Sustainable intensification of Brazilian livestock production through optimized pasture restoration

Grassland degradation compromises the profitability of Brazilian livestock production, and pasture recovery is a promising strategy for sustainable intensification of agriculture (SAI). Recovery increases carbon sequestration into the soil and can potentially avoid deforestation; thereby reducing emissions intensity (EI), but only at increased investment cost per unit of area. We develop a multi-period linear programming (LP) model for grazing beef production planning to represent a typical Cerrado stocking and finishing beef farm. We compare economic and environmental performance of two alternative optimized pasture management approaches relative to the traditional practice (TRP), which is based on restoring pasture after a full degradation cycle of 8years. The scenarios considered the difference made by access to subsidized credit through the Low Carbon Agriculture program (“Programa ABC”). The model estimates EI using upstream life cycle assessment (LCA), and dynamically estimates soil organic carbon (SOC) changes as a function of pasture management. The results show net present values (NPV) ranging from −67 Brazilian reals per hectare-year (R$·ha−1·yr−1) to around 300 R$·ha−1·yr−1, respectively for traditional and optimized pasture management strategies. Estimated EI of the TRP is 9.26 kgCO2 equivalent per kg of carcass weight equivalent (kgCO2e/kg CWE) relative to 3.59kgCO2e/kg CWE for optimized management. Highest emission abatement results from improved SOC sequestration, while access to credit could further reduce EI by around 20%. We consider the effects of alternative credit interest on both NPV and EI. The results provide evidence to inform the design of Brazil's key domestic policy incentive for low carbon agriculture, which is an important component of the country's Intended Nationally Determined Contributions (INDC) on emissions mitigation. The results also contribute to the global debate on the interpretation of SAI.


Introduction
Brazil is the world's second largest beef producer using systems that are predominantly pasture-based; i.e., around 90% of cattle are pasturefed only (Anualpec, 2013). Despite this, more than half of pasture area are degraded to some extent (De Oliveira et al., 2004). Gouvello et al. (2011) estimated that increasing beef productivity could provide the land needed for the expansion of crops for food and biofuel production in a near-zero deforestation scenario, while meeting increasing beef demand, at least up to 2040. Such actions are likely to reduce GHG emissions by lowering methane per unit of product, by avoiding deforestation and increasing soil organic carbon stocks (Gouvello et al., 2011).
Despite observed productivity gains made over the last three decades (Martha et al., 2012), challenges remain to reverse the economic losses from grassland degradation, while accommodating growing demand and simultaneously avoiding the conversion of natural habits. At around 73.5 kg of CWE/ha −1 ·yr −1 average Brazilian productivity is low relative to a potential of 294 kg CWE. ha −1 ·yr − 1 that could be reached if improved pasture management practices were adopted (Strassburg et al., 2014). Pastures can be restored by improving soil fertility and forage productivity by chemical and mechanical interventions. For example, improvements can be made by applying inputs (seeds, fertilizers) and through the use of machinery (e.g. mowing). As degradation advances, more drastic soil interventions are required to restore productivity.
Despite policy interest in reversing degradation, we note the absence of any farm-scale economic appraisals demonstrating the tradeoffs between investments in pasture restoration and the environmental returns, resulting from the potential increased soil organic carbon stocks (SOC) from restored pastures. Such assessment would ideally consider the dynamics of pasture degradation and restoration, and the cost-effectiveness of different management options. Existing farm and regional optimization models typically consider fixed forage productivity within production systems (e.g., extensive, semi-extensive and intensive) (Britz and Witzke, 2012;Dent et al., 2013;Weintraub and Romero, 2006). In such models the changes on SOC stocks are not modelled as a function of pasture management. An overly simplistic representation of production practices and failure to account for SOC provide a misleading picture of system productivity and GHG emissions.
