Maximizing profits while reducing environmental impacts in silvopastoral systems for Nellore: an idealized, simplified farm-level mathematical model

Lobo, A. A. G.; Akhtar, H. M. B.; Moreno, D. P. S.; Cortés, C. F. Alvarez; Cumbe, T. A.; Péra, T. G.; Gameiro, A. H.

doi:10.1590/1519-6984.288557

person A. A. G. Lobo *

schoolUniversidade Federal de São Carlos – UFSCar, Departamento de Biotecnologia e Produção Vegetal e Animal, Grupo de Estudos e Trabalhos em Agropecuária – GETAP, Araras, SP, Brasil

0000-0001-8691-9672

person H. M. B. Akhtar

schoolPakistan Agricultural Research Council, Punjab, Pakistan

0009-0005-1774-7500

person D. P. S. Moreno

schoolDepartment of Animal Production, Research Group Ruminantia, Faculty of Agricultural and Animal Sciences and Natural Resources, University of the Llanos, Meta, Colombia

0000-0002-4282-8864

person C. F. Alvarez Cortés

schoolUniversidad Cooperativa de Colombia , Seccional Villavicencio, Universidad Santo Tomás, ColombiaschoolUniversidad Santo Tomás, Colombia

0000-0001-7202-8422

person T. A. Cumbe

schoolUniversidade Zambeze – UniZambeze, Faculdade de Ciências Agrárias, Ulónguè, Tete, Moçambique

0000-0003-1552-1944

person T. G. Péra

schoolUniversidade de São Paulo – USP, Escola Superior de Agricultura “Luiz de Queiroz” – ESALQ, Piracicaba, SP, Brasil

0000-0001-8215-3606

person A. H. Gameiro

schoolUniversidade de São Paulo – USP, Faculdade de Medicina Veterinária e Zootecnia – FMVZ, Departamento de Nutrição e Produção Animal – VNP, Pirassununga, SP, Brasil

0000-0001-9015-5281

person*e-mail:
annelise.gomes.lobo@gmail.com

Editor:

