Week 1: One-locus Neutral Models (September 5)

Readings:

• Hartl and Clark 45-57 and 62-73 (Hardy-Weinberg)

Problems (due September 10):

• Hartl and Clark page 50: Problem 2.1 [Don't hand in].
• Hartl and Clark page 57: Problem 2.3 [Don't hand in].
• Hartl and Clark page 89: Problems 4, 9, 11 [Hand in].

Week 2: One-locus and Two-locus Models of Selection (September 10/12)

Readings:

• Hartl and Clark 199-225 (Selection)
• Hartl and Clark 73-87 (Two-locus neutral model)
• Hartl and Clark 239-240 (Epistasis)

Problems (due September 17):

• Hartl and Clark page 253: Problem 3.
• How many generations would it take for linkage disequilibrium to be less than 10% of its original value when r=1/2? When r=0.01? [Assume a two-locus model with random mating and no selection.]
• Compare Table 5.1 to 5.2 and equation 5.2 to 5.10 in Hartl and Clark. Equation 5.2 is the general solution to the haploid model and predicts the future ratio of allele frequencies based on the current ratio of allele frequencies and the amount of intervening time. (a) Show that equation 5.10 for the diploid model of selection cannot be written as (p'/q') = W*(p/q) where W is a constant that depends only on the fitnesses and not on the allele frequencies. (b) Show that W is a constant, however, when the fitness effects of each allele contribute multiplicatively to fitness such that w11 = w1*w1, w12 = w1*w2, and w22 = w2*w2. (c) For the model considered in (b), what would the ratio of allele frequencies equal after t generations of selection? (Compare your result to equation 5.2.)

Week 3: Mutation and Non-random Mating (September 17/19)

Readings:

• Hartl and Clark 151-157, 226-229, 182-187 (Mutation)
• Hartl and Clark 257-275, 294-295 (Non-Random Mating)

Optional reading:

• Drake et al (1998) Rates of spontaneous mutation. Genetics 148: 1667-1686.

Problems (due September 24):

• Hartl and Clark page 193: Problem 6, 9 (assume no selection).
• Hartl and Clark page 254: Problem 14.
• Hartl and Clark page 312: Problem 7, 10 (assume F₀ = 0), 13.

Week 4: Modifier models and the Coalescent (September 24/26)

Readings:

• Hartl and Clark 128-145 (Coalescent)
• The evolution of haploid and diploid life cycles (extracted from Otto and Day (2005) A Biologist's Guide to Mathematical Models, Princeton University Press)

Problems (due October 1):

• Question: In modifier models of recombination, where there is a modifier of recombination (M) that alters the recombination rate between two selected loci (A and B), the recombination rates are typically arbitrary between the loci, such that the recombination rate between the modifier locus and the A locus is set to R and the recombination rate between the A and B loci depends on the modifier genotype (say, r_MM, r_Mm, and r_mm). For clarity, assume that the species is haploid (coming together for a short diploid phase between syngamy and meiosis) and that the gene order is M-A-B. (a) As described, the modifier only influences the recombination rate between the A and B loci, but if the modifier's genotype alters the recombination rate between M and A as well (say, R_MM, R_Mm, and R_mm), then it turns out that two of these three recombination rates never enter into the recursion equations. Which ones and why? [Think about the genotypes in which recombination between M and A can affect offspring genotypes.] Consequently, say what R refers to in the standard model (R_MM, R_Mm, or R_mm)? (b) Felsenstein and Yokayama (1976) pointed out that in certain cases in this modifier model "there is no sharp distinction between individual selection and group selection." Specifically, if R = 0 and r_MM > 0, but r_Mm = r_mm = 0, then this haploid population can be split into two groups between which there is no gene flow: M individuals and m individuals. Explain why there is no gene flow between these sub-populations in this case.
• Hartl and Clark page 148: Problems 18, 20, 21.

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