Measuring Evolution: Population Genetics and Hardy-Weinberg Equilibrium
Introduction:
A population is a group of individuals of the same species living in a given area at a given
time. Since each individual in the population has a certain genotype, the population can be
studied from a genetic point of view by determining the frequency with which certain genes
occur in the total population. It is through such studies of population genetics that many
aspects of the process of evolution can be understood. Evolution is the change in the
frequencies of alleles (genes) within a population over time. As the frequencies of alleles
change within populations, so do the frequencies of the characteristics produced by those
alleles.
Population genetics looks at the genetic composition of a population rather than an
individual. All the various alleles of all the genes carried by the individual members of the
population constitute the gene pool. The genetic makeup of this gene pool can be described by
the relative frequency of each allele in the population. The way that these allele frequencies
change or remain stable from generation to generation can be studied. If allele frequencies are
changing from generation to generation, evolution is occurring within the population; if allele
frequencies remain stable from generation to generation, evolution is not occurring within the
population. Therefore, evidence of evolution lies within population allele frequency changes
over time.
In order to determine if allele frequencies of a population are changing over time, those
allele frequencies must be measured. In the following activities, you will calculate both allele
and genotype frequencies within a model population of moths as environmental variables are
manipulated.
Materials: (per group)
2 paper sacks
20 black beans
20 white beans
1 sheet of white paper
Activity 1: Hardy-Weinberg Equilibrium
It is important not to lose sight of the fact that allele frequencies within the gene pool of
a population are inherently stable. That is to say, allele frequencies do not change by
themselves. Despite the fact that evolution is a common occurrence in natural populations,
allele frequencies will remain unaltered indefinitely unless evolutionary mechanisms are active
within the population. A population in which allele frequencies are unchanging is said to be in
Hardy-Weinberg Equilibrium. Hardy and Weinberg concluded that a population will remain in
Hardy-Weinberg Equilibrium from generation to generation if, and only if, all of the following
conditions are met:
1. The population is large.
2. There are no mutations occurring within the population.
3. The population is isolated from neighboring populations (no gene flow).
4. No genetic drift is occurring.
5. Mating is random with every sexually mature male having an equal opportunity to
mate with every sexually mature female.
1
6. Natural selection is not occurring. That is, there is no selective pressure favoring one
phenotype over another.
Before Hardy and Weinberg, it was thought that dominant alleles must, over time, inevitably
force recessive alleles out of existence. This incorrect theory was called "genophagy" (literally
"gene eating"). According to this wrong idea, dominant alleles always increase in frequency
from generation to generation. Hardy and Weinberg were able to demonstrate with their
equation that dominant alleles can just as easily decrease in frequency within the population as
can recessive alleles.
Procedure:
To test Hardy-Weinberg Equilibrium, you will simulate a stable population and
determine if there is a change in allele frequency over several generations. To do this, you will
use a hypothetical population of moths living in a stable environment. In this moth population,
there are two phenotypes for color: black and white. The color difference is due to a pair of
alleles in which the allele for black (B) is dominant and the allele for white (b) is recessive.
Therefore, there is the potential for three different genotypes in the population: BB, Bb, and
bb. The hypothetical moth population has an equal number of males and females and all
members of the population have an equal opportunity of mating and producing offspring. In
the hypothetical moth population, the black bean represents the allele for black color and the
white bean represents the allele for white color. Begin with a population of ten individuals by
placing ten black and ten white beans into a paper bag. Mix the beans thoroughly by shaking
the bag. These beans represent the gene pool for the moth population with an allele frequency
of 0.5 for B and 0.5 for b. Keep in mind that each individual carries two alleles for the trait of
color. The 20 beans in the bag therefore represent the gene pool for the 10 members of the
parent generation in our model.
To produce the F1 generation, one member of your group, without peeking, will
randomly draw two beans out of the paper bag and place them on the lab table. Arrange the
beans on the table by genotype: BB, Bb, and bb. Continue drawing out pairs of beans until the
bag is empty. You should have 10 pairs of alleles arranged on the lab table in a manner similar
to Diagram 1. Using collected data, calculate the actual allele frequency for the F1 generation
using the following formula and record in Table 1.
Allele frequency =
BB
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒂 𝒔𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝒂𝒍𝒍𝒆𝒍𝒆
𝒕𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒂𝒍𝒍𝒆𝒍𝒆𝒔
Bb
bb
Diagram 1
2
Calculate F1 genotype frequencies using the following formula and record in Table 1.
