Model design

Bio-economic farm models can take the form of a simulation model or an optimization model (Janssen and van Ittersum, Reference Kanis, De Greef, Hiemstra and Van Arendonk2007). This paper develops a simulation model rather than an optimization model, since the degrees of freedom for optimization are limited in an intensive pig production system. We assumed that available farm resources, which are given (e.g. buildings and equipment), are optimally used and the farm operates at its optimum. The time period taken into account in the model is 1 year.

Figure 1 depicts the flow of inputs (feed and non-feed inputs) and outputs (both marketable and undesirable) and the production cycle of a sow and her piglets as it is modelled. Reproduction in the model starts with purchased replacement gilts from superior herd. Replacement gilts are mated (first mating) after a certain period of time from purchase. Conceived gilts join the sow pool. Gilts with problems (e.g. anoestrus, leg problems, udder problems, failed conception) are culled. The sow production cycle consists of conception, farrowing, lactation and weaning. After weaning, a sow will be mated or culled depending on her condition and performance. Weaned piglets pass through three growth stages – piglets (weaning to 23 kg), growing pigs (23 to 70 kg) and finishing pigs (70 kg to slaughter weight).

Figure 1

Flow chart of farrow-to-finish pig production system.

Variable costs of gilts and sows comprise costs of purchasing replacement gilts, feed, labour, veterinary, energy, semen, maintenance and repair, transport and others. Boar costs are included in gilt and sow costs. Variable costs of fattening pigs include costs of feed, labour, veterinary, energy, maintenance and repair, transport and others during the three growth stages. Fixed costs (depreciation and interest expenses) are included at farm level. In the social profit function, environmental costs of emission of GHGs from feed production and manure, and the fertilizer value of manure are also included. Returns consist of sales of culled gilts and sows, of fattening pigs, and of the fertilizer equivalent value of manure. Supplementary Material S1 provides the list of equations used to calculate the costs and returns of sows and fattening pigs.

Pig growth model

A pig growth model, InraPorc^® model, is incorporated in the BEFM to account for the biological aspects of growing-finishing pigs (23 kg to slaughter weight) using different diets. The model predicts growth performance of pigs (i.e. daily gain, feed conversion ratio, pork quality) for different types of diets used in the growing and finishing growth stages (Van Milgen et al., Reference Diesel, Miranda and Perdomo2008). Protein deposition (PD) and lipid deposition (LD) are the two key variables related to chemical and physical body composition of pigs for predicting growth response and carcass characteristics. The InraPorc^® model simulates nutrient partitioning for PD, LD and for other activities such as maintenance, physical activities and PD cost. The rate of PD and LD depends on potential PD, energy and amino acid supplies. Potential PD refers to PD when the pig is capable of expressing its full growth potential under ad libitum feeding. To predict feed intake in the InraPorc^® model, the equation Y=aX ^b was used; where Y is net energy intake in MJ/day, X the BW in kilogram, and a and b are parameters. The parameters a and b are estimated within InraPorc^® from given feed intakes at 50 and 100 kg BWs. Other parameters required for simulating growth performance in InraPorc^® are: initial age, initial BW, final age or final weight, precocity per day and mean PD per day.

Environmental cost of feed and manure

Feed production and manure are the largest contributors to global warming potential (GWP) in the pork production chain (Nguyen et al., Reference Omogbenigun, Nyachoti and Slominski2012; Cherubini et al., Reference Cherubini, Zanghelini, Alvarenga, Franco and Soares2015). The environmental cost of GWP, which is caused by emission of GHGs, from feed production and manure, is incorporated in the BEFM. Global warming potential is selected as it generally also acts as an indicator of other environmental categories (e.g. acidification and eutrophication) (Röös et al., Reference Serenius, Muhonen and Stalder2013). An efficient use of nitrogen leads to less acidifying and eutrophying substances being released to the environment and lower GHGs emission in the form of N₂O.

