Behavior of different numerical schemes for random genetic drift
| dc.contributor.author | Xu, S | |
| dc.contributor.author | Chen, M | |
| dc.contributor.author | Liu, C | |
| dc.contributor.author | Zhang, R | |
| dc.contributor.author | Yue, X | |
| dc.date.accessioned | 2023-05-31T07:29:22Z | |
| dc.date.available | 2023-05-31T07:29:22Z | |
| dc.date.issued | 2019-09-01 | |
| dc.date.updated | 2023-05-31T07:29:21Z | |
| dc.description.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. | |
| dc.identifier.issn | 0006-3835 | |
| dc.identifier.issn | 1572-9125 | |
| dc.identifier.uri | ||
| dc.language | en | |
| dc.publisher | Springer Science and Business Media LLC | |
| dc.relation.ispartof | BIT Numerical Mathematics | |
| dc.relation.isversionof | 10.1007/s10543-019-00749-4 | |
| dc.subject | Science & Technology | |
| dc.subject | Technology | |
| dc.subject | Physical Sciences | |
| dc.subject | Computer Science, Software Engineering | |
| dc.subject | Mathematics, Applied | |
| dc.subject | Computer Science | |
| dc.subject | Mathematics | |
| dc.subject | Random genetic drift | |
| dc.subject | Degenerate equation | |
| dc.subject | Conservations of probability and expectation | |
| dc.subject | Finite volume method | |
| dc.subject | Finite difference method | |
| dc.subject | Finite element method | |
| dc.subject | Numerical viscosity and numerical anti-diffusion | |
| dc.subject | DIFFUSION EQUATION | |
| dc.subject | FIXATION | |
| dc.title | Behavior of different numerical schemes for random genetic drift | |
| dc.type | Journal article | |
| duke.contributor.orcid | Xu, S|0000-0002-8207-7313 | |
| pubs.begin-page | 797 | |
| pubs.end-page | 821 | |
| pubs.issue | 3 | |
| pubs.organisational-group | Duke | |
| pubs.organisational-group | Duke Kunshan University | |
| pubs.organisational-group | DKU Faculty | |
| pubs.publication-status | Published | |
| pubs.volume | 59 |
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