Chapter 6
Practice Problems
6.1 Define genetic drift. What are the two main effects of genetic drift on the genetic
composition of populations?
6.2 (a) Why is allelic diversity lost faster than heterozygosity during a population bottleneck?
(b) What is the primary characteristic of an allele that will determine its probability of being lost
in a bottleneck?
6.3 Simulate genetic drift in a population (N=2) with one female (Aa) and one male (Aa) by
flipping a coin as shown in Figure 6.1 until the frequency of the A allele becomes one or zero.
Present your results as shown in Table 6.1. How many generations did it take before one allele
or the other became fixed? Which allele became fixed? If you did this simulation 100 times,
how many times would you expect the a allele to become fixed?
6.4 Simulate genetic drift in a population with one female and one male by flipping a coin
except this time begin with the female being AA and the male being Aa. Present your results as
shown in Table 6.1. How many generations did it take before one allele or the other became
fixed? Which allele became fixed? If you did this simulation 100 times, how many times would
you expect the a allele to become fixed?
6.5 There are a variety of computer programs available for simulating the effects of genetic
drift. Populus (Alstad 2001) is a particularly useful educational software package for simulating
genetic drift and other population genetic processes that we will use. You can download Populus
from http://www.cbs.umn.edu/populus/installer. Open the Mendelian Genetics/Genetic Drift
module of Populus and determine if your answers to the two previous questions are correct.
That is, what is the relationship between the initial allele frequency and the probability of an
allele eventually becoming fixed in a population. Set the number of loci to the maximum of 10
and vary the population size and initial allele frequency.
6.6 We saw in Example 6.3 that heterozygosities at individual loci may increase even though
overall heterozygosity will be reduced as predicted by equation 6.5. Set the initial allele
frequency with Populus at 0.26 with 10 loci and explore the observed pattern of genetic drift
with a population size of 25 for 100 generations. You should see that heterozygosity will
increase after one generation at approximately half of the loci. Remember, in this case
heterozygosity will increase if the allele frequency increases and will decrease if the allele
frequency decreases. How many generations does it take before the heterozygosity at all 10 loci
is less than in the initial population? How many loci do you think would be necessary to monitor
in a population to get an accurate measure of the size of a population?
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6.7 Kimura and Ohta (1969) have shown that the expected time until fixation occurs in a
population is approximately 4N generations. Use the simulation program PopG by Joe
Felsenstein and others for this exercise to explore this relationship. PopG can be downloaded
from http://evolution.gs.washington.edu/popgen/popg.html.
Set the initial allele frequency to 0.5 with 100 loci and explore if this expectation seems to hold.
It may be helpful to begin with very small population sizes and then explore results with larger
populations.
How sensitive is this result to the initial allele frequency?
6.8 The following allele frequencies were estimated at two microsatellite loci in brown bears
from Scandinavia (Waits et al. 2000):
Locus
Mu51
Alleles
102
110
112
114
116
118
120
122
0.241
0.098
0.011
0.006
0.098
0.408
0.057
205
207
211
0.472
0.301
0.227
0.080
Mu61
Assume that a new population of brown bears is founded on an island in the Baltic Sea from two
bears randomly selected from this population. Use expression 6.9 to predict the number of
alleles expected at these two loci in this newly founded population.
The expected heterozygosity at 19 microsatellite loci in this population was 0.66. What do you
expect the heterozygosity to be at these loci in the newly founded population after a generation
of random mating? Compare the proportion of alleles expected to be lost at these two loci to the
proportion of heterozygosity expected to be lost in a bottleneck of N=2.
6.9 Kurt Vonnegut (1985) wrote a science fiction novel (Galápagos) about a time in the future
when all humans are descended from two men and two women who happened to be on a cruise
to the Galápagos Islands in 1986. What proportion of the total heterozygosity in a population do
we expect to be retained after a bottleneck of four individuals (expression 6.5)? One could
argue on this basis that even extreme bottlenecks, such as four individuals, would not have a
major effect on populations or species. Do you agree with this argument? Why not?
