COMP 571
Bioinformatics: Sequence Analysis
Homework Assignment #4
Date Assigned: 28 October 2010.
Date Due: 4 November 2010.
1. Suppose that allele A is initially fixed in a population, and that it has a mutation rate of 10−5 to a, and that
there is no back (reverse) mutation. What will be the frequency of allele a in the population exactly after 2
generations? If there were back mutation, at the same rate as the forward mutation, what would the result be?
2. When A → a at rate 10−5 and a → A at rate 10−6 , what will be the equilibrium allele frequency in an infinitely
large population? How long will it take the population to move half way to its equilibrium starting from fixation
for A? How long will it take the population to move half way to its equilibrium starting from equal frequencies
of the two alleles?
3. Using the theory we developed for the coalescent with mutation, describe an algorithm for simulating the evolution of a set of alleles back in time, assuming the events that can occur are coalescence and mutation.
4. Assume a population at generation 0 in linkage equilibrium for two loci 1 (alleles A and a) and 2 (alleles B and
b), and the forward/backward mutation rates are u1 and v1 , respectively, for locus 1 and u2 and v2 , respectively,
for locus 2. Give formulas for the frequencies of AB, Ab, aB, and ab after mutation (no recombination). Is
there LD after mutation?
5. If we consider a population with partial self-fertilization (a randomly chosen fraction s of the population selfing
in each generation, and the rest mating at random), what will be the mutational equilibrium of allele frequency
and of genotype frequency?
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