Download Answer the following questions

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.