Behavior of different numerical schemes for random genetic drift

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

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

Fingerprint

Genetic Drift
Fixation
Numerical Scheme
Predict
Unconditionally Stable
Finite Volume Method
Probability Density
Equilibrium State
Diffusion equation
Paul Adrien Maurice Dirac
Difference Method
Convection
Viscosity
Finite volume method
Unstable
Finite Element Method
Singularity
Gene
Genes
Term

All Science Journal Classification (ASJC) codes

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

Cite this

Xu, Shixin ; Chen, Minxin ; Liu, Chun ; Zhang, Ran ; Yue, Xingye. / Behavior of different numerical schemes for random genetic drift. In: BIT Numerical Mathematics. 2019 ; Vol. 59, No. 3. pp. 797-821.
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Behavior of different numerical schemes for random genetic drift. / Xu, Shixin; Chen, Minxin; Liu, Chun; Zhang, Ran; Yue, Xingye.

In: BIT Numerical Mathematics, Vol. 59, No. 3, 01.09.2019, p. 797-821.

Research output: Contribution to journalArticle

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