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    The migration into a natural population of a controlled population, e.g., a transgenic population, is studied using a one island selection-migration model. A 2-dimensional system of nonlinear difference equations describes changes in allele frequency and population size between generations. Biologically reasonable conditions are obtained which guarantee the existence and uniqueness of a polymorphic equilibrium in the cases of complete dominance and no dominance in fitness. This model may provide some useful information about the migration of transgenes into a natural population.

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    Selgrade, James F.; Roberds, James H. 2009. Uniqueness of polymorphism for a discrete, selection-migration model with genetic dominance. Advanced Studies in Pure Mathematics 53:319-331.

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