Basic Properties of Populations Generated in the Frame of One-Parameter Discrete Model of Genetic Diversity

Abstract

Previously, when discussing the properties of one parameter discrete model of genetic diversity (M. Yu. Shchelkanov et al, J. Biomol. Struct. Dyn. 15, 887–894 (1998)), we took into account Hamming distance distribution only between precursor and arbitrary descendant sequences. However, really there are sets of sequence populations produced during amplification process. In the presented work we have investigated Hamming distance distributions between sequences from different descendant sets produced in the frame of one parameter discrete model. Two basic descendant generation operators (so called amplifiers) are introduced: 1) the last generation amplifier, [Lcirc], which produces descendants with precursor elimination; 2) all generations amplifier, Ĝ, which produces descendants without precursor elimination. Generalization of one-parameter discrete model for the case when precursor sequences do not coincide are carried out. Using this generalization we investigate the distribution of Hamming distances between [Lcirc]—and Ĝ -generated sequences. Basic properties of [Lcirc] and Ĝ operators, [Lcirc]/Ĝ-choice alternative problem have been discussed. Obtained results have common theoretical significance, but they are more suitable for high level genetic diversity process (for example, HIV diversity).