The objective of this work is to develop an equation to determine pasture restoration area based on beef demand and to use it to analyze the responses of pasture restoration to their conditioning factors in the Brazilian context.Coordenador: Roberto Giolo de Almeida. II SIGEE

BARIONI, L. G.

SILVA, R. de O.

English

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163An equation to determine demand-constrained pasture restoration areaAn equation to determine demand-constrained pasture restoration areaLuís Gustavo Barioni1*, Rafael de Oliveira Silva21Embrapa Agriculture Informatics, 2School of Mathematics, The University of Edinburgh*luis.barioni@embrapa.brIntroductionPasture restoration is a major part of the Brazilian NAMAs (Mozzer 2011) and INDCs (Brazil, 2015) and is operationally encouraged throu-gh a government-funded bank credit line for low carbon agriculture (Mozzer 2011). Beef production is the major grassland based activity in Brazil. Therefore, pasture restoration area targets should harmonize with projected demand for beef in order to avoid under and over pro-duction and negative impact on prices. Pasture restoration area has been previously estimated by large mathematical programming models (Oliveira Silva et al., 2016) but the development of a single equation mo-del is useful to improve understanding and transparency of the estima-tes and the interpretation of such large models’ results. The objective of this work is to develop an equation to determine pasture restoration area based on beef demand and to use it to analyze the responses of pasture restoration to their conditioning factors in the Brazilian context.Material and MethodsAn equation to estimate pasture restoration area (R, ha) as function of beef demand (D, kg CWE.yr-1) was deduced as follows.  Let  N be  the  number of animals  (N, heads) in  a   given pasture area. The variation in animal numbers (𝑁𝑓 − 𝑁𝑖) in a given period can be described by equation (1).𝑁𝑓    − 𝑁𝑖  = 𝛿𝑁   + 𝑁𝑖   − 𝑁out,                                                                         (1)164An equation to determine demand-constrained pasture restoration areawhere, Ni and Nf are the number of animals at the beginning and at the end of a period of time, respectively; 𝛿𝑁R  is the difference between the number of animals before and after recovering a pasture area (R, ha); 𝑁𝑖n  and 𝑁out   are the number of animals in areas where grasslands have expanded and contracted, respectively. Stocking rate (S) is defined as ratio between number of animals and grassland area (A, ha), i.e.  =  , therefore 𝑁 = 𝐴.  . So:𝛿𝑁R  = R.   (S𝑟  − S𝑑) = R.   𝛿S, and,                         (2)𝑁𝑖n  − 𝑁out  = 𝛿𝐴.  Sℎ                          (3)Substituting (2) and (3) in (1), and isolating R:R = 𝛿𝑁 −𝛿 𝐴.  Sℎ                                                                                 (4)Hereafter we assume production and demand are in equilibrium. Beef production is the product of the number of animals and production per animal (C, kg CWE.head-1.yr-1), i.e. D= C.   𝑁. Note that for the analy-sis herein, C represents the lifecycle average productivity of the herd. The variation in D is due to variations in N and in C as described in equation (5): 𝛿D = 𝛿𝑁.  C𝑖  + 𝑁𝑖.  𝛿C + 𝛿𝑁.  𝛿C             (5)A multiplier P, which is the proportion of production variation due to variation in N is useful to study the pathways of intensification. In a high time resolution, 𝛿𝑁.  𝛿C is very small relative to the other two com-ponents (lower than 1/50 for Δt = 1yr in the Brazilian conditions). So we can define P as, according to (6).:𝛿𝐷.  𝑃=𝛿𝑁.  𝐶𝑖∴𝛿𝑁=𝛿𝐷.  𝑃                   (6)Also, let’s define the ratios of final over initial, demand ( αD)  and animal numbers (αN), according to equations (7) and (8). 𝛼𝐷=𝐷𝑓 ∴𝛿𝐷=𝐷𝑖.  (𝛼𝐷−1)                                                                      (7)𝛿S𝐶𝑖𝐷𝑖165An equation to determine demand-constrained pasture restoration area to the other two components (lower than 1/50 for Δt = 1yr in the Brazilian conditions). So we can define P as, according to (6).: 𝛿𝛿𝛿𝛿.