HINT 20A: Fitness is proportional to *W* = (7/31)*v*_{A} + (24/31)*v*_{B}. Draw contours of fitness: For example, *W* = 1 = (7/31)*v*_{A} + (24/31)*v*_{B} is a downward-sloping straight line. The optimal survival maximizes fitness, given the constraint *v*_{A}^{2} + *v*_{B}^{2} ≤ 1, and is where fitness contours just touch the trade-off curve in Figure P20.1.

HINT 20B: The answer does not require calculation.

HINT 20C: Calculate α and {*v*_{A}, *v*_{B}} for both specialists and generalists.

HINT 20D: Assume that deleterious alleles are mainly eliminated in heterozygotes.

HINT 20E: What values of *J* and *A* maximize overall fitness? See Problem 20.1.i).

HINT 20F: Calculate the decrease in relative fitness.

HINT 20G: Half of the *T* alleles are transmitted randomly through females, and so are of type *T*^{p} with probability *p*. Of the other half, transmitted through males, a fraction (1 – *u*) are transmitted randomly through matings with *P*^{V} females and the remaining half are transmitted via *P*^{U} females and must be of type *T*^{P}.

HINT 20H: Because the preference gene is not directly selected, its frequency within the *T*^{P} background, *u*_{P}, does not change as a result of nonrandom mating; similarly for *u*_{Q}.

HINT 20I: Use the approximation that (1 + *x*/2) ~ _{}.

HINT 20J: Find the overall change, multiplying together the ratios over successive generations.

HINT 20K: The net fitness is the product of mating success and survival (Fig. 20.3A,B).

HINT 20L: This compromise between mating success and survival maximizes overall fitness.

HINT 20M: Plot male fitness as a function of male quality assuming different levels of display of antler size.