Download Lab 4 - University of Toronto Mississauga

Laboratory 4 EVOLUTIONARY MECHANISMS
& Hardy Weinberg Equilibrium
Before lab
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Review the mechanisms of evolution and the Hardy-Weinberg principle in your textbook
(Freeman Chapter 24, especially section 24.1).
Do the web/CD tutorial 24.1.
Read this lab. BRING a CALCULATOR TO LAB
Objectives After completing this exercise you should be able to:
1. Determine the allele frequencies for a gene in a model population.
2. Calculate observed and expected ratios of genotypes based on Hardy-Weinberg proportions.
3. Test hypotheses about the effect of evolutionary agents (natural selection, gene flow, genetic
drift, or mutation) on allele frequencies in a population.
4. Explain why the Hardy-Weinberg principle serves as a null hypothesis.
Evaluation—6%
1% Quiz at the beginning of lab
5% Group participation during lab & individual write up due in LAB 5.
Timeline
2:10 -- 2:30
2:30 -- 3:00
3:00 – 4:30
4:30 – 5:00
Quiz
Intro and Exercise 1
Exercise 2 (experiments 1, 2, and 3)
Discussion of thought questions plus clean up
Introduction
The Hardy-Weinberg Principle says that heredity itself cannot cause changes in the frequencies of
alternate forms of the same gene (alleles). If certain conditions are met, then the proportions of
genotypes that make up a population of organisms should remain constant generation after
generation according to Hardy- Weinberg equilibrium:
Genotype frequencies: p2 + 2pq + q2 = 1.0 (for two alleles)
If p is the frequency of one allele (A), and q is the frequency of the other allele (a), then
Allele frequencies: p + q=1.0
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4-2 Evolutionary Mechanisms
In nature, however, the frequencies of genes in populations are not static (that is, not unchanging).
Natural populations never meet all of the assumptions for Hardy-Weinberg equilibrium. The
assumptions for Hardy-Weinberg equilibrium are:
1. The organism in question is diploid.
2. Reproduction is sexual.
3. Mating is random.
4. Population size is very large.
5. Migration is negligible. (i.e., no immigration or emigration occurs)
6. No net changes in the gene pool due to mutation.
7. Natural selection does not affect the locus under consideration (i.e., all genotypes are
equally likely to reproduce).
Your text lists five conditions which must be met (which cover the same assumptions as listed
above):
1. No natural selection at the gene in question.
2. No genetic drift or random allele frequency changes affecting the gene in question.
3. No gene flow.
4. No mutation.
5. Random mating.
►Be able to explain the Hardy-Weinberg equilibrium and the reason for each condition.
Evolution is a process resulting in changes in the genetic makeup of populations through time;
therefore, factors that disrupt Hardy-Weinberg equilibrium are referred to as evolutionary agents.
In random mating populations, natural selection, gene flow, genetic drift, and mutation can all result
in a shift in gene frequencies predicted by the Hardy-Weinberg formula. Nonrandom mating can
also result in such changes. The exercises in this lab will demonstrate the effect of these agents
on the genetic structure of a simplified model population.
If a population is in Hardy-Weinberg equilibrium, then evolution is NOT happening;
therefore, the Hardy-Weinberg principle may be called the null hypothesis for evolution.
Hypothesis
In a large, randomly mating population with no mutation, migration, or selection, the allelic and
genotypic frequencies should remain at equilibrium.
Prediction
If a population is at Hardy-Weinberg equilibrium, then the frequencies of the alleles
(represented by beads in this lab) should not change.
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Summary of Materials
Per student group of 4:
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•
•
•
•
•
•
•
•
plastic dishpan (12" x 7" x 2")
50 large (10-mm diameter) white beads
50 large red/brown beads
50 large pink beads
4,000 small (8-mm diameter) white beads
pair of long forceps
coarse sieve (9.5-mm)
small bowl
2 small paper/opaque plastic bags
Exercise 1 Testing Hardy-Weinberg (HW) equilibrium (work in pairs)
Materials
Plastic/paper bag with 50 beads (mixture of white and red—different groups are given a different
proportion of red and white beads)
Introduction
Simulate a population using coloured beads and test whether this population is in HW equilibrium.