𝑃𝑃 = 𝛿𝛿𝛿𝛿.𝐶𝐶𝑖𝑖 ∴ 𝛿𝛿𝛿𝛿 =𝛿𝛿𝛿𝛿𝐶𝐶𝑖𝑖.𝑃𝑃  (6) Also, let’s define the ratios of final over initial, de and (αD) and animal numbers (αN), according to equations (7) and (8). 𝛼𝛼𝛿𝛿 = 𝛿𝛿𝑓𝑓𝛿𝛿𝑖𝑖 ∴ 𝛿𝛿𝛿𝛿 = 𝛿𝛿𝑖𝑖 . (𝛼𝛼𝛿𝛿 − 1)  (7) 𝛼𝛼𝛿𝛿 = 𝑁𝑁𝑓𝑓𝑁𝑁𝑖𝑖 ∴ 𝛿𝛿𝛿𝛿 = 𝛿𝛿𝑖𝑖 . (𝛼𝛼𝛿𝛿 − 1)  (8) Replacing appropriately the definitions in equations (6), (7) and (8) in equation (4), and assuming the average stocking rate for expansion and contraction grassland areas (𝑆𝑆ℎ) is equal to the initial stocking rate, i.e. 𝑆𝑆ℎ =𝛿𝛿i Ci.Ai , one can calculate R as in equation (9): 𝑅𝑅 = 𝛿𝛿𝑖𝑖𝛿𝛿𝛿𝛿.𝐶𝐶𝑖𝑖 ((𝛼𝛼𝛿𝛿 − 1).𝑃𝑃 − (𝛼𝛼𝐴𝐴 − 1)) =𝛿𝛿𝑖𝑖𝛿𝛿𝛿𝛿𝑖𝑖 ((𝛼𝛼𝛿𝛿 − 1).𝑃𝑃 − (𝛼𝛼𝐴𝐴 − 1))  (9) where 𝛿𝛿𝑌𝑌𝑖𝑖 =  𝛿𝛿𝑆𝑆.𝐶𝐶𝑖𝑖  is the difference in productivity between restored and degraded pastures.  Results and Conclusions According to Equation 9, the main factors defining the area of pasture restoration are the initial demand and its rate of growth, the overall variation in pasture area, the difference in productivity between recovered degraded areas and the rate of expected variation in animal performance.   Results of a sensitivity analysis of the rate of increase of demand to the specified factors, fixing initial demand (Di) to 10.0 MMT CWE, i.e. approximately the Brazilian current national production. The results highlight the importance of growth in beef demand to achieve the NAMAs target rates of pasture restoration in Brazil and suggest that if a high proportion of production increase is due to animal performance improvement, NAMA restoration targets may turn out to be unattainable (Figure 1). Comparing Figure 1 (a), (b) and (c) it is also possible to evaluate that pasture area expansion may also impair the target achievement.  Applying the expected range of Brazilian beef demand growth rates (1.25 – 2.00 %.yr-1), results presented in Table 1 indicate target rates of pasture restoration in Brazil (1.9 M ha.yr-1) would most likely be achieved in scenarios of pasture area contraction (i.e. αA < 1.0), associated with moderate levels of improvement of animal performance (≤ 50% of total productivity gain) and change in productivity of the recovered areas (≤ 80 kg CWE.ha-1.yr-1).  Results and ConclusionsAccording to Equation 9, the main factors defining the area of pasture r storation are the initial demand and its rate of growth, the overall va-riation in pasture area, the difference in productivity between recovered degra ed areas and the rate of expected variation in animal p rforman-ce.Resul s of a sensitivity analysis of the rate of incre se of demand to thespecified factors, fixing initial demand (Di) to 10.0 MMT CWE, i.e. approximately the Brazilian current national production. The results highlight the import nce of growth in beef dema d to achieve the NAMAs target rates of pasture restoration in Brazil and suggest that if  high propor i n of production increase is due to animal performance improvement, NAMA restoration targets may turn out to be unattaina-ble (Figure 1). Comparing Figure 1 (a), (b) and (c) it is also possible to evaluate that pasture area expansion may also impair the target achie-vement.Applying the expected range of Brazilian beef demand growth rates (1.25 – 2.00 %.yr-1), results presented in Table 1 indicate target rates of pasture restoration in Brazil (1.9 M ha.yr-1) would most likely be achieved in scenarios of pasture area contraction (i.e. 𝛼A < 1.0), as-sociated with moderate levels of improvement of animal performance (≤ 50% of total productivity gain) and change in productivity of the recovered areas (≤ 80 kg CWE.ha-1.yr-1).166An equation to determine demand-constrained pasture restoration areaProportion of productivity gain due to improved animal performance (P , dimensionless)Figure 1. Rate of beef demand growth (αD) required to achieve pasture restoration rates of 1.9 Mha.yr- 1 for different rates of variation in area (αA), difference in pro-ductivity of recovered – degraded pastures (δY) and proportion of production gain due to improved animal performance (1-P). αA values of 0.995, 1.000 and 1.005 correspond a variation of approx. (-0.79, 0 and +0.79 Mha.yr-1).Table 1. Intervals of area recovered (M ha.yr-1) for different levels of α, δY and P. Lower and upper limits correspond to annual rates of growth in demand of 1.25% and 2.00 %, respectively. Intervals in red indicate the range is lower than rates for pasture restoration proposed in the Brazilian NAMAs (direct + crop-livestock).  