Genotype frequency =
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒂 𝒔𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝒈𝒆𝒏𝒐𝒕𝒚𝒑𝒆
𝒕𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒈𝒆𝒏𝒐𝒕𝒚𝒑𝒆𝒔
In the hypothetical population, there are no mutations, no gene flow, no genetic drift,
mating is random, and natural selection is not occurring. To simulate a situation in which each
genotype has an equal chance of being eliminated by a predator or other natural factors, “kill”
half of each genotype that you draw from the gene pool sack by removing them from the
population. If there is an odd number of a particular genotype, subtract one from the number
and remove half of the remaining. For example, if there are three BB genotypes, subtract 1,
leaving two, and remove half of the remaining genotypes, i.e., one! If there is only one of a
particular genotype do not remove it. Return the surviving genotypes back to the population
gene pool sack. Replenish the gene pool in this manner: for each individual killed, place a black
allele (bean) and a white allele (bean) into the gene pool sack. For example, if a total of six
individuals were killed, add 6 black alleles and 6 white alleles to the sack. This restores the
population to 10 individuals. Mix the alleles thoroughly by shaking the sack. Continue the
simulation for six generations, calculating the allele and genotype frequency for each
generation and recording the data in Table 1.
Table 1
Moth Population Allele and Genotype Frequencies in Hardy-Weinberg Equilibrium
Generation
Allele Frequency
Genotype Frequency
B
b
BB
Bb
bb
Parent
0.5
0.5
F1
F2
F3
F4
F5
F6
1. Describe the results obtained.
2. Discuss possible reasons for the results obtained.
3. Would a similar result be expected regardless of the original frequencies of B
and b in the parent generation? Explain. (If not sure . . . experiment!)
3
Activity 2:
A. Natural Selection
The individual moths in the previous activity had an equal probability of surviving or not
surviving. Now let’s see what happens to allele frequencies if natural selection is occurring
within a population.
The population of moths is now living in a forest in which all the trees have dark bark,
either because light-barked trees have been removed by disease or human activity or because
pollution has darkened all tree trunks. When resting on a tree trunk, the dark moths are
difficult for predators to detect but the light moths are easily seen and preyed upon. What
effect will this have on allele frequencies within this population of moths?
To simulate this natural selection model, begin with 10 white alleles (beans) and 10
black alleles (beans) in the gene pool sack. These alleles represent ten parent individuals in the
population with a white allele frequency of 0.5 and the black allele frequency of 0.5. Randomly
draw pairs of alleles out of the gene pool sack as was done in Activity 1. Place the pairs of
alleles on the black lab table top to simulate moths on a dark tree trunk. After all the alleles (10
individuals) have been removed from the sack and placed on the black table top, calculate allele
and genotype frequencies for the F1 generation. Assume 100% predation on the white
phenotype (bb genotype) and remove these individuals from the population. Return the
surviving individuals to the gene pool sack and replace the genotypes lost to predation with one
black and one white allele. Continue for 10 generations, recording your results in Table 2.
Table 2
Moth Population Allele and Genotype Frequencies Undergoing Natural Selection
Generation
Allele Frequency
Genotype Frequency
B
b
BB
Bb
bb
Parent
0.5
0.5
F1
F2
F3
F4
F5
F6
F7
F8
F9
F10
1. Describe the results obtained.
2. Discuss possible reasons for the results obtained.
4
B. Natural Selection Pressure Reversed
What will happen to the moth population if the natural selection pressure is reversed as
the environment changes again? Assume now that there are some birch trees in the area where
the moth population lives. The birch trees have light-colored bark and white moths landing on
these trees will be less likely to be seen by predators than the black moths that happen to land
on the light-colored trees.
Assume that the woods are composed of an equal number of dark and light-colored
trees. Use a piece of white paper to represent the light-colored tree trunks and the dark lab
table top to represent the dark-colored tree trunks. This time begin with the allele frequencies
that were present in the tenth generation in the previous activity when natural selection
pressure was operating against the white allele. Enter the allele and genotype frequencies for
the F10 generation from the previous page in Table 3. Again, randomly draw a pair of alleles
from the gene pool sack and place them on the black table top to simulate a moth landing on a
dark-colored trunk. Place the next pair of alleles on the white piece of paper. Continue drawing
pairs of alleles from the gene pool sack and place them alternately on the black table top and
then on the white paper until all the alleles have been removed from the sack. When all the
alleles have been drawn, there should be five pairs of alleles on the white paper and five pairs
of alleles on the black table top, representing five individuals each. Calculate the allele
frequencies and genotype frequencies and record in Table 3 for the F11 generation.
