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Updated: Aug 15, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
Dynamical analysis of density-dependent selection in a discrete one-island migration model
1USDA Forest Service, Southern Research Station, Southern Institute of Forest Genetics, Harrison Experimental Forest, 23332 Hwy. 67, Saucier, MS 39574, USA. roberds@datasync.com
Abstract:
A system of non-linear difference equations is used to model the effects of density-dependent selection and migration in a population characterized by two alleles at a single gene locus. Results for the existence and stability of polymorphic equilibria are established. Properties for a genetically important class of equilibria associated with complete dominance in fitness are described. The birth of an unusual chaotic attractor is also illustrated. This attractor is produced when migration causes chaotic dynamics on a boundary of phase space to bifurcate into the interior of phase space, resulting in bistable genetic polymorphic behavior.
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