Download BIOL 464/GEN 535 Population Genetics

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BIOL 464/GEN 535 Population Genetics
Fall 2010
Test # 1, 09/30/2010
Please answer all questions unless otherwise specified. Show as much of your work as you can! Use the back
of the page and additional sheets as necessary.
1. Match each word to the correct definition by writing the corresponding letter in the box to the left. (10 pts)
Term
H Coefficient of
Relatedness
F Inbreeding
Coefficient
Definition
A A quantitative measure of one’s belief in the occurrence of a future event
B After one generation of random mating, genotype frequencies for a biallelic,
autosomal locus can be estimated as a binomial function of the allele
frequencies.
C Using general principles to reach conclusions about specific instances
D Different forms of an enzyme that are coded at the same locus
A Probability
J Mendel’s Law of
Independent
Segregation
G Coefficient of Kinship E The probability of sampling a heterozygous individual at a particular locus for a
population that is in Hardy-Weinberg Equilibrium
I Codominant
F The probability that two alleles at a locus will be identical by descent in a single
individual
B Hardy-Weinberg
G A measure of the relationship between two individuals, based on the probability
Principle
that an allele randomly selected from one individual will be identical by descent
to an allele randomly selected from the same locus in the other individual. This
is equivalent to the inbreeding coefficient of their hypothetical offspring
D Allozyme
H A measure of the relationship between two individuals, based on the proportion
of shared alleles that are identical by descent. This is equivalent to twice the
inbreeding coefficient of their hypothetical offspring
C Deductive Reasoning I Both alleles are apparent in a heterozygous genotype
E Expected
J During gamete formation, the segregation of alleles of one gene is independent
heterozygosity
of the segregation of alleles of another gene
2. The frequency of red-green color-blindness is 0.07 for men and 0.005 for women. If we sample one man and
one woman, calculate the probability that both will be color-blind. What are the assumptions of this
calculation? (10 points)
Note: you can take the shortcut of just multiplying the two genotype frequencies together, which yields the
same answer, but this is not strictly correct. But I still gave full credit for this approach.
3. a. What is the kinship coefficient of first cousins? (8 points)
b. What is the coefficient of relatedness of first cousins? (4 points)
4. A population of monkeyflowers (Mimulus guttatus) has 2 alleles (C1 and C2) for the locus CAX1, which
confers tolerance to heavy metals like Cd and Zn. The table below provides the number of genotypes
observed in seeds and seedlings collected from a strip mine near Nitro, West Virginia.
Genotype
C1C1
C1C2
C2C2
Number of Seeds
250
500
250
Number of Seedlings
225
450
10
a. Is there any evidence for departures of this locus from Hardy-Weinberg Equilibrium in the seeds? (10
points)
1
500
N12 250 
2
2  0.5.
p

N
1000
q=1-p = 1-0.5=0.5
N11 
O
250
500
250
E
p2
2pq
q2
E
250
500
250
Sum
chi-sq
0
0
0
0
p
q
0.5
0.5
No evidence for significant departures from Hardy-Weinberg expectations.
b. Is there any evidence for departures of this locus from Hardy-Weinberg Equilibrium in the seedlings? (10
points)
p
1
450
N 12 225 
2
2  0.66

