A differential equation, deduced from a DNA-type genetic algorithm with the lagging-strand-biased mutagenesis

Recent evidence indicated that the significant fidelity difference existed between the leading and lagging-strand. Using a 2-D DNA-type genetic algorithm (GA), we have shown that the lagging-stand-biased mutagenesis (disparity mutagenesis) has a significant advantage in the promotion of evolution, compared with the traditional parity mutagenesis model. Our aim of the present study was to deduce a differential equation which well reflected the result of simulations. The analytical solution of the differential equation obtained was in good agreement with the results of the simulation experiment. Comparing the results of the disparity mutagenesis with those of the parity one, the characteristics of the disparity mutagenesis were discussed in terms of relative mutation rates between the lagging and leading strands. Conditions of the extinction of a species were also discussed.