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At present, nucleotide sequences of 100 different Alu repeats are known, i.e. 0.01% of the total number of Alu repeats in the genome. It is clear that one can not refer the evolutionary characteristics of Alu repeats obtained from the analysis of the available limited sample to all Alu repeats comprised in the genome, without additional statistical estimations. For supplementary investigation of such average evolutionary characteristics as the extent of intraspecific divergence, the rate of Alu repeats transposition (insertion, excision), we used the method of imitation simulation of the process of Alu repeats transposition in the genome. As a result of simulation, phylogenetic relations were obtained among all Alu repeats. It was shown that the evolutionary characteristics evaluated for different samples of repeats were similar. It was proved that the extent of divergence of Alu repeats in the model is twice as small as that evaluated, according to the real data (0.15, instead of 0.3). Possible reasons for such discrepancy have been discussed.

The results of contextual analysis of 13 different mobile genetical elements (MGE) MDG1, MDG2, MDG3, MDG4, HOBO, P, F, MDG 17.6, H. M. S. Beagle, CIN1, BS1, TDD1, EV1 are presented. A search for regions revealing marked and statistically non-random homology with the consensus sequence of the heat-shock regulatory site (HSRS) has been carried out in these elements. Seven MGE (MDG1, MDG4, HOBO, P, CIN1, BS1, EV1) were shown to contain the regions of non-random homology with the HSRS consensus and the real HSRS. Evolutionary significance of connection between the environment and genetical cell system, based on the transcriptional activation of mobile genetical elements by heat-shock and some other factors, has been discussed.

A mathematical model of evolutionary dynamics of Alu repeats' number in the human genome has been worked out. The model permitted us to observe the dynamics of propagation of Alu repeats within the genome and to evaluate such important parameters of the process mentioned as the rates of transposition (insertion of new copies into the genome) and excision of repeats. The peculiarities of the control of Alu repeats' number in the genome have been discussed, based on the data obtained.

A mathematical model of the Markov's process type describing the duplicative transposition of mobile genetic elements (MGE) has been developed. The possible role of MGE containing regulatory sites activated under unfavourable conditions has been considered. An analysis of the model has shown that there may be such regimes of environmental changes (sharp but random changes of the environment parameters) when sufficiently reliable survival of population is dependent on such MGE.