This time you will simulate predation of the black and white phenotypes based on the
type of tree trunk they are on. On dark tree trunks assume that all black phenotypes escape but
half of the white phenotypes are preyed upon. Conversely, on the white background, assume
that all white phenotypes escape but half of the black phenotypes are preyed upon. If the
number of individuals open to predation is an odd number, subtract one from the total and
remove half of the remaining. If there is only one, do not remove it. Return the surviving
members to the gene pool sack and for each moth lost to predation, regardless of phenotype,
replace each with both a dark and light-colored allele. Mix the alleles well and repeat. Continue
through the F20 generation, calculating allele and genotype frequencies for each generation.
Table 3
Moth Population Allele and Genotype Frequencies Undergoing Natural Selection
Generation
Allele Frequency
Genotype Frequency
B
b
BB
Bb
bb
F10
F11
F12
F13
F14
F15
F16
F17
F18
F19
F20
5
1. Describe the results obtained.
2. Discuss possible reasons for the results obtained.
Activity 3: The Effect of Gene Flow
One of the conditions of Hardy-Weinberg equilibrium is that a population is isolated
from neighboring populations. When this condition is not met, gene flow can occur. Gene flow
refers to the movement of alleles from one population’s gene pool to another population’s
gene pool. This gene flow occurs when individuals leave one population (emigrate) and join a
neighboring population (immigrate). When this flow occurs randomly, the two populations
become more genetically similar.
To simulate gene flow, work with two paper sacks, one marked “Population A” and the
other marked “Population B”. In the Population A sack place 16 black beans and 4 white beans.
Record the allele frequencies for Population A in Table 4. In the Population B sack, place 4
brown alleles and 16 white alleles. Record the allele frequencies for Population B in Table 4.
Notice that the proportions of the two alleles in the two different populations are not the
same. This indicates that the two populations are genetically different. Mix the alleles well in
each population, then randomly draw four alleles from Population A while your partner
simultaneously draws four alleles from Population B. Transfer the alleles drawn from
Population A to the Population B gene pool and transfer the alleles drawn from Population B to
the Population A gene pool. Then, count the number of each allele in each population and
calculate the frequency of those alleles, recording results in Table 4. These alleles represent the
first wave of emigration and immigration. Repeat for the second, third and fourth waves. When
the activity is completed return beans to their original containers.
Table 4: The Effect of Gene Flow
Gene
Population A
Flow
B
b
Original
First Wave
Second Wave
Third Wave
Fourth Wave
1. Describe the results obtained.
2. Discuss possible reasons for the results obtained.
6
Population B
B
b
Activity 4: Determining Allele and Genotype Frequencies
Allele and genotype frequencies can be calculated using the Hardy-Weinberg equation.
In the Hardy-Weinberg equation, p represents the dominant allele and q represents the
recessive allele.
Hardy-Weinberg equation: p2 + 2pq + q2 = 1.0 (100%)
The equation simply states that the frequency of p (the dominant allele) within a
population plus the frequency of q (the recessive allele) within the same population equals 1.0
(100%).
(p + q) = 1.0
therefore,
(p +q)2 = 1.0
2
therefore, p + 2pq + q2 = 1.0
This concept makes perfectly good sense if you keep in mind that a pair of alleles
typically controls the expression of a trait. Therefore, the frequency of the dominant allele for
that trait, plus the frequency of the recessive allele for that trait must equal 100% of the alleles
for that trait within the population.
Let’s calculate the allele and genotype frequencies for the ability to taste the chemical
thiourea. The ability to taste thiourea is due to a dominant allele (T), while the lack of the ability
to taste thiourea is due to a recessive allele (t). Within a human population there are two alleles
present (T and t) and three possible genotypes (TT, Tt, and tt). Within the population, some of
the male sperm carry the dominant allele (T), while some of the sperm carry the recessive allele
(t). Therefore, the entire sperm population will be (T + t). The same applies to the eggs
produced by females within the population; some of the eggs are carrying the dominant allele
(T), while some of the eggs are carrying the recessive allele (t). Therefore, the entire egg
population will be (T + t). All possible matings within the population can thus be symbolized by
(T + t) x (T x t) = 1.0 (100%). Here we are ignoring individual matings and are instead considering
the entire population. The results of all possible matings in our actual population correspond to
the Hardy-Weinberg equation where TT corresponds to p2, Tt to 2pq, and tt to q2.