The need for investment to address the nexus of pasture degradation, low productivity and food security and emissions is recognised as a national policy priority in Brazil, with restoration encouraged through the creation of a government-funded bank credit line for low carbon agriculture, the Agricultura de Baixo Carbono (ABC) -Low Carbon Agriculture program (Mozzer, 2011). To date, this program has not been subject to any formal economic analysis considering the economic return to the adoption of restoration practices. The restoration issue is also of sufficient global prominence to have been central to Brazil's mitigation commitments under the United Nations Framework Convention on Climate Change. At the 15th Conference of the Parties (COP15) in 2009, the country proposed a voluntary emissions reduction target of around 40% relative to baseline emissions by 2020 to be achieved by its Nationally Appropriate Mitigation Actions (NAMAs) (Mozzer, 2011). At COP21 (2015), the commitment was nominally converted into an Independently Determined National Contribution (INDC) (Brazil, 2015), which proposed a further mitigation target of 43% reduction by 2030 relative to 2005 emissions. Both NAMAs and INDCs focus on reduced deforestation in the Amazon and the Cerrado, and include respectively the restoration of 15 million hectares (M ha) of degraded pastures between 2010 and 2020, and a further 15 M ha from 2020 to 2030.
This paper details an improved representation of pasture dynamics and environmental interactions, using an optimization model coupled with a full life cycle assessment approach (LCA) for a typical stocking and finishing beef cattle operation in the Cerrado biome. The objectives are: (i) to compare farmer's economic and environmental returns from investments in improved pasture restoration relative to traditional (baseline) practices; (ii) to understand how access to the ABC credit line improves the returns on investment; and (iii) to perform a sensitivity analyses of ABC interest rates on key economic parameters and emissions intensities.

Overview
Three versions of a LP model were developed to compare the economic and environmental performance subject to rural credit incentives and initial farm degradation levels: from severely degraded pasture to completely restored. Each version represents a restoration practice on a typical grazing system in the Brazilian Cerrado; the traditional pasture management and two alternative optimized restoration approaches. The model simulates beef production for a fattening and finishing system, accounting for herd dynamics, financial resources, feed budgeting, pasture recovery dynamics, and soil carbon stocks.

Mathematical modelling of restoration practices
Pasture degradation can be defined as the gradual loss of vigour, productivity and natural capacity for recovery to sustain production and quality of grass required by animals, and to overcome the detrimental effects of insects, diseases and weeds (Macedo and Zimmer, 1993). Traditional pasture management involves limited use of restoration practices, meaning that 50% to 80% of the Amazon and Cerrado pastures are currently degraded to some extent (Macedo et al., 2014;Peron and Evangelista, 2004). Grasslands are typically not managed with fertilizers or lime throughout the production period (Maia et al., 2009). Instead, restoration interventions can occur around every 5 to10 years (Maia et al., 2009). In this study, traditional pasture management is assumed as a cyclical intervention every 8 or 10 years of constant grazing use; i.e., when pasture and soil are visibly degraded and dry matter productivity reaches an ecosystem equilibrium level and stops degrading.
Based on the pasture degradation definition of Macedo and Zimmer (1993), the model imposes a deterministic decline in dry matter productivity (DMP) with time. DMP levels (in tonnes of dry matter per hectare year) are represented by {P1,P2,P3,P4,P5,P6,P7,P8,P9,P10,P11}. As the symbols are ordered in decreasing levels of DMP, the degradation process is represented as the annual transference between consecutive levels, i.e., P1 degrades to P2 after one year of formation of pasture P1, if no interventions are undertaken; P2 degrades to P3 in the following year, and so forth, until P10, which degrades to P11, the minimum degradation level (ecosystem equilibrium), thus P11 "degrades" to P11. Because there are 11 DMP levels and each level is one-year "distance" from its consecutive, the whole degradation process takes 10 years. The traditional restoration practice (TRP) is equivalent to restoration only when P10 or P11 are reached.
In contrast this paper models other two optimized approaches: The Fractional Restoration Practice (FRP) and the Uniform Restoration Practice (URP). URP permits restoration of the whole pasture at any point during the degradation process, e.g., DMP level P5 could be restored to P4, P3, P2 or P1 or maintained at P5 instead of degrading to P6 at any time. FRP extends URP and allows for fractions of pasture area to be restored to different DMP levels, e.g., any fraction of pasture P5 could be restored to P1, other fractions to P2 and P5, and even a fraction may degrade to P6. In this way, a given pasture area is then partitioned into sub-areas instead of a uniform area as is the case in TRP and URP. The annual average values of the DMP levels are presented in

. Model's overview
Pasture management is optimized using a multi-period linear programming model for grazing beef production planning, with an application to a representative stocking and finishing beef cattle operation in the Cerrado.
