Bridging Wright-Fisher and Moran models

TL;DR

This paper introduces a new model that unifies the Wright-Fisher and Moran models in population genetics, providing analytical insights into fixation probabilities, times, and coalescent processes.

Contribution

It presents a simple, tractable model bridging two fundamental population genetics models and extends it to include fluctuating parameters and selection effects.

Findings

Derived fixation probabilities and times under the new model.

Showed convergence to Kingman's coalescent.

Extended model to include fluctuating population parameters and selection.

Abstract

The Wright-Fisher model and the Moran model are both widely used in population genetics. They describe the time evolution of the frequency of an allele in a well-mixed population with fixed size. We propose a simple and tractable model which bridges the Wright-Fisher and the Moran descriptions. We assume that a fixed fraction of the population is updated at each discrete time step. In this model, we determine the fixation probability of a mutant and its average fixation and extinction times, under the diffusion approximation. We further study the associated coalescent process, which converges to Kingman's coalescent, and we calculate effective population sizes. We generalize our model, first by taking into account fluctuating updated fractions or individual lifetimes, and then by incorporating selection on the lifetime as well as on the reproductive fitness.