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Overview
Population Genetics and Evolution
In this lab, you will:
1. learn about the Hardy-Weinberg law of genetic equilibrium, and
2. study the relationship between evolution and changes in allele frequency by using a computer simulation to represent
a sample population.
Objectives
After doing this lab you should be able to:
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Calculate allele and genotype frequencies using the Hardy-Weinberg equation.
Discuss the effect of natural selection on allelic frequencies.
Explain and predict the effect on allelic frequencies of selection against the homozygous recessive.
Discuss the relationship between evolution and changes in allele frequencies as measured by deviations from the
Hardy-Weinberg principle of genetic equilibrium
Background
In 1908, G.H. Hardy and W. Weinberg independently suggested a scheme whereby evolution could be viewed as changes
in the frequency of alleles in a population of organisms. They reasoned that if A and a are alleles for a particular gene
locus and each diploid individual has two such loci, then p could be designated as the frequency of the A allele and q as
the frequency of the a allele. Thus, in a population of 100 individuals (each with two copies of the gene) in which 40% of
the genes are A, p would be 0.40. The rest of the genes (60%) would be a, and q would be equal to 0.60 (i.e. p + q = 1.0).
These are referred to as allele frequencies. If certain conditions are met, the frequency of the possible diploid
combinations of these alleles (AA, Aa, aa) should equal p2 + 2pq + q2 = 1.0. Hardy and Weinberg also argued that if five
conditions are met, the population's allele and genotype frequencies will remain constant from generation to generation.
These conditions are:
1.
2.
3.
4.
5.
The population is very large. The effects of chance on changes in allele frequencies is thereby greatly reduced.
Individuals show no mating preference for A or a (mating is random).
There are no new mutations of the alleles for the gene.
There is no immigration or emigration of individuals and their genes in or out of the population.
All genotypes have an equal chance of surviving and reproducing (there is no selection).
Basically, the Hardy-Weinberg equation describes the status quo. If the five conditions are met, then no change will occur
in either allele or genotype frequencies in the population. It provides a yardstick by which changes in allele frequency, and
therefore evolution, can be measured. One can look at a population and ask: Is evolution occurring with respect to a
particular gene locus? The Hardy-Weinberg principle allows for the detection of changes in the population's gene
frequency over time (evolution).
Installing Populus—Populus is a population modeling program developed at the University of Minnesota. If you are doing
this lab activity in class, it should already be installed on your computer; if you're doing it at home, a basic level of
“computer savvy” is assumed. You can get the program at http://www.cbs.umn.edu/populus/. If you need help, ask Mr.
Lyman-Buttler. Populus requires the Java Runtime Environment to be installed in order to run; you can check to see
whether this is the case at http://www.javatester.org/version.html.
Genetic Drift: Monte Carlo Model
This simulation uses a random number generator to sample genes from a parental population and pass them on to
offspring. Population size is assumed to remain constant from generation to generation.
Suppose that a population consists of one male and one female, and that both are heterozygous at a locus with two
mutant alleles. There are four alleles in the total gene pool, 2 A alleles and 2 a alleles, so p = q = 0.5. The female will
produce A and a eggs in equal frequency, and the male will produce half A and half a sperm. If gametes are chosen at
random and fused to form a filial population of 2 individuals, the probability that the first individual will be an AA is (0.5*0.5)
= 0.25, and the probability that both progeny will be AA's is (0.5*0.5)*(0.5*0.5) = 0.0625. Thus if population size = 2, there
is 1 chance in 16 that allelic frequency will change from p = 0.5 to p = 1.0 in a single generation simply through the random
sampling of gametes.
In addition to the drift from p = 0.5 to p = 1.0, there are other possible outcomes; p could change to 0, 0.25, or 0.75, and
the likelihood of these events is calculated similarly (you should be able to do it). A computer model which uses random
numbers to mimic this unpredictable sampling process is called a "Monte Carlo Simulation."
1) Select “Model” from the main menu. Go to the Mendelian Genetics menu and select “Genetic Drift.” This will bring
up a box that lets you set initial conditions (population size, starting allele frequency, etc.)
2) Set the population size to 10 and the number of loci to 10. Leave the other parameters as they are.
3) Click the “View” button, and observe the graph. Notice how the allele frequencies change randomly. Sometimes,
an allele frequency will reach 1.0 or 0.0. When this happens, an allele has become “fixed” in the population: only
one allele for that trait remains, and the other one has been eliminated, never to return.
4) Open up a spreadsheet (such as Microsoft Excel or OpenOffice Calc) and use it to keep track of your data. The
data-tracking scheme that you use is up to you; I want you to measure the average number of alleles fixed per
generation. This is one way to measure the loss of genetic diversity over time. Some possible considerations:
• How many trials should I conduct to get good results, statistically speaking? (Another way of looking at this: if
everyone in the class runs the simulation enough times, everyone should get the same results. How long is
this?) To run another trial, click “Iterate.”
• How can I get the computer to keep track of the average for me, so I don't have to?
• Can I set up the spreadsheet to record a running average, so that I can stop recording data when it seems the
average isn't moving anymore?
Note that the simulation is set to run for 3 times as many generations as the population size; so, for example, for a
population of 50, 150 generations are simulated. This will be the same for every iteration. Therefore, in this case,
you can just take the number of alleles fixed during the course of the simulation, and divide 150.