Takako Matsumura Tundisi

Parameters	Values	Units balanced	Literary domain	Meaning	Sets
densidadev(v) - Tithonia diversifolia	14100	plants.ha^-1	Rivera et al. (2015), Vázquez (2023), Chará et al. (2017), Mauricio et al. (2019)	plant density	vegetal
densidadev(v) - Gliricidia sepium	2800	plants.ha^-1	Herrera et al. (2021), Oliveira et al. (2018b), Costa et al. (2021), Palma (2009)	plant density	vegetal
densidadev(v) - Urochloa brizantha	2700000	plants.ha^-1	Santos (2022)	plant density	vegetal
pricel(l) – growing	239.2	R$.@^-1	USP (2024)	animal price	livestock
pricel(l) - fattening	287.52	R$.@^-1	USP (2024)	animal price	livestock
costv(v) - Tithonia diversifolia	2295	R$.ha^-1	AGRO EM QUESTÃO: Revista de Iniciação Científica da Faculdade CNA (2017)	implantation cost	vegetal
costv(v) - Gliricidia sepium	1180	R$.ha^-1	Costa et al. (2004)	implantation cost	vegetal
costv(v) - Urochloa brizantha	1300	R$.ha^-1	Scot Consultoria (2015)	implantation cost	vegetal
costl(l) - growing	1812.3	R$.head^-1	Santos and Grzebieluckas (2014)	animal cost	livestock
costl(l) - fattening	1223.16	R$.head^-1	Santos and Grzebieluckas (2014)	animal cost	livestock
costf(f) - nitrogen	933	R$.t^-1	Nativa Agronegócios (2024)	fertilizer cost	fertilizer
costf(f) - phosphorus	934	R$.t^-1	Nativa Agronegócios (2024)	fertilizer cost	fertilizer
costf(f) - potassium	933	R$.t^-1	Nativa Agronegócios (2024)	fertilizer cost	fertilizer
costf(f) - calcium	70.46	R$.t^-1	Mato Grosso do Sul (2022)	fertilizer cost	fertilizer
costf(f) - magnesium	110	R$.t^-1	Mato Grosso do Sul (2022)	fertilizer cost	fertilizer
costs(s) - mineralsuple	3723.3	R$.t^-1	Matsuda (2024)	feed cost	feed
costs(s) - protsuple	3186.4	R$.t^-1	Matsuda (2024)	feed cost	feed
livestockweight(l) - growing	210	kg.animal^-1	Barbero et al. (2021)	animal weight	livestock
livestockweight(l) - fattening	520	kg.animal^-1	Barbero et al. (2021)	animal weight	livestock
produtivRainy(v) - Tithonia diversifolia	31.5	t of NM.ha^-1	Soares (2021)	biomass productivity	vegetal
produtivRainy(v) - Gliricidia sepium	20	t of NM.ha^-1	Silva et al. (2020)	biomass productivity	vegetal
produtivRainy(v) - Urochloa brizantha	33.5	t of NM.ha^-1	Barbosa (2020)	biomass productivity	vegetal
produtivDry(v) - Tithonia diversifolia	24.7	t of NM.ha^-1	Calsavara et al. (2016)	biomass productivity	vegetal
produtivDry(v) - Gliricidia sepium	9.7	t of NM.ha^-1	Silva et al. (2022)	biomass productivity	vegetal
produtivDry(v) - Urochloa brizantha	13.4	t of NM.ha^-1	Barbosa (2020), Rodrigues (2004)	biomass productivity	vegetal
drymatterrequirement(l) - growing	5	kg.day^-1	NASEM (2016)	dry matter requirement	livestock
drymatterrequirement(l) - fattening	11	kg.day^-1	NASEM (2016)	dry matter requirement	livestock
period(l) - growing	240	days	Oliveira et al. (2023)	season length	livestock
period(l) - fattening	120	days	Oliveira et al. (2023)	season length	livestock
drymattercompositionrainy(v) - Tithonia diversifolia	0.15	%	Odedire and Oloidi (2014)	vegetals dry matter during the rainy	vegetal
drymattercompositionrainy(v) - Gliricidia sepium	0.22	%	Valadares Filho et al. (2018)	vegetals dry matter during the rainy	vegetal
drymattercompositionrainy(v) - Urochloa brizantha	0.33	%	Valadares Filho et al. (2018)	vegetals dry matter during the rainy	vegetal
drymattercompositiondry(v) - Tithonia diversifolia	0.15	%	Odedire and Oloidi (2014)	vegetals dry matter during dry	vegetal
drymattercompositiondry(v) - Gliricidia sepium	0.22	%	Valadares Filho et al. (2018)	vegetals dry matter during dry	vegetal
drymattercompositiondry(v) - Urochloa brizantha	0.33	%	Valadares Filho et al. (2018)	vegetals dry matter during dry	vegetal
drymattercompositionfeed(s) - mineralsuple	0.99	%	Valadares Filho et al. (2018)	feed dry matter	feed
drymattercompositionfeed(s) - protsuple	0.92	%	Valadares Filho et al. (2018)	feed dry matter	feed
proteinrequirement(l) - growing	0.44	kg.day^-1	NASEM (2016)	crude protein nutritional requirement	livestock
proteinrequirement(l) - fattening	0.861	kg.day^-1	NASEM (2016)	crude protein nutritional requirement	livestock
proteincontentrainy(v) - Tithonia diversifolia	0.21	% of DM	Odedire and Oloidi (2014)	vegetals crude protein during the rainy	vegetal
proteincontentrainy(v) - Gliricidia sepium	0.17	% of DM	Valadares Filho et al. (2018)	vegetals crude protein during the rainy	vegetal
proteincontentrainy(v) - Urochloa brizantha	0.08	% of DM	Valadares Filho et al. (2018)	vegetals crude protein during the rainy	vegetal
proteincontentdry(v) - Tithonia diversifolia	0.21	% of DM	Odedire and Oloidi (2014)	vegetals protein during dry	vegetal
proteincontentdry(v) - Gliricidia sepium	0.17	% of DM	Valadares Filho et al. (2018)	vegetals protein during dry	vegetal
proteincontentdry(v) - Urochloa brizantha	0.08	% of DM	Valadares Filho et al. (2018)	vegetals protein during dry	vegetal
proteincontentfeed(s) - mineralsuple	0	% of DM	Not applicable	feed crude protein	feed
proteincontentfeed(s) - protsuple	0.3	% of DM	Matsuda (2024)	feed crude protein	feed
energyrequirement(l) - growing	4.5	Mcal.day^-1	NASEM (2016)	nutritional requirement for metabolizable energy	livestock
energyrequirement(l) - fattening	8.2	Mcal.day^-1	NASEM (2016)	nutritional requirement for metabolizable energy	livestock
energycontentrainy(v) - Tithonia diversifolia	2360	Mcal.t^-1.DM^-1	Val (2019)	vegetals metabolizable energy during the rainy	vegetal
energycontentrainy(v) - Gliricidia sepium	2340	Mcal.t^-1.DM^-1	Valadares-Filho et al. (2016)	vegetals metabolizable energy during the rainy	vegetal
energycontentrainy(v) - Urochloa brizantha	1960	Mcal.t^-1.DM^-1	Valadares-Filho et al. (2016)	vegetals metabolizable energy during the rainy	vegetal
energycontentdry(v) - Tithonia diversifolia	1850	Mcal.t^-1.DM^-1	Val (2019)	vegetals metabolizable energy during dry	vegetal
energycontentdry(v) - Gliricidia sepium	2340	Mcal.t^-1.DM^-1	Valadares-Filho et al. (2016)	vegetals metabolizable energy during dry	vegetal
