ЗАСТОСУВАННЯ НЕЛІНІЙНИХ РЕГРЕСІЙНИХ МОДЕЛЕЙ У СЕЛЕКЦІЙНИХ ТЕХНОЛОГІЯХ ДОБОРУ БАТЬКІВСЬКИХ ПАР ДЛЯ СТВОРЕННЯ ГІБРИДІВ F1ОВОЧЕВИХ ВИДІВ РОСЛИН

Abstract

The construction of non-linear regression relationships between the characteristics of the manifestation of quantitative traits in parental forms and their hybrid progeny in the breeding of vegetable plant species, which allow the formation of prognostic models for the selection of parental pairs for crossing in order to achieve the maximum effect in terms of the level of manifestation of quantitative traits in the obtained progeny. The purpose of the article is to demonstrate the prognostic capabilities of the method of planning multifactorial experiments according to the compositional plan of the complete factorial experiment (CFE) of the 3rd order for the construction of polynomial regression models, which express in the breeding of vegetable plant species the functional relationship of one quantitative trait of the progeny depending on three quantitative traits of the original parental forms. Methodology of the study is based on general scientific methods: analysis and synthesis; induction and deduction; observations and abstractions used to systematize research results in the natural sciences. Special methods: evaluation of the biochemical composition of sweet pepper fruits in the phase of biological ripeness; determination of patterns of formation of valuable quantitative traits and their variability in parental forms and derivatives of hybrids F1 of sweet pepper; mathematical and statistical – planning of a multifactorial experiment; programming; construction of nonlinear regression models. Results of the research demonstrate the high efficiency of the calculated regression models for establishing the regularities of the manifestation of quantitative traits between the original forms and their progeny in the selection of sweet pepper. Research samples of sweet pepper created at the Institute of Vegetable and Melon Growing of the National Academy of Sciences were used for the regression analysis. The parental forms and hybrids F1 derived from them were used as objects of statistical calculations. Data from the biochemical evaluation of fruits in the phase of biological ripeness obtained during 2021–2022 were used for statistical calculations. Polynomial regression was used to study the regularities of the total sugar content in the fruits of hybrid F1 plants depending on the content of biochemical components (dry matter, total sugar, and vitamin C) in the fruits of the parental forms. Finally, the results of mathematical modeling allow us to draw the following conclusions: the dominant influence on the expression of the studied trait (the maximum content of total sugar in the fruits of F1 hybrids) provides a similar level of the content of this valuable biochemical component in the parental forms of plants; when analyzing the data of the two-year studies by the degree of influence of the dry matter content in the parent forms of the plants, the optima of the manifestation of the investigated trait in the hybrids F1 were found; the graphical representation of the model functions according to the data of 2021 (Ymod1) and according to the data of 2022 (Ymod2) in the 3-dimensional coordinate system indicates the absence of a linear relationship between the investigated factors-arguments with a predominantly parabolic form of the relationship when displaying the resulting characteristic. Practical implications. In order to calculate mathematical and statistical models that reflect the patterns of manifestation of valuable quantitative traits between parental forms of vegetable plant species and hybrids derived from them, an effective algorithm for building a system of regression equations based on the matrix of the planning of a complete factorial experiment (CFE) of the 3rd order is proposed. Value/originality. The proposed modification of the planning elements of a full factorial experiment of the 3rd order, which provides for the unequal repetition of the number of parallel experiments in the planning matrix and the method of varying the levels of the argument factors (x1, x2, x3), made it possible to calculate multifactorial nonlinear regression equations, the application of which in the breeding of vegetable plant species allows optimal selection of parental components for crossbreeding with the maximum effect of manifestation of the investigated quantitative trait in their hybrid progeny.