# When Can The Discrete Moran Process May Bereplaced By Wright-fisher Diffusion?

## TL;DR

This paper quantifies the error when approximating the discrete Moran process with the Wright-Fisher diffusion in population genetics, especially under weak selection and immigration, extending to Markovian processes.

## Contribution

It provides a quantitative large population limit of the approximation error, including cases with Markovian selection and immigration processes.

## Key findings

- Error bounds for diffusion approximation under weak selection and immigration
- Extension to Markovian processes with jump or diffusion limits
- Robust approach applicable to various population dynamics

## Abstract

The Moran discrete process and the Wright-Fisher modelare the most popular models in population genetics. It is common tounderstand the dynamics of these models to use an approximating diffusionprocess, called Wright-Fisher diffusion. Here, we give a quantitativelarge population limit of the error committed by using the approximationdiffusion in the presence of weak selection and weak immigrationin one dimension. The approach is robust enough to consider the casewhere selection and immigration are Markovian processes, with limitsjump or diffusion processes.