The bag of beads represents the gene pool for the population; each bead is a single allele (in a
single gamete) and the two colours represent the two alleles for that gene in the population. For
this simulation we will call red/brown (R) dominant to white (r)
Hypothesis: (re-state the Hardy-Weinberg theory)
Prediction: Predict the genotype frequencies of the population in future generations (If/then)
The code number of the outside of your bag is ___________
Count the actual number of alleles in your population:
______ # red/brown beads (alleles)
‘allele’ frequency of R =___________
______ # white beads (alleles)
‘allele’ frequency of r = ___________
______ total # beads
How many diploid individuals are represented in this population? ______
Example: diploid individuals; 25 individuals in the population
Allele frequency p+q=1.0
40 red
allele frequency of R = 35/50 = 0.8 (p)
10 white allele frequency of r = 15/50 = 0.2 (q)
--50 total ‘alleles’ for 25 diploid individuals
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Expected genotype frequency p2 + 2pq + q2 = 1.0
(0.8) 2 + 2(0.8x0.2) + (0.2) 2 = 1
0.64 + 0.32 + 0.04 = 1
Homozygous red = 0.64 or 16 individuals in a population of 25
Heterozygous = 0.32
or 8 individuals
Homozygous white = 0.04 or 1 individual
Expected phenotype frequency
“red” 0.64 + 0.32 = 0.96 or 24 individuals in a population of 25
White 0.04
or 1 individual
Procedure
1. Without looking, randomly remove two beads from the bag. These two beads represent one
diploid individual in the next generation. Record the genotype in Table 1a.
2. Return the beads to the bag, shake before selecting two more beads. Why? (see
explanation below-‘sampling with replacement’)
3. Continue steps 1 & 2 until you have recorded the genotypes for 20 individuals.
Results
1. Determine the expected frequencies of alleles and genotypes for the population from the
original allele frequency: [see sample calculations above]
Expected allele frequencies: p + q=1.0
p (freq of R) = ______ q (freq of r) = ________
2
2
Expected genotype frequencies ( p + 2pq + q = 1.0 (for two alleles)) and the
expected number of individuals of each genotype. [use the number you counted above]
Expected freq RR______Rr_______ rr______
# individuals
RR______Rr_______ rr______
2. Calculate the observed frequencies from the observed number of individuals of each
genotype obtained from your experiment.
# individuals
RR______Rr_______ rr______
Observed freq
RR ______ Rr _______ rr ______
3. To determine whether the observed frequencies were consistent with what was
expected,use the Chi-Square statistical test. (See sample calculation in Table 3a)
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Table Ia The # of individuals with the three genotypes after one generation—comparing the
observed versus expected # of individuals
# RR
#Rr
#rr
Observed (o)
Expected (e)
Deviation (o-e)= d
d2
d2//e
Chi-square = sum d2//e
_____
Discussion
4. Do the results of your statistical analysis suggest that the frequencies of genotypes in your
population are significantly different from expected?
5. Were your results consistent with your hypothesis and prediction?
6. What would you expect to happen to the frequencies if you continued the simulation for 25
generations?
7. Is this population evolving? Explain your answer.
8. How does this simulation meet the conditions for the population to be in HW equilibrium?
Answer yes or no for each condition: Random mating____; Large population ____; no gene
flow ____; no selection____
Sample data, calculations, and discussion:
Table Ib Example for 50 individuals randomly selected with an initial allele frequency or p=q
# RR
#Rr
#rr
Observed (o)
22
22
6
Expected (e)
18
24
8
Deviation (o-e)= d
4
2
2
d2
16
4
4
d2//e
0.89
0.16
0.5
Chi-square = sum d2//e
1.55 (degrees of freedom = 2 because 3
genotypes -1 = 2),
level of significance p=0.05) NOT Significant
Table Ic Critical values for the χ2 - distribution
Degrees
Level of probability
of
0.10
0.05
0.01
freedom
6.64
3.84
2.71
1
9.21
5.99
4.61
2
11.34
7.82
6.25
3
13.28
9.49
7.78
4
Discussion: The observed results are consistent with the expected results. The data support the
hypothesis; the observed distribution is not significant from expected under the Hardy-Weinberg
theory. Any minor differences can be attributed to change of sampling error. (This population is not
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evolving.)
