American Institute of Mathematical Sciences

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April  2019, 6(2): 119-129. doi: 10.3934/jdg.2019009

An application of a dynamical model with ecological predator-prey approach to extensive livestock farming in uruguay: Economical assessment on forage deficiency

Francisco Dieguez 1,, and  Hugo Fort 2,

1. 

Facultad de Veterinaria, Departamento de Nutricion, Universidad de la Republica, Ruta 1 km 42.500, Libertad, CP 80.100, San Jose, Uruguay
2. 

Facultad de Ciencias, Instituto de Fisica, Universidad de la Republica, Igua 4225, CP 11.400, Montevideo, Uruguay

* Corresponding author: Francisco Dieguez

Received  October 2018 Revised  March 2019 Published  April 2019

Extensive livestock farmers have to manage climate risk. Therefore, there is a need to generate quantitative tools to evaluate the biophysical and economic impacts on extensive farming based on native grasslands. We present an ecological model based on the predator-prey approach, used to simulate the effect of forage deficiency on the farm's economic performance. Different scenarios of animal stocking rate and carrying capacity of grassland are considered to assess the impact of forage deficiency in spring. Results suggest a cubic response of Gross product per hectare as function of Gross margin, according Mott's theoretical model for meat production on grassland systems in response to stocking rate. The maximum value of this cubic response function strongly depends on the initial grass height and climate scenarios. The initial grass height is critical to maximize secondary productivity and farm economic results. Scenarios including grass reserves can buffer the deficiency on grass growth rates and pasture offer, as occurs in drought periods at the time when farmers try to make animals gain liveweight. Our analysis reinforces the usefulness of forage assignment adjustment by modulating stocking rate to improve liveweight gain and economic results under climate change conditions.

Keywords: Modeling, drought, resilience, cattle production systems.
Mathematics Subject Classification: Primary: 49K15, 91B74; Secondary: 92D40.
Citation: Francisco Dieguez, Hugo Fort. An application of a dynamical model with ecological predator-prey approach to extensive livestock farming in uruguay: Economical assessment on forage deficiency. Journal of Dynamics and Games, 2019, 6 (2) : 119-129. doi: 10.3934/jdg.2019009
References:
[1]

E. Berretta and M. Bemhaja, Produccion estacional de comunidades naturales de Basalto de la unidad Queguay Chico, Serie tecnica INIA, 102 (1998), 16-28. 

[2]

P. Booysen, Optimizacion de la carga de ganado y el manejo del pastoreo, Pastos, 5 (1975), 372-381. 

[3]

P. Carvalho, D. dos Santos and F. Neves, Oferta de forragem como condicionadora da estructura do pasto e do desempenho animal, in Anais do II Simposio de Forrageiras e Produo Animal Rio Grande do Sul, Brasil, (2007), 25–59.

[4]

A. Daza and R. Martin, Estimacion de la carga ganadera economicamente optima en fincas de ganado vacuno de carne del ecosistema de la Dehesa, ITEA, 28 (2007), 294-296. 

[5]

DIEA Direccion de Estadisticas Agropecuarias, in Anuario Estadistico Agropecuario, Ministerio de Ganaderia Agricultura y Pesca, Montevideo, Uruguay, 2007. Available from: http://www.mgap.gub.uy/sites/default/files/anuario2007.zip.

[6]

DIEA Direccion de Estadisticas Agropecuarias, in La ganaderia en Uruguay: Contribucion a su conocimiento, Ministerio de Ganaderia Agricultura y Pesca, Montevideo, Uruguay, 2003. Available from: http://www2.mgap.gub.uy/portal/afiledownload.aspx?2,5,99,O,S,0,170%3BS%3B9%3B40,.

[7]

DIEA Direccion de Estadisticas Agropecuarias, in Anuario Estadistico Agropecuario, Ministerio de Ganaderia Agricultura y Pesca, Montevideo, Uruguay, 2018. Available from: https://descargas.mgap.gub.uy/DIEA/Anuarios/Anuario2018/Anuario_2018.pdf.