The model focuses on optimizing decisions for pasture management while maximizing profit subject to biological and financial constraints. Stocking rates and, therefore, total output depend on feed production from pasture and consumption patterns driven by herd dynamics. The model accounts for intra-and inter-annual variations of pasture productivity and represents the processes of pasture degradation and restoration to optimize decisions on restoration from an economic perspective. The model was implemented in AIMMS algebraic language (Bisschop, 2011), comprising approximately 7000 variables and 4300 constraints for a 20 year planning period, and was solved using the CPLEX solver (CPLEX, 2009).
Tables 1-3 provide the general notation used to describe the model. 2.3.2 Pasture dynamics The area of each DMP level p in a given year t is represented by Z t,p and the level of productivity of a partition for each month M in {Jan, Feb, Mar, …, Dec} of the calendar is represented by ρ p,M .
The degradation process is represented as the annual transition of pasture levels in Ω = {P1,P2,P3,P4,P5,P6,P7,P8,P9,P10,P11}. In the case of FRP the model is designed to allocate proportions of the area optimally by either (i) maintaining productivity at the current level (i.e. keep a sub-area in the same level), and (ii) improving productivity to any other more productive level, or (iii) letting it degrade. Accelerated degradation due to overgrazing was not considered since the model adjusts the stocking rates according to what the animals consume and the available dry matter. Let Z t,p represent the area of pasture p in year t; and RZ t,p,q be the pasture area that is transferred (restored) from partition p to partition q in year t, t pasture inter-annual productivity dynamics are given by: where p and q indexes correspond to the order of elements in Ω; q is auxiliary index in the same set as p. The first term in the right hand side (RHS) of Eq. (1) represents degradation. The second term in the RHS represents the restoration dynamics; the first term in the sum Σ RZ t,q,p represents the area transferred from all other partitions to p and Σ RZ t-1,p,q sums up the area that is removed from p (restored) to any more productive level q.
Since the grassland restored area RZ t,p,q comes from the available area Z t-1,p , it is required that ∑ q RZ t;q;p ≤Z t−1;q ∀q; t The pasture productivity level at the end of the planning period was constrained not to be less than its initial value: At the beginning of production, it is necessary to initialize the pasture partitions, thus:

Herd dynamics and stocking rates
The model represents animal growth by defining age cohorts k with fixed attributes (e.g. body weight and feed intake, Table 4). Fattening is modelled as the transfer from age cohorts as follows: The third term in the RHS transfers all the purchased animals from previous cohorts {k − 1, k − 2, k − 3, …} to the current cohort k, in month m. The fourth term in the RHS is similar, but it represents the transference from age cohort k to the successive cohorts {k + 1, k + 2, …}. As each age cohort corresponds to three months, the mortality rate from one cohort to another is accumulated via a relation of three months (fourth term in the RHS).
In the case of k = 10 (slaughter age cohort), the number of steers is given by: Stocking rates are limited by the amount of available forage. Letting W m be the dry matter transferred from one month to the next. and: Eq. (9) is used to constraint the above-ground biomass inaccessible to the animals, i.e., there is a minimum value of forage per area that will have to be transferred to the following month: 2.3.3. Revenue flow Income (G m ) is generated from steers sold for slaughter.
Expenses (H m ) is composed of farm fixed maintenance costs, cattle maintenance costs, purchasing cattle and investments in pasture restoration. Thus: where PI m is a parameter vector used to discount the annual investments in pasture restoration in the selected month and PI m is equal to 1 if m a payment month, or 0 if m is not a payment month.
At the first month of the planning period, cash flow is given by: And the credit lines must meet the credit limit: The credit line in Eq. (12) (variable V t ) is paid in 5 instalments (PV t ) after the third year of contract: Along the planning period, cash flow is given by: Similarly to TI m , PI m is used to set the months in which credit payments occur according to the number of instalments. A discount rate of 6% per annum (0.5% per month) is applied to represent the opportunity cost.
At the end of the planning period, all steers are sold. Furthermore the farm has to pay costs of pasture post-production, i.e., pasture restoration investments necessary to let farm productivity be greater than or equal to the value of the initial year.
The objective function is to maximize the final cash:

GHG emissions and SOC stocks
The model estimates GHG using emissions factors for activities within the notional farm gate. Emissions associated with farm activities are: (a) CH 4 from cattle enteric fermentation (CH 4 from excreta is not accounted); (b) Direct and indirect N 2 O from manure; (c) Direct and indirect N 2 O emissions from N fertilization; (d) CO 2 from changes in SOC stocks; and (e) LCA factors for inputs and farm operations applied in land use change and restoration practices. Items (a) and (b) depend on herd composition: each age cohort has an associated emission factor of CH 4 and N 2 O (Eq. (18)).
