Behavior of different numerical schemes for random genetic drift

Shixin Xu, Minxin Chen, Chun Liu, Ran Zhang, Xingye Yue

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In the problem of random genetic drift, the probability density of one gene is governed by a degenerated convection-dominated diffusion equation. Dirac singularities will always be developed at boundary points as time evolves, which is known as the fixation phenomenon in genetic evolution. Three finite volume methods: FVM1-3, one central difference method: FDM1 and three finite element methods: FEM1-3 are considered. These methods lead to different equilibrium states after a long time. It is shown that only schemes FVM3 and FEM3, which are the same, preserve probability, expectation and positiveness and predict the correct probability of fixation. FVM1-2 wrongly predict the probability of fixation due to their intrinsic viscosity, even though they are unconditionally stable. Contrarily, FDM1 and FEM1-2 introduce different anti-diffusion terms, which make them unstable and fail to preserve positiveness.

Original languageEnglish (US)
Pages (from-to)797-821
Number of pages25
JournalBIT Numerical Mathematics
Volume59
Issue number3
DOIs
StatePublished - Sep 1 2019

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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