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An introduction to the mathematical structure of the Wright-Fisher model of population genetics.

Tran TD, Hofrichter J, Jost J - Theory Biosci. (2012)

Bottom Line: In this paper, we develop the mathematical structure of the Wright-Fisher model for evolution of the relative frequencies of two alleles at a diploid locus under random genetic drift in a population of fixed size in its simplest form, that is, without mutation or selection.We establish a new concept of a global solution for the diffusion approximation (Fokker-Planck equation), prove its existence and uniqueness and then show how one can easily derive all the essential properties of this random genetic drift process from our solution.Thus, our solution turns out to be superior to the local solution constructed by Kimura.

View Article: PubMed Central - PubMed

Affiliation: Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany. trandat@mis.mpg.de

ABSTRACT
In this paper, we develop the mathematical structure of the Wright-Fisher model for evolution of the relative frequencies of two alleles at a diploid locus under random genetic drift in a population of fixed size in its simplest form, that is, without mutation or selection. We establish a new concept of a global solution for the diffusion approximation (Fokker-Planck equation), prove its existence and uniqueness and then show how one can easily derive all the essential properties of this random genetic drift process from our solution. Thus, our solution turns out to be superior to the local solution constructed by Kimura.

Show MeSH
Behaviour of the discrete solution in time  and k = 32 with p = 0.5
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Fig2: Behaviour of the discrete solution in time and k = 32 with p = 0.5

Mentions: This behaviour coincides with the discrete one (Figs. 2, 3):


An introduction to the mathematical structure of the Wright-Fisher model of population genetics.

Tran TD, Hofrichter J, Jost J - Theory Biosci. (2012)

Behaviour of the discrete solution in time  and k = 32 with p = 0.5
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4269093&req=5

Fig2: Behaviour of the discrete solution in time and k = 32 with p = 0.5
Mentions: This behaviour coincides with the discrete one (Figs. 2, 3):

Bottom Line: In this paper, we develop the mathematical structure of the Wright-Fisher model for evolution of the relative frequencies of two alleles at a diploid locus under random genetic drift in a population of fixed size in its simplest form, that is, without mutation or selection.We establish a new concept of a global solution for the diffusion approximation (Fokker-Planck equation), prove its existence and uniqueness and then show how one can easily derive all the essential properties of this random genetic drift process from our solution.Thus, our solution turns out to be superior to the local solution constructed by Kimura.

View Article: PubMed Central - PubMed

Affiliation: Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany. trandat@mis.mpg.de

ABSTRACT
In this paper, we develop the mathematical structure of the Wright-Fisher model for evolution of the relative frequencies of two alleles at a diploid locus under random genetic drift in a population of fixed size in its simplest form, that is, without mutation or selection. We establish a new concept of a global solution for the diffusion approximation (Fokker-Planck equation), prove its existence and uniqueness and then show how one can easily derive all the essential properties of this random genetic drift process from our solution. Thus, our solution turns out to be superior to the local solution constructed by Kimura.

Show MeSH