}}$ (+5%) and gross energy content $\overline{e_{j=grass,k}}$ (+5%).

## 3. Results

### 3.1 Trade-offs revealed by sensitivity analysis on cereals and grass intake

Exploring the modelling outputs across joint gradients of cereal and grass highlight
some trade-offs related to dietary composition. In Fig. 2 desirable outcomes are
depicted in blue, denoting highest benefit indicators (such as WG and gross energy)
and lowest cost indicators (including emissions, total feed import, and feed-food
competition indicators). Conversely, undesired outcomes are depicted in red,
signifying lowest benefit indicators and highest cost indicators. Point O designates
the *baseline* scenario in Bourbonnais, characterized by a grass-based diet
representing an extensive cattle system. The nominal cattle diet in *baseline* is
detailed in table 1. Outputs in *baseline* were WG, $3.58 \times 10^4$ tons; total emissions,
$2.19 \times 10^5$ tons CO$_2$ equivalent; human-edible feed consumed per kg WG, 0.67 kg;
food-competing land per kg WG, $1.04 \times 10^{-3}$ ha; total feed imports, $1.52 \times 10^4$ tons. To
gain deeper insights into the trade-offs among different indicators linked to grass and
cereals intake, we introduced the isoline (OA) of WG passing through point O,
representing all possible cereals/grass combinations yielding the same nominal WG
level as in the *baseline* scenario. Further, we identified another point on this isoline,
labelled as A, to help explore trade-offs. Point B symbolizes the converse of the
*baseline* scenario—depicting a cereal-based diet—representing the most intensive
cattle system. Moving across the isoline OA and the dashed line OB allows exploring
the trade-offs related to cereal-based diet vs. grass-based diet.
a)

<figure><img src="image_3.png" /></figure>

b)

<figure><img src="image_4.png" /></figure>

c)

<figure><img src="image_5.png" /></figure>

d)

<figure><img src="image_6.png" /></figure>

e)

<figure><img src="image_7.png" /></figure>

f)

<figure><img src="image_8.png" /></figure>

g)

<figure><img src="image_9.png" /></figure>
**Fig. 3** (a–h) Heatmaps showing relevant model outputs as a function of the variation of cereals and grass quantities in the cattle’s diets. The blue end of the color scale corresponds to positive effects (i.e., higher values of gross energy intake and WG and lower values of emissions, feed importation, human-edible feed per WG and food-competing land per WG), and the red end corresponds to negative effects. Line OA is an isoline representing a constant total WG as baseline, and overlaps the heatmaps corresponding to the other outputs. Dashed line OB is a trend from baseline O (representing the grass-intensive diet scenario) to point B (representing the grain-intensive diet scenario).

Moving along the x and y axes in the plots correspond to both a variation in dietary composition and total dry matter intake. All the outputs sensitive to both these parameters exhibit important variations (e.g., for emissions from $1.9 \times 10^5$ tons to plus ~24%). On the contrary, digestibility is only sensitive to dietary composition (and not affected by the quantity) and exhibits a modest variation (from 0.69 to plus ~2.9%).

Through the WG isoline OA, from point O to A, for the same WG level, cereals intake increases and grass intake decreases; and some indicators show improvement, such as increased digestibility, decreased emissions. However, other indicators show undesired effects, i.e., decreased gross energy, higher total feed imports and an increase in human-edible feed and food-competing land per kg WG. Moving from point O to point B, we observe that several indicators improved, such as increased digestibility (0.7125) and decreased emissions ($2.07 \times 10^5$ tons), while several indicators worsen, including decreased WG ($3.69 \times 10^4$ tons); higher feed importations ($5.50 \times 10^4$ tons) and increased human-edible feed (2.1 kg/kgWG) and food-competing land per kg WG ($1.27 \times 10^{-3}$ ha/kgWG). Trade-offs are revealed in the WG isoline OA and in line OB as a transition from a grass-intensive diet to a grain-intensive diet, with indicators displaying contrasting directions of change.
## 3.2 Contribution of each feed type to model outputs

