Biological growth and spread modeled by systems of recursions. II. Biological theory.

The mathematical theory developed in Part I is applied to a selection-migration model in population genetics with sex-linked locus and to the host-vector or venereal disease epidemic model. In both models, a constant c*(xi) is found for each unit vector xi. The mathematical results imply that under certain initial conditions, the frequency of the advantageous gene in the male and female gametic outputs or the epidemic will spread at a speed c*(xi) in the direction xi as time goes to infinity. Time is measured in discrete nonoverlapping generations. In most cases, we can find a formula for c*(xi).