Abstract
A dynamic optimization model for weed infestation control using selective herbicide application in a corn crop system is presented. The seed bank density of the weed population and frequency of dominant or recessive alleles are taken as state variables of the growing cycle. The control variable is taken as the dose–response function. The goal is to reduce herbicide usage, maximize profit in a pre-determined period of time and minimize the environmental impacts caused by excessive use of herbicides. The dynamic optimization model takes into account the decreased herbicide efficacy over time due to weed resistance evolution caused by selective pressure. The dynamic optimization problem involves discrete variables modeled as a nonlinear programming (NLP) problem which was solved by an active set algorithm (ASA) for box-constrained optimization. Numerical simulations for a case study illustrate the management of the Bidens subalternans in a corn crop by selecting a sequence of only one type of herbicide. The results on optimal control discussed here will give support to make decision on the herbicide usage in regions where weed resistance was reported by field observations.
Similar content being viewed by others
References
Anderson DD, Nissen SJ, Martin AR (1998) Mechanism of primisulfuron resistance in a shattercane (Sorghum bicolor) biotype. Weed Sci 46(1):158–162
Birgin EG, Martínez JM (2002) Large-scale active-set box-constrained optimization method with spectral projected gradients. Comput Optim Appl 23(1):101–125
Birgin EG, Martínez JM, Raydan M (2000) Nonmonotone spectral projected gradient methods on convex sets. SIAM J Optim 10(4):1196–1211
Britton NF (2003) Essential mathematical biology. Springer Undergraduate Mathematics Series, London, UK
Byrd RB, Lu P, Nocedal J, Zhu C (1995) A limited memory algorithm for bound constrained optimization. SIAM J Sci Comput 16(5):1190–1208
Carvalho FT, Moretti TB, Souza PA (2010) Eficácia e seletividade de associações de herbicidas utilizados em pós-emergência na cultura do milho. Rev Bras Herbic 9(1):35–41
Christensen S, Streibig JC, Haas H (1990) Interaction between herbicide activity and weed suppression by spring barley varieties. In: Seventh European Weed Research Society Symposium, Helsinki, 367–374
Christiaans T, Eichner T, Pething R (2007) Optimal pest control in agriculture. J Econ Dyn Control 31(12):3965–3985
Christoffoleti PJ (2002) Curvas de dose-resposta de biótipos resistente e suscetível da Bidens pilosa L. aos herbicidas inibidores da ALS. Sci Agric 59(3):513–519
Christoffoleti PJ (2008) Aspectos de resistêcia de plantas daninhas a herbicidas, 3rd edn. Associação Brasileira de Ação à Resistência de Plantas Daninhas, Piracicaba, SP
Cousens R (1985) A simple model relating yield loss to weed density. Ann Appl Biol 107(2):239–252
Dan HA, Procópio ALL, Dan SO, Finotti TR, Assis RL (2010) Seletividade do atrazine à cultura do milheto Pennisetum glaucum, Planta Daninha, 28 no. spe, 1117–1124
Diggle AJ, Neve PB, Smith FP (2003) Herbicides used in combination can reduce the probability of herbicide resistance in finite weed populations. Weed Res 43(5):371–382
Gazziero DLP, Santos AMB, Voll E, Adegas FS (2008) Resistência de picão—preto (Bidens subalternans) ao herbicida atrazine, in: Congresso Brasileiro da Ciência das Plantas Daninhas e Congresso de la Associacón Latinoamericana de Malezas, Ouro Preto, 7
Gressel J (2009) Evolving understanding of the evolution of herbicide resistance. Pest Manag Sci 65(11):1164–1173
Gressel J, Segel LA (1978) The paucity of plants evolving genetic resistance to herbicides: possible reasons and implications. J Theor Biol 75(3):349–371
Hager WW (2009) Source code for ASA-CG version 1.3, Available at: http://www.math.ufl.edu/~hager/papers/Software
Hager WW, Zhang H (2006) A new active set algorithm for box constrained optimization. J Optim 17(2):526–557
Heap I (2011) The international survey of herbicide resistant weeds, Available at: http://www.weedscience.com
