WHEN CAN THE DISCRETE MORAN PROCESS BE REPLACED BY WRIGHT-FISHER DIFFUSION?
Résumé
The Moran discrete process and the Wright-Fisher model
are the most popular models in population genetics. It is common to
understand the dynamics of these models to use an approximating diffusion
process, called Wright-Fisher diffusion. Here, we give a quantitative
large population limit of the error committed by using the approximation
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, with limits
jump or diffusion processes.
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