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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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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