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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2009/714701 |
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| Summary: | 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. |
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| ISSN: | 1687-952X 1687-9538 |