IMEA (2014) Custo de produ ção de milho—Safra 2013/14, Available at: http://www.imea.com.br/upload/publicacoes/arquivos/R410-2013-01-CPMilho.pdf
Jones R, Cacho OJ (2000) A dynamic optimization model of weed control. 44th Annual Conference of the Australian Agricultural and Resource Economics. Australia, Sydney, pp 1–17
Jones R, Cacho OJ, Sinden J (2006) The importance of seasonal variability and tactical responses to risk on estimating the economic benefits of integrated weed management. Agric Econ 35(3):245–256
Karam D (2011) Manejo de plantas daninhas resistentes na cultura do milho. Plantio Direto 20(124):40–46
Karam D, Lara JFR, Magalhães PC, Filho IAP, Cruz MB (2004) Seletividade de carfentrazone-ethyl aos milhos doce e normal. Rev Bras Milho e Sorgo 3(1):62–68
Kennedy JOS (1986) Dynamic programming: applications to agriculture and natural resources. Elsevier, New York, NY
Kotani K, Kakinaka M, Matsuda H (2009) Dynamic economic analysis on invasive species management: Some policy implications of catchability. Math Biosci 220(1):1–14
Kotani K, Kakinaka M, Matsuda H (2011) Optimal invasive species management under multiple uncertainties. Math Biosci 233(1):32–46
Lin CJ, Moré JJ (1999) Newton’s method for large bound-constrained optimization problems. SIAM J Optim 9(4):1100–1127
Maxwell BD, Roush ML, Radosevich SR (1990) Predicting the evolution and dynamics of herbicide resistance in weed populations. Weed Technol 4(1):2–13
Medd R, Nicol HI, Cook A (1995) Seed kill and its role in weed management system: A case study of seed production, seed banks and population growth of avena species (wild oats). Ninth European Weed Research Society Symposium, Budapest 2:627–632
Moss S (2010) Detecting herbicide resistance, Available at: http://www.hracglobal.com/Publications/DetectingHerbicideResistance/tabid/229/~Default.aspx
Neve P, Norsworthy JK, Smith KL, Zelaya IA (2011) Modelling evolution and management of glyphosate resistance in Amaranthus palmeri. Weed Res 51(1):99–112
Oliveira AT, Santos JB, Camelo GM, Botelho RG, Lázri TM (2009) Efeito da interação do nicosulfuron e Chlorpyrifos sobre o banco de sementes e os atributos microbianos do solo. Rev Bras Ciência do Solo 33(3):563–570
Pandey S, Medd R (1990) Integration of seed and plant kill tactics for control of wild oats: An economic evaluation. Agric Syst 34(1):65–76
Powles SB, Preston C (2011) Herbicide cross resistance and multiple resistance in plants, Available at: http://www.hracglobal.com/~Publications/~HerbicideCrossResistanceandMultipleResistance~/tabid/224/Default.aspx
Powles SB, Shaner DL (2001) Herbicide resistance and world grains. CRC Press, London, UK
Rafikov M, Balthazar JM (2005) Optimal pest control problem in population dynamics. Comput Appl Math 24(1):65–81
Ralebitso TK, Senior E, Verseveld HWV (2002) Microbial aspects of atrazine degradation in natural environments. Biodegradation 13(1):11–19
Seefeldt SS, Jensen JE, Fuerst EP (1995) Log-logistic analysis of herbicide dose–response relationships. Weed Technol 9(1):218–227
Streibig JC, Kudsk P (1993) Herbicide bioassays. CRC Press, Boca Raton, FL
Tind T, Mathiesen TJ, Jensen JE, Ritz C, Streibig JC (2009) Using a selectivity index to evaluate logarithmic spraying in grass seed crops. Pest Manag Sci 65(11):1257–1262
Tranel PJ, Wright TR (2002) Resistance of weeds to ALS-inhibiting herbicides: what have we learned? Weed Sci 50(6):700–712
Acknowledgments
The authors acknowledge the support given by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) under the Programa Nacional de Cooperação Acadêmica (PROCAD).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Natasa Krejic.
Rights and permissions
About this article
Cite this article
Stiegelmeier, E.W., Oliveira, V.A., Silva, G.N. et al. Optimal weed population control using nonlinear programming. Comp. Appl. Math. 36, 1043–1065 (2017). https://doi.org/10.1007/s40314-015-0280-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40314-015-0280-x