Eq. (18) accounts for emissions converted to carbon dioxide equivalent for each cattle age cohort k, where ce m is the total cattle emissions in month m; CH 4k and N 2 O k are the emissions factors for CH 4 and N 2 O (in kg hd − 1 mth − 1 ) for steers of age cohort k (Table 4), 21 and 310 are Dry matter intake of animal of steer age cohort k Table 4 kg·hd −1 ·mth −1 η q,p Cost of restoration from pasture level q to level p Table 4 R$·ha −1 λ k Cattle maintenance cost for age cohort k Table 4 R$·hd −1 μ k Mortality rate of steer age cohort k Table 4 Dimensionless π Transaction cost of purchasing cattle 30 R$·hd −1 ρ p,M Productivity of pasture level p in calendar month M Table 5 kg·ha −1 ·mth −1 σ M Fraction of herbage mass loss due to senescence 0.00014 Dimensionless θ k Selling price of steer age cohort k Fraction of herbage mass loss due to grazing animals (grazing efficiency) 0.6 Dimensionless a Amortization parameter was calculated using the formula γ ¼ irð1− 1 ð1þirÞ np Þ −1 , where ir represents the ABC program interest rate (5.5% per annum) and np the number of payments.

Table 4
Steer bioeconomic and emissions data.
Age cohort  Arruda and Corrêa (1992). b Average shrunk body weight (Avg SBW) as proposed by Costa et al. (2005). c Dry matter intake (DMI) as estimated by the National Research Council model (NRC, 2000).  Table S1.
respectively the CH 4 and N 2 O equivalence in CO 2 e -in global warming potential for 100 years (GWP-100). Due to the lack of studies in Brazilian conditions, for (c), we used the Intergovernmental Panel on Climate Change -IPCC Tier 1 default factor of 1% and 0.2% (Eggleston et al., 2006), respectively for direct and indirect N emissions.
Eq. (19) accounts for the emissions from N based fertilizers in year t (fe t ). The term inside the sum gives the amount of N applied for all pasture restoration options. The factor cv N→N2O corresponds to the proportion of N converted into N 2 O.
For (d), the emissions are calculated by modelling SOC dynamics. The model works with equilibrium values of the C stock for each pasture type ( Table 5). The equilibrium values and equilibrium time horizon were calculated exogenously, using simulations from the CENTURY model (Parton et al., 1987) applied to Cerrado biophysical characteristics and using the annual dry mater productivity calculated for each pasture DMP level.
Detailed derivation of the soil organic carbon model developed in this analysis is presented below.
Based on equilibrium values and parameter that represents bioclimatic conditions, the model dynamically simulates SOC accumulation sensitive to pasture management. We first develop a version of SOC stock for a fixed DMP level p over time, then we generalise to a heterogeneous pasture area by calculating weighted average values.
Let c t,p be the SOC stock of pasture p in year t (in tonnes per hectare), the changes in SOC stocks over time (dc t /dt) can be represented as function of an annual carbon input flux through photosynthesis (I t ), and the respiratory losses due to decomposer organisms (r t ), where r t. is proportional to the amount of SOC in t, i.e., r t. = ρc t ; and ρ is the fraction of SOC which is lost by plant respiration, as proposed by Vuichard et al. (2007): Assuming i t = F fixed and nothing that respiration losses are proportional to C t : At steady state dc t / dt = 0: where C* t,p = ε p is the SOC of pasture p at equilibrium. Thus Eq. (21) can be written as: Writing as difference equations (discrete-time analogue):   Thus, SOC accumulation is given by: Given the equilibrium values of each pasture DMP level (ε p ), carbon respiration losses (ρ p ) and initial SOC stock (c 0 , p ), Eq. (25) estimates SOC at any time t. The parameter ρ p can be calibrated to adjust an assumed equilibrium time, or obtained exogenously, e.g., by calibrating against the CENTURY model (Parton et al., 1987).