energycontentdry(v) - Urochloa brizantha	1960	Mcal.t^-1.DM^-1	Valadares-Filho et al. (2016)	vegetals metabolizable energy during dry	vegetal
energycontentfeed(s) - mineralsuple	0	Mcal.t^-1.DM^-1	Not applicable	feed metabolizable energy	feed
energycontentfeed(s) - protsuple	3480	Mcal.t^-1.DM^-1	Valadares-Filho et al. (2018)	feed metabolizable energy	feed
totaldigestiblenutrientsrequirement(l) - growing	3	kg.day^-1	NASEM (2016)	TDN nutritional requirement	livestock
totaldigestiblenutrientsrequirement(l) - fattening	6	kg.day^-1	NASEM (2016)	TDN nutritional requirement	livestock
totaldigestiblenutrientscontentrainy(v) - Tithonia diversifolia	0.61	% of DM	Silva et al. (2018)	vegetals TDN during the rainy	vegetal
totaldigestiblenutrientscontentrainy(v) - Gliricidia sepium	0.61	% of DM	Valadares-Filho et al. (2016)	vegetals TDN during the rainy	vegetal
totaldigestiblenutrientscontentrainy(v) - Urochloa brizantha	0.56	% of DM	Valadares-Filho et al. (2016)	vegetals TDN during the rainy	vegetal
totaldigestiblenutrientscontentdry(v) - Tithonia diversifolia	0.61	% of DM	Silva et al. (2018)	TDN of vegetables during dry	vegetal
totaldigestiblenutrientscontentdry(v) - Gliricidia sepium	0.61	% of DM	Valadares-Filho et al. (2016)	TDN of vegetables during dry	vegetal
totaldigestiblenutrientscontentdry(v) - Urochloa brizantha	0.56	% of DM	Valadares-Filho et al. (2016)	TDN of vegetables during dry	vegetal
totaldigestiblenutrientscontentfeed(s) - mineralsuple	0	% of DM	Not applicable	feed TDN	feed
totaldigestiblenutrientscontentfeed(s) - protsuple	0.57	% of DM	Matsuda (2024)	feed TDN	feed
manureproduction(l) - growing	0.0125	t.animal-1.day^-1	Pagliari et al. (2020)	manure produced	livestock
manureproduction(l) - fattening	0.0303	t.animal-1.day^-1	Pagliari et al. (2020)	manure produced	livestock
CO₂eqvegetal(v) - Tithonia diversifolia	-26.6	t.ha^-1	Montagnini et al. (2013)	ton of CO₂ equivalent per hectare of vegetal	vegetal
CO₂eqvegetal(v) - Gliricidia sepium	-26.6	t.ha^-1	Montagnini et al. (2013)	ton of CO₂ equivalent per hectare of vegetal	vegetal
CO₂eqvegetal(v) - Urochloa brizantha	-26.5	t.ha^-1	Eri et al. (2020)	ton of CO₂ equivalent per hectare of vegetal	vegetal
CO₂eqfertilizer(f) - nitrogen	0.65	t.ha^-1	Gissi (2017)	ton of CO₂ equivalent per ton of fertilizer (100 kg.N.ha-1)	fertilizer
CO₂eqfertilizer(f) - phosphorus	0.71	t.ha^-1	Kumar et al. (2012)	ton of CO₂ equivalent per ton of fertilizer	fertilizer
CO₂eqfertilizer(f) - potassium	0.46	t.ha^-1	Kumar et al. (2012)	ton of CO₂ equivalent per ton of fertilizer	fertilizer
CO₂eqfertilizer(f) - calcium	1.4	t.ha^-1	Silva et al. (2014)	ton of CO₂ equivalent per ton of fertilizer	fertilizer
CO₂eqfertilizer(f) - magnesium	0.13	t.ha^-1	Silva et al. (2014)	ton of CO₂ equivalent per ton of fertilizer	fertilizer
CO₂eqlivestock(l) - growing	0.27	t.animal^-1	Lobo (2023)	ton of CO₂ equivalent per head (during the cycle 240 days)	livestock
CO₂eqlivestock(l) - fattening	0.67	t.animal^-1	Méo Filho (2020)	ton of CO₂ equivalent per head	livestock
manurenutrients(f) - nitrogen	0.006	%	Sandoval Paixão et al. (2020)	amount of manure weight in nutrients	fertilizer
manurenutrients(f) - phosphorus	0.052	%	Sandoval Paixão et al. (2020)	amount of manure weight in nutrients	fertilizer
manurenutrients(f) - potassium	0.025	%	Sandoval Paixão et al. (2020)	amount of manure weight in nutrients	fertilizer
manurenutrients(f) - calcium	0.01	%	Sandoval Paixão et al. (2020)	amount of manure weight in nutrients	fertilizer
manurenutrients(f) - magnesium	0.003	%	Sandoval Paixão et al. (2020)	amount of manure weight in nutrients	fertilizer
FertililzerRequirement(v,f) - Tithonia diversifolia - nitrogen	0.14	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Tithonia diversifolia - phosphorus	1.17	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Tithonia diversifolia - potassium	0.56	t.ha^-1	Eifediyi et al., 2023, Sandoval Paixão et al., 2020	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Tithonia diversifolia - calcium	0.23	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Tithonia diversifolia - magnesium	0.07	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Gliricidia sepium - nitrogen	0.135	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Gliricidia sepium - phosphorus	1.17	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Gliricidia sepium - potassium	0.562	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Gliricidia sepium - calcium	0.225	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Gliricidia sepium - magnesium	0.0675	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Urochloa brizantha - nitrogen	0.135	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Urochloa brizantha - phosphorus	1.17	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Urochloa brizantha - potassium	0.562	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Urochloa brizantha - calcium	0.225	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
FertililzerRequirement(v,f) - Urochloa brizantha - magnesium	0.0675	t.ha^-1	Eifediyi et al. (2023), Sandoval Paixão et al. (2020)	fertilizer consumption per plant in tons of fertilizer per hectare of plant	vegetal,fertilizer
costgee	100	R$.t^-1	DATAGRO (2024)	methane cost in CO₂eq	scalar
totalarea	56	ha	Rivera-Acosta and Xiuchuan (2023), Simioni et al. (2022a, b), Resende et al. (2020)	farm-level area	scalar
mortalityrate	11.05	%	Portes et al. (2020), Marín-Garzon et al. (2021)	animal mortality rate	scalar
stockingrate	0.45	ha.animal^-1	Neves (2020)	animal stocking rate	scalar
slaughterweight	520	kg	Kul et al. (2020)	slaughter weight	scalar
minimum_tithonia	0.3	%	Pazla et al. (2021)	minimum amount of Tithonia diversiflora in DMI	scalar
minimum_gliricidia	0.1	%	Tahuk et al. (2022)	minimum amount of Gliricidia sepium in DMI	scalar
minimum_pasture	0.6	%	Marsetyo et al. (2021)	minimum amount of Urochloa brizantha in DMI	scalar
DMI_G	5	kg	NASEM (2016)	dry matter intake by growing animals	scalar
DMI_F	11	kg	NASEM (2016)	dry matter intake by fattening animals	scalar

