# Consider a population with two types, X and Y, with a payoff table as follows: (a) Find the fitness.

Consider a population with two types, X and Y, with a
payoff table as follows:

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Consider a population with two types, X and Y, with a payoff table as follows: (a) Find the fitness.
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(a) Find the fitness for X as a function of x, the
proportion of X in the population, and the fitness for Y as a function of x.
Assume that the population dynamics from generation to generation conform to
the following model:

where xt is the proportion of X in the population in
period t, xt+1 is the proportion of X in the population in period t + 1, FXt is
the fitness of X in period t, and FYt is the fitness of Y in period t.

(b) Assume that x0, the proportion of X in the
population in period 0, is 0.2. What are FX0 and FY0?

(c) Find x1, using x0, FX0,
FY0, and the model given above.

(d) What are FX1 and FY1?

(e) Find x2 (rounded to five decimal places).

(f) What are FX2 and FY2 (rounded
to five decimal places)?