.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.
