Vol. 12(3). Feb. 2021, No. 2, pp. 1-14.

MARKOV AND NON-MARKOV HEREDITARY PROCESSES IN ASEXUAL AND RANDOM MATING SEXUAL POPULATIONS
Vol. 12(3) ICMSFC Feb. 2021, No. 2, pp. 1-14
E. A. ABDEL-REHIM, R. M. HASSAN, A. M. A. EL-SAYED

Abstract

In this paper, we numerically investigate the Hereditary processes in the sexual and asexual mating. The genetic diffusion models of the two cases are described by partial differential equations. The solutions of these equations are considered as the conditional probability of finding the specific genes at a certain generation with a certain frequency. We also investigate the effects of the selection and mutations as well as the dependence on the memory on the sexual random mating and on the self proliferation of the asexual case. The effects of the wild-type mutation rate and mutator mutation rate per genome on the asexual proliferation is also numerically discussed. To do so, the common finite difference rules (FDM) will be utilized. The convergence of the discrete approximate solutions on the short and long run, i.e. the dependence on the memory, are also discussed and numerically investigated. The reversibility property for both models is theoretically and numerically discussed. Finally, a concrete conclusion will be given to summarize our numerical results and their relations to the real life problems.


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