Prediction of populational dynamics of phytophages in agroecosystems using Markov chains

  • A. V. Fokin National University of Life and Environmental Sciences of Ukraine, Ukraine
  • N. N. Dolya National University of Life and Environmental Sciences of Ukraine, Ukraine
  • V. F. Drozda National University of Life and Environmental Sciences of Ukraine, Ukraine
Keywords: number of insects; agrocenosis; modeling; plant protection; depressive state of the population

Abstract

It is shown that the effectiveness of protective technologies can be predicted using Markov chains, that is, on the basis of the application of probabilistic approaches in the phase transitions of the dynamics of the abundance of insect phytophages population (outbreak of number, depression, etc.) and assuming that changes in the state of the system occur at certain moments of time. The probability of transitions between states corresponds to the sum of the effectiveness of insecticides and the parameters of the system of predictors, which will allow to take into account the problem of incompleteness in accordance with the second theorem of Gödel (Gödel incompleteness theorem). One of these problems is the prediction of the dynamics of the number of insects, since it is impossible to construct a predictive model of the dynamics of the total number, based only on the number data, depending on the system level (population, agrocenosis, biocenosis, etc.); to solve this problem, it is necessary to involve the external predictors (modifying and regulating). In this context, it is important the right choice of predictors to obtain an adequate prediction of the behavior of the system at one level or another. Therefore, it is quite possible to use the basic provisions of the factorial dynamics of population theories (parasitic, biocenotic and climatic), the stochastic and the regulation theory of the dynamics of the population, the trophic and biogeocenotic theory of dynamics of populations. It is important to correctly estimate the level of the predictable system and to form the complex of additional predictors that are not its elements, in order to maximize the intensification of the predictive model. Based on the data on the abundance of the population and the effectiveness of the selected measure (chemical protection, biological agent, agrotechnical measure), it is possible to predict the probability of the population transition to a steady depressive state and the multiplicity of application of means for controlling the number of phytophages for its achievement

References

Beletsky, E. N., & Stankevich, S. V. (2018). Politsiklichnost', sinkhronnost' i nelineynost' populyatsionnoy dinamiki nasekomykh i problemy prognozirovaniya [Polycyclicity, synchronicity and non-linearity of insect population dynamics and problems of prediction]. Premier Publishing s.r.o., Vienna (in Russian).

Bolanos-Espinoza, A., Bravo-Mojica, H., Equihua-Martinez, A., Trinidad-Santos, A., Ramirez-Valverde, G., & Dominguez-Valenzuela, J. A. (2001). Densidad y danos de plagas del maiz, bajo labranza convencional y de conservacion. Acta zool. mex, 83, 127–141.

Buysens, S., Martens, K., Lefebure, D., De Schoenmakere, M., & Spiessens, K. (2000). Op weg naar een beredeneerde tripsbestrijding (Thrips tabaci Lindeman) in de preiteelt (Allium ampeloprasum L.). Parasitica, 56(2‒3), 77–83.

Cranshaw, W., Bartolo, M., & Schweissing, F. (2001). Control of squash bug injury: Management manipulations at the base of Pumpkin. Southwestern Entomologist, 26(2), 147–150.

Fokin, A. V. (2011). Optimízatsíya strukturi zakhistu roslin víd shkídnikív [Optimization of structure for plant protection of the insects-pests]. Kolobіg, Kyiv (in Ukrainian).

Fokin, A. V. (2015). Principles of fractal phytosanitary diagnostics of agrocenosis [Printsipi fraktal'noí fítosanítarnoí díagnostiki agrotsenozu]. Karantin i Zahist Roslin, 4, 16‒18.

Kelbert, M. Y., & Sukhov, Y. M. (2010). Veroyatnost' i statistika v primerakh i zadachakh [Probability and statistics in examples and problems]. T. II: Markov chains as the starting point of the theory of random processes and their applications. MTSNMO, Moscow (in Russian).

Kolomeichenko, V. V., & Lysenko, N. N. (2001). Adaptivnyye podkhody k zashchite rasteniy [Adaptive approaches to plant protection]. Agricultural biology. Series “Plant Biology”, 1, 3–12 (in Russian).

Kostryukov, S. P., Arefyev, V. P., & Kvasyuk, N. Y. (2001). Osobennosti zashchity kartofelya ot bolezney, vrediteley i sornyakov [Features of potato protection from diseases, pests and weeds]. Potatoes and vegetables, 1, 31 (in Russian).

Li, J., Lu, Z., Wang, D., & Tian, C. (2005). Succession and its mechanism of cotton pests in Xinjiang. Chinese Journal of Ecology, 24(3), 261–264.

Mascarette, L. A., Badiali, C. W., & Raetano, C. G. (1999). Avaliacao da eficiencia de inseticidas para o controle de traca-do-tomateiro Tuta absoluta (Meyrick, 1917) (Lepidoptera – Gelechiidae). Cientifica, 27(1–2), 129–136.

