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Diffusion limit for the phenomenon of random genetic drift. (English) Zbl 0994.35019
Summary: The paper deals with mathematical modelling of population genetics processes. The formulated model describes the random genetic drift. The fluctuations of gene frequency in consecutive generations are described in terms of a random walk. The position of a moving particle is interpreted as the state of the population expressed as the frequency of appearance of a specific gene. This leads to a continuous model on the microscopic level in the form of two first order differential equations (known as the telegraph equations). Applying the modified Chapman-Enskog procedure we show the transition from this system to a macroscopic model which is a diffusion type equation. Finally, the error of approximation is estimated.
MSC:
35B25 Singular perturbations in context of PDEs
92D10 Genetics and epigenetics
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