MATHEMATICAL MODEL OF WINTER WHEAT PRODUCTIVITY IN THE RAINFED CONDITIONS OF THE SOUTH OF UKRAINE DEPENDING ON THE CROP’S VARIETAL TRAITS

Abstract

Abstract The paper is devoted to elucidation of the results of mathematical modeling of winter wheat yields, cultivated in the rain fed conditions of the South of Ukraine, depending on the varietal traits of the crop. The purpose of the study is the development of the mathematical equation of winter wheat varieties yields in the rain fed conditions of the steppe zone depending on such varietal traits of the crop as winter resistance, resistance to lodging, shedding, and drought. Methods.The methodology of multiple regression analysis was applied to conduct the research and develop the mathematical model of winter wheat ideotype. Experimental basis for mathematical modeling was represented by the results of ecological varietal testing, conducted in the rain fed conditions at the fields of PC «Zoria» and SE «Illich-Agro Zaporizhzhia». Evaluation of the model’s fitting quality and prediction accuracy was performed by the values of the multiple determination coefficient and mean absolute percentage error. To understand the influence of the studied traits on winter wheat productivity, rank correlations were calculated, and to establish the relationship and affinity between the varietal traits a matrix of Fechner’s correlation coefficients was computed. Mathematical computations were performed within Microsoft Excel 365 spreadsheets processor and BioStat v.7 statistical toolkit. Results. Mathematical evaluation of the studied varietal traits of winter wheat allowed to establish that the highest positive value in the crop’s yield formation in the rainfed conditions of the steppe zone of Ukraine is attributed to drought tolerance (Pearson’s pairwise correlation coefficient is +0.19), while other factors play a secondary role or have negative effect on the crop’s productivity. Evaluation of the multiple regression model confirms the above results and additionally significant positive effect of shedding resistance. The multiple regression model has high adequacy (multiple correlation coefficient is 0.9791; determination coefficient is 0.9587; adjusted determination coefficient is 0.8463) and prediction accuracy (mean absolute percentage error is 18.45%). Conclusions. According to the results of multiple regression analysis and rank correlation calculations, the strongest effect on the crop’s productivity in the mentioned agro-productive conditions is provided by such a varietal trait as drought tolerance, while the minimum effect has cold (winter) resistance. The proposed mathematical model of winter wheat productivity in the rainfed conditions of the South of Ukraine has high fitting quality and moderately high prognostic value. Key words: winter resistance, ideotype of a variety, mathematical model, drought resistance, regression analysis, resistance to lodging, shedding resistance, yielding capacity.