[8]

F. Dieguez and H. Fort, Towards scientifically based management of extensive livestock farming in terms of ecological predator-prey modelling, Agric. Sys., 153 (2017), 123-137. 

[9]

F. Dieguez and R. Terra, Aplicacion del Modelo de una Explotacion Ganadera Extensiva (MEGanE) para el estudio de la sensibilidad de la produccion ganadera a la amplitud de la variabilidad de la oferta de forraje, in Anuario del 6 Congreso Argentino de Agro Informatica Buenos Aires, Argentina, (2014), 50–63.

[10]

M. do Carmo, Mejorando el campo natural: ajuste de la oferta de forraje a la escala predial, in Produccion animal sostenible en pastoreo sobre campo natural - MGAP Montevideo, Uruguay, (2013), 84–87.

[11]

FAO Food and Agriculture Organization, Grassland of the world, in Plant Production and Protection Series No. 34 (eds. Suttie, Reynolds and Batello), FAO, Rome, Italy, 2005. Available from: http://www.fao.org/3/y8344e/y8344e00.htm.

[12] J. Forrester, Industrial Dynamics, MIT Press, Cambridge, Massachusetts, EEUU, 1961. 
[13]

H. Fort, On predicting species yields in multispecies communities: Quantifying the accuracy of the linear Lotka-Volterra generalized model, Ecol. Modelling, 387 (2018), 154-162.  doi: 10.1016/j.ecolmodel.2018.09.009.

[14]

INAC Instituto Nacional de Carnes, Anuario Estadistico, Montevideo, Uruguay, 2017.

[15]

IPA Instituto Plan Agropecuario, Resultados del ejercicio 2016–2017, Montevideo, Uruguay, 2018.

[16]

IPA Instituto Plan Agropecuario, Evaluacion de una metodologia de modelacion y simulacion participativa para contribuir a la comprension y comunicacion del fenomeno de la sequia y mejorar la capacidad de adaptacion de productores ganaderos del basalto, Montevideo, Uruguay, 2011.

[17]

LART Laboratorio de Teledeteccion de La Universidad de Buenos Aires, Proyecto Observatorio Forrajero, Buenos Aires, Argentina, 2018. Available from: http://lart.agro.uba.ar/proyectos/.

[18]

G. Maraschin, E. Moojen, C. Ecosteguy, F. Correa, E. Apesteguia, I. Boldrini and J. Riboldi, Native pasture, forage on offer and animal response, in Proceedings of the XVII International Grassland Congress Saskatoon, Canada, (1997), 288.

[19]

G. May, R. Jones, M. Langemeier and K. Dhuyvetter, Influence of grazing lease terms on economic optimal stocking rates, Jour. Range. Manag., 55 (2002), 461-468. 

[20]

MGAP Ministerio de Ganaderia, Agricultura y Pesca, Pautas para el manejo del campo natural, Montevideo, Uruguay, 2011. Available from: https://www.planagropecuario.org.uy/web/24/librillos/pautas-para-el-manejo-del-campo-natural.html.

[21]

MGCN Mesa de Ganaderia sobre Campo Natural, Produccion Animal Sostenible en pastoreo sobre campo natural, Montevideo, Uruguay, 2013. Available from: http://www.mgap.gub.uy/sites/default/files/multimedia/libro_campo_natural_final_en_baja.pdf.

[22]

J. Mieres, Guia para la alimentacion de rumiantes, Serie Tecnica INIA, 142 (2004), 18-47. 

[23]

P. Modernel, W. Rossing, M. Corbeels, S. Dogliotti, V. Picasso and P. Tittonell, Land use change and ecosystem service provision in Pampas and Campos grasslands of southern South America, Environ. Res. Letters, 11 (2016), 1-22.  doi: 10.1088/1748-9326/11/11/113002.

