Prediction of populational dynamics of phytophages in agroecosystems using Markov chains

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