Lab 11: Population Genetics
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OBJECTIVES:
 To gain a general understanding about the field of population genetics and how it can be
used to study evolution and population dynamics.
 Understand the concepts of evolution, fitness, natural selection, genetic drift and
mutations.
 To simulate Hardy-Weinberg equilibrium conditions.
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INTRODUCTION:
A population is a group of individuals of one species that occupy a defined geographical
area and share genes through interbreeding. Within a large population, new, genetically distinct
subpopulations can arise through isolation by distance (IBD). In this mechanism, as the
subpopulations become geographically isolated, genetic differentiation between groups in the
general population increases. These groups, more commonly referred to as local populations or
demes, consist of members that are far likelier to breed with each other than with the remainder
of the population. As such, their gene pool differs significantly from that of the general
population and with continued isolation, demes may eventually evolve into new species. Demes
also arise from other mechanisms including geographical, ecological, temporal and/or behavioral
isolation (Fig. 1).
Figure 1. Mechanisms of isolation
Population genetics is a direct extension of Mendel’s laws of inheritance, Darwin’s ideas
of natural selection, and the concepts of molecular genetics. It focuses on the population to
which an individual belongs rather than on the individual. Within any given population, every
individual has its own set of alleles, and collectively, every individual’s set of alleles comprises
the population’s gene pool. The role of a population geneticist is to study the allelic and
genotypic (Formulas 1 and 2, respectively) variation present within a population’s gene pool and
to assess how this variation changes from one generation to the next.
1. Allelic frequency =
# of copies of an allele in a population
Total # of all alleles for that gene in a population
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2. Genotypic Frequency = # of individuals with a particular genotype in a population
Total # of all individuals in a population
Example:
In a population of 100 individuals, 64 are PTC tasters with genotype TT, 32 are PTC tasters with
genotype Tt and the last 4 are non-tasters with genotype tt.
a. What is the allelic frequency t?
Allelic frequency of t = 2*[# inds. w/ recessive genotype (tt)] + # inds. w/ heterozygous genotype (Tt)
Total # of individuals in the population
=
2[4] + 32
2[100]
=
40
200
=
0.2 or 20%
b. What is the genotypic frequency of tt?
Genotypic frequency of tt =
# of tt individuals
Total # of individuals in the population
=
4
64 + 32 + 4
=
4
100
=
0.04 or 4%
In general, populations are dynamic units that change from one generation to the next. To
predict how a gene pool changes in response to fluctuations in size, geographic location and/or
genetic composition, population geneticists have developed mathematical models that quantify
these parameters. The most recognized of these are the Hardy-Weinberg (HW) equations:
(p + q)2 = 1 and p2 + 2pq + q2 = 1
These equations relate allele and genotype frequencies in a population and indicates the
proportion of each allele combination that should exist within a population. In this formula,
p = the frequency of the dominant allele (e.g. B)
q = the frequency of the recessive allele (e.g. b)
p2 = the frequency of the homozygous dominant genotype (e.g. BB)
q2 = the frequency of a recessive genotype (e.g. bb)
2pq = the frequency of a heterozygote genotype (e.g. Bb)
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The HW equation predicts equilibrium, i.e., the allelic and genotypic frequencies remain
constant over the course of many generations, if the following five assumptions are met:
(1) Large population size
(2) Random mating
(3) No mutation
(4) No migration
(5) No natural selection
In reality, no population ever satisfies HW equilibrium completely.
Example 1:
If in a population of 100 cats, 16 individuals express the recessive phenotype (white fur), then
the frequency of the black phenotype is 0.84 and of the white phenotype is 0.16.
a.
Using the HW equation, calculate the frequencies of alleles B and b.
frequency of white (bb) cats = 16/100 = 0.16
q2 = 0.16 therefore q = √0.16 = 0.4
since p + q =1, then p = 1 – q
therefore, p =1- 0.4 = 0.6
b.
Using the HW equation, calculate the frequencies of the BB and Bb genotypes.
From part a, we know that p = 0.6 and q = 0.4
therefore, the frequency of BB cats is p2 = (0.6)2 = 0.36
and the frequency of Bb cats = 2pq = 2(0.6)(0.4) = 0.48
Fig. 11.10
To check: since p2 + 2pq + q2 = 1, then 0.36 + 0.48 +0.16 = 1
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Example 2:
In a population of fruit flies, the genotypes of individuals present are: 50 RR, 20 Rr and 30 rr
where R = red eyes and r = white eyes. Assuming the population is in Hardy-Weinberg
equilibrium, the proportion of each genotype would be determined as follows:
a. Using Formula 1, calculate the frequency of each allele, in this case R and r.