[24]

G. Mott, Grazing pressure and measurement of pasture production, in Proc. 8th Int. Grassland Congress Reading, England, (1960), 601-611.

[25]

NetLogo, The Center for Connected Learning and Computer-Based Modeling, Illinois, USA, 2018. Available from: http://ccl.northwestern.edu/netlogo/.

[26]

J. Pastor, Mathematical ecology of populations and ecosystems, A John Wiley & Sons, Ltd, Sussex, UK, 2011

[27]

M. Pereira and F. Larratea, Campo natural, informacion satelital, uso de la regla, Serie tecnica INIA, 240 (2018), 49-55. 

[28]

G. Quintans, Algunas estrategias para disminuir la edad al primer servicio en vaquillonas, Serie tecnica INIA, 174 (2008), 53-55. 

[29]

J. Ritten, C. Bastian and M. Fraiser, Economically optimal stocking rates: A bioeconomic grazing model, Rangeland Ecol. Manag., 63 (2010), 407-414.  doi: 10.2111/08-253.1.

[30]

B. Rosengurtt, Praderas naturales: los problemas de su manejo, Rev. Asoc. Ing. Agr., 21 (1949), 11-16. 

[31]

S. Saldanha, Manejo del pastoreo en campos naturales sobre suelos medios de Basalto y suelos arenosos de Cretacico, Serie tecnica INIA, 151 (2005), 75-84. 

[32]

F. Sganga, C. Cabrera, M. Gonzalez and S. Rodriguez, Produccion Familiar Agropecuaria Uruguaya y Sus Productores Familiares, a Partir De Los Datos Del Censo General Agropecurio y el Registro de Productores Familiares, MGAP. Montevideo, Uruguay, 2014. Available from: http://www2.mgap.gub.uy/portal/afiledownload.aspx?2,10,821,O,S,0,10981%3BS%3B1%3B76,.

[33]

P. Soca, M. Carriquiry, M. do Carmo, S. Scarlato, A. Astessiano, C. Genro, M. Claramunt and A. Espasandin, Oferta de forraje del campo natural y resultado productivo de los sistemas de cria vacuna del Uruguay: I- produccion, uso y conversion del forraje aportado por campo natural, Serie tecnica INIA, 208 (2013), 97-117. 

[34]

Z. Sun, I. Lorscheid, J. D. Millington, S. Lauf, N. R. Magliocca, J. Groeneveld, S. Balbi, H. Nolzen, B. Mller, J. Schulze and C. M. Buchmann, Simple or complicated agent-based models? A complicated issue, Environ. Modelling & Software, 86 (2016), 56-67.  doi: 10.1016/j.envsoft.2016.09.006.

[35]

B. Turner, R. Rhoades, L. Tedeschi, R. Hanagriff, K. McCuistion and B. Dunn, Analyzing ranch profitability from varying cow sales and heifer replacement rates for beef cow-calf production using system dynamics, Agric. Sys., 114 (2013), 6-14.  doi: 10.1016/j.agsy.2012.07.009.

[36]

J. Vayssieres, M. Vigne, V. Alary and P. Lecomte, Integrated participatory modelling of actual farms to support policy making on sustainable intensification, Agric. Sys., 104 (2011), 146-161.  doi: 10.1016/j.agsy.2010.05.008.

show all references

References:
[1]

E. Berretta and M. Bemhaja, Produccion estacional de comunidades naturales de Basalto de la unidad Queguay Chico, Serie tecnica INIA, 102 (1998), 16-28. 

[2]

P. Booysen, Optimizacion de la carga de ganado y el manejo del pastoreo, Pastos, 5 (1975), 372-381. 

[3]

P. Carvalho, D. dos Santos and F. Neves, Oferta de forragem como condicionadora da estructura do pasto e do desempenho animal, in Anais do II Simposio de Forrageiras e Produo Animal Rio Grande do Sul, Brasil, (2007), 25–59.