Sampling with replacement
By replacing the beads each time after sampling, the size of the gene pool stays the same and the
probability of selecting any allele should remain equal to its frequency.
Exercise 2 Simulating Evolutionary Change (work in teams of 3-4)
Under the conditions specified by the HW-model, the allele frequencies should not change, and
evolution should not occur. In this exercise, you will modify each of the conditions to determine the
effect on allele and genotype frequencies in subsequent generations using the bead model.
The General Model
The populations you will be working with are composed of coloured beads representing individuals
as follows:
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White beads are homozygous for the white allele (CW CW).
Red beads are homozygous for the red allele (CRCR)
Pink beads are heterozygotes (CWCR).
These beads exist in "ponds" that are represented by plastic dishpans filled with smaller beads.
The smaller beads can be strained to retrieve all the "individuals" that make up the model
population. When the individuals are recovered, the frequencies of the colour alleles can be
determined using the Hardy-Weinberg formula.
The alleles in our population are codominant. Thus, each white bead contains two white alleles;
each pink bead, one white and one red; and each red bead, two red alleles. The total number of
colour alleles in a population of twenty individuals is forty. If such a population contains five white
beads and ten pink beads, the frequency of the white allele is:
p = (2 x 5) + 10
40
= 0.5
Because p + q = 1.0, the frequency of the red allele (q) must also be 0.5 if there are only two colour
alleles in this population.
Experiment 1 Natural Selection by simulated predation
Natural selection disturbs Hardy-Weinberg equilibrium by discriminating between individuals with
respect to their ability to produce young. Those individuals that survive and reproduce will
perpetuate more of their genes in the population. These individuals are said to exhibit greater
fitness than those who leave no offspring or fewer offspring. We will model the effect of natural
selection by simulating predation on our population.
1. The initial population:
• ten large white beads,
• ten large red beads
• twenty large pink beads
Put into a dishpan filled with small white beads (to a depth of at least 5 cm).
2. One student is the predator. After the beads are mixed, the predator searches the pond and
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removes as many prey items (large beads) as possible in 30 seconds. In order to more closely
model the handling time required by real predators, you must search for and remove beads
with a pair of long forceps.
3. Because some of the large beads are cryptically coloured (they blend into the environment),
the proportions of beads taken may not reflect the original proportions. Sift the pond with the
sieve, count the number of large white, pink, and red beads, and record the totals in Table 1.
Use these counts to calculate the frequencies of the white (p) and red (q) alleles remaining in
the population after selection and record them in Table 2. For example, if five white, eight pink,
and eight red beads remain, the frequency of the white allele is:
p = (2 x 5) + 8 = 0.43
42
4. Using the new values for allele frequencies, calculate genotype frequencies for homozygous
white (p2), heterozygous pink (2pq), and homozygous red (q2) individuals, and record them in
Table 2. For example, if p now equals 0.43, the frequency of homozygous white individuals is:
p2 = (0.43)2 = 0.18
Assuming that fifty individuals comprise the next generation, calculate the number of white, pink,
and red individuals needed to create the population of a new pond and record these numbers in
Table 5.1. For example, if p2 = 0.18, the number of white beads is:
p2 x 50 = 0.18 x 50 = 9.0
Using these numbers, construct a new pond.
5. Repeat steps 2 – 4 for three more rounds. Stop when Tables 1 and 2 are filled in completely.
A different student should be the predator in each round. When you are finished, plot the
frequency of the red allele over time in Figure1.
Thought Question 1
How would the gene frequencies change, if you started with small red beads as a background?
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Table 1 Counts of large beads before and after four rounds of simulated predation (Part B).