Two steps are required to calculate the environmental costs of feed and manure: determining the amounts of GWP from feed production and manure, and monetizing GWP. The GWP of feed productions were taken from Ali et al. (Reference Ali, van Zanten, Berentsen, Bastiaansen, Bikker and Oude Lansink2017). The GWP of feed production included emissions from extraction of raw materials (e.g. fertilizer, pesticide and energy), cultivation of crop ingredients (including emissions from direct land use change), drying and processing of ingredients, manufacturing of concentrated feed and transportation in all stages until the pig farm. The GWP from manure depends on manure management and the type of diets used (Dourmad et al., 2003; Rigolot et al., Reference Röös, Sundberg, Tidåker, Strid and Hansson2010). The calculation of this GWP for the different diets is presented in the ‘Model application’ section below. The three GHGs: CO₂, CH₄ and N₂O were expressed in kilogram of CO₂ equivalent (CO₂-eq) using weights of 1, 28 and 265 for CO₂, CH₄ and N₂O, respectively (assuming 100 years life span; Intergovernmental Panel on Climate Change (IPCC), 2015).

Monetizing GWP was done by using the shadow price of CO₂ emission. Several studies estimated the cost of CO₂ release to the atmosphere (for an overview see Tol, Reference Van Milgen, Valancogne, Dubois, Dourmad, Sève and Noblet2008). These costs are associated with the impact of CO₂ release on the environment, human health and economy. There is a huge variation among the estimates in the literature (see Tol, Reference Van Milgen, Valancogne, Dubois, Dourmad, Sève and Noblet2008). Although a shadow price represents the costs of damages on environment, resources and human health caused by CO₂ release, it is also a politically negotiated price for carbon. In this study, we used estimates from Gurgel and Paltsev (Reference Houška, Wolfová and Fiedler2014) for Brazil. During the 2009 Copenhagen meeting, Brazil agreed to reduce GHG emissions by between 36.1% and 38.9% by 2020. Gurgel and Paltsev (Reference Houška, Wolfová and Fiedler2014) examined a sectoral carbon tax, carbon tax on land use change, and establishing a carbon market for emission allowance trading from the agricultural and energy sectors together with a carbon tax on land use change to achieve this target. In this study, we used the average of the 2015 carbon tax for the livestock sector (about 0.07 US$/kg CO₂-eq) and carbon market price (about 0.02 US$/kg CO₂-eq). Even though two prices cannot exist together from economic point of view, we used the average of carbon tax and carbon market price since the carbon market price that Gurgel and Paltsev (Reference Houška, Wolfová and Fiedler2014) estimated does not account for emissions from land use change caused by the livestock sector. The shadow price that we used in this study (0.045 US$/kg CO₂-eq) is comparable with the shadow price estimated by Price et al. (Reference Rezitis and Stavropoulos2007) for United Kingdom (0.048 US$/kg CO₂-eq for 2015). For manure, we considered the financial gains due to the replaced fertiliser and reduction in GHGs emissions after taking account of GHG emissions from manure (refer to the ‘Model application’ section below for the Brazilian situation).

Stochastic variables

The BEFM accounts for the stochasticity of the main economic parameters (i.e. feed prices, the price of replacement gilt and the selling price of finished pig). The reason for choosing these stochastic parameters is that these variables fluctuate over time and they are expected to have substantial influence on the economic results as feed cost accounts >75% in pig cost of production and as sales of finished pigs are the main source of revenue. Fluctuations in feed prices follow the fluctuation of corn and soybean meal prices, which are the main feed ingredients.

The stochasticity of biological parameters (i.e. InraPorc^® model parameters – mean PD, precocity per day, and net energy intakes at 50 and 100 kg live weights) was also considered. Performance variation among growing-finishing pigs is one of the main problems encountered by pig producers, which ultimately results in heterogeneous slaughter weights. For example, feed intake, nutrient utilization and daily growth vary between growing-finishing pigs, which in turn result in different nutrient excretions. The inclusion of stochasticity in the InraPorc^® model parameters captures the variations in performance among growing-finishing pigs (e.g. daily growth, feed intake, feed conversion and excretion of nutrients). Since the model is for a typical farm, we believe that there will be no random variations in management practices over time. Only variations external to the farm (e.g. prices and biological variations between pigs) are considered. We assumed that the performance of sows in the same age structure is the same and hence random variation between the performances of sows is negligible. Introduction of stochasticity in models requires average values, the variation of the stochastic variables and the correlation among these variables. For prices, standard deviations and correlation coefficients can be derived from annual data by removing the effect of the trend term. For the InraPorc^® model parameters, standard deviations and correlation coefficients can be computed from data recorded on a given farm.