[4]

A. Daza and R. Martin, Estimacion de la carga ganadera economicamente optima en fincas de ganado vacuno de carne del ecosistema de la Dehesa, ITEA, 28 (2007), 294-296. 

[5]

DIEA Direccion de Estadisticas Agropecuarias, in Anuario Estadistico Agropecuario, Ministerio de Ganaderia Agricultura y Pesca, Montevideo, Uruguay, 2007. Available from: http://www.mgap.gub.uy/sites/default/files/anuario2007.zip.

[6]

DIEA Direccion de Estadisticas Agropecuarias, in La ganaderia en Uruguay: Contribucion a su conocimiento, Ministerio de Ganaderia Agricultura y Pesca, Montevideo, Uruguay, 2003. Available from: http://www2.mgap.gub.uy/portal/afiledownload.aspx?2,5,99,O,S,0,170%3BS%3B9%3B40,.

[7]

DIEA Direccion de Estadisticas Agropecuarias, in Anuario Estadistico Agropecuario, Ministerio de Ganaderia Agricultura y Pesca, Montevideo, Uruguay, 2018. Available from: https://descargas.mgap.gub.uy/DIEA/Anuarios/Anuario2018/Anuario_2018.pdf.

[8]

F. Dieguez and H. Fort, Towards scientifically based management of extensive livestock farming in terms of ecological predator-prey modelling, Agric. Sys., 153 (2017), 123-137. 

[9]

F. Dieguez and R. Terra, Aplicacion del Modelo de una Explotacion Ganadera Extensiva (MEGanE) para el estudio de la sensibilidad de la produccion ganadera a la amplitud de la variabilidad de la oferta de forraje, in Anuario del 6 Congreso Argentino de Agro Informatica Buenos Aires, Argentina, (2014), 50–63.

[10]

M. do Carmo, Mejorando el campo natural: ajuste de la oferta de forraje a la escala predial, in Produccion animal sostenible en pastoreo sobre campo natural - MGAP Montevideo, Uruguay, (2013), 84–87.

[11]

FAO Food and Agriculture Organization, Grassland of the world, in Plant Production and Protection Series No. 34 (eds. Suttie, Reynolds and Batello), FAO, Rome, Italy, 2005. Available from: http://www.fao.org/3/y8344e/y8344e00.htm.

[12] J. Forrester, Industrial Dynamics, MIT Press, Cambridge, Massachusetts, EEUU, 1961. 
[13]

H. Fort, On predicting species yields in multispecies communities: Quantifying the accuracy of the linear Lotka-Volterra generalized model, Ecol. Modelling, 387 (2018), 154-162.  doi: 10.1016/j.ecolmodel.2018.09.009.

[14]

INAC Instituto Nacional de Carnes, Anuario Estadistico, Montevideo, Uruguay, 2017.

[15]

IPA Instituto Plan Agropecuario, Resultados del ejercicio 2016–2017, Montevideo, Uruguay, 2018.

[16]

IPA Instituto Plan Agropecuario, Evaluacion de una metodologia de modelacion y simulacion participativa para contribuir a la comprension y comunicacion del fenomeno de la sequia y mejorar la capacidad de adaptacion de productores ganaderos del basalto, Montevideo, Uruguay, 2011.

[17]

LART Laboratorio de Teledeteccion de La Universidad de Buenos Aires, Proyecto Observatorio Forrajero, Buenos Aires, Argentina, 2018. Available from: http://lart.agro.uba.ar/proyectos/.

[18]

G. Maraschin, E. Moojen, C. Ecosteguy, F. Correa, E. Apesteguia, I. Boldrini and J. Riboldi, Native pasture, forage on offer and animal response, in Proceedings of the XVII International Grassland Congress Saskatoon, Canada, (1997), 288.

[19]

G. May, R. Jones, M. Langemeier and K. Dhuyvetter, Influence of grazing lease terms on economic optimal stocking rates, Jour. Range. Manag., 55 (2002), 461-468. 

