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  • 1
    Electronic Resource
    Electronic Resource
    The population genealogy of the infinitely-many neutral alleles model (1987)
    Springer
    Journal of mathematical biology 25 (1987), S. 381-391 
    Details
    ISSN: 1432-1416
    Keywords: Coalescent ; K-allele diffusions ; Population genealogy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A process analogous to Kingman's coalescent is introduced to describe the genealogy of populations evolving according to the infinitelymany neutral alleles model. The process records population frequencies in old and new classes, and labels the new classes in order of decreasing age. Its marginal distribution is characterized in a form which is amenable to explicit calculations and the transition densities of the associated K-allele models follow readily from this representation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00277163
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Dual processes and an invariance result for exchangeable models in population genetics (1985)
    Springer
    Journal of mathematical biology 23 (1985), S. 103-118 
    Details
    ISSN: 1432-1416
    Keywords: Dual processes ; Lines of descent ; Diffusion approximations ; Exchangeability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract By means of a representation as interactive particle systems, dual processes are constructed for a large class of exchangeable models in population genetics. It is shown that as the population size becomes large these dual processes tend in distribution to a particularly tractable limiting dual process. Properties of the models are analyzed using the duality relationship and approximate expressions are obtained for various quantities. Diffusion approximations follow easily from the invariance result.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276560
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The Wright-Fisher model with temporally varying selection and population size (1985)
    Springer
    Journal of mathematical biology 22 (1985), S. 21-29 
    Details
    ISSN: 1432-1416
    Keywords: Wright-Fisher model ; selective advantage ; ultimate homozygosity ; martingale methods ; coupling techniques ; fixation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Wright-Fisher model is considered in the case where the population size is random and the magnitude of the selective advantage of one of the alleles varies with time. The central question addressed is the possibility of ultimate genetic polymorphism. Partial results are obtained in the general case and complete results in the case where the population size and selective advantage are not density dependent. Bounds on the fixation probability are obtained when the selective advantage is constant.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276544
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    Paper (German National Licenses)
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