# Evolution Chapter 17 Hints

HINT 17A: The ratio (p/q) is initially very close to p0 = 10–5 and changes each generation by a factor 1.1.

HINT 17B: Find an expression for pt + 1/qt + 1 in terms of pt, and then consider the change in frequency of the P type in discrete time Δp = pt + 1pt.

HINT 17C: First, think of the rates of increase due to mutation and selection separately.

HINT 17D: Use the expression for t from iii).

HINT 17E: You only need to find W for the two genotypes at a few points (N = 0, 0.5, 1, 2, say) and draw a smooth curve between these.

HINT 17F: Compare the fitness of both types.

HINT 17G: Find expressions for the number of individuals in each class from year to year and use this to construct a table of the population.

HINT 17H: The average excess of an allele is defined as the the average fitness of genes carrying that allele, minus the overall average.

HINT 17I: At equilibrium, the two patterns must give equal fitness.

HINT 17J: Calculate the change in phenotype frequency over one generation; start by considering the fitness of each allele.

HINT 17K: Check the fitness of the population at p = 1/2.

HINT 17L: Think about the fitnesses of the two alleles.

HINT 17M: You need to assume that selection is weak (i.e., s << 1).

HINT 17N: See Box 28.2. The first step is to think of elapsed time as a function of allele frequency:

HINT 17O: Assume that the alleles are combined randomly, in linkage equilibrium; this is a fairly good approximation for unlinked loci. Then, for each pair of allele frequencies, work out the frequencies of the four genotypes and hence the average fitness. By writing out the mean fitness on a grid (say, at pA, pB = 0, 0.25, 0.5, 0.75, 1), you can sketch the contours of mean fitness.

HINT 17P: Differentiate the expression for in i) with respect to pA.

HINT 17Q: Substitute the rate of increase back into the expression from i).

HINT 17R: The ratio of allele frequencies with WP/WQ = 1.2 is given by Eq. 17.2 (p. 468); thus, work out the allele frequency after t generations.

HINT 17S: Graphs can be sketched quickly by finding allele frequencies at a few chosen times and filling in between—for example, choosing p0 = 0.01, t = 0, 10, 20, 30, 40.