The parameter ρ p is fixed across the pasture levels in Ω = {P1,P2,P3,P4,P5,P6,P7,P8,P9,P10,P11}, since Ω represents productivity levels of the same pasture species and bioclimatic conditions. Given ρ p fixed, we show that the SOC under a heterogeneous pasture area composed of pastures p in Ω is equivalent to the weighted average of the individual areas of pastures p (Z t,p ) and SOC of pastures p (c t,p ). Let represent the fraction of pasture p in the total area; and c H t represents the total SOC accumulated in the total pasture area. Then: Applying Eq. (25) in Eq. (26): Substituting Eq. (26) into Eq. (27): Since the total area is fixed (∑ p Z t;p ¼ A), Eqs. (26)-(28) are linear relations.
Below we present the proof that summing the individual SOC variations Δc t,p of a pasture area composed of sub-areas of pastures with different dry matter productivity (DMP) levels is equivalent to calculating the weighted average between the individual areas of pastures p (Z t,p ) and SOC of pastures p (c t,p ). This is equivalent to proving the relation (29).
From Eq. (27): Imposing that w t,p (ε q − c t − 1,q ) = 0 if p ≠ q, Eq. (30) can be rearranged as: Since ∑ p w t;p ¼ 1 Item (f), the LCA emissions associated with inputs and farm operations applied in the farm are calculated according to: Eq. (34) gives the annual LCA emissions of (f) by accounting for the total application of a given input (or farm operation) inp in year t (term inside the double sum) and multiplying it by the input LCA emission factor, and then summing over inp. Where lca inp represents the emission factor of input inp; INA p,q the amount of applied input inp associated with pasture restoration from pasture p to q (variable RZ t,p,q ).

Data
The typical system represented is a 600 ha grazing beef cattle farm in the city of Campo Grande (20.4683°S, 54.6225°W) in the state of Mato Grosso do Sul, Brazil, which was taken as a reference for climate and bioeconomic data. The analysis used a planning period of 20 years and a budget limited to retained capital or the ABC credit line. The aim is to fatten, finish and sell Nellore steers with diet based solely on forage from pasture Brachiaria brizantha cv. Marandu.
Direct cattle CH 4 emissions (Table 4) were calculated using Tier 2 methodology (Eggleston et al., 2006). Direct N 2 O emissions from manure were estimated using a modified IPCC Tier 2 method. This follows recommendations in previous studies, e.g. Lessa et al. (2014) suggesting that urine and faeces have significantly different emissions factors under typical low protein content diets in Brazil, and that under such conditions, N excretion can be higher in faeces than urine (Xavier et al., 2014). Lessa et al. (2014) estimated N excretion separately for urine and faeces with respective emission factors derived from Brazilian studies (Cardoso et al., 2016).
Pasture productivity (Table 5) for each level in Ω = {P1,P2,P3,P4,P5,P6,P7,P8,P9,P10,P11} was estimated using the Invernada software (Barioni, 2011), which uses monthly averages of historical climate data and the amount of N applied to estimate forage potential accumulation rates, according to the model of Tonato et al. (2010) for the main grass species used in Brazil.
The restoration costs (in R$-2012 per hectare) in Table 6 (the values of η p,q ) were calculated as a function of the individual application of inputs and services employed in restoration practices. We assume the cost of restoring pasture from p to q, where p and q can be any element in Ω, is given by the cost of inputs/machinery used to maintain pasture p (because the restoration decision is made at the moment of degradation) added the cost required to restore one hectare from degraded level P11 to q, less the cost of inputs to restore one hectare from level P11 to p, but only positive differences in the amount of inputs/machinery are accounted for. Let ap inp,P11,q be the amount of inputs/machinery required to restore one hectare of pasture level P11 to level q. Then η p,q is given by: The LCA emission coefficients for the inputs and machinery operations account for all upstream involved GHG emissions in their life cycle, from extraction of natural resources to production at the farm gate, except for purchased calves. Purchased calves are not specific but constant for the restoration practices, therefore not affecting the optimal solution. Base process data was collected from the inventory Ecoinvent v.2.2 (Ecoinvent, 2014) and processed in SimaPro v. 7.3.3 software ("SimaPro Analyst,", 2011). We followed the IPCC v. 1.02 Fig. 1. Comparison of economic returns depending on initial degradation scenarios (LPP, IPP, and HPP) and access to ABC credit. (A) Net present value (R$2012·ha −1 ·yr −1 ) (B) Stocking rates (AU·ha -1 ) (C) Average restoration investments (10 3 R$·yr −1 ) (D) Average pasture restoration (ha·yr −1 ) (E) Average beef productivity (kg CWE·ha −1 ·yr −1 ) methodology for calculating emissions in GWP over a 100 year timespan (Eggleston et al., 2006). The list of all inputs and farm operations included in the analysis and associated LCA emissions factors (lca inp ) can be found in De Oliveira Silva et al. (2016).
