Dynamical Analysis of Density-dependent Selection in a Discrete one-island Migration Model

James Roberds; James F. Selgrade

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Dynamical Analysis of Density-dependent Selection in a Discrete one-island Migration Model

Informally Refereed

Authors:

James Roberds, James F. Selgrade

Year:

2000

Type:

Scientific Journal

Station:

Southern Research Station

Source:

Mathematical Biosciences 164 (2000) l-15

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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.

Keywords

selection, migration, genotype, density-dependence, bifurcation

Citation

Roberds, James H.; Selgrade, James F. 2000. Dynamical Analysis of Density-dependent Selection in a Discrete one-island Migration Model. Mathematical Biosciences 164 (2000) l-15