The sensitivity indices, expressed as percentages, indicate the proportion of each feed type to the contribution to the variability observed in the respective model outputs, as presented in Fig. 4. Oil protein has a significant impact on various model outputs, contributing notably to all outputs (gross energy, 26%; digestibility, 43%; nitrogen content 34%; WG, 35%; nitrogen emissions, 36%; feed importation, 32%; human-edible feed per kg WG, 44%; food-competing land per kg WG, 43%. Oilseed meals contribute greatly to nitrogen content (33%), nitrogen emissions (32%) and feed importation (40%). Cereals contribute greatly to digestibility (45%), WG (17%) and human-edible feed per kg WG, 51%. Forage and grass contribute greatly to total emissions (37% in total).

<figure><img src="image_10.png" /></figure>

**Fig. 4.** Sensitivity indicators for each feed type quantity on different model variables and final indicators. Sensitivity indicators are expressed in percentages representative of the contribution to the variable or indicator.

## 3.3 Scenarios results

Model outputs are represented in Fig.5 for the *baseline* and the three other scenarios. In the *dry seasons* scenario, total WG decreased (-2.58%); total emissions
decreased (-0.22%) with enteric methane, methane from manure and nitrous oxide from manure management -0.72%, -0.73% and + 3.36% respectively; human-edible feed per WG and food-competing land per WG increased by 149g and 5.5×10⁻⁴ ha per kg WG respectively. Compared to the *baseline* scenario, the region was no longer self-sufficient in forage and required extra importation of 109592 tons, including additional import requirements of 1,611 tons of oil protein and 5320 tons of oilseed meals. In the *grazing improvement* scenario, compared with the *baseline*, WG increased by 6.02% and total emissions decreased by 3.03% overall with enteric methane, methane from manure and nitrous oxide from manure management -3.71%, -4.78% and + 1.85% respectively; human-edible feed per WG and food-competing land per WG decreased by 37g and 5.7×10⁻⁵ ha/kg WG respectively. Compared with *baseline*, there was no need for extra importation of any feed type. For *mixed* scenario, total WG increased (+1.22%); total emissions decreased (-3.25%) with enteric methane, methane from manure and nitrous oxide from manure management -3.92, -4.93% and + 1.59% respectively; human-edible feed per WG decreased by 9g/kgWG and food-competing land per WG increased by 2.43 × 10⁻⁴ ha/kgWG. Additional importation of oil-protein, oilseed meals and forage were required but less than dry seasons scenario with a reduced requirement of 1060 tons for oil-protein, 2276 tons for oilseed meals, and a substantial decrease of 2276 tons for forage.

In the *dry seasons* scenario, there was a decrease in WG; however, when combined with grazing improvement in the scenario, WG increased instead, and the *mixed* scenario exhibited the least emissions. Furthermore, in terms of feed-food competition and feed import requirements, the *grazing improvement* scenario outperformed others.
<figure><img src="image_11.png" /><figcaption>b) Feed surplus and importation requirements [tons]</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>c) Feed-food competition</figcaption></figure>

<figure><img src="image_13.png" /></figure>

Fig. 5. Results of the scenarios (scenarios correspond to baseline (orange), dry seasons (yellow), grazing improvement (green) and mixed (blue); a) WG and emissions with values expressed as proportions of the indicators observed in the baseline (set equal to 1); b) feed surplus (positive values) and feed import needs (negative values) in tons; c) feed-food competition.
561 **4. Discussion**

562 We developed a model at the regional scale linking cattle diet to WG (proxy of beef
563 production), emissions and land use impacts. Diet properties are linked with the
564 properties of the agricultural production in the region. We could observe that dietary
565 composition modulates a trade-off between production, emission and land use
566 impacts (Research question (i)). In particular, higher digestibility and gross energy
567 content allowed for higher productivity and lower emissions; however, because we
568 adopted a regional-scale approach, we also observed that more digestible diets were
569 also more impacting on land, requiring more feed to be imported and exacerbating
570 feed-food competition. Scenario exploration (related to Research Question (ii))
571 showed that climatic events can have, through provoking dietary changes, impacts
572 on land use and some management strategies (i.e., grazing improvement) can
573 mitigate the trade-off between animal performance and land use impact. These
574 observations highlighted some elements worth being discussed and raised some
575 ideas for setting management principles.