We assumed the farm has fixed costs proportional to pasture area. Fixed costs are associated with expenses for cattle (veterinarian equipment), labor and infrastructure and taxes for a beef production system in the state of Mato Grosso do Sul (Table 7).
To start production, the farmer is allowed to take a loan (variable V t,cr ) in the first year from the ABC program. The credit conditions for cattle breeders investing in pasture restoration are a limit of 1 million Brazilian reals (R$) and the payment can be made in 5 instalments  with a three year grace period and an interest rate of 5.5% per annum (http://www.bndes.gov.br/apoio/abc.html).

Farm initial state scenarios
The quality of the pastures (or the level of degradation) before production starts, is an important factor when assessing the effectiveness of restoration practices. Three initial farm degradation scenarios are assumed: the Low Pasture Productivity (LPP), with initial pasture area corresponding to the whole area at DMP level P7 (8.7 t DM·ha −1 ·yr −1 ); the Intermediate Pasture Productivity (IPP), with initial pasture area at DMP level P5 (12.6 t DM·ha − 1 ·yr −1 ); and the High Pasture Productivity (HPP), with initial pasture area at DMP level P1 (19.6 t DM·ha −1 ·yr −1 ). We compared the traditional pasture management with the proposed optimized restoration practices with initial investments subjected to available capital with and without government subsidies for intensification through access to ABC credit.

Shadow price of carbon
A carbon value is not included in the optimization model because there is currently no carbon market entry points for this mitigation effort. However, the methodology allows the implicit calculation of a carbon value. The restoration practices comparison assumes no emissions limit, but we use an emission limit E BAU , corresponding to the total emissions of the unconstrained solution, to calculate the shadow price (of carbon) implied by this emissions constraint (Eq. (36)). We also constrain the model to produce the same beef output as in the unconstrained solution. Ae shadow price is estimated as the change in the objective function from relaxing the emission constraint by one tonne of CO 2 e in relation to the total emissions of the unconstrained solution.
where the terms in the left hand side are respectively emissions from cattle, SOC, fertilizers, the use of inputs and farm operations.

Results
NPV for TRP ranges from −67 R$·ha −1 ·yr −1 to 53.5 R$·ha −1 ·yr −1 , depending on the initial degradation level and access to ABC credit. A negative NPV arising as a result of grassland degradation is actually observed for some beef stocking and finishing systems in Mato Grosso do Sul (Crespoline dos Santos, 2015).
The results indicate that investing in beef production is highly sensitive to the initial level of degradation if TRP is adopted. The LPP scenario implies a negative NPV of −67 R$·ha· −1 ·yr −1 (Fig. 1A, LPP). Under LPP access to ABC credit does not alter the optimum farm decisions since no credit is taken if decisions are based on profit maximization. This is because revenues generated in the first years are insufficient to repay the loan instalments and to cover farm costs, i.e., first payment of five, after three years of credit uptake, as it was modelled in line to ABC credit contract policies (See farm costs section). Instead by using their own capital, payment is made at the end of production, i.e., at the end of 20th year of production.
Under IPP and HPP, the TRP NPV is sensitive to credit access. The NPV of 10.2 R$·ha −1 ·yr −1 is around 4 times greater than production without access to ABC (Fig. 1A, IPP).
In contrast to TRP, optimizing pasture restoration though FRP or URP reduces the importance of the initial degradation level; NPV of 273.4 R$·ha −1 ·yr − 1 and 274.5 R$·ha − 1 ·yr − 1 , respectively for LPP and HPP initial productivity scenarios (without ABC credit). As expected, the annual average stocking rates are also less dependent on initial productivity. The reason is that taking the alternative restoration practices leads to optimal stocking rates more efficiently, with minimum costs and less time required. The average stocking rates were around 1.6 animal units per hectare (AU·ha −1 ), 1 which accords with carrying capacity suggested by Strassburg et al. (2014).
