# Diffusion limit for the phenomenon of random genetic drift

Applicationes Mathematicae (2000)

- Volume: 27, Issue: 1, page 81-101
- ISSN: 1233-7234

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topMarciniak, Anna. "Diffusion limit for the phenomenon of random genetic drift." Applicationes Mathematicae 27.1 (2000): 81-101. <http://eudml.org/doc/219261>.

@article{Marciniak2000,

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.},

author = {Marciniak, Anna},

journal = {Applicationes Mathematicae},

keywords = {genetic drift; telegraph equations; singularly perturbed systems; diffusion equation; random walk; modified Chapman-Enskog procedure},

language = {eng},

number = {1},

pages = {81-101},

title = {Diffusion limit for the phenomenon of random genetic drift},

url = {http://eudml.org/doc/219261},

volume = {27},

year = {2000},

}

TY - JOUR

AU - Marciniak, Anna

TI - Diffusion limit for the phenomenon of random genetic drift

JO - Applicationes Mathematicae

PY - 2000

VL - 27

IS - 1

SP - 81

EP - 101

AB - 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.

LA - eng

KW - genetic drift; telegraph equations; singularly perturbed systems; diffusion equation; random walk; modified Chapman-Enskog procedure

UR - http://eudml.org/doc/219261

ER -

## References

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- [9] D. Ludwig, Stochastic Population Theories, Lecture Notes in Math. 3, Springer, Berlin, 1974.
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- [14] E. Zauderer, Partial Differential Equations of Applied Mathematics, Wiley, 1988. Zbl0551.35002

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