576 **4.1 Role of diet digestibility and gross energy**

577 High digestibility is crucial for efficient feed utilization in beef production, as it
578 optimizes the gross energy and nutrient availability from the feed for net energy
579 utilization in growth, resulting in higher WG for a given intake. Meanwhile, high feed
580 use efficiency lead to a reduced fraction leaving for converting to methane and less
581 nitrogen being excreted as waste, and subsequently lower emissions of methane and
582 nitrous oxide (Cantalapiedra-Hijar et al., 2018; De la Torre et al., 2019). The positive
583 influence of digestibility and gross energy on production is given by the following
584 positive feedback loop. Increased digestibility and gross energy intake increase the
daily WG, which induces a higher diet intake requirement; in turn, more diet intake corresponds to a higher daily gross energy intake from the diet and consequently further increase in WG. This positive feedback might be exacerbated in presence of a diet which is energy-dense (i.e., rich in oil-protein and oilseed meals) (Fig. 4). Such energy-dense feed types lead to higher nitrogen content, higher gross energy density and higher digestibility. Indeed, nitrogen emissions increase with nitrogen content; and methane emissions decrease with digestibility and increase with gross energy (Moraes et al., 2014; Grossi et al., 2018; Eugène et al., 2021)). For calculation of enteric methane emissions, we adopted the IPCC Tier 2 approach and introduced a methane conversion factor, defined as the percentage of gross energy from feed converted to methane. For calculation of methane emissions from manure management, based on IPCC Tier 2 approach, higher digestibility will bring about less VS excretion rate and therefore and subsequently less methane emissions from manure management. Therefore, an optimal diet digestibility and gross energy content should be addressed in order to find a good balance between these two diet properties.

Diet digestibility and gross energy content and, subsequently, their impacts on model outputs, are determined by diet quantity and composition, as revealed by our sensitivity analyses. The sensitivity analysis on cereals vs grass showed that higher proportion of concentrates in the diet increased digestibility and thereby improved the impact on beef cattle production and emissions (Fig. 3), in line with other studies (Clark and Tilman, 2017; Grossi et al., 2018). Our sensitivity analysis of all feed types showed that even though oil protein comprises the smallest proportion of the diet (Fig. 4), it exerts the most influence on average gross energy content (26%), followed by oilseed meals 19%, forage 15%, grass 14%, coproducts 14% and cereals 12%.
Moreover, oil protein (43%) and cereals (45%) have the greatest influence on average diet digestibility.

## 4.2 Trade-off between digestibility and land use impacts

Adopting a regional scale allowed showing that while more digestible feed types (i.e., cereals, oil-protein crops and meals) might be win-win solutions for increased production and reduced emissions, they also increase the negative impact on land use, requiring more imported feed and causing feed-food competition. Energy-rich feed crops impact considerably on land on a global scale, representing 185Mha as estimated by Govoni et al. (2023) (reference year 2016-2018). The addition of cereals in the diet was accompanied by competition with human consumption (Fig. 3). The extra importation triggers land displacement, necessitating the utilization of land in other regions or countries, which, in turn, causes increased emissions from feed production and transportation to other regions (Davis et al., 2015; Meyfroidt et al., 2013).

