doi: 10.15389/agrobiology.2022.3.500eng

UDC: 631.559:631.153.7:51-76:519.7



I.M. Mikhailenko, V.N. Timoshin

Agrophysical Research Institute, 12, Grazhdansky Prosp., St. Petersburg, 195220 Russia, e-mail (✉ corresponding author),

Mikhailenko I.M.
Timoshin V.N.

Received January 28, 2022

In modern crop production, a traditional paradigm of separate management of crops and weeds as part of single agrocenosis dominates. However, mineral fertilizers simultaneously stimulates the growth and development of crops and weeds, and herbicides suppress the growth of both cultivated plants and weeds. This leads to significant yield losses and waste of fertilizers and herbicides. The purpose of this study is to develop a theoretical basis for solving the problem of managing agrocenoses, which include the main crop and weeds. The solution of this problem is aimed at eliminating the limitations of the existing paradigm of separate management of crops and weeds in the agrocenosis. Previously, we have developed a theory of management of agro-technologies, in which the object of management is an agricultural crop without considering the role of weeds in the agrocenoses. In accordance with this theory, the crop management is carried out at strategic, program and real-time levels. In the presented work, for the first time, the problem of managing agrocenoses at the program level during one growing season is posed and solved. The essence of the approach lies in the development of the programs, which are sequences of technological operations for the application of mineral fertilizers, irrigation and herbicide treatments, providing a given crop yield with minimal expenditure of resources. To solve this problem, in the previously developed theory, mathematical models for crop parameters are modified to reflect the effect of herbicides. In addition, a model of the parameters of dominant weed species was introduced into the control task, in which, in addition to the doses of herbicide treatments, the effect of the doses of mineral fertilizers is reflected. The mathematical model for the soil environment, which takes into account the influence of the parameters of the state of the cultivated crop and weeds, has also undergone significant refinement. The problem is solved on the example of sowing spring wheat as part of an agrocenoses. The presence of several spring wheat phenological phases needs to transform the structure and parameters of the mathematical models used for all phenophases. This, in turn, needs to solve the problem of forming optimal programs for managing agrocenoses separately for each interphase period and combine the received private programs into a single program. As a method for solving the problem, the Pontryagin’s maximum principle is used in combination with a dynamic programming scheme (from the end of the growing season to its beginning). The structural complexity of the control object, which is an agricultural field with agrocenoses, necessitates solving the problem of program control in three stages. At the first stage, a program is formed to change the parameters of the soil environment, which ensures the achievement of the required crop yield. At this stage, the effect of herbicide treatments on the state of crop sowing is not considered. At the second stage, a sequence of technological operations is found that provides the best approximation of soil parameters to the optimal program obtained at the first stage. Finally, at the third stage, the optimal sequence of herbicide treatments performed simultaneously with other technological operations is found. To consider the influence of these processing, the programs obtained at the first two stages are refined until the convergence of the solution of the entire problem is obtained.  

Keywords: program control, agrocenoses, mineral fertilizers, herbicides, mathematical models, control algorithms.   