Determine the average number of alleles fixed per generation for populations of size 10, 100, and 500. Record data here:
Now, e-mail a copy of your spreadsheet to [email protected].
Analysis questions:
1) Generally speaking, what is the effect of drift on genetic diversity in a population?
2) Were the populations you simulated at Hardy-Weinberg equilibrium? Why or why not?
3) How do the effects of drift on genetic diversity very with population size?
4) Did it appear that any of the alleles conferred a selective advantage, or were they all equally likely to be lost?
Explain.
5) Which Hardy-Weinberg assumption is violated in this simulation?
6) Describe 2 possible events in nature that could cause a population to experience a significant amount of drift.
Drift and Selection
Now we are going to examine two different causes of evolution at the same time. This gets our model a little closer to a
real-world population, and it will also help us understand the relative importance of different causes of evolution a little
better. Unlike the previous model, this one is programmed to track only a single allele. Because selection is involved, there
are three new variables: WAA, WAa, and Waa, which stand for the relative fitness of the homozygous dominant,
heterozygous, and homozygous recessive genotypes, respectively. In this simulation, the allele frequency is the frequency
of the dominant (A) allele.
What does relative fitness mean? ______________________________________________________________________
A recessive deleterious mutation
Many new alleles in a gene pool originate as recessive mutations. These mutations are usually deleterious, that is to say,
they reduce the relative fitness of the organism. Let's model the emergence of a new deleterious allele in a population, and
track its progress through future generations. Set a population size of 500, an initial allele frequency of 0.999 (this
corresponds to 499 normal individuals and 1 person with 1 normal + 1 mutant allele), and relative fitness values of 1.0. 1.0,
and 0.5 for AA, Aa, and aa, respectively. Click “View” to run the simulation. Click “View” again to run it again.
1) Run the simulation several times, until you start to notice a pattern. What happens? Why?
2) Now, change the population size to 10, and the allele frequency to 0.95 (this still corresponds to a single allele in
the gene pool). Are your results different? How? Why?
3) Now change the relative fitness of the homozygous recessive genotype to 0.99. (This is not that much worse than
the dominant phenotype!) Run the simulation several times. What do the results tell you about the power of natural
selection?
4) Which Hardy-Weinberg assumption is violated in this simulation?
Heterozygote advantage
The sickle-cell allele is a well-known example of heterozygote advantage. People with two copies of the allele have sicklecell disease, which significantly shortens life span and reduces relative fitness. People with one normal allele and one
sickle-cell allele, on the other hand, suffer few ill effects but have increased resistance to malaria, which confers a
significant advantage in environments where malaria is present. Set a population size of 500, an initial allele frequency of
0.999 (this corresponds to 499 normal individuals and 1 person with 1 normal + 1 mutant allele), and relative fitness values
of 0.9. 1.0, and 0.5 for AA, Aa, and aa, respectively. Click “View” to run the simulation. Click “View” again to run it again.
You may need to do this 20 or more times before getting interesting results.
1) Most of the time, the line remains flat at 1.0. Why?
2) When the recessive allele does spread in the population, what frequency does it tend towards? (Remember, the
graph shows the frequency of the dominant allele.) Is it approximately the same every time? Why do you think it
behaves this way?
3) The line usually remains flat at 1.0, but sometimes the allele spreads. What does this suggest about the number of
times this mutation has originated in the human population?
4) Suppose you live in sub-Saharan Africa where malaria is common. Which would you rather have, the normal (but
malaria-susceptible) phenotype, or sickle-cell disease (homozygous recessive)? Why?
5) Let's revisit our population. Suppose we go to northern Europe, where historically there has been no malaria. How
could you change the relative fitness (W) values to reflect this? What effect does this have on the simulations?
Additional Population Genetics Problems
Calculate answers to the following population genetics problems. Assume that Hardy-Weinberg equilibrium applies in each
case. Show your work and set-ups.
1. The frequency of two alleles in a gene pool is 0.3 (A) and 0.7 (a). What is the percentage of heterozygous
individuals in the population, assuming that the population is in Hardy-Weinberg equilibrium?
2. Allele (B) for white wool is dominant over allele (b) for black wool. In a sample of 1800 sheep, 1782 are white and
18 are black. Estimate the allelic frequencies in this sample, assuming the population is in equilibrium.
3. In a population that is in Hardy-Weinberg equilibrium, the frequency of the recessive homozygote genotype of a
certain trait is 0.49. What is the percentage of individuals homozygous for the dominant allele?
4. In Drosophila, the allele for normal length wings is dominant over the allele for vestigial wings. In a population of
1000 individuals, 360 show the recessive phenotype. How many individuals would you expect to be homozygous
dominant and heterozygous for this trait?
5. The allele for the ability to roll one's tongue is dominant over the allele for the lack of this ability. In a population of
5000 individuals, 35% show the recessive phenotype. How many individuals would you expect to be homozygous
dominant and heterozygous for this trait?
6. In humans, Rh positive blood is produced by a dominant gene (R) while Rh negative blood is produced by the
recessive allele (r). In a population that is in Hardy-Weinberg equilibrium, if 94% of the individuals are Rh positive,
what are the frequencies of the two alleles?
7. In corn, yellow kernel color is governed by a dominant allele; white by its recessive allele. A random sample of
5,000 kernels from a population that is in equilibrium reveals that 4000 are yellow and 1000 are white. What are
the frequencies of the alleles in this population? What is the percentage of heterozygote kernels?