Prognostication in plant protection. Review of the past, present and future of nonliner dynamics method

By carrying out a theoretical synthesis of the information on the regularities of population dynamics of some insect pests of agricultural plants and based on the past and present the authors have analysed the dynamics of many years in the number of the insect populations. An attempt to determine the presence of synchronism of outbreaks of the insects’ mass reproduction with the years of sharp changes in the solar activity has been made; the relationship between the changes in the number of the insects and meteorological and heliographic factors has been analysed. An analysis of the dynamics of the sun pest reproduction taking into account the duration of sunshine on the materials of one of the outbreaks (local population) in the Kupiansk district of the Kharkiv region showed the unreliability of this index as a predicate of the prognosis; and the reproduction rate of the local population of the sun pest does not change depending on the duration of the solar radiance. It is determined that this principle is also unsuitable for forecasting the dynamics in the number of this pest. The linear differential equations, in which not only the meteorological factors but also the indices of the solar activity (global factor) were used as variables were unsuitable for prognostication the dynamics in the number of the insects. The examples listed in the article confirm the fundamental regularity, namely the polycyclic dynamics of various natural systems and the synchronism in their development. The synchronization is inevitable because all objects of inanimate and living nature consist of the same chemical elements, and the conservation and conversion of energy is universal in nature. Based on the methodology of the cyclic dynamics it is possible to develop the algorithms for prognostication the regular mass reproduction of harmful insects.


Introduction
At the beginning and in the middle of the twentieth century in the former USSR, including Ukraine, the mass reproductions of multi-facated and specialised insect pests of agricultural crops, fruit and forest stands were noted. Among them the webworm beetle dominanted. In 1912 and 1920 the mass reproduction of this pest over a vast territory was one of the prerequisites for organizing the prognostication in plant protection. The beginning of prognostication in plant protection in Ukraine was in 1913.
Since this year the entomological bureau of the Kharkiv provincial zemstvo headed by V. Averin has begun to publish the "Newsletter on agricultural pests and measures to control them" with a separate section "On the expected appearance of pests" (Averin, 1913). In 1925, under the People's Land Commissariat in Ukraine (Kharkiv) the plant protection departments under the guidance of V.H. Averin and the Central Plant Protection Station were organised. In 1925-1929 the station was headed by A.A. Mihulin; under his guidance the "All-Ukrainian network of observation points" (OP) was created in 1925 and its information and methodical support was developed. Ukrainian ecologists took an active part in organizing and establishing the prognostication in plant protection. In 1925, Averin published the article "The Periodic Appearance of the Most Important Pests of Agriculture in Ukraine" and the article "The Waves of Life of the Most Important Pests in Ukraine", where he showed the wave (cyclic) nature of the harmful insect mass reproduction. In 1930 N.A. Grossheim described the history of the mass reproduction of multi-faceted and specialised pests, emphasizing their unexpected appearance and sharply criticizing the climatic, parasitic and trophic theories of the insect populations' dynamics. He recommended using the periodicity as a criterion for the forecasting (Grossheim, 1930). In 30s, the fundamental studies of the population ecology under the guidance of Professor A.H. Lebediev began at the Department of Ecology of the Terrestrial Animals of the Institute of Zoology of the Academy of Sciences of Ukraine. In the article "On the Importance of Forecast as for Harmful Insects" he also noted the periodicity of the harmful insects' mass reproductions and their probable association with the space and meteorological factors (Lebediev, 1930). The theoretical foundations and prognostication methods in plant protection were first substantiated by S.P. Ivanov in 1936 in his work "The Mass Reproductions of Pests and Methods of Their Forecast" (Ivanov, 1936).