[20]

MGAP Ministerio de Ganaderia, Agricultura y Pesca, Pautas para el manejo del campo natural, Montevideo, Uruguay, 2011. Available from: https://www.planagropecuario.org.uy/web/24/librillos/pautas-para-el-manejo-del-campo-natural.html.

[21]

MGCN Mesa de Ganaderia sobre Campo Natural, Produccion Animal Sostenible en pastoreo sobre campo natural, Montevideo, Uruguay, 2013. Available from: http://www.mgap.gub.uy/sites/default/files/multimedia/libro_campo_natural_final_en_baja.pdf.

[22]

J. Mieres, Guia para la alimentacion de rumiantes, Serie Tecnica INIA, 142 (2004), 18-47. 

[23]

P. Modernel, W. Rossing, M. Corbeels, S. Dogliotti, V. Picasso and P. Tittonell, Land use change and ecosystem service provision in Pampas and Campos grasslands of southern South America, Environ. Res. Letters, 11 (2016), 1-22.  doi: 10.1088/1748-9326/11/11/113002.

[24]

G. Mott, Grazing pressure and measurement of pasture production, in Proc. 8th Int. Grassland Congress Reading, England, (1960), 601-611.

[25]

NetLogo, The Center for Connected Learning and Computer-Based Modeling, Illinois, USA, 2018. Available from: http://ccl.northwestern.edu/netlogo/.

[26]

J. Pastor, Mathematical ecology of populations and ecosystems, A John Wiley & Sons, Ltd, Sussex, UK, 2011

[27]

M. Pereira and F. Larratea, Campo natural, informacion satelital, uso de la regla, Serie tecnica INIA, 240 (2018), 49-55. 

[28]

G. Quintans, Algunas estrategias para disminuir la edad al primer servicio en vaquillonas, Serie tecnica INIA, 174 (2008), 53-55. 

[29]

J. Ritten, C. Bastian and M. Fraiser, Economically optimal stocking rates: A bioeconomic grazing model, Rangeland Ecol. Manag., 63 (2010), 407-414.  doi: 10.2111/08-253.1.

[30]

B. Rosengurtt, Praderas naturales: los problemas de su manejo, Rev. Asoc. Ing. Agr., 21 (1949), 11-16. 

[31]

S. Saldanha, Manejo del pastoreo en campos naturales sobre suelos medios de Basalto y suelos arenosos de Cretacico, Serie tecnica INIA, 151 (2005), 75-84. 

[32]

F. Sganga, C. Cabrera, M. Gonzalez and S. Rodriguez, Produccion Familiar Agropecuaria Uruguaya y Sus Productores Familiares, a Partir De Los Datos Del Censo General Agropecurio y el Registro de Productores Familiares, MGAP. Montevideo, Uruguay, 2014. Available from: http://www2.mgap.gub.uy/portal/afiledownload.aspx?2,10,821,O,S,0,10981%3BS%3B1%3B76,.

[33]

P. Soca, M. Carriquiry, M. do Carmo, S. Scarlato, A. Astessiano, C. Genro, M. Claramunt and A. Espasandin, Oferta de forraje del campo natural y resultado productivo de los sistemas de cria vacuna del Uruguay: I- produccion, uso y conversion del forraje aportado por campo natural, Serie tecnica INIA, 208 (2013), 97-117. 

[34]

Z. Sun, I. Lorscheid, J. D. Millington, S. Lauf, N. R. Magliocca, J. Groeneveld, S. Balbi, H. Nolzen, B. Mller, J. Schulze and C. M. Buchmann, Simple or complicated agent-based models? A complicated issue, Environ. Modelling & Software, 86 (2016), 56-67.  doi: 10.1016/j.envsoft.2016.09.006.

[35]

B. Turner, R. Rhoades, L. Tedeschi, R. Hanagriff, K. McCuistion and B. Dunn, Analyzing ranch profitability from varying cow sales and heifer replacement rates for beef cow-calf production using system dynamics, Agric. Sys., 114 (2013), 6-14.  doi: 10.1016/j.agsy.2012.07.009.

