(Use of spreadsheet software recommended) This problem explores more thoroughly the…

(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:

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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.

 

 

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