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The Infinitely-Many-Alleles Model with Selection as a Measure-Valued Diffusion

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Stochastic Methods in Biology

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 70))

Abstract

In [4], a diffusion model is constructed for a genetic system in which all alleles are selectively neutral and all mutants are new. The state of this model is the vector of order statistics of the gene frequencies. This reordering of the frequencies is necessary because of the assumption on mutation. Fixing the order of the alleles results in a model in which the sum of the gene frequencies is less than one for all positive time. Unfortunately, reordering makes it virtually impossible to study models with selection using this approach.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Utah, Salt Lake City, UT, 84112, USA

    S. N. Ethier

  2. Department of Mathematics, University of Wisconsin, Madison, Madison, WI, 53706, USA

    T. G. Kurtz

Authors
  1. S. N. Ethier
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  2. T. G. Kurtz
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Editor information

Editors and Affiliations

  1. National Institute of Genetics, Yata 1, 111 Mishima, Shizuoka-ken, 411, Japan

    Motoo Kimura

  2. Center for Stochastic Processes, Department of Statistics, University of North Carolina, 27514, Chapel Hill, NC, USA

    Gopinath Kallianpur

  3. Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya, 464, Japan

    Takeyuki Hida

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© 1987 Springer-Verlag Berlin Heidelberg

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Ethier, S.N., Kurtz, T.G. (1987). The Infinitely-Many-Alleles Model with Selection as a Measure-Valued Diffusion. In: Kimura, M., Kallianpur, G., Hida, T. (eds) Stochastic Methods in Biology. Lecture Notes in Biomathematics, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46599-4_6

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  • DOI: https://doi.org/10.1007/978-3-642-46599-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17648-0

  • Online ISBN: 978-3-642-46599-4

  • eBook Packages: Springer Book Archive

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