# Evolution Chapter 20 Hints

HINT 20A: Fitness is proportional to W = (7/31)vA + (24/31)vB. Draw contours of fitness: For example, W = 1 = (7/31)vA + (24/31)vB is a downward-sloping straight line. The optimal survival maximizes fitness, given the constraint vA2 + vB2 ≤ 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 {vA, vB} 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 Tp with probability p. Of the other half, transmitted through males, a fraction (1 – u) are transmitted randomly through matings with PV females and the remaining half are transmitted via PU females and must be of type TP.

HINT 20H: Because the preference gene is not directly selected, its frequency within the TP background, uP, does not change as a result of nonrandom mating; similarly for uQ.

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.