Global dynamics of a selection model for the growth of a population with genotypic fertility differences
A population growth model is considered for a one locus two allele problem with selection based entirely on fertility differences. A local stability analysis is carried out for the critical points — which include possible polymorphic states — of the resulting nonlinear differential equations. The methods of dynamical systems theory are applied to obtain limiting genotypic proportions for every initial state. Thus the results are global and there are no periodic solutions.