  1. Mikhaylenko I.M. Teoreticheskie osnovy i tekhnicheskaya realizatsiya upravleniya agrotekhnologiyami [Theoretical foundations and technical implementation of agricultural technology management]. St. Petersburg, 2017 (in Russ.).
  2. Mikhaylenko I.M., Timoshin V.N. Agrokhimiya, 2020, 8: 86-93 CrossRef (in Russ.).
  3. Nemchenko V.V., Rybina L.D., Gilev S.D., Kungurtseva N.M., Stepnykh N.V., Kopylov A.N., Kopylova S.V. Sovremennye sredstva zashchity rasteniy i tekhnologii ikh primeneniya [Modern plant protection products and technologies for their application]. Kurtamysh, 2006 (in Russ.).
  4. Emel’yanov Yu.Ya., Kopylov E.V., Kirillova E.V. Nivy Zaural’ya, 2914, 6(106): 18-23 (in Russ.).
  5. Korsakov K.V., Strizhkov N.I, Pron’ko V.V. Vestnik Altayskogo gosudarstvennogo agrarnogo universiteta, 2013, 4(120): 24-32 (in Russ.).
  6. Kazakov I.E. Metody optimizatsii stokhasticheskikh sistem [Methods for optimizing stochastic systems]. Moscow, 1987 (in Russ.).
  7. Jouven M., Carrère P., Baumont R. Model predicting dynamics of biomass, structure and digestibility of herbage in managed permanent pastures. 1. Model description. Grass & Forage Science, 2006, 61(2): 112-124 CrossRef
  8. Oliver M. An overview of precision agriculture. In: Precision agriculture for sustainability and environmental protection /M. Oliver, T. Bishop, B. Marchant (eds.). Routledge, 2013: Chapter 1 1-17 CrossRef
  9. Sanderson M.A., Rotz C.A., Fultz S.W., Rauburn E.B., Estimating forage mass with a commercial capacitance meter, rising plate meter, and pasture ruler. Agronomy Journal, 2001, 93: 1281-1286 CrossRef
  10. Roudier P., Tisseyre, B., Poilvé, H., Roger J.-M. A technical opportunity index adapted to zone-specific management. Precision Agriculture, 2011, 12: 130-145 CrossRef
  11. Kim K., Chavas J.P. Technological change and risk management: an application to the economics of corn production. Agricultural Economics, 2003, 29(2): 125-142 CrossRef
  12. Derby N.E., Casey F.X.M., Franzen D.E. Comparison of nitrogen management zone delineation methods for corn grain yield. Agronomy Journal, 2007, 99(2): 405-414 CrossRef
  13. Heatherly L.G., Elmore T.W. Managing inputs for peak production. In: Soybeans: improvement, production and uses /J.E. Specht, H.R. Boerma (eds.). ASA-CSSA-SSSA, Madison, 2004: 451-536 CrossRef
  14. Paoli J.N., Tisseyre B., Strauss O., McBratney A. A technical opportunity index based on the fuzzy footprint of a machine for site-specific management: an application to viticulture. Precision Agriculture, 2010, 11: 379-396 CrossRef
  15. Sun W., Whelan B., McBratney A., Minasny B. An integrated framework for software to provide yield data cleaning and estimation of an opportunity index for site-specific crop management. Precision Agriculture, 2013, 14: 376-391 CrossRef
  16. Tisseyre B., McBratney A.B. A technical opportunity index based on mathematical morphology for site-specific management: an application to viticulture. Precision Agriculture, 2008, 9: 101-113 CrossRef
  17. Bohanec M., Cortet J., Griffiths B., Žnidaršič M., Debeljak M., Caul S., Thompson J., Krogh P.H. A qualitative multi-attribute model for assessing the impact of cropping systems on soil quality. Pedobiologia, 2007, 51(3): 239-250 CrossRef
  18. Steven M. Satellite remote sensing for agricultural management: opportunities and logistic constraints. ISPRS Journal of Photogrammetry and Remote Sensing, 1993, 48(4): 29-34 CrossRef
  19. Bohanec M., Cortet J., Griffiths B., Žnidaršič M., Debeljak M., Caul S., Thompson J., Krogh P.H. A qualitative multi-attribute model for assessing the impact of cropping systems on soil quality. Pedobiologia, 2007, 51(3): 239-250 CrossRef
