Bridging Wright-Fisher and Moran models

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 in the diffusion approximation, as well as the effective population size. 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.