Model application

The developed stochastic BEFM is applied to an independent (i.e. farrow-to-finish) pig farm in Minas Gerais to assess the impact of using alternative feed sources on private and social profits. Pig producers in Minas Gerais (and the southeast region) generally follow a farrow-to-finish production system. In Brazil, such producers are named ‘independent producers’ as these producers do not have contractual agreements with agribusinesses for receiving inputs (e.g. feed and piglets) or supplying their finished pigs. In Minas Gerais, the size of farms varies significantly ranging from 50 sows to more than 5000 sows. We assume that a typical farm in our model owns 1500 productive sows with annual replacement rate of 45% (Martins et al., Reference Monteiro, Garcia-Launay, Brossard, Wilfart and Dourmad2012). Embrapa Swine and Poultry Centre (Reference Gunjal and Legault2016) also assumes 1500 productive sows in their monthly reports of swine cost of production for Minas Gerais.

Definition of cases

A reference case and two alternative cases (macaúba and co-products) are designed to assess the impact of using co-products in the diets of finishing pigs on private and social profits. The reference case represents the current feeding practice in Minas Gerais, Brazil. Table 1 shows the complete diet compositions used in the three cases.

Table 1

Diet compositions for pigs in Minas Gerais, Brazil (% of diet in kilogram product)

¹ A corn–soybean meal, macaúba kernel cake- and co-product-based finishing diets were used in the reference, macaúba and co-products cases, respectively. Diets of sows, piglets and growing pigs, which were the same in the three cases, were considered. Net energy intakes were the same.

² Cherubini et al. (Reference Cherubini, Zanghelini, Alvarenga, Franco and Soares2015).

³ The growing and reference finishing pig diets were formulated based on data from a feed company by Gabriel Rocha. The alternative finishing diets were taken from Ali et al. (Reference Ali, van Zanten, Berentsen, Bastiaansen, Bikker and Oude Lansink2017).

⁴ Equivalent to 500 FTU phytase/kg diet.

⁵ Mycotoxin binders, flavours and sweetener agent (not included in the environmental impact analyses).

⁶ Standardised ileal digestible lysine.

A three-stage feeding regime is assumed for fattening pigs based on piglets (weaning to 23 kg live weight), growing pigs (23 to 70 kg) and finishing pigs (70 kg to slaughter weight). Although it is possible to predict growth performance from 15 kg to slaughter using the InraPorc^® model, we assumed that the piglet stage (weaning to 23 kg) is exogenous to the model to match with the Brazilian production system. The three cases have a common part (i.e. the diets for sows, piglets and growing pigs) and a specific part (i.e. diets for finishing pigs). The cases are specific for only the finishing stage because the digestibility of co-products (which are used in the alternative finishing diets) is lower compared with corn and soybean meal, whereas the digestive capacity of finishing pigs is better than that of piglets and growing pigs. Moreover, a significant amount of feed is used in the finishing stage. The growing pig and the reference finishing pig diets were formulated to represent the current feeding practices in Minas Gerais. The finishing pig diet in the reference case mainly consists of corn and soybean meal. In the macaúba and co-products cases, a macaúba kernel cake- and a co-product-based diets are used during the finishing stages, respectively. The alternative finishing pig diets were taken from Ali et al. (Reference Ali, van Zanten, Berentsen, Bastiaansen, Bikker and Oude Lansink2017). Total net energy intakes are set to be equal in the three cases.

Management, biological and economic input parameters

A farm that owns 1500 productive sows with an annual replacement rate of 45% is assumed. The average (2006-15) litter size born alive and pre-weaning mortality rates are about 12 piglets and 8.74%, respectively. Table 2 presents the values of management and biological input parameters of the model. Total net energy intakes are set to be equal in the three cases through the parameters net energy intakes at 50 and 100 kg BWs. We assumed that net energy intakes of growing-finishing pigs are 21.07 and 28.94 MJ/day at 50 and 100 kg BWs, respectively (Monteiro et al., Reference Nguyen, Hermansen and Mogensen2016). As the alternative diets of finishing pigs (macaúba kernel cake- and co-product-based diets) contain lower net energy concentrations (9.83 MJ/kg, Table 1) compared with the reference diet (10.26 MJ/kg, Table 1), pigs are allowed for a higher feed intake under alternative cases to realize the same net energy intake as the reference case. However, the higher feed intakes also result in increased feed costs and GHGs emissions.

Table 2

Management and biological inputs of pig production in Minas Gerais, Brazil

¹ Derived from annual sow replacement rate, replacement gilt culling and death rates, and sow death rate.