Beads
Initial Population
Before
White
Pink
Red
Total
10
20
10
40
After
Second Population
Before
50
After
Third Population
Before
50
After
Fourth Population
Before
50
After
Table 2 Allele and genotype frequencies due to selection by simulated predation.
Population
Initial population
First
generation after selection
Second
generation after selection
Third
generation after selection
Fourth
generation after selection
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p
q
p2
2pq
q2
0.5
0.5
0.25
0.5
0.25
Frequency of red allele (q)
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1.0
0.5
1
3
2
Time (in generations)
4
Figure 1 Effects of predation on allele frequencies.
Selection that favors one extreme phenotype over the other and causes allele frequencies to
change in a predictable direction is known as directional selection. When selection favors an
intermediate phenotype rather than one at the extremes, it is known as stabilizing selection.
Selection that operates against the intermediate phenotype and favors the extreme ones is called
disruptive selection.
It is important to realize that selection operates on the entire phenotype so that the overall fitness
of an organism is based on the result of interactions of thousands of genes.
The model presented here is very simple. Occasionally simple genetic differences like the one you
have modeled are critical to the survival of different phenotypes
Thought Question 2
If two identical populations were in different environments (such as in our red and white ponds),
how would the frequency of the colour genes in each pond compare after a large number of
generations?
As two populations become genetically different through time (divergence), individuals from these
populations may lose the ability to interbreed (=reproductive isolation). If this happens, two species
form from one ancestral species. This process is called speciation.
Results & Discussion—working draft for your assignment due in Lab 5
Experiment 1 Natural selection by predation
1. State your hypothesis:
2. State your prediction:
3. Which of the conditions necessary for Hardy-Weinberg equilibrium were met?
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4. Which condition (s) changed?
5. Describe the changes in allele frequencies of p and q over time and compare the end
frequencies to starting frequencies.
6. Describe the changes in genotype frequencies and compare the end frequencies to starting
frequencies.
Experiment 2 Natural Selection and Gene Flow (migration)
The frequencies of alleles in a population also change if new organisms immigrate and interbreed,
or when old breeding members emigrate. Gene flow due to migration may be a powerful force in
evolution. To demonstrate its effect:
1. Establish an initial population as in Experiment 1 Step 1.
2. Begin selection as before, except in this part of the exercise add five new red beads to each
generation before the new allele frequencies are determined. These beads represent migrants
from a population where the red allele confers greater fitness. Record the counts before and
after predation (with the five new red beads added) in Table 3 and the frequencies of alleles in
Table 4.
3. For each generation, record in Table 5 the frequencies of the red allele obtained with both
selection and migration.
Thought Question 3
How does migration influence the effectiveness of selection in this example?
Some level of gene flow is necessary to keep local populations of the same species from becoming
more and more different from each other. Things that serve as barriers to gene flow may
accelerate the production of new species. Migration may also introduce new genes into a
population and produce new genetic combinations. Imagine the result of a black allele being
introduced into our model population and the new heterozygotes (perhaps gray and dark red) it
would produce.
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Table 3 Counts of large beads before and after four rounds of simulated predation with gene
flow.
Beads
Initial Population
Before
White
Pink
Red
Total
10
20
10
40
After
Second Population
Before
50
After
Third Population
Before
50
After
Fourth Population
Before
50
After
Table 4 Allele and genotype frequencies due to selection by simulated predation with addition of
gene flow .
Population
Initial population
First
generation after selection
Second
generation after selection
Third
generation after selection
Fourth
generation after selection
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p
q
p2
2pq
q2
0.5
0.5
0.25
0.5
0.25
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Table 5 Frequency of red allele due to selection and migration.
Generation
Selection Alone
(Experiment 1)
Selection and migration
(Experiment 2)
1
q =
q =
2
q =
q =
3
q =
q =
4
q =
q =
Experiment 2: Natural selection with gene flow (migration) working draft
7. State your hypothesis:
8. State your prediction:
9. Which of the conditions necessary for Hardy-Weinberg equilibrium were met?
10. Which condition (s) changed?
11. Describe the changes in allele frequencies of p and q over time and compare the end
frequencies to starting frequencies.