This trade-off was also visible in the *dry season* scenario. In line with the findings of other research (Salmoral et al., 2020; Accatino et al., 2022) and real cases in France (Nettier et al., 2010), we assumed that farmers might need to purchase additional concentrates and forage from external sources or alternate regions to maintain consistent diet intake for their cattle, ensuring the sustenance of the existing stock and growth rate considering long-term economic returns (Beulter, 2006). This assumption is based on the knowledge that neighboring regions are not significantly affected by dry seasons and could potentially supply the necessary feed imports. Consequently, farmers have the option to retain their entire cattle stock. However, we acknowledge that in real situations farmers could opt for destocking or to mix
634 destocking and buying external feed, therefore this assumption may lead to an
635 overestimation of the total feed requirements. However, with this scenario we
636 showed the potential effect of the dietary change potentially induced by a drought
637 event of moderate gravity. The increased proportion of concentrates in the feed
638 elevated average feed digestibility, promoting more energy used for body growth and
639 less emissions (Fig.5.). However, this has been compensated by a slower growth
640 rate with WG decreasing 2.58% . Moreover, enhanced reliance on concentrates
641 engendered amplified human-edible feed utilization, demanding more land to sustain
642 the production of food-competing feed. In regions characterized by grassland-based
643 practices, like Bourbonnais, our findings highlighted the necessity of feed importation
644 or better livestock management strategies during dry seasons. This is attributed to
645 local feed production from crops proving inadequate to substitute lost grass
646 production. Similar constraints have been identified in various studies of pasture-
647 based systems (Ifejika Speranza, 2010; Ferris, 2007).

648 **4.3 Trade-off mitigation strategies**

649 Our findings suggested that possible strategies for improving the sustainability of
650 beef cattle systems are those that can improve average diet digestibility without
651 extending the impact on land and without increasing feed-food competition.

652 **4.3.1 Grazing improvement**

653 In the *grazing improvement* scenario, we improved feed digestibility and grass gross
654 energy as well as grass yield and finally feed conversion ratio (Morais et al., 2018);
655 therefore, the same level of diet intake was associated with increased diet
656 digestibility and gross energy. Concrete practices to make grass more digestible and
657 for sustainably intensify grasslands include the manipulation of grass species
658 (Cardoso et al. 2016, Morais et al., 2018), grazing at optimal maturity (Fynn et al., 659 2017), rotational grazing (Badgery et al., 2016; Cardoso et al. 2016), among other 660 strategies. Some benefits of this scenario were increased animal productivity and 661 reduced emissions (Fig.5.), in line with the conclusions of other studies (Grainger and 662 Beauchemin, 2011; Beauchemin and McGinn, 2008). These enhancements in the 663 *grazing improvement* scenario were achieved without augmenting total feed 664 consumption or exploiting extra land to grow more feed, which reduces dependence 665 on an external feed supply and minimizes the consumption of human-edible feed. 666 Hristov et al. (2013) conducted a comprehensive review of mitigation options and 667 concluded that increasing grazing quality might be an effective mitigant of the 668 produced per unit of animal products.

669 Management strategies related to the sustainable intensification of pastures allow for 670 valuing existing grasslands, especially those that cannot be converted to croplands, 671 which are the ones for which beef cattle provide a net contribution to human nutrition 672 (Mottet et al., 2017). In addition, for beef cattle, grass diets match their natural 673 metabolism and evolutionary behaviours (Rutter, 2010). Eating grass is *what cattle 674 are good at* (van Zanten et al., 2018) —converting human-ingedible resources to 675 human-edible food and converting nutrients that humans cannot absorb into human- 676 absorbable nutrients. Grass-based cattle systems have the potential to more 677 sustainably contribute to future food security than their grain-based counterparts 678 (Van Zanten et al., 2018). It is also to be considered that while the lower digestibility 679 of grass (compared to cereals) makes pasture-based systems higher in emissions 680 than feedlot systems, some studies highlight the positive impact of grasslands on 681 carbon sequestration (e.g., Wang et al., 2015). Starting from this, Liang et al. (2020)
also call for a systemic approach in modelling and evaluating cattle systems and
provide empirical evidence about maintenance of soil carbon by grazing cattle.

### 4.3.2 Increasing grassland resilience to dry periods

The *dry season* scenario showed that the impact on land use of cattle dietary need can be exacerbated in case of climatic events such as droughts or extended dry periods, decreasing pasture productivity and pushing farmers to buy external feeds.