N
685
N 11 
q=1-p = 1-0.66=0.34
O
225
450
10
E
p2
2pq
q2
E
chi-sq
296
309
80
Total
16.9 p
64.6 q
61.9
143.4
0.66
0.34
Reject the null hypothesis of no difference between observed and expected genotype frequencies. Therefore,
there is evidence for significant departures from Hardy-Weinberg expectations for the seedlings.
4. (continued)
c. What is the relative fitness of each genotype? (8 points)
N 11s
N12s
N 22 s
225
450
10
N 11
N
N
11 
 250  1
12  12  500  1
22  22  250  0.044
N
225
N
225
N
225
Ms
Ms
Ms
250
250
250
N
N
N
M
M
M
where N11S is the frequency after selection (i.e., in seedlings), and NM is the frequency of the best-performing
genotype.
d. What is the value of h? (4 points)
12 1  hs
1=1-hs
1=1-h(0.956) (see part e)
h=0
e. What is the value of s? (4 points)
22 1  s
0.044=1-s
s=0.956
Note: I should have asked this question before question d.
f. Provide a reasonable biological hypothesis to explain the observed genotype frequencies? (5 points)
The soils in the strip mine contain a high concentration of heavy metals, which can decrease survival of
monkeyflower seedlings. One of the CAX1 alleles, C1, confers tolerance to heavy metals and acts in a
completely dominant manner. Therefore, seedlings lacking the C1 allele (i.e., those with a C2C2 genotype)
had substantially lower survival than the other two genotypes, which caused a deviation from HardyWeinberg expectations due to the effects of selection against C2C2 seedlings.
5. In a large, isolated, randomly-mating population of cottonwood trees, you examine 10,000 seedlings and
discover 10 albinos. Assume that albinism is caused by a recessive allele at a single locus. When this
allele is homozygous, seedlings will die well before the age of reproduction (i.e., s = 1). This allele is
completely recessive, with no discernible difference in fitness between heterozygotes (carriers) and
individuals who do not carry the allele.
a. What is the frequency of carriers of the albino allele in this population? You can assume this population is
in Hardy-Weinberg equilibrium. (10 points)
b. How would you expect the frequency of this allele to change over time? Hint: no calculation is required (2
points)
This allele should gradually decline in frequency over time. However, it will persist for many generations at a
low frequency in heterozygous state, where it will essentially be invisible to selection.
Since I stated in part A that the population is in Hardy-Weinberg equilibrium, this second part of the question
was confusing, so nobody lost credit for it.
c. You want to start a breeding program using 10 individuals from this population. What is the probability of
choosing one or more carriers of this allele in your sample? (5 points)
*****PLEASE READ THIS*****
Short Answer. Graduate students answer any 3. Undergraduates answer any 2. Please aim for no more than a
paragraph (less than 150 words) per answer. (Undergrads: 15 points each; Grads: 10 points each)
6. How does the average fitness of a population change in response to directional selection? What assumptions
must be met for this condition to be maintained over evolutionary time?
The average fitness for a population should increase in response to directional selection, provided that 0≤h≤1
and there is genetic variation for the loci under selection. This will be maintained over evolutionary time as long
as diversity is maintained in the population, usually through mutation and gene flow.
7. What were the two major laws derived from Mendel’s work? Why were these essential to the development
of Population Genetics as a science of central importance for studies of organismal evolution?
1. Mendel’s Law of Independent Segregation: two members of a gene pair (alleles) at a single locus
segregate independently into gametes so that half of the gametes carry one allele and half carry the
other.
This provided the theoretical basis for predicting genotype and phenotype frequencies in future generations
based on current frequencies. This is fundamentally important in modeling evolution based on genetic variation,
a central tenet in Population Genetics.
2. Mendel’s Law of Independent Assortment: During gamete formation, the segregation of alleles of one
gene is independent of the segregation of alleles of another gene.
This laid the theoretical foundation for combining the effects of individual loci to extend the principles of
particulate inheritance so that they could explain variation in quantitative traits and gradual changes in
phenotype in response to selection. This law was incorrect, strictly speaking, for linked loci, but it did provide a
simple starting point for Mendelians in modeling phenotypic evolution.
8. What effect is inbreeding likely to have over many generations on:
a. Genotype frequencies in the absence of selection?
The frequency of heterozygote genotypes will decrease and homozygotes will increase due to inbreeding in the
absence of selection.
b. Allele frequencies in the absence of selection?
Allele frequencies should be unchanged assuming large population size, random mating, and no selection.
c. Expected heterozygosity?
Expected heterozygosity is a direct function of allele frequencies, and therefore should not change due to
inbreeding alone.
9. What determines the equilibrium genotype frequencies in an organism with a mixed mating system in the
absence of selection? What is the equilibrium frequency of heterozygotes in a population that is undergoing
complete selfing?
The selfing rate and the starting allele frequencies will determine the equilibrium frequency of heterozygotes in
such a population, assuming all other Hardy-Weinberg assumptions are met. Under complete selfing, there is
only a trivial equilibrium point at H=0. Heterozygosity will be eliminated in the absence of gene flow and
mutation.
10. Human beings typically carry many recessive lethal alleles in their genomes. How can you explain the
abundance of such alleles, given that they can cause such a drastic reduction in fitness? Be sure to use
principles that you have learned in this class thus far in justifying your answer.
Recessive alleles are essentially invisible to selection when in a heterozygous state because their effect is
masked by the dominant alleles. Therefore, such alleles can persist for a very long time at low allele frequencies
because the majority of individuals carrying these alleles will also have a wild-type allele that confers fitness
equivalent to wild-type homozygotes.
11. Hardy-Weinberg Equilibrium is almost invariably taught within the first couple of weeks of Population
Genetics classes. What is this law, and why is it fundamentally important in Population Genetics?
The law states that if a population is subject to random mating, a very large (theoretically infinite) size, no
migration, no selection (fecundity + mortality), and no mutation, then the allele frequencies will remain
constant, and the genotype frequencies will be a binomial expansion of the allele frequencies in the next
generation. This is fundamentally important because it serves as a null hypothesis for all phenomena in
population genetics. It also provides a mechanism for directly estimating genotype frequencies from allele
frequencies in populations that do not have severe departures from the assumptions. This has allowed the
derivation of a large number of equations describing the effects of processes such as genetic drift, selection,
and gene flow. The law also has practical implications, such as allowing the estimation of allele frequencies
for dominant loci based solely on the frequency of homozygous recessive genotypes, which can be estimated
directly from phenotypes.