Note: For full credit you must show your work.(1) (25 pts) Inbreeding coefficients in the classics. Unless stated otherwise, assume all ancestors
have inbreeding coefficients of zero (fA = 0 ). Sketch the pedigree for each problem. Label the
inbreeding loops clearly.
0.004
# of Windows
0 300 700
7
9
23
25
27
29
33
35
37
5
3
0.000
7
9
23
25
27
29
33
35
37
5
3
0.004
0.000
Chromosome
Heterozygosity (bp )
0.000 0.005
Heterozygosity (bpï)
# of Windows
0 300 700
7
9
23
25
27
29
33
35
37
5
3
Plot 2
Isle RoyDOH0
Chromosome
0.004
# of Windows
0 300 700
Ethiopia
7
9
23
25
27
29
33
35
37
5
3
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uploaded
0.000
0.005 or distributed.
Chromosome
F
# of Windows
0 300 700
7
9
23
25
27
29
33
35
37
3
0.000 0.005 0.000 0.005
ï
Chromosome Heterozygosity (bp
Heterozygosity
(bpï)
)
5
0.004
0.000
Heterozygosity (bpï)
70.000
0.004
9
3
5
7
9
23
25
27
29
33
35
37
# of Windows
23
25 0 300
700
27
29
33
35
37
D
0.000
3
5
Heterozygosity
(bpï)
1
Mexico PlotMinnesota
Chromosome
Heterozygosity (bpï)
0.004
0.000
# of Windows
0 300 700
0.000 0.005
Heterozygosity (bpï)
0.000
7
9
23
25
27
29
33
35
37
F
B
0.000 0.005
Heterozygosity (bpï)
0.004
# of Windows
0 300 700
E
(2) (10 pts) Below plots of the heterozygosity across the genome of two different wolves.
Essentially the genome was divided into many windows and the proportions of SNPs in that
window that are heterozygous is plotted. One plot is from a wolf population that has experienced
extensive inbreeding over the past few generations. The other plot is from a wolf population that
0.000
0.000 0.005
has not experienced inbreeding. Which
plot0.005
is from
the genome from the inbred wolf population
ï
Chromosome
Chromosome
Heterozygosity
(bp
)
Heterozygosity
(bpï)
(plot 1 or plot 2)? Why? Be sure to explain what inbreeding does to heterozygosity across the
genome.
5
3
0.004
0.000
Heterozygosity (bpï)
(d) Assume there is a recessive allele that causes a genetic disease. The frequency of the
D
allele is 1/150. What is the probability that Katherine will be affected by the disease?
Tibet Joffrey (under both scenarios you calculated in c)?
Ethiopia
Paddy?
C
# of Windows
0 300 700
Heterozygosity (bpï)
(c) In Game of Thrones, the evil king Joffrey is secretly the son of twins Jaime and Cersei
Lannister. First, calculate the inbreeding coefficient of Joffrey if Jaime and Cersei are
non-identical twins. Second, for the sake of argument, calculate it assuming Jaime and
0.000 0.005
Cersei are identical twins (though
of course
this isn’t biologically possible).
ï
Chromosome
Heterozygosity (bpï)
Heterozygosity (bpï)
(b) In the classic coming-of-age film Blue Lagoon, first cousins Richard (Chris Atkins)
B
and Emmeline (Brooke Shields) are stranded on an island and develop an attraction to
Xinjiang
Minnesota
each other in which Emmeline eventually ends up bearing a child,
Paddy. What is the
inbreeding coefficient of Paddy?
A
# of Windows
0 300 700
(a) In the classic award winning film Chinatown that takes place in Los Angeles in the
1930s, the main character Evelyn (Faye Dunnaway) admits in a climactic scene to Jake
Gittes (Jack Nicholson) about her relationship to the character Katherine: “She’s my sister
and my daughter!” Evelyn bore Katherine to her own father Noah Cross when she was
15. What is Katherine’s inbreeding coefficient?
Heterozygosity (bpï)
# of Windows
0 300 700
EEB 135/235: POPULATION GENETICS – HOMEWORK 2
Heterozygosity (bpï)
0.000 0.005
Heterozygosity (bpï)
(3) (25 pts) (a) Asian rice (Oryza sativa) is an important crop that can self-fertilize. At a particular
locus, the three genotypes have the following frequencies:
AA = 0.49
AB = 0.36
BB = 0.15
What are the genotype frequencies after 2 generations of self-fertilization? What are the allele
frequencies after 2 generations of self-fertilization?
(b) Other plants have a mixture of mating systems. This means they can self-fertilize or cross
pollinate. Wild soybeans (Glycine soja) are an example of a plant having a mixed mating system.
They self-fertilize approximately 87% of the time, but outcross 13% of the time.
Given the same initial genotype frequencies as stated above, what are the genotype frequencies
after 2 generations of mating where 87% of the plants self-fertilize and 13% outcross? What are
the allele frequencies after 2 generations of this mating?
(4) (15 pts) Imagine that you start with a population of completely heterozygous individuals (i.e.
they all have the Aa genotype) that can only self-fertilize. (a) Derive an equation to reflect the
frequency of the heterozygous genotype in an arbitrary generation t as a function of the initial
heterozygosity in generation 0. (b) How many generations will it take for the AA homozygous
genotype to reach a frequency of at least 0.5? You may use a spreadsheet program for this part of
the question (Excel or Google doc, etc), but please save and submit your output. You can also
tackle part b analytically, if you prefer.
(5) (25 pts) As part of the 1000 Genomes Project, you collect data from two different pairs of
SNPs. The two SNPs within each pair are 28kb apart.
At the first pair of SNPs, the following haplotype frequencies are observed:
PAB
PAb
PaB
Pab
= 0.00
= 0.20
= 0.60
= 0.20
Calculate (a) the allele frequencies at each locus, (b) the coefficient of linkage
disequilibrium, D, and (c) r2 (d) and D’.
At the second pair of SNPs, the following haplotype frequencies are observed:
PAB
PAb
PaB
Pab
= 0.50
= 0.20
= 0.15
= 0.15
Calculate (e) the allele frequencies at each locus, (f) the coefficient of linkage
disequilibrium, D, (g) r2 , (h) D’, (i) and the χ2 test statistic, degrees of freedom, and pvalue for a test of linkage disequilibrium. Assume a sample size of 400 individuals. Are
the loci in linkage equilibrium?
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(i) Which pair of SNPs (the first pair, or the second pair) shows evidence for
recombination? Why?
(6) (Graduate student question: Extra Credit for undergrads, 25 pts) Imagine a pair of brothers.
Assume that the alleles in their parents are not IBD with each other. (a) Calculate the probability
that the brothers will share 2 alleles Identical by Descent (IBD). (b) Calculate the probability that
the brothers will share 1 allele IBD. (c) Calculate the probability that the brother share 0 alleles
IBD. (d) One of the brothers has the 17,18 genotype at the D18S51 locus. Calculate the
probability that the other brother has that same genotype. Note, the frequency of the 17 allele in
the population is 0.1556 and the frequency of the 18 allele is 0.0918.
I thank John Novembre and Chuck Taylor for several of these problems.
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