Ukrainian Journal of Ecology, 10(4), 2020 The criteria proposed in his work are still being used by the experts of the phytosanitary monitoring and prognostication service of Ukraine, although they are outdated and do not meet the methodology of modern studies of the population ecology of the insects. In addition S.P. Ivanov was the the first who called the one-year forecast the "long-term" one as it was accepted in meteorology; and even now it is being widely used in the plant protection forecast without any specification, although the work "Prognostication. Terminology" (Lisichkin, 1990) was published about 30 years ago. In 1938 a collective monograph by S.P. Ivanov, M.M. Levitt and Ye.M. Yemchuk "Mass Reproductions of Animals and Gradation Theories" was published. This is the first work containing a critical analysis of the theoretical concepts of domestic and foreign ecologists on the population dynamics at the example of the harmful insects' mass reproduction with an analysis of 325 domestic and 686 foreign literature sources. One of the chapters of this monograph is devoted to an acute debatable problem, namely to the periodicity of the insects mass reproduction and to a critical analysis of the existing in the 1930s theoretical ideas about the connection of the mass reproductions outbreakes with the climate dynamics and the appearance of the sun-spots (Ivanov, 1938). The authors of this monograph did not deny the possible connection of "Sunny weather" (the definition of the solar activity by O. L. Chizhevskyi) with the dynamics of the insect populations, but they indicated that it has not yet been determined (late 30s of the last century). By the way till now the question as for the connection of the solar activity with the processes and phenomena occurring in the biosphere, biogeocenoses and populations remains acute debatable despite the fact that most researchers of the solar-terrestrial relations continued and are still continuing to indicate its presence. In 1940 and 1950 on the initiative of the Ukrainian ecologists (A.F. Kryshtal and others) and taking into account the urgency of the mass reproduction problem the All-Union Ecological Conferences on the problem of "Mass Reproduction of Animals and Their Forecast" were held in Kyiv on the basis of the T.H. Shevchenko State University. At the same time the works "On the Mass Reproduction of Insects" (Belanovskyi, 1940) and "Features of the Mass Reproduction of Insects and the Principles of Their Prognostication" (Ivanov, 1936) were published. The authors critically summarised the earlier works of the Ukrainian ecologists and made the important conclusions for prognostication in plant protection; they are as follows: -if the forecast is developed on the basis of the quantitative data obtained from the autumn surveys, then one should not take into account the weather conditions forecasted for the next year because weather forecast for such a long period can only be probabilistic, and therefore it has no prospects to compare the meteorologic factors of this winter, next spring and insect phenology; -the results of the autumn surveys must be compared with the dynamics of the previous years; -a qualitative assessment of the population variation of the insects (average weight and sex ratio) should be made; -it is necessary to determine the infection of the hibernating stage of the insects with the parasites and the affection caused by the pathogens. These criteria are still taken into account by the specialists of the monitoring and forecasting services. Afterwards the ecologists tried to explain the reasons of the mass reproduction of the insects by their reaction to the environmental factors, mainly air temperature and humidity in the laboratory, transferring the results of the laboratory studies to the natural conditions, and it was a gross methodological error. Air temperature and humidity really create a natural background against which the development of the biological systems, including the insects, takes place. However this does not mean that these factors play a leading role in the dynamics of the populations. The famous American ecologist Kenneth Watt wrote: "In thousands of scientific articles the temperature and humidity have been assigned a leading role as the main factors affecting the development of various organisms. However this enourmous work has not yet led to the fact that their influence could be used in the population models" (Watt, 1971). In 1954 "The theory of changing the vital activity of the populations at the example of mouse-like rodents" was substantiated by the famous Russian ecologist I.Ya. Poliakov. Its essence, the vital activity of the populations (their ecological and morphophysiological structure) in a given period, is determined by the conditions under which the age groups it consists of developed in the past. In his opinion the main and fundamentally new thesis of this theory is that the latter allows one to judge the dynamics of the population and the probable factors that can affect it according to the state of the forage reserve, physical environment, and morphophysiological structure of the populations (Poliakov, 1954). Based on this theory the annual forecasts in plant protection (regarding harmful rodents and insects) were developed and are still being developed. In relation to the mass reproductions of the insects, namely the pests of the agricultural crops, fruit and forest stands, he replaced the prognostication of the mass reproduction with the economic resource prognostication, and more often with a prospective assessment of the phytosanitary condition of a given territory for the purpose of planning and organizing plant protection (Maksimov, 1984). The failure of these forecasts was confirmed 3 years later. In 1957 an unprecedented in the history of domestic entomology the outbreak of the mass reproduction of the owlet moth (Hadena sordida Bkh) was noted. It covered all the regions of Northern Kazakhstan, some regions of Western Siberia, Altai Territory, Trans-Urals and Bashkiria. Only during 1957 the caterpillars of the owlet moth destroyed 150 million poods of grain in the virgin regions of Kazakhstan and Siberia; and the territory populated by this pest exceeded 10 million hectares (Grigorieva, 1965;Shek, 1965). In Northern Kazakhstan the main breeding ground was concentrated in the eastern part of the Kustanai and southeastern part of the Kokchetav regions with the caterpillars' density of 300 and more specimens per square meter. In 1957 there was a "sudden", unexpected mass reproduction of the webworm beetle; according to I. Ya. Poliakov (Poliakov, 1964) this pest was not considered a mass any more. I.Ya. Poliakov (Poliakov, 1980) made an attempt to identify the reasons of this mass reproduction, substantiate the forecast of its population dynamics and solve the immidiate tasks to improve the prognostication. At the same time he noted that until 1929 this pest had appeared on a mass scale with an interval of 5-10 years. From 1853 to 1935 (for 82 years) nine great increases in its number were noted in the European part of the USSR; each of them lasted from one to five years. The last outbreak occurred after a 35-year interval. There were no such long depressions Ukrainian Journal of Ecology, 10(4), 2020 before. However this is not true. In the literary sources the local mass reproductions of this pest were recorded in Ukraine and Russia in 1947-1950and in 1956-1957(Shvareva, 1963Dobretsov, 1980;Knor, 1981;Triebel, 1989;Kravchenko, 2002;Biletskyi, 2006;Frolov, 2010;Biletskiy, 2015). I.Ya. Poliakov made the following assumptions. The mass reproduction of the webworm beetle in the former USSR was due not only to the condition of climatic factors (these factors are not indicated). According to the fundamental studies of the climatologists the climatic factors include solar radiation (SR), atmospheric circulation (AC) and the underlying surface (US) (Shvareva, 1963;Borisenkov, 1982). One of the main reasons was the radical transformations of the landscape in the thirties which were taking place under the influence of the socialist reconstruction of the agricultural production and its further intensification. The stations for the development of the webworm beetle were significantly reduced aafter the organization of collective and state farms. The wave of the regular mass reproduction of this pest was presumably associated with the creation of the shelterbelt forest on the area of more than 2 million hectares, large areas of irrigated and watering land, and the expansion of crops of perennial legume grasses and row crops. In addition there were no methods for long-term forecasts of the webworm beetle spreading, phenology and harmfulness as the bases for the decision-making; and also the methods to protect the agricultural crops from this pest have not been developed (Poliakov, 1980). At the same time I.Ya. Poliakov defined the tasks of further improving the forecasts regarding the appearance and spreading of the webworm beetle; they are the followings: -a complete transition to the mathematical modeling of the population dynamics of the webworm beetle; -planning the protective treatments and determining the time and place of their conducting using a computer; -organization of automated collection and processing of the information concerning the status of this pest (number and phenology); -improving the methods for calculating the butterflies and caterpillars in order to ensure the accuracy of up to ± 40% at the lowest labour costs. The first task is too optimistic. The famous French mathematician Jacques Hadamard (Hadamard, 1970) wrote in this connection: "the construction of the prognostication models in ecology using the differential equations looks like a parody of Physics"; and G. G. Winberg (Winberg, 1981) noted the difficulties in formalising the biological systems (at the example of the populations) using the mathematical methods. We used the available data on the population dynamics of some insect pests in agricultural plants to to determine the presence of synchronism in insects mass reproduction outbreaks regards the years of sharp changes in the solar activity. The relationship between the changes in the insect numbers, meteorological and heliographic factors has been analysed.

