Practice Problems s4

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?

1 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 Alleles

Mu51 102 110 112 114 116 118 120 122 0.09 0.01 0.00 0.09 0.40 0.05 0.080 0.241 8 1 6 8 8 7 Mu61 205 207 211 0.47 0.22 0.301 2 7

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?

2 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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4 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