English

Quantitative diffusion approximation for the Neutral $r$-Alleles Wright-Fisher Model with Mutations

Probability 2024-07-15 v1

Abstract

We apply a Lindeberg principle under the Markov process setting to approximate the Wright-Fisher model with neutral rr-alleles using a diffusion process, deriving an error rate based on a function class distance involving fourth-order bounded differentiable functions. This error rate consists of a linear combination of the maximum mutation rate and the reciprocal of the population size. Our result improves the error bound in the seminal work [PNAS,1977], where only the special case r=2r=2 was studied.

Keywords

Cite

@article{arxiv.2407.09102,
  title  = {Quantitative diffusion approximation for the Neutral $r$-Alleles Wright-Fisher Model with Mutations},
  author = {Peng Chen and Jie Xiong and Lihu Xu and Jiayu Zheng},
  journal= {arXiv preprint arXiv:2407.09102},
  year   = {2024}
}
R2 v1 2026-06-28T17:38:23.481Z