Mascarette, L. A., Badiali, C. W., & Raetano, C. G. (1999a). Avaliacao da eficiencia de inseticidas para o controle de broca-pequena-do-tomateiro Neoleucinodes elegantalis (Guenee, 1854) (Lepidoptera – Pyralidae). Cientifica, 27(1–2), 117–128.

Medina, P., Budia, F., Del Estal, P., Adan, A., & Vinuela, E. (2004). Toxicity of fipronil to the predatory lacewing Chrysoperla carnea (Neuroptera: Chrysopidae). Biocontrol Science and Technology, 14(3), 261–268. doi: 10.1080/09583150410001665141

Nikolova, I. (2003). The impact on nyakoi agrotechnical measures on the arsenal of chromosomals on the harm of harvests (Heteroptera: Miridae, Pentatomidae) on the soyate of Glycine max L. (Merrill) and on the extent of damage to the seeds. Acta Entomologica Bulgarica, 9(3–4), 16–21.

Olfert, O. (1999). Influence of farming practices on arthropods. Proc. Entomol. Soc. Manit., 55, 36.

Purvis, G., Fadl, A., & Bolger, T. (2001). A multivariate analysis of cropping effects on Irish ground beetle assemblages (Coleoptera: Carabidae) in mixed arable and grass farmland. Annals of Applied Biology, 139(3), 351–360. doi: 10.1111/j.1744-7348.2001.tb00149.x

Reichmuth, C. (2000). Es gibt Vor- und Nachteile. Praktische Schadlingsbekampfer, 52(6), 22–23.

Schmitz, P. M., & Wronka, T. C. (2000). Landwirtschaft ohne Chemie? – Eine okonomische Betrachtung. Mitt. Biol. Bundesanst. Land- und Forstwirt. Berlin-Dahlem., 371, 25–30.

Shamanskaya, L. D., Oderova, E. V., & Ludtseva, N. V. (2005). Problemy i perspektivy polucheniya ekologicheski chistogo urozhaya oblepikhi [Problems and prospects of obtaining a clean harvest of sea buckthorn]. Siberian Herald of Agricultural Science, 1, 64–69 (in Russian).

Shen, B., & Ren, S. (2004). Impact of various control measures on Bemisia tabaci populations and cucumber yields. Acta Agriculturae Universitatis Jiangxiensis, 25(5), 728–731.

Sigvald, R. (2003). Forecasting and warning systems for pests and diseases in Sweden. Crop Protection Workshop “Pests, Direases and Weeds” (St. Petersburg–Pushkin, Oct. 28–29, 2003), 45–46.

Szendrei, Z., Mallmpalli, N., & Isaacs, R. (2005). Effect of tillage on abundance of Japanense beetle, Papillia japonica Newman (Coleoptera, Scarabaeidae) larvae and adults in high bush blueberry fields. Journal of Applied Entomology, 129(5), 258–264. doi: 10.1111/j.1439-0418.2005.00961.x

Vasilieva, L. A., & Niyazov, O. D. (2007). Integrirovannyy kontrol' chislennosti vishnevoy mukhi – osnovnogo vreditelya chereshni i vishni [Integrated control of the number of cherry flies ‒ the main pest of cherries and cherries]. Achievements of entomology in the service of the agro-industrial complex, forestry and medicine. Krasnodar (in Russian).

Vereshchagina, O., & Veretelnik, E. (2004). Vrediteli ozimykh kolosovykh v Slavyanskom rayone i perspektivy ikh rasprostraneniya [Pests of winter crops in the Slavic region and the prospects for their distribution]. Topical issues of plant protection, agrochemistry, agrarian soil science and insect faunistics in the Krasnodar Territory, 186, 27–29.

Wilde, G. E., Whitworth, R. J., Claassen, M., & Shufran, R. A. (2001). Seed treatment for control of wheat insects and its effect on yield. J. Agric. Urb. Entomol., 18(1), 1–11.

Williams, I. H. (2006). Integrating parasitoids into management of pollen beetle on oilseed rape. Agron. Res., 4, 465–470.

Youssef, A. I., Nasr, F. N., Stefanos, S. S., Elkhair, S. S., Shehata, W. A., Agamy, E., Herz, A., & Hassan, S. A. (2004). The side-effects of plant protection products used in olive cultivation on the hymenopterous egg parasitoid Trichogramma cacoeciae Marchal. Journal of Applied Entomology, 128(9‒10), 593–599. doi: 10.1111/j.1439-0418.2004.00892.x

Uspenskij, V. A. (1982). Teorema Gjodelja o nepolnote [Gödel's incompleteness theorem]. Nauka, Moscow.

Published
2019-04-10
How to Cite
Fokin, A., Dolya, N., & Drozda, V. (2019). Prediction of populational dynamics of phytophages in agroecosystems using Markov chains. Agrology, 2(2), 100–105. https://doi.org/10.32819/019014
Section
Оriginal researches