(Use of spreadsheet software recommended) This problem explores more thoroughly the generation-by-generation population dynamics seen in Exercise S8. Since the math can quickly become very complicated...

(Use of spreadsheet software recommended) This problem explores more thoroughly the generation-by-generation population dynamics seen in Exercise S8. Since the math can quickly become very complicated and tedious, it is much easier to do this analysis with the aid of a spreadsheet. Again, consider a population with two types, X and Y, with a payoff table as follows:

Recall that the population dynamics from generation to generation are given by:

Consider an evolutionary game between green types and purple types, with a payoff table as follows:

In terms of the parameters a, b, c, and d, find the conditions that will guarantee a stable polymorphic equilibrium.