Geodesic
Diffusion limit for the phenomenon of random genetic drift
Applicationes Mathematicae, Tome 27 (2000) no. 1, pp. 81-101.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/am-27-1-81-101
Keywords: genetic drift, telegraph equations, singularly perturbed systems, diffusion equation, random walk

Anna Marciniak 1

1 
@article{10_4064_am_27_1_81_101,
     author = {Anna Marciniak},
     title = {Diffusion limit for the phenomenon of random genetic drift},
     journal = {Applicationes Mathematicae},
     pages = {81--101},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {2000},
     doi = {10.4064/am-27-1-81-101},
     zbl = {0994.35019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am-27-1-81-101/}
}
TY  - JOUR
AU  - Anna Marciniak
TI  - Diffusion limit for the phenomenon of random genetic drift
JO  - Applicationes Mathematicae
PY  - 2000
SP  - 81
EP  - 101
VL  - 27
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am-27-1-81-101/
DO  - 10.4064/am-27-1-81-101
LA  - en
ID  - 10_4064_am_27_1_81_101
ER  - 
%0 Journal Article
%A Anna Marciniak
%T Diffusion limit for the phenomenon of random genetic drift
%J Applicationes Mathematicae
%D 2000
%P 81-101
%V 27
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/am-27-1-81-101/
%R 10.4064/am-27-1-81-101
%G en
%F 10_4064_am_27_1_81_101
Anna Marciniak. Diffusion limit for the phenomenon of random genetic drift. Applicationes Mathematicae, Tome 27 (2000) no. 1, pp. 81-101. doi : 10.4064/am-27-1-81-101. http://geodesic.mathdoc.fr/articles/10.4064/am-27-1-81-101/

Cité par Sources :