Equilibrium in Wright-Fisher models of population genetics

TL;DR

This paper introduces a new way to analyze equilibrium states in multivariate Wright-Fisher models by using probability ratios and transforms the drift component into a cubic parabola, offering a novel perspective on gene frequency dynamics.

Contribution

It presents a new formulation of equilibrium states using probability ratios and transforms the drift component into a cubic parabola in Wright-Fisher models.

Findings

Defined equilibrium states via probability ratio fluctuations

Transformed drift component into a cubic parabola

Provided new mathematical insights into gene frequency dynamics

Abstract

For multivariant Wright-Fisher models in population genetics, we introduce equilibrium states, expressed by fluctuations of probability ratio, in contrast to the traditionally used fluctuations, expressed by the difference between the current value of the random process and its equilibrium value. Then the drift component of the dynamic process of gene frequencies, primarily expressed as a ratio of two quadratic forms, is transformed into a cubic parabola with a certain normalization factor.