The model of bacterial selection includes no frequency-dependence, meaning that the per capita production of the different types does not depend on the fraction of types in the population. Each of the following discrete-time dynamical systems for the number of mutants at and the number of wild type bt depends on the fraction of mutants pt. For each, explain in words how each type is affected by the frequency of the mutants, find the discrete-time dynamical system for pt, find the equilibria, evaluate their stability, and plot a cobweb diagram. Do any of them oscillate?
Suppose
at + 1 = 2(1 - pt)2at
bt + 1 = (1 + pt)bt.