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