|
Problem 13.1
Cystic fibrosis is caused by recessive alleles at a single gene, CFTR. In populations of European descent, it has an incidence at birth of up to approximately 1 in 2000 (p. 358).
|
| *i) |
What is the frequency of the recessive allele that is responsible for this disease?
|
| *ii) |
What fraction of marriages are at risk of bearing offspring with this disease?
|
|
Problem 13.2
A total of 2000 bp of homologous mitochondrial DNA were sequenced from ten individuals (1–10), which had been sampled from the same population of flightless beetles. Within this sample, 24 sites were polymorphic; these are shown in Table P13.1, together with the corresponding sites from an individual of a closely related species, labeled X. This second species also differed at 52 other sites that were identical within the sample of ten from the study species.
|
| *i) |
What is the chance that a site will be polymorphic?
|
| **ii) |
What is the chance that a randomly chosen pair of sequences will differ at a random site? In other words, what is the nucleotide diversity, π?
|
| **iii) |
What is the genealogy that describes the relationship between these sequences? Assume that each site has experienced only a single mutational change. HINT 13A
|
| **iv) |
Each of the two species in this study is found only on one oceanic island; these islands were originally joined, but they were separated by a rise in sea level 0.5 million years ago (Mya). Estimate the rate at which these sequences have accumulated mutations. HINT 13B
|
| **v) |
Estimate how long ago the most recent common ancestor (MRCA) of the sample of ten beetles lived.
|
| **vi) |
How accurate is the assumption that each site has experienced only one mutational change (a) within the study species and (b) between the species? What errors may be made by ignoring multiple mutational changes?
|
|
Problem 13.3
Figure 13.14 shows a genealogy of the region around the Adh gene in Drosophila melanogaster. This was estimated from data on 14 sequence variants, labeled as “+” or “–,” plus the fast/slow amino acid polymorphism (labeled “F” or “S”). HINT 13C (Table P13.2 shows a subset of these data: 27 sampled chromosomes showed 13 different haplotypes (labeled a–m).
|
| *i) |
Construct a genealogy connecting chromosomes a–k. How many mutational changes are there on this genealogy?
|
| **ii) |
How many mutational changes are needed to include l and m on this genealogy?
|
| **iii) |
If chromosomes l and m were produced by recombination, how many mutational changes must be assumed? HINT 13D
|
| **iv) |
Are there any pairs of sites where all four possible combinations are found (i.e., --, -+, +-, ++)? How could these be produced?
|
|
Problem 13.4
|
| *i) |
In a random DNA sequence, how often will stop codons occur?
|
| **ii) |
Suppose that a sequence coding for a protein 300 amino acids long is duplicated, so that there is no longer any selection to maintain its function. If random mutations occur at a rate of 10–8 per base pair per generation, how long will it be before a stop codon arises, and terminates translation prematurely? HINT 13E
|
|
Problem 13.5
Comparison of the rat and mouse sequences shows that the chance that these carry the same base at neutral sites is approximately 0.79. Similarly, comparison between mouse and human genomes gives a probability of identity at a single site of approximately 0.67.
|
| *i) |
Assuming that the rate of substitution at neutral, unconstrained sites is 3 × 10–9 per year, estimate the time when the common ancestor of rat and mouse lived and similarly for human and mouse.
|
| **ii) |
Figure P13.1 shows the relationship between these three species; α is the chance that a site does not change between the common ancestor of mouse and rat and either descendant species, and β is the chance that this common ancestor has the same state as in humans.
Write the probabilities of identity between mouse and rat and between human and mouse, given above, in terms of α and β, and hence estimate α and β. HINT 13F
|
| **iii) |
What is the chance that a neutral site would be the same in human, rat, and mouse?
|
| **iv) |
About 5000 segments of 100 bp are exactly the same among human, rat, and mouse. Is this number more than you would expect by chance? (The human genome has 2.9 × 109 bp.)
|
|
Problem 13.6
The genetic code is redundant: 64 possible triplets code for 20 amino acids and the stop signal that terminates translation (see Figs. 2.23 and 2.26).
|
| *i) |
What is the chance that a mutation at the first position of a triplet codon will not alter the amino acid that is coded (i.e., what is the chance that the mutation is synonymous)? HINT 13G
|
| **ii) |
Similarly, what is the chance that a mutation at the second or third positions is synonymous?
|
| ***iii) |
What would these probabilities be if the code were entirely random? HINT 13H
|