  20. Bagavathiannan M.V., Beckie H.J., Chantre G.R., Gonzalez-Andujar J.L., Leon R.G., Neve P., Poggio S.L., Schutte B.J., Somerville G.J., Werle R., Van Acker R. Simulation models on the ecology and mana gement of arable weeds: structure, quantitative insights, and applications. Agronomy, 2020, 10: 1611 CrossRef
  21. Sattin M., Zanin G., Berti A. Case history for weed competition/population ecology: velvetleaf (Abutilon theophrasti) in corn (Zea mays). Weed Technology, 1992, 6(1): 213-219 CrossRef
  22. Spitters C.J.T., Krop M., de Groot W. Competition between maize and Echinochloa crus-galli analysed by a hyperbolic regression model. Annals of Applied Biology, 1989, 115: 541-551 CrossRef
  23. Cousens R. An empirical model relating crop yield to weed and crop density and a statistical comparison with other models. The Journal of Agricultural Science, 1985, 105(3): 513-521 CrossRef
  24. Colbach N., Collard A., Guyot S.H.M., Meziere D., Munier-Jolain N. Assessing innovative sowing patterns for integrated weed management with a 3D crop:weed competition model. European Journal of Agronomy, 2014, 53: 74-89 CrossRef
  25. Christensen S. Crop weed competition and herbicide performance in cereal species and varieties. Weed Research, 1994, 34(1): 29-36 CrossRef
  26. Krop M.J., Spitters J.T. A simple model of crop loss by weed competition from early observations on relative leaf area of the weeds. Weed Research, 1991, 31(2): 97-105 CrossRef
  27. Afifi M., Swanton C. Early physiological mechanisms of weed competition. Weed Science, 2012, 60(4): 542-551 CrossRef
  28. Ziska L.H. Could recent increases in atmospheric CO2 have acted as a selection factor in Avena fatua populations? A case study of cultivated and wild oat competition. Weed Research, 2017, 57(6): 399-405 CrossRef
  29. Wiles L.J., King R.P., Sweizer E.E., Lybecker D.W., Swinton S.M. GWM: General weed management model. Agricultural Systems, 1996, 50(4): 355-376 CrossRef
  30. Parsons D.J., Benjamin L.R., Clarke J., Ginsburg D., Mayes A., Milne A.E., Wilkinson J. Weedmanager—a model-based decision support system for weed management in arable crops. Computers and Electronics in Agriculture, 2009, 65(2): 155-167 CrossRef
  31. Oriade C., Forcella F. Maximizing efficacy and economics of mechanical weed control in row crops through forecasts of weed emergence. Journal of Crop Production, 1999, 2(1): 189-205 CrossRef
  32. Scursoni J.A., Forcella F., Gunsolus J. Weed escapes and delayed weed emergence in glyphosate-resistant soybean. Crop Protection, 2007, 26(3): 212-218 CrossRef
  33. Schutte B.J., Hager A.C., Davis A.S. Respray requests on custom-applied, glyphosate-resistant soybeans in Illinois: How many and why. Weed Technology, 2010, 24(4): 590-598 CrossRef
  34. Nowell L.H., Moran P.W., Schmidt T.S., Norman J.E., Nakagaki N., Shoda M.E., Mahler B.J., Van Metre P.C., Stone W.W., Sandstrom M.W., Hladik M.L. Complex mixtures of dissolved pesticides show potential aquatic toxicity in a synoptic study of Midwestern U.S. streams. Science of the Total Environment, 2018, 613-614: 1469-1488 CrossRef
  35. Pandey S., Medd R.W. A stochastic dynamic programming framework for weed control decision making: an application to Avena fatua L. Agricultural Economics, 1991, 6(22): 115-128 CrossRef 
  36. Lodovichi M.V., Blanco A.M., Chantre G.R., Bandoni J.A., Sabbatini M.R., Vigna M., López R., Gigón R. Operational planning of herbicide-based weed management. Agricultural Systems, 2013, 121: 117-129 CrossRef
  37. Berti A., Bravin F., Zanin G. Application of decision-support software for postemergence weed control. Weed Science, 2003, 51(4): 618-627 CrossRef
