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ArticleOriginal scientific text

Title

Diffusion limit for the phenomenon of random genetic drift

Authors 1

Affiliations

  1. Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Abstract

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.

Keywords

ENG
genetic drift, telegraph equations, singularly perturbed systems, diffusion equation, random walk

Bibliography

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Applicationes Mathematicae
2000/27/1
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Pages:
81-101
Main language of publication
English
Received
1999-01-15
Accepted
1999-11-09
Published
2000
Exact and natural sciences