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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
39/2014

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

Tat Dat Tran, Julian Hofrichter and Jürgen Jost

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.

Received:
Mar 21, 2014
Published:
Apr 7, 2014

Related publications

inJournal
2013 Journal Open Access
Tat Dat Tran, Julian Hofrichter and Jürgen Jost

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

In: Theory in biosciences, 132 (2013) 2, pp. 73-82