\sum_{v} p r o d u t i v D r y (v) x X_{v e g e t a l} (v) x x d r y m a t t e r c o m p o s i t i o n d r y (v) x p r o t e i n c o n t e n t d r y (v) \geq p r o t e i n r e q u i r e m e n t (' f a t t e n i n g') x p e r i o d (' f a t t e n i n g') x X_{l i v e s t o c k} (' f a t t e n i n g') / 1000

\sum_{v} p r o d u t i v D r y (v) x X_{v e g e t a l} (v) x x d r y m a t t e r c o m p o s i t i o n d r y (v) x t o t a l d i g e s t i b l e n u t r i e n t s c o n t e n t d r y (v) = t o t a l d i g e s t i b l e n u t r i e n t s r e q u i r e m e n t (' f a t t e n i n g') x p e r i o d (' f a t t e n i n g') x X_{l i v e s t o c k} (' f a t t e n i n g')

X_{g e e} = \sum_{v} C O 2 e q v e g e t a l (v) x X_{v e g e t a l} (v) + \sum_{f} C O 2 e q f e r t i l i z e r (f) x X_{f e r t i l i z e r} (f) +

\sum_{l} C O 2 e q l i v e s t o c k (l) x X_{l i v e s t o c k} (l)

Maximizing profits while reducing environmental impacts in silvopastoral systems for Nellore: an idealized, simplified farm-level mathematical model

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