Figure 1. Rate of beef demand growth (αD) required to achieve pasture restoration rates of 1.9 Mha.yr-1 for different rates of variation in area (αA), difference in productivity of recovered – degraded pastures (δY) and proportion of production gain due to improved animal performance (1-P). αA values of 0.995, 1.000 and 1.005 correspond a variation of approx. (-0.79, 0 and +0.79 Mha.yr-1).  Table 1. Intervals of area recovered (M ha.yr-1) for different levels of α, δY and P. Lower and upper limits correspond to annual rates of growth in demand of 1.25% and 2.00 %, respectively. Intervals in red indicate the range is lower than rates for pasture restoration proposed in the Brazilian NAMAs (direct + crop-livestock).   References  BRAZIL. 2015. Intended Nationaly Determined Contribution (INDCs). Library of Congress.http://www4.unfccc.int/submissions/INDC/Published Documents/Brazil/1/BRAZIL iNDC english FINAL.pdf. OLIVEIRA SILVA, R. de; BARIONI, L. G.; HALL, J. A. J.; FOLEGATTI MATSUURA, M. Y.; ZANETT ALBERTINI, T; FERNANDES, F. A.; MORAN, D. Increasing beef production could lower greenhouse gas emissions in Brazil if decoupled from deforestation. Nature Climate Change, v. 6, p. 493-498, 2016. DOI 10.1038/NCLIMATE2916 MOZZER, G B. Agriculture and Cattle Raising in the Context of a Low Carbon Economy. In Motta, R.S. (Ed.) CLIMATE CHANGE IN BRAZIL: Economic, Social and Regulatory Aspects. Brasília, DF: IPEA. 2011, Cap 4, p. 107 – 122. https://www.ipea.gov.br/agencia/images/stories/PDFs/livros/livros/livro_climatechange_ingles.pdf#page=108. -0.5% 0 0.5% -0.5% 0 0.5% -0.5% 0 0.5%40 [3.6 , 5.0] [2.3 , 3.8] [1.1 , 2.5] [2.8 , 3.8] [1.6 , 2.5] [0.3 , 1.3] [2.0 , 2.5] [0.8 , 1.3] [-0.5 , 0.0]60 [2.4 , 3.3] [1.6 , 2.5] [0.7 , 1.7] [1.9 , 2.5] [1.0 , 1.7] [0.2 , 0.8] [1.4 , 1.7] [0.5 , 0.8] [-0.3 , 0.0]80 [1.8 , 2.5] [1.2 , 1.9] [0.5 , 1.3] [1.4 , 1.9] [0.8 , 1.3] [0.2 , 0.6] [1.0 , 1.3] [0.4 , 0.6] [-0.2 , 0.0]100 [1.4 , 2.0] [0.9 , 1.5] [0.4 , 1.0] [1.1 , 1.5] [0.6 , 1.0] [0.1 , 0.5] [0.8 , 1.0] [0.3 , 0.5] [-0.2 , 0.0]Proportion of productivity gain due to variation in animal performance (1-P)Area variation (α)δY (kg.ha.yr-1)25% 50% 75%Proportion of productivity gain due to improved animal performance (P, dimensionless) (a) αA = 0.995 (b) α A= 1.000 (c) αA = 1.005 Rate of increase in demand (%.yr-1) 167An equation to determine demand-constrained pasture restoration areaReferencesBRAZIL. 2015. Intended Nationaly Determined Contribution (INDCs). Library of Con-gress.http://www4.unfccc.int/submissions/INDC/Published Documents/Brazil/1/BRAZIL iNDC english FINAL.pdf.OLIVEIRA SILVA, R. de; BARIONI, L. G.; HALL, J. A. J.; FOLEGATTI MATSUURA, M.  Y.; ZANETT ALBERTINI, T; FERNANDES, F. A.; MORAN, D. Increasing beef production could lower greenhouse gas emissions in Brazil if decoupled from deforestation. Nature Climate Change, v. 6, p. 493-498, 2016. DOI 10.1038/NCLIMATE2916MOZZER, G B. Agriculture and Cattle Raising in the Context of a Low Carbon Economy. In Motta, R.S. (Ed.) CLIMATE CHANGE IN BRAZIL: Economic, Social and Regulatory Aspects. Brasília, DF: IPEA. 2011, Cap 4, p. 107 – 122. https://www.ipea.gov.br/agencia/images/stories/PDFs/livros/livros/livro_climate-change_ingle s.pdf#page=108.

An equation to determine demand constrained pasture restoration area.

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An equation to determine demand constrained pasture restoration area.

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