[36]

J. Vayssieres, M. Vigne, V. Alary and P. Lecomte, Integrated participatory modelling of actual farms to support policy making on sustainable intensification, Agric. Sys., 104 (2011), 146-161.  doi: 10.1016/j.agsy.2010.05.008.

Figure 1.  Screen capture of the predator-prey livestock model causal diagram (stocks and flow) implemented on NetLogo [25]
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Figure 2.  Frequency histogram for the climatic coefficient (coefClima) occurrence for Uruguayan basaltic region (serie 2000–2018 [17])
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Figure 3.  Gross product (USD per head and per hectare; top) and Gross margin (USD per hectare) (down) for scenarios varying Stocking rate (GU/ha) and initial Grass height (cm) for three values (coefClima) parameter (1.0, 0.5, 0.25 and 0.125)
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Figure 4.  Monthly evolution of coefClima parameter for the basaltic region of Uruguay, economic year 2016–2017
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Table 1.  Annual production costs for the economical year 2016–2017 published by IPA [16]. Asterisk indicates those considered as variable costs. Not marked items were considered as fix costs
Item USD/ha/year
Workforce expenses 29.00
Infrastructure conservation 3.50
Equipment, tools and vehicle devaluation and expenses 13.00
Taxes 12.25
Miscellaneous system expenses 18.00
Pasture conservation* 9.50
Direct cattle expenses (health)* 7.00
Nutrition expenses* 3.50
Total cost 95.75
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Item USD/ha/year
Workforce expenses 29.00
Infrastructure conservation 3.50
Equipment, tools and vehicle devaluation and expenses 13.00
Taxes 12.25
Miscellaneous system expenses 18.00
Pasture conservation* 9.50
Direct cattle expenses (health)* 7.00
Nutrition expenses* 3.50
Total cost 95.75
Table 2.  Economic-productive indicators result for economic year 2016–2017 from IPA [16] monitoring program
Indicator Value
Meat production (kg/ha) 113
Stocking rate (GU/ha) 0.79
Surface (ha) 1374
Herd size (total GU) 1073
Gross margin (USD/ha) 58
Gross production (USD/ha) 154
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Indicator Value
Meat production (kg/ha) 113
Stocking rate (GU/ha) 0.79
Surface (ha) 1374
Herd size (total GU) 1073
Gross margin (USD/ha) 58
Gross production (USD/ha) 154
Table 3.  Maximal GM/ha per hectare and Stocking rate that its value is reached (IGH: initial Grass height; R2: Coefficient of determination; S: Stocking rate)
IGH (cm) coefClima R2 Maximum GM (USD/ha) S (GU/ha)
3 1 0.99 31.35 0.82
3 0.5 1.00 12.46 0.72
3 0.25 1.00 -29.86 0.52
3 0.125 1.00 -79.75 0.24
5 1 0.99 107.78 1.03
5 0.5 0.99 71.58 0.9
5 0.25 1.00 1.90 0.64
5 0.125 1.00 -68.62 0.32
7 1 0.99 146.27 1.13
7 0.5 0.99 99.82 0.97
7 0.25 1.00 16.30 0.69
7 0.125 1.00 -63.85 0.35
Table Options

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IGH (cm) coefClima R2 Maximum GM (USD/ha) S (GU/ha)
3 1 0.99 31.35 0.82
3 0.5 1.00 12.46 0.72
3 0.25 1.00 -29.86 0.52
3 0.125 1.00 -79.75 0.24
5 1 0.99 107.78 1.03
5 0.5 0.99 71.58 0.9
5 0.25 1.00 1.90 0.64
5 0.125 1.00 -68.62 0.32
7 1 0.99 146.27 1.13
7 0.5 0.99 99.82 0.97
7 0.25 1.00 16.30 0.69
7 0.125 1.00 -63.85 0.35
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