  38. Wilkerson G.C., Wiles L.J., Bennett A.C. Weed management decision models: Pitfalls, perceptions, and possibilities of the economic threshold approach. Weed Science, 2002, 50(4): 411-424 CrossRef
  39. Lindsay K., Popp M., Norsworthy J., Bagavathiannan M., Powles S., Lacoste M. PAM: decision support for long-term Palmer amaranth (Amaranthus palmeri) control. Weed Technology, 2017, 31(6): 915-927 CrossRef
  40. Lacoste M., Powles S. Beyond modeling: considering user-centered and post-development aspects to ensure the success of a decision support system. Computers and Electronics in Agriculture, 2016, 121: 260-268 CrossRef
  41. Kristensen K., Rasmussen I.A. The use of Bayesian network in the design of a decision support system for growing malting barley without use of pesticides. Computers and Electronics in Agriculture, 2002, 32: 197-217 CrossRef
  42. Neuhoff D., Schulz D., Köpke U. Potential of decision support systems for organic crop production: WECOF-DSS, a tool for weed control in winter wheat. In: Proceedings of the International Scientific Conference on Organic Agriculture, Adelaide, Australia, 21-23 September 2005. Adelaide, 2005: 1-4.
  43. Zambrano-Navea C., Bastida F., Gonzalez-Andujar J.L. A cohort-based stochastic model of the population dynamic and long-term management of Conyza bonariensis in fruiting tree crops. Crop Protection, 2016, 80: 15-20 CrossRef
  44. Bennett A.C., Price A.J., Sturgill M.C., Buol G.S., Wilkerson G.C. HADSS, Pocket HERB, and Web HADSS: decision aids for field crops. Weed Technology, 2003, 17(2): 412-420 CrossRef
  45. Lyon L.L., Keeling J.W., Dotry P.A. Evaluation and adaptation of the HADSS® computer program in Texas Southern High Plains cotton. Weed Technology, 2004, 18(2): 315-324 CrossRef
  46. Ford A.J., Dotray P.A., Keeling J.W., Wilkerson J.B., Wilcut J.W.  Gilbert L.V. Site-specific weed management in cotton using WebHADSS. Weed Technology, 2011, 25(1): 107-112 CrossRef
  47. Gonzalez-Andujar J.L., Fernandez-Quintanilla C., Bastida F., Calvo R., Izquierdo J., Lezaun J.A. Assessment of a decision support system for chemical control of annual ryegrass (Lolium rigidum) in winter cereals. Weed Research, 2011, 51(3): 304-309 CrossRef
  48. Gonzalez-Andujar J.L., Fernandez-Quintanilla C., Bastida F., Calvo R., Gonzalez-Diaz L., Izquierdo J., Lezaun J.A., Perea F., Sanchez del Arco M.J., Urbano J.M. Field evaluation of a decision support system for herbicidal control ofAvena sterilis ssp. ludoviciana in winter wheat. Weed Research, 2010, 50(1): 83-88 CrossRef
  49. Bessette D., Wilson R., Beaudrie C., Schroeder C. An online decision support tool to evaluate ecological weed management strategies. Weed Science, 2019, 67(4): 463-473 CrossRef
  50. Benjamin L.R., Milne A.E., Parsons D.J., Cussans J., Lutman P.J.W. Using stochastic dynamic programming to support weed management decisions over a rotation. Weed Research, 2009, 49(2): 207-216 CrossRef
  51. Lacoste M., Powles S. RIM: Anatomy of a weed management decision support system for adaptation and wider application. Weed Science, 2015, 63(3): 676-689 CrossRef
  52. Jørgensen L.N., Noe E., Langvad A.M., Jensen J.E., Ørum J.E., Rydahl P. Decision support systems: barriers and farmers’ need for support. EPPO Bulletin, 2007, 37(2): 374-377 CrossRef
  53. Kanatas P., Travlos I.S., Gazoulis I., Tataridas A., Tsekoura A., Antonopoulos N. Benefits and limitations of decision support systems (DSS) with a special emphasis on weeds. Agronomy, 2020, 10(4): 548 CrossRef







Full article PDF (Rus)

Full article PDF (Eng)