² Derived from weaned piglets per sow per year, number of finished pigs per sow per year and mortality rates in the finishing stage.

³ For gilts with standard performance.

The economic input parameters of the model are presented in Table 3. The expected prices of replacement gilts and of finished pigs are the averages of annual prices in the period 2006-15. Annual prices of feeds for piglets, growing pigs, finishing pigs and sows were only available for the year 2015 from Ali et al. (Reference Ali, van Zanten, Berentsen, Bastiaansen, Bikker and Oude Lansink2017) who computed them using information on the composition and the prices of feed ingredients. Other information available were the annual feed costs of finished pigs from a database of Embrapa swine and poultry centre for the entire period 2006-15. The missing feed prices in the period 2006-14 were computed in two steps. First, we computed the annual percentage change in the feed costs of finished pigs for the period 2006-15. Next, we used the annual changes in feed cost to compute feed prices for the period 2006-14 from the 2015 prices of feeds. By doing this, we assumed that the annual changes in feed cost per finished pig over the period 2006-15 are entirely due to changes in feed prices between the same years.

Table 3

Economic input values of pig production in Minas Gerais, Brazil

R$=Brazilian Real.

¹ Average feed prices (2006-15) derived from annual feed cost of finished pig (Embrapa swine and poultry centre, Reference Gunjal and Legault2016).

² Derived based on the relative price of live weight of culled gilts (R$3.45/kg) and sows (R$2.22/kg) compared to the average price of live weight of finished pigs (R$3.45/kg) from January to July 2016 in Passos, MG.

Stochastic input parameters

Feed prices, the price of replacement gilts and the selling price of finished pigs were assumed to be stochastic in the BEFM. Annual data (2006-15) were used to compute the means, standard deviations and correlations among these stochastic parameters. Prices were de-trended (i.e. the systematic increase or decrease in prices was removed from the original prices) to generate a price series that was used for computing the standard deviations and correlations.

For the InraPorc^® model parameters, the mean values were taken from Monteiro et al. (Reference Nguyen, Hermansen and Mogensen2016) which were estimated from the Brazilian production system. For the standard deviations and correlation coefficients among these parameters, values were adopted from Saintilan et al. (Reference Skorupski, Garrick, Blair and Smith2015) who derived them based on experimental data from France. As the Brazilian production system is also based on high-potential breeds using modern technologies, we assume that the values reflect the variation in Brazil. Therefore, the variance captures performance differences between individual pigs. A normal distribution was assumed for both economic and biological parameters. Table 4 summarizes the mean values, standard deviations and correlation coefficients of the stochastic parameters. As prices and biological parameters cannot be negative, the distributions of the parameters were truncated at zero (i.e. the minimum value is 0). Simulations were conducted using @Risk, an add-in in MS Excel (Palisade Corporation, Ithaca, NY, USA).

Table 4

Mean values, standard deviation and correlation coefficients among stochastic parameters

R$=Brazilian Real.

Environmental cost of feed and net return from manure

The GWP (including emissions from direct land use change) of feed ingredients were taken from Ali et al. (Reference Ali, van Zanten, Berentsen, Bastiaansen, Bikker and Oude Lansink2017). Using the emission factors of feed ingredients and diet compositions, GWP of each diet was derived. Manure is the second source of GHGs emission in pig production. For storage of manure, an open slurry tank (without a natural crust cover) is assumed, as this is the most commonly used form of pig manure management system in Brazil. The liquid manure is assumed to be removed daily or weekly from the channels of the building through pipes to the external deposit (slurry tank) where it is kept for about 120 days for partial stabilization and subsequent field application (Kunz et al., Reference Louhichi, Kanellopoulos, Janssen, Flichman, Blanco, Hengsdijk, Heckelei, Berentsen, Lansink and Van Ittersum2009; Cherubini et al., Reference Cherubini, da Silva, Zanghelini, Alvarenga, Galindro, de Léis and Soares2014). For estimating CH₄ and (indirect) N₂O emissions from manure, the tier 2 approach of IPCC was used by using country- and diet-specific data and IPCC (Reference Janssen and van Ittersum2006) default values. The country-specific data concern the volatile solids and nutrient excretions of sows and piglets. For sows and piglets, these data were taken from Cherubini et al. (Reference Cherubini, da Silva, Zanghelini, Alvarenga, Galindro, de Léis and Soares2014) and Diesel et al. (Reference Dourmad, Pomar and Massé2002). For pigs in the growing and finishing stages, the mathematical models of Rigolot et al. (Reference Röös, Sundberg, Tidåker, Strid and Hansson2010) and Dourmad et al. (2003) were included in the BEFM to calculate the amounts of volatile solids and nutrient excretions for the specific diets used. There is no direct N₂O emission since manure is stored in an open slurry tank without natural crust cover (IPCC, Reference Janssen and van Ittersum2006; Cherubini et al., Reference Cherubini, da Silva, Zanghelini, Alvarenga, Galindro, de Léis and Soares2014). Supplementary Material S2 and Supplementary Table S2 provide the details of calculations for estimating volatile solids, nutrient excretions and GWP of manure.

