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The Dynamics of Migration–Selection Models

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Tutorials in Mathematical Biosciences IV

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 1922))

The evolution of the gene frequencies at a single multiallelic locus under the joint action of migration and selection is reviewed. The three models treated are in (1) discrete space and discrete time; (2) discrete space and continuous time; and (3) continuous space and continuous time. These models yield, respectively, a system of (1) nonlinear, first-order difference equations; (2) nonlinear, first-order differential equations; and (3) semilinear, parabolic partial differential equations. Among the questions discussed are the loss of a specified allele, the maintenance of a specified allele or every allele, the existence and stability of completely polymorphic equilibria, the weak- and strong-migration limits, and uniform (i.e., location-independent) selection. Many examples and unsolved problems are discussed.

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Authors and Affiliations

  1. Department of Ecology and Evolution, The University of Chicago, 1101 East 57th Street, Chicago, IL, 60637, USA

    T. Nagylaki

  2. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA

    Y. Lou

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  1. T. Nagylaki
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  2. Y. Lou
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Editors and Affiliations

  1. Mathematical Biosciences Institute, Ohio State University, 231 West 18th Avenue, Columbus, OH, 43210-1292, USA

    Avner Friedman

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Nagylaki, T., Lou, Y. (2008). The Dynamics of Migration–Selection Models. In: Friedman, A. (eds) Tutorials in Mathematical Biosciences IV. Lecture Notes in Mathematics, vol 1922. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74331-6_4

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