Frequency of r allele =
2[30] + 20
2[100]
=
80
200
= 0.4
Therefore, q, the frequency of the recessive allele, equals 0.4.
b. Since q is known, the p + q = 1 is equation is used to determine p, the frequency of
the dominant allele.
since p + q =1, then p = 1 – q
therefore, p = 1 – 0.4 = 0.6
c. Now using the HW equation, we can calculate the proportion of RR, Rr and rr
individuals in the population.
From part a and b, we know that p = 0.6 and q = 0.4
therefore, the frequency of RR individuals is p2 = (0.6)2 = 0.36
the frequency of those with the Rr genotype = 2pq = 2(0.6)(0.4) = 0.48
and the frequency of rr flies = q2 = (0.4)2 = 0.16
d. Since there are 100 flies in our population, when the population is in HW
equilibirium, 36 flies are homozygous dominant (RR), 48 are heterozygous (Rr) and
the remaining16 are homozygous recessive (rr).
The genetic composition of a population’s gene pool can be affected by several
evolutionary factors, including mutations, migration, non-random mating, genetic drift and
natural selection. Mutations, changes in the DNA sequence, are the ultimate source of genetic
variation in a population’s gene pool, but because mutation rates are generally low, mutations
alone do not usually result in changes in allele frequency. Allelic distributions in a particular
group can also fluctuate due to migration, i.e. the movement of individuals either into
(immigration) or out of (emigration) a population, resulting in either the addition or loss of
alleles, respectively. Diversity within a population is also affected by random events, a process
referred to as genetic drift. Two examples of genetic drift are (1) founder effects (Fig. 2A) and
(2) genetic bottlenecks (Fig. 2B). In the first scenario, a small group of individuals leave the
original population and start a new population in a different location. In contrast, a bottleneck
occurs when the original population is drastically reduced in size as a result of some type of
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natural disaster (e.g. fires, hurricanes, disease, etc.). In addition, non-random mating (e.g.
inbreeding/self-fertilization - increases homozygosity) and natural selection also alter the
genetic variation within a population.
A.
B.
Figure 2. A. Founder effect and B. Bottleneck effect
In summary, the various techniques employed by population geneticists enable them to
determine the frequency of gene interaction (gene flow) among different populations and
examine the effects of natural selection, migration and mutations, on the genetic composition of
these groups. Overall, population genetics attempts to explain how adaptation and speciation
shape biological populations over time. In today’s lab you will use the concepts and techniques
of population genetics to answer questions about the genetic composition of particular
populations.
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TASK 1 - Genotypic Frequencies and Hardy Weinberg (HW) Equilibrium
You can use the HW equations and your knowledge about allelic and genotypic
frequencies to address many population genetics questions. The four problems below provide
examples.
Exercise 1: Gene and Genotype Frequencies
In addition to the ABO antigens you learned about in Lab 8, several other classes of
glycoproteins are present on the surface of red blood cells. Examples include the MN, Rh, Duffy
and Lewis antigens. For this exercise, we will focus on the MN blood protein system. The MN
antigens, like the ABO blood proteins, display codominant inheritance where both alleles (i.e., M
and N) are expressed simultaneously. In a group of 100 people, 49 are MM, 42 are MN, and 9
are NN. If, M = p and N = q, answer the questions that follow and show all calculations:
a.
How many M alleles are present among the group?
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b.
How many N alleles are present among the group?
c.
What is the frequency of the M allele?
d.
What is the frequency of the N allele?
e.
What are the frequencies of MM, MN and NN genotypes?
Exercise 2: Gene Frequencies in a Medical Application
The island of Madagascar has a total population of 1300 people, including 13 individuals who
are afflicted by Cystic Fibrosis (CF), a recessively inherited disease. Researchers are interested
in knowing how many people in the Madagascar populace are carriers of CF, and have requested
your assistance as the resident physical anthropologist. If the C allele is dominant and the c allele
is recessive, answer the questions that follow. (Show all calculations)
a. What is the frequency of recessive individuals in the Madagascar populace?
b. What is the frequency of dominant individuals in this population?
c. What is the frequency of the Cc genotype in Madagascar?
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d. How many people in this population are normal (i.e. not carriers)?
e. How many people in this population are carriers?
Exercise 3: Examine Your Own Traits
Using yourself and your lab mates, complete Tables 1, 2 and 3.
Table 1: Individual Observation
Representative
Trait
phenotype
Allele
Inheritance
Your Phenotype
Your
Character
Pattern
(check one)
possible
genotype
DOM = dominant, REC = recessive
DOM
Widow’s Peak
W
dominant
a
recessive
Darwin’s Ear
Point
E
dominant
Cleft Chin
c
recessive
Attached
Earlobes
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REC
Ability to detect the
bitter taste of
phenylthiocarbamide
(PTC).