In Brazil, manure is applied on land as organic fertilizer and thereby avoids the production and use of artificial fertilizer (Kunz et al., Reference Louhichi, Kanellopoulos, Janssen, Flichman, Blanco, Hengsdijk, Heckelei, Berentsen, Lansink and Van Ittersum2009; Cherubini et al., Reference Cherubini, Zanghelini, Alvarenga, Franco and Soares2015). To calculate the returns from manure we assume that the avoided fertilizers are urea (46% N), superphosphate (42% P₂O₅) and potassium chloride (60% K₂O). Efficiency rates of 0.75 for urea (Nguyen et al., Reference Nguyen, Hermansen and Mogensen2010), 1 for superphosphate and 1 for potassium chloride were assumed to estimate the amounts of avoided fertilisers. The amounts of avoided chemical fertilisers are then calculated as:

(1) $$F_{{\rm N}} \,{\equals}\,{{0.75{\times}{\rm N}_{{{\rm Manure}}} } \over {0.46}}$$

(2) $$F_{{{\rm P}_{{\rm 2}} {\rm O}_{5} }} \,{\equals}\,{{1{\times}{\rm P}_{2} {\rm O}_{5}}_{{{\rm Manure}}} \over{0.42}}$$

(3) $$F_{{{\rm K}_{2} {\rm O}}} \,{\equals}\,{{1{\times}{\rm K}_{2} {\rm O}_{{{\rm Manure}}} } \over {0.60}}$$

where F _N is the amount of urea, N_Manure the total N excretion in the manure adjusted for N volatilisation during storage, $F_{{{\rm P}_{2} {\rm O}_{5} }} $ the amount of superphosphate, P₂O_5Manure the amount of P₂O₅ in the manure, $F_{{{\rm K}_{2} {\rm O}}} $ the amount of potassium chloride and K₂O_Manure the amount of K₂O in the manure. Then, the net return from manure is computed as:

(4) $$\eqalignno { {\rm Net\,\,return\,\,from\,\,manure}\,{\equals} & \,\sum P_{i} {\times}F_{i} {\plus}\sum {SP} {\times}GWP_{{F_{i} }} \cr&\; {\minus}SP {\times}GWP_{{{\rm Manure}}} $$

where P _i is price of artificial fertilizer i; i refers to N, P₂O₅ and K₂O; F _i the amount of avoided fertilizer i; SP the shadow price of GWP; $GWP_{{F_{i} }} $ is GWP of artificial fertilizer production and GWP _Manure is GWP of manure. The first term $( {\sum P_{i} {\times}F_{i} } )$ refers to the fertilizer value of manure, the second term $( {\sum {SP}{\times}GWP_{{F_{i} }} } )$ implies the avoided environmental cost due to the avoided production of artificial fertilizer and the last term (SP×GWP _Manure) is the environmental cost of manure. Supplementary Table S3 provides the details of calculations and parameter values for computing the net return from manure.

Sensitivity analysis

We checked the sensitivity of private profit due to a change in the price of the macaúba kernel cake-based diet. As discussed in Ali et al. (Reference Ali, van Zanten, Berentsen, Bastiaansen, Bikker and Oude Lansink2017), the price of macaúba kernel cake was based on only processing cost as the product is non-existent in market. Commercialization of the production and processing system of macaúba, however, might make it a competitive product. Therefore, in the sensitivity analysis we assumed an increase of the price of the macaúba kernel cake-based finishing diet by 14%. This increase would make the price of the macaúba kernel cake-based diet equal to the price of the reference diet.