Discussion
These works are still remained unknown for many ecologists who studied and are studing the regularities of the population dynamics of the harmful insects. Moreover the year of 1975 served as a powerful stimulus for the intensification of the researches in the field of solar and biospheric relations taking into account the results of studies carried out before 1975. To develop the forecasts the ecologists used the indices of long-term dynamics of the solar activity expressed in the relative Wolf system numbers (W) ( Table 1, Appendix). In 2009, S.V. Dovhan (Dovhan, 2009) performed a statistical generalization of the long-term quantitative data presented by the Republican Phytosanitary Monitoring Service and the forecast of the dynamics of the average density of some widespread harmful insects in Ukraine in order to develop the quantitative models for their prognosticatin for the next year (season). The indices of temperature, precipitation, relative humidity and duration of sunshine were used as the predicates (factors). The linear regression equations served as the prognostic models. To analyse the authenticity of the number dynamics correlation of some insect pests we partially used the information presented in the monograph (Dovhan, 2008) without giving the prognostic equations of the linear regression; some data are presented in Tables 2-4.  1980,1983,1985,[1996][1997][1998][1999][2000]2004 0.086 0.86 European corn borer 1974, 1975, 1978-1979, 1989-1994, 2000-20040.215021.56 Webworm beetle 1975-1976, 1988-1990, 2003-2004, 2004 Mamestra cabbage moth 1973-1975, 1978-1979, 1985, 1990-1991,1998-20070.160516.05 Sun pest 1969, 1984, 1987, 1993-1996, 2001, 2007-20090.3772 37.72 Scarab beetles 1980, 1985, 1987-1988, 2000, 2004 Corn ground beetle 1976-1977, 1981-1982, 1989-1990, 1996-1997, 2000, 2002-2004 0.1382 13.82 Apple moth 1968, 1977, 1981-1983, 1989, 1997-1998, 2005-2006 0.0983 0.983 Ukrainian Journal of Ecology, 10(4), 2020  1976, 1984, 1987, 1999-2001, 20030.270727.0 European corn borer 1971, 1980, 1984, 1991, 1994, 20060.270727.0 Webworm beetle 1973-1974, 1977, 1989-1990, 2008-20090.207920.7 Mamestra cabbage moth 1970, 1994, 1997-19980.18485 18.5 Sun pest 1969, 1986-1988, 1998, 2003-20070.230223.0 Scarab beetles 1983-1986, 1988-1994, 1999-20000.1294 Corn ground beetle 1973-1974, 1983-1984, 1991-1993, 2001-20030.4935 49.3 Beet root weevil 1973, 1978, 1980, 1987, 2005 0.0673 6.73 Grey beet weevil 1984-1990, 1994-1996, 2000-2002 0.3495 34.9 Apple moth 1970, 1972, 1976-1977, 1980-1988, 1994-1996, 2001-2008 0.2994 29.9 The analysis of the linear regression data presented in Table 2 indicates the absence of dependence of the regular increase in the number of harmful insects on the meteorological factors (duration of sunshine, temperature and humidity) in the Zaporizhzhia region. In the Cherkasy region (Table 3) some dependence was noted regarding the corn ground beetle (49,3%); in the Volyn region this dependence can be noted in the cases of the gnawing moths, mamestra cabbage moth, scarab beetles, corn ground beetle, beetroot weevil and apple moth. The unauthenticity of the obtained results when conducting the traditional linear modeling of the dynamics in the number of some harmful insects testifies to the fact that the insect populations are complex and nonlinear systems and the linear method is not suitable for the mathematical modeling of the dynamics. Moreover the methodology of availability forecasting is outdated. The population dynamics is closely related to the cyclic recurrence and aggravated rates (mass reproduction) which must be detected in proper time using the phytosanitary monitoring (Kniazeva, 2002;Chaika, 2012).  1972-1979, 1996-1997, 1999-2009 0.5499 54.9 Corn ground beetle 1974-1975, 1987, 1992, 1996-2009 1973, 1980, 1986, 1991-1994, 1997-2009 0.797 17.9 Apple moth 1973, 1976, 2004-2008 0.7611 76.1 At one time at the example of modeling the dynamics in the number of the sun pest in the Kharkiv region it was shown that the linear modeling is also not suitable for the prognostic purposes (Bіletskyi, 2006). Based on the quantitative data on the average density of the sun pests in the hibernating places a quantitative model which is an equation of a multiple regression equation was proposed: y = 3.0126 -0.0141252×W+0.00014457×W², where "y" is an average density of the bugs in the hibernating places; "W" is a Wolf number (an index of the number of sunspots on the visible disk of the Sun).