ABC credit promotes profitable and sustainable production only when combined with appropriate pasture management. Taking the ABC credit could increase NPV from 2.7 R$·ha − 1 ·yr −1 to 10.2 R$·ha −1 ·yr −1 , when compared to no access for TRP (Fig. 1A). Fig. 1C shows that FRP could require less investment in restoration than TRP; e.g., investments are 62,700 R$ and 69,800 R$ per year, respectively for the FRP and the TRP under LPP (no ABC), while the  average restoration area is around 3 times greater for the FRP than TRP (Fig. 1D).
Although the credit promotes more investment per year in restoration, Fig. 1D shows less area is restored per year when the credit is available. Because ABC increases cash incomes, more intensive restoration options are undertaken, reducing the average restoration area but improving forage productivity. Fig. 1E shows that the TRP beef productivity ranges from 96 to 104.7 kg CWE·ha −1 ·yr −1 (without ABC) and 167.6 kg CWE·ha −1 ·yr −1 (with ABC). Optimizing pasture restoration could double or triple beef productivity if combined with the ABC credit (Fig. 1E). Fig. 2A-C provide graphical representation of the pasture management practices, i.e., pasture composition in terms of pasture types defined in Table 6, and the associated forage productivity in tonnes of dry matter per hectare per year (t DM·ha − 1 ·yr −1 ), under the LPP scenario.
Figs. 3A − C shows that FRP has more consistent productivity, allowing for optimal relation between forage productivity and stocking rates over the production time. Fractionating pastures also require less cash inflow for investments, a barrier to the adoption of sustainable intensification measures (de Oliveira Silva et al., 2015;Moran et al., 2013) In both FRP and URP the optimum level of productivity is around 18.3 t DM·ha −1 ·yr −1 . Pasture degradation and restoration dynamics can cause SOC to switch from a sink to a source of CO 2 (Smith, 2014). Fig. 3 shows TRP oscillates between losses and gains in SOC stocks, resulting in a slight increase from 45.2 to 47.2 t of carbon per hectare (t-C·ha −1 ), while SOC increased from 45.2 to 60.5 t-C·ha −1 for URP and FRP.
We use the LPP scenario to compare the life cycle assessment emissions intensity of the alternative pasture management practices. The results show that SOC plays a major role in reducing both the absolute total, and emissions per kilogram, while LCA associated with the use of farm inputs, e.g., nitrogen, seed distribution, internal transport, are of minor importance -in relation to direct cattle emissions and SOC. Optimizing pasture management though FRP could double production from 96.0 kg of carcass-weight equivalent per hectare year (kg-CWE·ha − 1 ·yr − 1 ) to 213.4 kg of CWE·ha − 1 ·yr −1 while decreasing the TRP emissions of 494.34 t of CO 2 e per year (tCO 2 -e·yr −1 ) by 30%. Optimizing through URP could increase production to 207.4 kg of CWE·ha −1 ·yr −1 while reducing average annual emissions by 45%. Fig. 4 shows EI as an aggregation of the main GHG emissions sources from the stocking and finishing beef systems, i.e. excluded purchased calves related emissions. Emissions intensities were calculated with and without access to ABC credit under the LPP scenario. Due to the high initial level of degradation in the LPP scenario, even the TRP restoration means pastures are (moderately) intensified during the production period. Estimated EI is 9.26 kg CO 2 -e/kg CWE. Fig. 4 shows that adopting the optimized pasture management practices could reduce these to around 3.59 kg CO 2 -e/kg CWE, with emissions abatement resulting from SOC sequestration from improved grasses. Note that direct cattle emissions account for around 11.87 kg CO 2 -e/kg CWE, whereas SOC sequestration abates 3.8 kg CO 2e/kg CWE, or 30% of cattle EI under TRP. If FRP or URP is adopted, gains in SOC stocks could abate 80-85% of cattle direct emissions (CH 4 and N 2 O).
On average, access to ABC credit reduces EI by around 20% when compared to the same pasture management practice, assuming that producers risk investing their own capital to optimally manage pastures in the scenario without ABC credit. This is because ABC credit provides more incentive for intensification (as seen in Fig. 1C-D), and SOC stocks are higher than without the credit.
