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Uniqueness of polymorphism for a discrete, selection-migration model with genetic dominance. (English) Zbl 1177.92028

Elaydi, Saber (ed.) et al., Advances in discrete dynamical systems. Proceedings of the 11th international conference on difference equations and applications (ICDEA 06), Kyoto, Japan, July 24–28, 2006. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-49-5/hbk). Advanced Studies in Pure Mathematics 53, 319-331 (2009).
Summary: 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.
For the entire collection see [Zbl 1170.39300].

MSC:

92D15 Problems related to evolution
39A60 Applications of difference equations
37N25 Dynamical systems in biology
39A10 Additive difference equations
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