A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher Models
Discrete ancestral problems arising in population genetics are investigated. In the neutral case, the duality concept has been proved of particular interest in the understanding of backward in time ancestral process from the forward in time branching population dynamics. We show that duality formula...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
|
| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2009/714701 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832548888905515008 |
|---|---|
| author | Thierry E. Huillet |
| author_facet | Thierry E. Huillet |
| author_sort | Thierry E. Huillet |
| collection | DOAJ |
| description | Discrete ancestral problems arising in population genetics are investigated.
In the neutral case, the duality concept has been proved of
particular interest in the understanding of backward in time ancestral process
from the forward in time branching population dynamics. We show that
duality formulae still are of great use when considering discrete nonneutral
Wright-Fisher models. This concerns a large class of nonneutral models with
completely monotone (CM) bias probabilities. We show that most classical
bias probabilities used in the genetics literature fall within this CM class or
are amenable to it through some “reciprocal mechanism” which we define.
Next, using elementary algebra on CM functions, some suggested novel evolutionary
mechanisms of potential interest are introduced and discussed. |
| format | Article |
| id | doaj-art-6a64e315176f4dd9aab1e8b2cbf7779e |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-6a64e315176f4dd9aab1e8b2cbf7779e2025-02-03T06:12:44ZengWileyJournal of Probability and Statistics1687-952X1687-95382009-01-01200910.1155/2009/714701714701A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher ModelsThierry E. Huillet0Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRS-UMR 8089, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, FranceDiscrete ancestral problems arising in population genetics are investigated. In the neutral case, the duality concept has been proved of particular interest in the understanding of backward in time ancestral process from the forward in time branching population dynamics. We show that duality formulae still are of great use when considering discrete nonneutral Wright-Fisher models. This concerns a large class of nonneutral models with completely monotone (CM) bias probabilities. We show that most classical bias probabilities used in the genetics literature fall within this CM class or are amenable to it through some “reciprocal mechanism” which we define. Next, using elementary algebra on CM functions, some suggested novel evolutionary mechanisms of potential interest are introduced and discussed.http://dx.doi.org/10.1155/2009/714701 |
| spellingShingle | Thierry E. Huillet A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher Models Journal of Probability and Statistics |
| title | A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher Models |
| title_full | A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher Models |
| title_fullStr | A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher Models |
| title_full_unstemmed | A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher Models |
| title_short | A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher Models |
| title_sort | duality approach to the genealogies of discrete nonneutral wright fisher models |
| url | http://dx.doi.org/10.1155/2009/714701 |
| work_keys_str_mv | AT thierryehuillet adualityapproachtothegenealogiesofdiscretenonneutralwrightfishermodels AT thierryehuillet dualityapproachtothegenealogiesofdiscretenonneutralwrightfishermodels |