12. Describe the changes in genotype frequencies and compare the end frequencies to starting
frequencies.
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Experiment 3 Natural Selection with Genetic Drift (founder or bottleneck
effect)
Chance is another factor that affects the kind of gametes in a population that are involved in
fertilization. As a result, shifts in gene frequencies can occur between generations just because of
the random aspects of fertilization. This phenomenon is known as genetic drift. In this portion of the
experiment, we will simulate genetic drift.
1. Establish an initial population as in Experiment 1 Step l.
2. One student in the group should, without looking, place his or her hand in the bowl and choose
ten large beads at random.
3. Record the allele frequencies in Table 6 that would result from the ten individuals you have
chosen.
Table 6 Allele frequencies produced by genetic drift.
Expected frequencies
Actual Frequencies
(n = 10)
Actual Frequencies
(n = 30)
p = 0.5
p =
p =
q = 0.5
q =
q =
Thought Question 4
If the individuals you selected were the only individuals to reproduce in this generation, what would
be the effect on allele frequencies compared to those initially present in the population?
4. Now replace the ten beads you removed in step 2. Select beads at random again, but this time
select thirty beads.
5. Calculate the allele frequencies from the thirty beads and record these frequencies in Table 6.
Thought Question 5
How do these frequencies for 30 individuals compare to those generated in step 3 for 10
individuals?
Generally, the larger the breeding population, the smaller the sampling effect that we call genetic
drift. In small populations, genetic drift can cause fluctuations in gene frequencies that are great
enough to eliminate an allele from a population, such that p becomes 0.0 and the other allele
becomes fixed (q = 1.0). Genetic variation in such a population is reduced. Populations that
become very small may lose much of their genetic variation. This is known as a bottleneck effect.
Another way in which chance affects allele frequencies in a population is when new populations
are established by migrants from old populations.
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6. To model this effect, choose at random six individuals from an initial population as in Part B1 to
represent the migrants.
7. Move these individuals to a new unoccupied pond. It is not necessary to actually set up a new
pond for this demonstration; just use your imagination.
8. Now calculate the allele frequencies in the new pond and record them in Table 7.
Table 7 Allele frequencies in a founder population.
Initial Population
Founder Population
p = 0.5
p =
q = 0.5
q =
Thought Question 7
How do they compare with the frequencies that were characteristic of the pond from which these
migrants came?
The genetic makeup in future generations in the new population will more closely resemble the six
migrants than the population from which the migrants came. This effect is known as the founder
effect. The founder effect may not be an entirely random process because organisms that migrate
from a population may be genetically different from the rest of the population to begin with. For
example, if wing length in a population of insects is variable, one might expect insects with longer
wings to be better at founding new populations because they may be carried farther by winds.
Experiment 3 natural selection and genetic drift (founder and
bottleneck) working draft
13. State your hypothesis:
14. State your prediction:
15. Which of the conditions necessary for Hardy-Weinberg equilibrium were met?
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16. Which condition (s) changed?
17. Describe the changes in allele frequencies of p and q over time and compare the end
frequencies to starting frequencies.
18. Describe the changes in genotype frequencies and compare the end frequencies to starting
frequencies.
Review of Chi-square χ2 test
The chi-square (χ2 pronounced kye-square) test is one way to test an hypothesis in an experiment in
which the data collected are frequency data, rather than continuous data ( t -test). Genetic and
behavioural experiments often measure the frequency of occurrence of events; for instance, an
experimenter may want to compare the number of animals responding to some stimulus to the
number of animals that did not respond. Note that the χ2; analysis uses raw data only, not
percentages or proportions.
The χ2 formula is
(observed - expected) 2
χ =∑
expected
2
Table 6. Critical values for the χ2 - distribution
Degrees
Level of probability
of
0.10
0.05
0.01
freedom
6.64
3.84
2.71
1
9.21
5.99
4.61
2
11.34
7.82
6.25
3
13.28
9.49
7.78
4
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