The results are given in Table 5. From the data presented in the table it is seen that the quantitative model in which the indices of the solar activity of the Wolf number (w) were used as a predicate in order to forecast the density of the bugs in the hibernating places was unreliable; the error, that is the deviation of the prognostic density from the actual one was from 0.1 to
To prove the synchronism of the vast majority of insects there is no need to use the Chi-square criterion. Both the regional and global synchronizations with the years of sharp changes in the solar activity were noted in the case of the above-mentioned insects. With the years of sharp changes in the solar activity the climate-forming factors (solar reaction and atmospheric circulation), meteorological elements (weather factors such as temperature, precipitation, atmospheric pressure, duration of sunshine), annual growth of trees and yield capacity of the agricultural crops have been synchronised (Tables 8, 9).  Table 8. Fracture rates of long-term course of natural processes on the Earth and statistic assesments of fractures connection with sharp changes in solar activity (Druzhynin, 1969;Influence ..., 1971;Druzhynin, 1974) Process name The data presented in the table indicate that the fracture rates during the years of solar benchmarks (during the years of sharp changes in the solar activity) are 8-23% higher than the frequencies in other years with high chi-square criteria (from 7.5 to 154) and, accordingly the probabilities of chance differences in the fractures in the years with sharp changes in the solar activity and in other years are low (from 1 to 0.01) which allows us to assert the non-randomness and synchronization of the long-term

Prognostication in plant protection
Ukrainian Journal of Ecology, 10(4), 2020 course of natural processes in the years of solar benchmarks with the probability from 99 to 99.9%. We have obtained the analogous results as for the Kharkiv region (Table 9). The data given in Table 9 also allow asserting the synchronization of the atmospheric processes and the yield capacity of winter crops (wheat and rye) with the years of sharp changes in the solar activity. The global mass reproductions of some insect pests are synchronous with the sharp changes in the solar activity or solar benchmarks (Table 10).  1901-1905 1909-1914 1923-1929 1931-1933 1936-1941 1948-1957 1964-1970 1972-1981 1984-1991 1997-1998 100 The beginning of the regular (global) mass reproduction of all 12 species of the widespread pests was synchronous with the years of sharp changes in the solar activit (Table 10). In addition they are polycyclic. The cyclic character has been currently determined in the development of many natural systems (biological, environmental, economic and social) and even in the scientific work (Yahodynskyi, 1981;Aliakrynskyi, 1985;Vernadskyi, 1988). Analysing the results of the scientific work of the world-Ukrainian Journal of Ecology, 10(4), 2020 famous scientists V.I. Vernadskyi (Vernadskyi, 1988) noted the following: "The explosions of scientific work are recurred over the centuries, they are accumulated in one of the few generations in one or in many countries when the gifted individuals create a force changing the biosphere ..." (Vernadskyi, 1988). This fact was confirmed by Yu.V. Yakovets (Yakovets, 2002): "If we look at Russia in the first quarter of the 20th century through the prism of the past decades then the cluster of great figures of the world science, a generation of talents will be striking. They are I.P. Pavlov, N.I. Vavilov, V.I. Vernadskyi, P.A. Kropotkin, K.E. Tsiolkovskyi, O.L. Chizhevskyi, P.A. Sorokin, N.D. Kondratiev, A.A. Bohdanov, N.A. Berdaiev, and many others. They made a breakthrough in many branches of knowledge, founded the immense knowledge of a new scientific paradigm which would be completed in the new century" (Yakovets, 2002).

Conclusions
The analysis of the dynamics of the sun pest reproduction, in the Kupiansk district, Kharkiv region, showed the unreliability of this index as a forecast predicate; the reproduction rate of the sun pest local population is not changed depending on the sunshine duration. We determined that this principle is also unsuitable for prognostication of the dynamics in the number of this pest. The linear differential equations, in which not only the meteorological factors but also the indices of the solar activity (a global factor) were used as variables, were unsuitable for forecasting the dynamics in insect numbers. The cases described in this article confirmed the fundamental regularity, namely the polycyclic dynamics of various natural systems and the synchronism in their development. The synchronization is inevitable because all objects of inanimate and living nature consist of the same chemical elements, and the conservation and conversion of energy is universal. Based on harmful pest cyclic dynamics it is possible to prognose their regular mass reproduction.