How can one determine the allele frequencies within the population? Begin by
calculating the frequency of the recessive allele, t. This is done by first calculating the frequency
of the homozygous recessive genotype. Calculate the frequency of tt by counting the number of
individuals who are non-tasters within the population. In our sample population, let’s say that
there are 20 non-tasters in a population of 100. The frequency of tt = 20/100 = 0.20 (20%).
Since the frequency for tt is 0.20, then the frequency of the t allele is √𝑡𝑡 = √0.20 = 0.45.
Since the Hardy-Weinberg equation says (p+q) = 1.0 (100%), then:
(T + t) = 1.0
T = 1.0 – t
T = 1.0 - .45
T = 0.55
7
In this sample population, the frequency of the dominant T allele is 0.55 and the
frequency of the recessive t allele is 0.45. Therefore:
p = 0.55 and q = 0.45
(p + q) = 1.0
(.55 + .45) = 1.0 (100%)
We can now use these known allele frequencies to calculate the genotypic frequencies
in the population by using the Hardy-Weinberg equation. To do so simply plug the known allele
frequencies into the equation.
p2 + 2pq + q2 = 1.0
(0.55 x 0.55) + 2(0.55 x 0.45) + (0.45 x 0.45) = 1.0
0.30
+
0.50
+
0.20
=1.0
TT
Tt
tt
Calculated frequencies of genotypes within the population:
TT = 0.30
Tt = 0.50
Tt = 0.20
1.0 (100%)
Summary:
1. Calculating allele frequencies within a population:
a. Determine the number of individuals within the population that are
homozygous recessive for the trait. This is easy to do because these individuals
possess the recessive phenotype.
b. Calculate the frequency of the homozygous recessive individuals within the
population. Do this by dividing the number of homozygous recessive
individuals by the total number of individuals within the population.
c. Determine the frequency of the recessive allele within the population by
calculating the square root of the frequency of the homozygous recessive
individuals.
d. Determine the frequency of the dominant allele in the population by
subtracting the frequency of the recessive allele from 1.0. Remember that
p + q = 1.0, therefore p = 1 – q.
2. Calculating genotypic frequencies within a population:
Once you have calculated the recessive and dominant allele frequencies,
simply plug those values into the Hardy-Weinberg equation. Keep in mind that
p equals the frequency of the dominant allele, and q equals the frequency of
the recessive allele.
8
Problems
1. What does the Hardy-Weinberg equation predict about allele frequencies in a population
isolated from disturbing influences?
2. What happens to allele frequencies in a population when a condition of the Hardy-Weinberg
Equilibrium is not met?
3. Explain how recessive alleles can persist in a population even when they are selected against.
4. What is meant by “gene flow”?
5. What would be the effect of gene flow between two populations, A and B, if there is flow
from B to A but there is no flow from A to B?
6. The characteristic of male-pattern baldness is produced by the recessive allele, n.
Normal hair is the dominant characteristic and is produced by a dominant allele, N. A
survey found that out of 1000 men, 360 had male pattern baldness while the other 640
had normal hair. Show your work!!!!!
a. What are the phenotypic ratios?
b. Using this information find the allele frequencies for alleles N and n.
c. What are the expected genotype frequencies?
9
7. One in 1700 U. S. Caucasian newborns have cystic fibrosis. Normal (N) is the dominant allele
whereas (n) is the recessive allele for cystic fibrosis.
a. What percent of the U. S. Caucasian population has cystic fibrosis?
b. Based on the incidence of cystic fibrosis in the U. S. Caucasian population, calculate the
following allele and genotype frequencies:
1) N
2) n
3) NN
4) Nn
5) nn
8. It has been discovered that individuals possessing a heterozygous condition (Nn) are better
able to survive diseases which produce severe diarrhea. What would happen to the
frequency of the n allele if there was an epidemic of cholera or other type of diarrheaproducing disease? Would allele n frequency increase? Decrease? Remain the same?
Explain.
9. Is it possible to mathematically determine if evolution is occurring in a population? If so,
explain how.
10