The formation of optimal crop rotations is virtually unsolvable from the standpoint of the classical methodology of experimental research. Here, we deal with a mathematical model based on expert estimates of “predecessor-crop” pairs’ efficiency created for the conditions of irrigation in the forest-steppe of Ukraine. Solving the problem of incorporating uncertainty assessments into this model, we present new models of crop rotations’ economic efficiency taking into account irrigation, application of fertilisers, and the negative environmental effect of nitrogen fertilisers’ introduction into the soil. For the considered models we pose an optimisation problem and present an algorithm for its solution that combines a gradient method and a genetic algorithm. Using the proposed mathematical tools, for several possible scenarios of water, fertilisers, and purchase price variability, the efficiency of growing corn as a monoculture in Ukraine is simulated. The proposed models show a reduction of the profitability of such a practice when the purchase price of corn decreases below 0.81 EUR∙kg ^–1 and the price of irrigation water increases above 0.32 EUR∙m ^–3 and propose more flexible crop rotations. Mathematical tools developed in the paper can form a basis for the creation of decision support systems that recommend optimal crop rotation variations to farmers and help to achieve sustainable, profitable, and ecologically safe agricultural production. However, future works on the actualisation of the values of its parameters need to be performed to increase the accuracy.

The aim of performed research was to evaluate weed seedbank in soil under the influence of four different winter wheat tillage systems. Winter wheat was grown in the following cultivation systems: A – monoculture with direct drilling into white clover mulch; B – monoculture with direct drilling into wheat stubble; C – monoculture with conventional tillage; D – crop rotation with conventional tillage. It was shown that pre-sowing wheat tillage had a more considerable effect on weed species and weed seedbank in soil than type of crop rotation. The least seedbank was observed when plough system was replaced by direct drilling. In the soil layer of 0–20 cm, under wheat no-plough tillage, 20.3% less weed diaspores wasfound compared to monoculture with plough tillage and by 40.1% lessthan in crop rotation. The plough tillage increased amount of weed diaspores in the whole plough layer, while direct drilling increased it only in 0–1 cm of soil layer. After direct drilling of wheat into stubble (B) the number of weed diaspores in 1 dcm³ of soil in 0–1 cm layer was over twofold higher than in direct sowing in mulch (A), and threefold higher than in crop rotation (D) and almost six times higher than in wheat monoculture with conventional tillage (C). Dominating weed species in the soil over the types of wheat cultivation systems were: Chenopodium album L., Amaranthus retroflexus L., Apera spica-venti L., Lamium purpureum L., and Viola arvensis Murr.

Straw, particularly cereal straw, is a valuable by-product of crop production, which can be used for various purposes, e.g. as livestock feed and bedding or for making fuels, however it should primarily be retained on farmland in order to prevent soil organic matter (SOM) losses and thus to maintain or improve soil quality. The aim of this study was to analyze effects of the frequency of crop residues (straw) incorporation into the soil on the content of soil organic matter and on crop yields. There were the following experimental treatments: SR – straw of all crop in the rotation removed, S1 – straw of one crop per rotation incorporated, S2 – straw of two crops in the rotation incorporated, and S3 – straw of three crops incorporated into the soil (loamy sand). After 21 years of crop rotation with straw removal (SR) the SOM level in the soil slightly decreased to 14.4 g∙kg ^–1 soil DM, compared to that in 1997 (14.6 g∙kg ^–1). However, when straw of one crop (rape) per rotation was incorporated (S1) the content of SOM increased to 15.0 g∙kg ^-1 soil DM, and to 15.6 and 16.0 g∙kg ^–1 in S2 and S3 treatments respectively. Straw retention had also a beneficial effect on the content of labile fractions of SOM (hot water extractable C and N). Grain yields and yield components of wheat and triticale, and seed yields of rape in the SR treatment were not significantly different from those obtained in S1, S2 and S3 treatments.