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

Francisco Dieguez; Hugo Fort

doi:10.3934/jdg.2019009

Article Contents

2019, Volume 6, Issue 2: 119-129. Doi: 10.3934/jdg.2019009

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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
^* Corresponding author: Francisco Dieguez

Received: October 2018

Revised: March 2019

Published: April 2019

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Abstract

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.

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Mathematics Subject Classification: Primary: 49K15, 91B74; Secondary: 92D40.

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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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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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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

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