2011
DOI: 10.1080/15326349.2011.593411
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Population Genetics Models with Skewed Fertilities: A Forward and Backward Analysis

Abstract: Discrete population genetics models with unequal (skewed) fertilities are considered, with an emphasis on skewed versions of Cannings models, conditional branching process models in the spirit of Karlin and McGregor, and compound Poisson models. Three particular classes of models with skewed fertilities are investigated, the Wright-Fisher model, the Dirichlet model, and the Kimura model. For each class the asymptotic behavior as the total population size N tends to infinity is investigated for power law fertil… Show more

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Cited by 27 publications
(51 citation statements)
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“…Mathematically, this is described as follows: in a Kingman coalescent, Ne scales linearly with N, whereas for MMC models, Ne can be a fraction of N or scales on the order of log(N) (Huillet & Möhle 2011). In other words, it is expected that under MMC models, the effective population size measured from polymorphism data yields significantly smaller values than the number of observable individuals N in the population or the species (see below for example).…”
Section: Patterns Of Polymorphism Under MMCmentioning
confidence: 99%
“…Mathematically, this is described as follows: in a Kingman coalescent, Ne scales linearly with N, whereas for MMC models, Ne can be a fraction of N or scales on the order of log(N) (Huillet & Möhle 2011). In other words, it is expected that under MMC models, the effective population size measured from polymorphism data yields significantly smaller values than the number of observable individuals N in the population or the species (see below for example).…”
Section: Patterns Of Polymorphism Under MMCmentioning
confidence: 99%
“…Note that (4) corrects the erroneous formula at the top of p. 536 of the original paper [1] , and that (5) is the simpler formula that appeared in the original paper but is valid only in special cases. In the following it is clarified which compound Poisson models satisfy (5).…”
Section: Correctionsmentioning
confidence: 99%
“…[1] does not hold for arbitrary symmetric compound Poisson models. It should be replaced by the following Theorem 2.3, which clarifies that many symmetric compound Poisson models are in the domain of attraction of the Kingman coalescent.…”
Section: Correctionsmentioning
confidence: 99%
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