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Updated: Dec 14, 2025

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
Published on: September 5, 2019
Quantitative approximation of the discrete Moran process by a Wright-Fisher diffusion
Gorgui Gackou1, Arnaud Guillin1, Arnaud Personne2
1Laboratoire de Mathématiques Blaise Pascal, CNRS UMR 6620, Université Clermont-Auvergne, Avenue des Landais, 63177, Aubière, France.
Abstract:
The Moran discrete process and the Wright-Fisher model are the most popular models in population genetics. The Wright-Fisher diffusion is commonly used as an approximation in order to understand the dynamics of population genetics models. Here, we give a quantitative large-population limit of the error occurring by using the approximating diffusion in the presence of weak selection and weak immigration in one dimension. The approach is robust enough to consider the case where selection and immigration are Markovian processes, whose large-population limit is either a finite state jump process, or a diffusion process.
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