The *mixed* scenario showed that improving grazing quality can simultaneously improve animal production, emissions and land use impacts, even when facing extreme events such as dry seasons. Improving grazing by enhancing the adaptive capacity and resilience of grassland to drought is another promising coping strategy (Mathijs et al., 2022; Ferris, 2007). An example of strategy consists in promoting (intra- and inter-specific) diversity in plant composition, as more diverse forage mixtures have been observed to be less drought-stressed than less diverse mixtures (Lüscher et al., 2022). Moreover, improved grazing systems with more sustainably exploited grassland increase the opportunities for higher carrying capacities (Grainger and Beauchemin, 2011; Piipponen et al. 2022).

### 4.3.3 Other mitigation strategies

A straightforward strategy for trade-off mitigation is reducing the herd size (see the scenario of reduced beef consumption by Morais et al. (2021)). Considering feed management, other ideas raise from the principles highlighted by our results, i.e., increasing diet digestibility without using more land. This could consist of e.g., employing feed processing techniques, adjusting feed frequency or utilizing feed additives, substituting energy-rich feed components with industrial by-products which
705 do not increase the impact on land or human food wastage and grazing on cover
706 crops (Grossi et al., 2018; Pinotti et al. 2021; Yan et al., 2024).

707 **4.4 Limitations and future perspectives**

708 Our model specifically focused on feed digestibility and gross energy content as the
709 key factors impacted by feed intake and composition. Despite the recognized
710 importance of protein content in defining livestock diets and its use in some animal
711 models (Faverdin et al., 2011; Huuskonen et al., 2013), we made a deliberate choice
712 not to include it into our analysis to avoid expanding the scope of the model
713 excessively. We did not consider emissions from feed production and post-farm
714 activities due to lack of region-specific data on feed importation sources and beef
715 exportation sources. These are indeed important considerations that warrant future
716 exploration to achieve a more thorough understanding of the environmental impact of
717 beef production. Nonetheless, the results of feed requirement can serve as a proxy to
718 imply the intensity of emissions for feed production. Our model is designed for a one-
719 year timeframe, and does not delve into specific age-related or season-related
720 variations in cattle diet. While we have proportionally adjusted the feed intake
721 quantity for cattle at different age, sex and functions, we acknowledge the limitations
722 of lack of specificity and potential impacts in cattle behavior and nutritional needs.
723 Rather than aiming at realistic predictions, our objective was to establish connections
724 between production, emissions, and land use impacts through the perspective of
725 livestock diet, while emphasizing the trade-offs between these aspects. The model
726 could be improved by including other emissions from the beef production sector and
727 making the indicators for land use impacts more representative and comprehensive.

728 **5 Conclusions**
729 Our results showed that more digestible diets can conciliate production with emission reduction (if the gross energy intake is not too high). However, being more digestible diets mostly based on cereals and soybean meals, they are more dependent on feed imports and cause more feed food competition. Our study suggests that strategies at the regional scale for alleviating the trade-offs linked to beef production should be based on improving average diet digestibility with land uses that do not cause feed-food competition. Possible strategies for softening trade-offs related to cattle diet is making grass resource more digestible to beef cattle and improve the resilience of grasslands to droughts.

738 Acknowledgements

739 This work benefited from the French state aid managed by the ANR under the "Investissements d'avenir" programme with the reference ANR-16-CONV-0003.The
740 Doctoral School ABIES also provided the financial support to the first author for her
741 PhD training.

743 Author contribution

744 **Ruizhen Wang**, Conceptualization, Data Curation, Formal analysis, Methodology, Validation, Visualization, Writing – original draft. **Laurence Puillet**, Conceptualisation, Supervision, Validation, Writing – Review & editing. **Corentin Pinsard** Validation, Writing – Review & editing **Philippe Lescoat**: Conceptualisation, Supervision, Validation, Writing – Review & editing. **Francesco Accatino**: Conceptualization, Funding acquisition, Methodology, Supervision, Validation, Writing – original draft, Writing – Review & editing

751
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