Chew on PTC paper
to find out your
phenotype.
Unpigmented
Iris (blue)
b
recessive
Tongue Rolling
R
dominant
Tongue Folding
f
recessive
Hitchhiker’s
Thumb
h
recessive
Freckles
F
dominant
Mid-Digital
Hair
M
dominant
Dimples
D
dominant
PTC tasting
T
dominant
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Table 2: Observations for Your Class
Trait
Total
Number
Number of
Dominant
Phenotypes
% of
Total
Number of
Recessive
Phenotypes
% of
Total
1. Widow’s Peak
2. Attached Earlobes
3. Darwin’s Ear Point
4. Cleft Chin
5. Unpigmented Iris
6. Tongue Rolling
7. Tongue Folding
8. Hitchhiker’s Thumb
9. Bent Little Finger
10. Mid-Digital Hair
11. Dimples
12. PTC tasting
Table 3: Expected Allele and Genotype Frequencies* for Your Class
Trait
Allele Frequencies
p
q
Genotype Frequencies
p2
2pq
q2
1. Widow’s Peak
2. Attached Earlobes
3. Darwin’s Ear Point
4. Cleft Chin
5. Unpigmented Iris
6. Tongue Rolling
7. Tongue Folding
8. Hitchhiker’s Thumb
9. Bent Little Finger
10. Mid-Digital Hair
11. Dimples
12. PTC tasting
*Note: these are the expected genotypic frequencies if the population is in HW equilibrium.
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TASK 2 - Beetles Natural Selection Exercise
One of the benefits of population genetics and the HW equation is that you can
objectively measure the effect of changes in gene frequency due to factors such as natural
selection. This concept will be demonstrated using an isolated beetle population with three color
variants (red, orange and yellow) in experiments 1, 2 and 3. Note that mating in the beetles is
random and only one offspring is produced per mating pair. The colors of offspring follow the
pattern below:
Mating Pair
Red x Red
Red x Yellow
Red x Orange
Orange x Orange
Orange x Yellow
Yellow x Yellow
Offspring Produced
Red
Orange
50% Red; 50% Orange
50% Orange; 25% Red; 25% Yellow
50% Yellow; 50% Orange
Yellow
The selection pressure being simulated here is predation.
Experiment 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
Start the Beetles 2 program by double clicking on the icon on the desktop.
Once the program has opened, select New Experiment from the file menu.
Ensure that you have a Predator Diet Ratio of 3:3:3.
Set a Beetle Population of 30.
Set Initial Beetle Numbers to 8:14:8.
Model the population by clicking on the ‘10 Generations’ button until Generation 20.
Graph your data on the computer and record trend(s).
Select "New Experiment" and change the Beetle Population to 60. Repeat the experiment.
Select "New Experiment" and change the Beetle Population to 120. Repeat the
experiment.
Questions:
a. Did each experiment show the same trends?
b. Which population size showed the greatest variation? Why?
c. Which population size was the most stable? Why?
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d. From these experiments, what can you conclude about genetic variation within a small
population as compared to larger ones?
e. Is limited diversity an advantage for long term survival of a small isolated population?
Explain.
Experiment 2: Rates of Predation
1.
2.
3.
4.
5.
6.
Select New Experiment from the file menu.
Ensure that you have a Predator Diet Ratio of 3:2:1.
Set a Beetle Population of 30.
Set Initial Beetle Numbers to 10:10:10.
Model the population by clicking on the ‘10 Generations’ button until Generation 20.
Graph your data on the computer and record trend(s).
Questions:
a.
Why might a predator feed on more red beetles than other colored beetles?
b. Why does the number of orange beetles tend toward zero after the red beetle numbers
have done so?
c.
In a natural population, does an individual’s chance of surviving vary from year to
year? Explain.
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Experiment 3: Changing Rates of Predation
1. Select New Experiment from the file menu.
2. Ensure that you have a Predator Diet Ratio of 3:3:3.
3. Set a Beetle Population of 120.
4. Set Initial Beetle Numbers to 30:60:30.
5. Model the population by clicking on the ‘5 Generations’ button.
6. Set the Predator Diet Ratio to 6:1:3.
7. Model the population by clicking on the ‘5 Generations’ button until Generation 10.
8. Set the Predator Diet Ratio to 6:6:1.
9. Model the population by clicking on the ‘5 Generations’ button until Generation 15.
10. Graph your data on the computer and record trend(s).
11. Select "New Experiment" and repeat Steps 2 to 10 three times or combine your data with
three other groups.
Questions:
a. Did increasing the predation rate of red beetles affect the population? Explain.
b. Let’s say that red beetles have been selected against. Could they ever completely
disappear from the population?
c. Can an uncommon variety still be maintained within a population? Explain.
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