I. THEORETICAL BASIS OF GENOTYPES IDENTIFICATION ON THEIR PHENOTYPES DURING SELECTION IN SEGREGATING GENERATIONS I.M. Mikhailenko, V.A. Dragavtsev Agrophysical Research Institute, Russian Academy of Agricultural Sciences, 14, Grazhdanskii prosp., St. Petersburg, 196220 Russia, e-mail: ilya.mihailenko@yandex.ru Received August 22, 2011 S u m m a r y The authors presented the formalized theory for identification of genotypes on phenotypes in modern breeding technologies. <...> As a base the authors proposed the mathematical models of «genotype—environment» interaction, for which they solves an inverse informational problem during the estimation of sizes of no observed action of seven genetic-physiological system on selected quantitative traits to be improved. <...> Basic principles of modeling the system of “genotype-environment” interaction and possible ways of using the proposed models in solving basic problems of modern genetics and breeding were discussed in detail previously (1). <...> The most important tasks solved my means of these models are (Figure 1): evaluation of the mechanisms of transgressions and selection of parental pairs for obtaining a desired result of crossing; estimation of the contributions (eg., to productivity) of genetic-physiological systems of the parents; prediction of transgressions of breeding traits in offspring; crossing and obtaining F2 population; identification of genotypes on the base of phenotypes. <...> Development of the theory for solving this problem may open a prospect for significant advances of modern genetics . 1. <...> Evaluation of the mechanisms of transgressions and selection of parental pairs from the collection of varieties 2. <...> Estimation of the contributions of parental genetic-physiological systems to an improved character 3. <...> Prediction of the breeding traits of transgression genotypes 5. <...> Identification of individual genotypes by phenotypes and comparison of selected transgressions with forecasts 4. <...> The first step is selection of parental pairs capable to provide the desired result of crossing; this process can be optimized using the task of predicting results of such cross. <...> Each of these stages operates by mathematical models of “genotype-environment” interaction. <...> Its target is identification (or creation) of a genotype having the maximum number of positive expressions of specified breeding traits (BRT). <...> That’s why the algorithm of this task is based on the principle of background traits (2) and the principle of multi-directional shifts of an individual’s quantitative character caused by genetic and environmental causes in two-dimensional coordinates of a trait (3). <...> An ideal background <...>