Today the major oil producing crops from the Brassicaceae family in the world and Ukraine are winter rape (Brassica napus oleifera bienis D. C.) and spring rape (Brassica napus oleifera annua Metzg.). At present the acreage of these crops in the world is over 40 million hectares, and in Ukraine there are more than 1 million hectares. Less common crops are white mustard (Sinapis alba L.) and Chinese mustard (Brassica juncea Gzem.). The world acreage under the mustard crops is about 3,0 million hectares (in Ukraine there are about 100 thousand hectares). Other oil producing crops from the cabbage family such as spring winter cress (Brassica campestris L.), winter rape (Brassica rapa oleifera DC), winter false flax (Camelina sativa subsp. pilosa N. Zinge), spring false flax (Camelina sativa var. Glabrata (DC.), oily radish (Raphanus sativus L. var. oleiformis Pers) and black mustard (Brassica nigra (L.) Koch) occupy only a small area, while the Abyssinian mustard (Crambe abyssinica Hosts. ex. RE Fr.) is not grown in our country at all. It is impossible to obtain high and stable yields of all agricultural crops without protection of plants from the harmful insects. The losses of the crops due to the pests are huge, especially during the mass reproduction of the insects. The entomocomplex of agroceonoses of oil producing cabbage crops is extremely rich and contains several hundred species. As a result of their vital functions more than 50% of the crops can be lost and as far as 25-55% growth increase in the yield can be reached due to the pollinating insects. Despite the short-term existence of agroceonoses of spring oil producing cabbage crops (90-120 days) their entomofauna is characterised by a considerable diversity of species composition. During the vegetation periods in 2007–2019 in the fields of the Educational, Research and Production Centre “Research Field” of Kharkiv National Agrarian University named after V.V. Dokuchaiev and the State Enterprise “Research Farm “Elitne” of the Institute of Plant Growing named after V.Ya. Yuriev of the National Academy of Agrarian Sciences of Ukraine we have found 54 species of specialised and multi-faceted pests of oil producing cabbage crops that belong to eight lines and 22 families. Among them 29 species are the specialised pests and 25 are multi-faceted ones. The frequency of the pest species occurrence on the crops is the following: eight species (15%) populate the crops on a mass scale, six species (11%) are moderately spread, and 40 species (74%) have a low population density. The cabbage bug, mustard bug, ground cabbage aphid, rose chafer, rape blossom beetle, mesographe flea beetle, flea beetle and diamond black moth belong to the species that populate the crops on a mass scale. Among them four species belong to the Coleoptera line, two species belong to the Hemiptera line, one species belong to the Homoptera line and one species belong to the Lepidoptera line. The representatives of the Coleoptera line dominate; their proportion in the entomological community structure is 48% (26 species). The economic importance of these pests is not the same and greatly depends on the population density and phenophase of the crop development as well as on weather conditions.

The history of the formation and development of the Department of Zoology and Entomology named after B. M. Lytvynov of the Kharkiv National Agrarian University named after V. V. Dokuchaiev since 1840 is presented. The activity of the heads of the department and leading scientists in different periods is characterized. The scientific schools of V. G. Averin, A. A. Migulin, B. M. Litvinov, Ye. N. Beletskiy are described, which cover a wide range of issues of population dynamics of phytophagous insects, protection of fruit, cruciferous and other agricultural crops. The directions of research of the current teaching staff are highlighted.

One of the most dangerous pests of cabbage crops which can damage plants in the budding and flowering phases in all areas of their cultivation is a rape blossom beetle (Meligethes aeneus Fabricius, 1775). The pest is widespread throughout Ukraine; it causes significant damage to the crops every year and reduces the seed yields. It should be noted that the rape blossom beetle is not new to our country and as a pest of rape and other crops from the cabbage family has been mentioned since 1845, and a detailed description of its morphology, biology and ecology can be found in the works of the nineteenth century. It is established that in the Eastern Forest-Steppe of Ukraine the first individuals of the rape blossom beetle appear on the flowering wild growing plants (first of all on dandelion and buttercup) when the average daily temperature exceeds 8 °C, it is the middle of the first decade of April and the beginning of the third decade of April. The mass emergence of the rape blossom beetles takes place when the daily average temperatures are at the range of 9–13 °C and the sum of the effective temperatures above 5 °C is at the range of 100–113 °C, it is the middle of the second decade of April and the end of the third decade of April. The females of the rape blossom beetle usually lay 2–3 eggs into one bud of spring rape or mustard. When protecting the crops from the rape blossom beetle the highest technical efficiency was noted when applying the binary mixture of the microbiological preparation Actophyte, 0.25 % of emulsion concentrate in the dose of 4.8 L/ha and systemic insecticide Biscaya, 24 % of oily dispersion (0.25 L/ha) and in 14 days after spraying it was 76.6 % on white mustard, 74.3 % on Chinese mustard and 76.2 % on spring rape. The highest growth increase in the yield capacity was observed in the same variant; for white mustard it was 0.431 t/ha, for Chinese mustard it was 0.265 t/ha and for spring rape the growth increase amounted to 0.277 t/ha. As a result of the researches it is established that the weight of 1000 healthy seeds is 2,6996 g, and the weight of the seeds damaged by the larvae of the rape blossom beetle is 0.4213 g, so it is reduced by 84.4 %. The filling of the damaged seeds is 6.8 times more, which indicates that they are smaller in diameter and frail. The undamaged seeds of spring rape contain 35.92 % of fat, and the damaged seeds contain only 17.48 %, which is 2.05 times less. The protein content in the undamaged seeds was 30.97 % and in the damaged ones it was 32.23 %, that is 1.04 times more. The germination rate of the undamaged seeds of spring rape under the laboratory conditions on the eighth day was 90.0 %, and the germination rate of the damaged ones amounted to 58.0 % and was lower by 32.0 %.

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The authors have analysed the theoretical possibilities of prognostication the dynamics in the number and mass reproduction of some species of harmful insects. A theoretical synthesis of the information on the regularities of the population dynamics of the most common insect pests of agricultural plants from the point of view of the methodology of nonlinear dynamics and synergetics has been done. Based on the past and present an analysis of the many-year dynamics in the number of the insect populations has been carried out and an attempt to develop the algorithms for prognostication the seasonal and annual changes in the number of the insects has been made. To do this the authors recommend a scenario-based method of prognostication and making decisions in plant protection. Using the phytosanitary monitoring they determine the beginning of the regular mass reproduction (the appearance of an aggravated rate) and then, based on the phytosanitary prognosis, an aggravation of the situation that has developed or is being developing on the farm, in the district or in the region is made; after that on the base of the short-term prognosis (signaling) it is recommended to make the optimal decision to protect a particular crop taking into account the economic threshold of harmfulness. According to the authors this approach, based on the methodology of nonlinear dynamics (synergetic paradigm), makes it possible to determine in advance the breeding grounds of the aggravated rates and make the optimal decisions in plant protection. The predicted scenario will not be a prognostication of the future, but the elements of an evolutionary process inherent in nature.