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Population Genetics — BI 515 — Exam 1, Spring 2013 Answer the following questions. Do you own work. Please type your answers in this document and submit electronically. All of the questions can be answered with one or a few sentences and/or numerical results. 1. Early doubters of Mendelian genetics pointed to the general lack of 3:1 phenotypic ratios in natural populations as evidence that Mendel’s results on peas were not generally applicable. Why is this argument flawed? 2. Provide a simple verbal explanation for why the probability of fixation for a new, neutral mutation is 1/(2N). 3. Explain the distinction between the terms autozygous and homozygous. 4. What factors influence effective population size in natural populations and what is the direction of their effects? 5. We have not yet considered models of natural selection, but you should be able to solve this problem using basic Mendelian and Hardy-Weinberg logic. Strong selection is one possible reason for a population deviating from Hardy-Weinberg equilibrium. Suppose that a gene has a dominant allele (A) and a recessive allele (a) and that survival during early life stages for individuals homozygous for the recessive allele is only 80% as high as for individuals with the dominant phenotype. hints: critical value for the χ2 a) If the population allele frequency is 0.7 A and 0.3 a in distribution with 1 df and pgeneration 1 adults, what are the expected proportions value = 0.05 is 3.84 of the three genotypes in generation 2 zygotes? 2 observed - expected) ( b) What are the allele frequencies and expected 2 c =å proportions of the three genotypes in generation 2 expected adults? (Assume that a very large number of offspring is produced and that 20% of aa individuals dies immediately, before a random sample of the remaining individuals is selected to form the adult population for the next generation.) c) Would a sample size of 1000 adults be enough to detect a significant deviation from Hardy-Weinberg equilibrium in the generation 2 adults? 6. Using the data presented in Table 2.3 in your text (pg. 20), calculate the probability that a randomly selected individual would match the genotype show in the table at right, which was derived from a blood smear at a crime scene: a) Probability: __________ b) If a suspect who was Asian had a matching genotype, how would you argue the case if you were the prosecutor? c) Likewise, if you were the defense attorney? Locus D3S1358 vWA D21S11 D18S51 D13S317 FGA D8S1179 D5S818 D7S820 Allele 1 15 17 30 13 11 20 13 11 9 Allele 2 15 19 32 16 11 24 13 12 12 Population Genetics — BI 515 — Exam 1, Spring 2013 7. Two genes with two alleles (A, a and B, b) are located on the same chromosome. a) If the frequency of “gametes” or “chromosomes” in a sample of 500 individuals (=1000 chromosomes) is as follows: AB 620, Ab 180, aB 80, ab 120, what is the level of linkage disequilibrium between the two genes as measured by D and r2? b) We did not discuss statistical tests for linkage, but can you describe an approach that could be used to test whether there is statistically significant linkage disequilibrium in the above sample (i.e., greater than expected by chance if the genes were unlinked)? c) OK, go ahead and calculate the test statistic and show your result. 8. The equation for Wright’s fixation index for a random-breeding population of size N is as follows: 1 æ 1 ö Ft = + ç1÷Ft-1 2N è 2N ø a) Explain in words the basic logic of this equation. b) Assuming F0 (F at time zero) = 0, what is the expected value of F after 10 generations for a population of size 50? 9. Consider the following sample of 6 gene sequences, with the alignment below showing only the variable positions along a sequence of 1000 bases. a) Calculate the number of segregating sites (S) and nucleotide diversity (∏ = the average number of pairwise mismatches)? b) Give two estimates of θ that can be derived from these data? c) Why might the two estimates of θ not match? Sample1 Sample2 Sample3 Sample4 Sample5 Sample6 A A A A T T A A A G A A G G G A A A C C C T T T C C T T T T T T T T C C G G G A A A T T T C C C G A A A A A T T T C C C 10. Briefly describe the Wright-Fisher model of random genetic drift. a) An experimental study using Drosophila randomly selected 8 males and 8 females to produce each successive generation, thus maintaining a constant population size of 2N = 32. The expected and observed results for this experiment are shown in Fig. 3.11 in your test. There is overall a reasonably good fit between observation and theory, but drift appears to have proceeded more quickly than expected in the experimental populations. What is a likely explanation for the discrepancy? Population Genetics — BI 515 — Exam 1, Spring 2013 11. (Fill in the blank!) In generations, the average time to coalescence for two randomly sampled alleles is the reciprocal of the probability of coalescence in a single generation (= _______ generations). Now consider the case where k alleles have been sampled. Why does it make sense that the average time until 2 of the k alleles coalesce is may want to use both words and equations to explain this. 4N ? You k(k -1) 12. The family patriarch Beauregard had two wives, with whom he had a son and daughter, respectively. They fell for the daughter and son, respectively, of Charles and Delilah, but the families became estranged and drifted apart. Years later, Elwood married Fiona, not realizing she was his half cousin once removed. a) What is the inbreeding coefficient of their son Alfonse? (you may want to redraw the genealogy to more clearly show all lines of descent) b) If the frequency of a genetic disorder (phenotype) caused by a completely recessive allele is 1 in a 1000 in the general population, how much more likely is A to be affected by this disease? 13. DeGiorgio et al. (2009, PNAS) examined genetic diversity in human populations. This is a portion of a figure from their paper, with each dot showing values for a different human population. a) Why do African and Native American populations differ so much in overall heterozygosity and linkage disequilibrium? Population Genetics — BI 515 — Exam 1, Spring 2013 14. CHALLENGE QUESTION: Download the CoalescentSimulator.py python code from the course web page and test whether it is producing results that are consistent with theoretical expectations. Specifically, how does tree height and tree length vary with k and N? A perfect answer will be two graphs, one showing tree height as a function of N with results for different values of k (both theoretical expectations and simulated results with standard errors) plotted as different data series, and the other the same for tree length. 15. SUPER CHALLENGE QUESTION: Download the CoalescentSimulator2.py python code from the course web page and test whether it is producing results that are consistent with theoretical expectations. This code adds the simulation of DNA sequences and mutations along the genealogy. The results of interest in this case are the number of segregating sites (S) and nucleotide diversity (π). Again, how do they vary with k and N and do the simulated results match theoretical expectation? ** A really good answer for both of these questions will require summarizing the results of lots of simulated data sets. To do this efficiently, you may need to add some lines of code to automate the process, calculate the parameters of interest, and output the data you need. If you know what you need to do but are not sure about how, I’m happy to give you some help on the coding.