Equilibrium and nonequilibrium attractors for a discrete, selection-migration model
This study presents a discrete-time model for the effects of selection and immigration on the demographic and genetic compositions of a population. Under biologically reasonable conditions, it is shown that the model always has an equilibrium. Although equilibria for similar models without migration must have real eigenvalues, for this selection-migration model we illustrate a Hopf bifurcation which produces longterm stable oscillations in allele frequency and population density. The interplay between the selection parameters in the fitness functions and the migration parameters is displayed by using migration parameters to reverse destabilizing bifurcations that occur as intrinsic density parameters are varied. Also, the rich dynamics for this selection-migration model are illustrated by a period-doubling cascade resulting in a pulsating strange attractor.