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 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.

28 pages, 8 figures

References in corpus (4)

• Most undirected random graphs are amplifiers of selection for Birth-death dynamics, but suppressors of selection for death-Birth dynamics
• The duality of spatial death-birth and birth-death processes and limitations of the isothermal theorem
• Clonal interference and Muller's ratchet in spatial habitats
• Frequent asymmetric migrations suppress natural selection in spatially structured populations