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6.10 Johnson (1988) reported the following allele frequencies at 25 allozyme loci in the land
snail Theba pisana that was introduced from Europe into western Australia in the 1890s (see
Example 6.2). Describe the amounts of genetic variation in these three samples (heterozygosity
and allelic diversity). Assume that all of the loss in heterozygosity was caused by the initial
founding events; that is, assume that there has been no additional loss of heterozygosity in the
mainland Australia or Rottnest Island populations because of small population size. What is the
number of founders in the two founding events that would explain the differences in
heterozygosities in these three populations? The picture below of this snail was taken by the
senior author on Rottnest Island.
-------------------------------------------------Australia
------------------Locus Allele
France
Perth
Rottnest
-----------------------------------------------G6PDH 105
0.03
--100
0.97
1.00
1.00
IDH-1 110
0.14
--100
0.79
0.92
0.77
90
0.07
0.08
0.23
LDH
100
0.97
1.00
1.00
77
0.03
--LAP-1 106
0.35
--103
0.26
--100
0.39
1.00
1.00
LGP-2 127
0.11
--118
0.09
--109
0.09
--100
0.69
1.00
1.00
82
0.02
--LTP-1 100
0.78
0.88
1.00
96
0.22
0.12
-LTP-2 105
-0.06
-100
0.40
0.29
0.80
95
0.44
0.65
0.20
90
0.16
--LTP-3 111
0.02
--100
0.70
0.60
1.00
91
0.26
0.40
-84
0.02
--MDH-3 100
0.97
1.00
1.00
70
0.03
--PGM-2 130
0.07
0.10
0.34
117
0.21
--100
0.72
0.90
0.66
PGM-3 225
0.03
--175
0.21
0.60
0.71
155
0.34
--140
0.02
--100
0.40
0.40
0.29
14 loci 100
1.00
1.00
1.00
--------------------------------------------------
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Assignment Problems
6.11 We have seen that the proportion of heterozygosity remaining after a bottleneck of a single
generation is (1-1/2N), regardless of the number of alleles present and their frequencies.
However, the amount of allelic diversity expected to remain after a bottleneck does depend on
allele frequencies. Show that the number of alleles expected to remain after a bottleneck of N=2
differs at a locus with two alleles if one of the alleles is rare (say q=0.1 and p=0.9) in comparison
to when the two alleles are equally frequent (p=q=0.5).
6.12 Lake trout were introduced into Flathead Lake in western Montana in the early 20th
century. They have had a devastating effect on native fish species after they invaded other lakes
in the Flathead drainage. Kalinowski et al. (2010) described genetic variation at 11
microsatellite loci in a non-native population of lake trout in Swan Lake, Montana. This
population was recently established by a few migrant individuals from the nearby Flathead Lake
population. The lake trout in Swan Lake had greatly reduced average heterozygosity (0.68)
compared to the average heterozygosity in lake trout from Flathead Lake (0.88). Assume that all
of the loss in heterozygosity was caused by the initial founding event; that is, assume that there
has been no additional loss of heterozygosity because of small population size. What is the
estimated number of founders based upon the observed reduction in heterozygosity?
6.13 Gibbs et al. (1991) have described 37 nearly equally frequent alleles at the hypervariable
major histocompatibility (MHC) locus in a sample of 77 adult blackbirds from Ontario (Figure
6.11). How much genetic variation would you expect to be retained at this locus if this
population went through a very small population bottleneck (say 10 breeding individuals) and
then quickly recovered to over 100 individuals? Consider both heterozygosity and allelic
diversity.
6.14 Several new populations of koalas have been introduced to islands to help conserve the
species (Seymour et al. 2001). Populations of koalas that have gone through founding
bottlenecks when introduced to islands show an increased frequency of testicular aplasia (a
failure of testicular development) and other indications of inbreeding depression.
The two plots below show the distributions of allele frequencies present at six microsatellite loci
in two populations of koalas from South Australia. One of these samples is from a large natural
population of koalas and the other sample is from a newly founded island population. Which of
these two populations is most likely to be a recently founded island population? Explain the
basis for your answer.
NOTE: The bar on the far left of each plot that is directly above zero (0.0) on the allele
frequency axis indicates the number of alleles whose frequency is greater than zero and less than
0
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