The free energy method and the Wright-Fisher model with 2 alleles.

We systematically investigate the Wright-Fisher model of population genetics with the free energy functional formalism of statistical mechanics and in the light of recent mathematical work on the connection between Fokker-Planck equations and free energy functionals. In statistical physics, entropy increases, or equivalently, free energy decreases, and the asymptotic state is given by a Gibbs-type distribution. This also works for the Wright-Fisher model when rewritten in divergence to identify the correct free energy functional.

The evolution of moment generating functions for the Wright-Fisher model of population genetics.

We derive and apply a partial differential equation for the moment generating function of the Wright-Fisher model of population genetics.

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

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.