Average annual emissions for the FRP is 473.2 t of CO 2 e per year (t CO 2 e·yr −1 ). The shadow price analysis suggests a value of 30.8 R$ per tonne of abated CO 2 e (or 15.1 US$). This can be interpreted as the minimum value farmers would have to be paid per tonne of CO 2 e to maintain profitability as shown in the objective function. Fig. 5 shows a sensitivity analysis of ABC interest rates against NPV, emissions intensity and beef productivity for FRP.
The NPV is highly sensitive to variations in the ABC interest rate. If the rate increases from the baseline value of 5.5% to 8% per year (p.y), NPV decreases by 11.5%, emissions intensity increases by around 8% and beef productivity decrease by around 7%. Reducing the interest rate to 3% p.y increases NPV and beef productivity by around 7% and 3.4%, respectively, while reducing emissions intensity by 4%.

Discussion
Sustainable agricultural intensification rhetoric has highlighted the inherent multi-dimensional trade-offs in meeting increasing food demand by optimizing production while minimizing external costs. Existing literature is largely conceptual, e.g. Loos et al. (2014), and less specific about the relevant scale of analysis. Farm scale optimization is clearly necessary to demonstrate the economic feasibility of any transition from traditional production practices to intensified alternative pasture-based systems. To date however, data on the full extent of pasture degradation in Brazil are patchy and this handicaps more accurate calculation of current average dry matter productivity and SOC stocks.
Our results inform the economics of the 30 M ha restoration target (2010−2030) defined in Brazil's by NAMAs/INDC commitments, and suggest significantly increased profitability and reduced emission through strategic partitioned pasture restoration. Note that this method could be realistically applied at farm level by fenced partition of pasture area and that the result holds without including any notional monetary value that might in future be associated with farm carbon credits. Note that there are currently no significant agricultural carbon credit schemes in Brazil. The ABC program offers an incentive for technology adoption but does not calculate any carbon benefits from increased productivity.
Calculated emission intensities are consistent with De Figueiredo et al. (2017), which show estimates including SOC sequestration in Brachiaria pastures. Our estimates are significantly lower than previous studies (Cederberg et al., 2009;Ruviaro et al., 2014;Cardoso et al., 2016;Gerber et al., 2013) this is partially because we modelled a stockingfinishing system in contrast to whole cycle systems. However, most of the differences in the emission estimates are explained by the fact the other studies do not incorporate SOC sequestration into emission intensities. Indeed, De Oliveira Silva et al. (2016) suggest that accounting for SOC in improved grazing systems could lead to a counter-intuitive result where increasing production could actually lead lower emissions than decreased stocking in some particular beef systems. Although, it is well known that SOC doesn't accumulate ad infinitum and in the long, term the benefits of SOC are likely to be negligible (Brandão et al., 2013;Smith, 2014). A deterministic model has limitations in not capturing the effects of price fluctuations. Further, the focus on profit maximization is potentially contestable, and observed behaviours in relation to the demand for ABC credit to date suggests that alternative satisficing and risk minimization behaviours might warrant exploration as part of a broader sensitivity analysis of key model parameters. Indeed Brazilian farmers have a poor appreciation of the complexity of beef systems and are generally averse to new technologies (SPRP, 2014). In this respect, a robust extension service is essential for planning, on the ground, pasture restoration and beef system improvement, which would benefit from the application of appropriate mathematical optimization.
The farm level focus of this analysis means that we ultimately do not consider the extent to which systems intensification will influence deforestation rates through less extensive land use. Sparing land that could then be used for alternative production options clearly opens up the potential for other market mediated effects that could be just as extensive (Cohn et al., 2014;Gouvello et al., 2011). SAI technologies alone are unlikely to reduce land expansion if unaccompanied by targeted land management incentives and effective deforestation control policies (Arima et al., 2014).

Conclusion
The analysis provides evidence of the importance of pasture management decisions for grazed beef production systems and highlights how improved pasture management could enhance both economic and environmental outcomes relative to the traditional management scenario.
Improved pasture management has a potential role to play in SOC sequestration, potentially decreasing EI in stocking and finishing systems. The results also provide evidence of the importance of public policy to promote sustainable beef production. The ABC credit can significantly influence profitability and GHG emissions. But under highly degraded conditions and the traditional practice, access to the credit may be insufficient to encourage intensification measures. The results thus provide some of the credit conditions that may be necessary to achieve Brazil's international INDCs commitments, which hitherto have not been informed by any farm scale analysis. The results could be extended beyond Brazil to inform sustainable intensification in countries and regions with similar grazing production systems.