Name _______________________________________
Period ______________
Lab 8: Population Genetics and Evolution
Introduction
In 1908, G.H. Hardy and W. Weinberg independently suggested a
scheme whereby evolution could be viewed as changes in
frequency of alleles in a population of organisms. In this scheme, if
A and a are alleles for a particular gene locus and each diploid
individual has two such loci, then p can be designated as the
frequency of the A allele and q as the frequency of the a allele. For
example, in a population of 100 individuals (each with two loci) in
which 40% of the alleles are A, p would be 0.40. The rest of the
alleles would be (60%) and q would be equal to 0.60. Therefore p + q=1. These are referred to as allele
frequencies. The frequency of the possible diploid combinations of these alleles (AA, Aa, aa) is expressed as
p2 +2pq +q2 = 1.0. Hardy and Weinberg also argued that if 5 conditions are met, the population's alleles and
genotype frequencies will remain constant from generation to generation. These conditions are as follows:
1)
2)
3)
4)
5)
The breeding population is large. (Reduces the problem of genetic drift.)
Mating is random. (Individuals show no preference for a particular mating type.)
There is no mutation of the alleles.
No differential migration occurs. (No immigration or emigration.)
There is no selection. (All genotypes have an equal chance of surviving and reproducing.)
The Hardy-Weinberg equation describes an existing situation. Of what value is such a rule? It provides a way
by which changes in allelic frequencies can be measured.
If a population's allelic frequencies change, it is undergoing evolution.
Part I: Estimating Allele Frequencies for a Specific Trait (Taster vs. Non-Taster)
The PTC gene, TAS2R38, was discovered in 2003. There are two common forms (or alleles) of the PTC
gene, and at least five rare forms. One of the common forms is a tasting allele, and the other is a non-tasting
allele. Each allele codes for a bitter taste receptor protein with a
slightly different shape. The shape of the receptor protein determines
how
strongly it can bind to PTC. Since all people have two copies of every
gene,
combinations of the bitter taste gene variants determine whether
someone finds PTC intensely bitter, somewhat bitter, or without taste
at all.
PTC stands for phenylthiocarbamide. Also known as phenylthiourea,
the
chemical structure of PTC resembles toxic alkaloids found in some
poisonous plants..
Using the class as a sample population, the allele frequency
of a
gene controlling the ability to taste PTC can be estimated. Tasting
PTC
is evidence of the presence of a dominant allele in either a
homozygous (AA) or heterozygous (Aa) condition. The inability to
taste
PTC is dependent on the presence of the two recessive alleles (aa). To estimate the frequency of the being a
“Taster” allele in the population, one must find p. To find p, one must first determine q (the frequency of the
non-tasting allele).
Procedure:
1. Determine whether you are a taster or a non-taster
2. A decimal number representing the frequency of tasters (p2+2pq) should be calculated by dividing the
number of tasters in the class by the total number of students in the class.
3. A decimal number representing the frequency of the non-tasters (q2) can be obtained by dividing the
number of non tasters by the total number of students.
4. You should then record these numbers in Table 1.
5. Use the Hardy-Weinberg equation to determine the frequencies (p and q) of the two alleles. The
frequency q can be calculated by taking the square root of q2. Once q has been determined, p can be
determined because 1-q=p.
6. Record these values in Table 1 for the class and also calculate and record values of p and q for the North
American population.
Phenotypic Proportions of Tasters and Non-Tasters and Frequencies of the Determining Alleles
Table 1
Phenotypes
2
Taster (p +2pq)
Class Population
North American
Population
(#)
(%)
0.75
Allele Frequency
2
Non-Taster(q )
(#)
p
q
(%)
0.25
(North American Population: 528,720,588)
Data
1. Fill in the missing data in the table above based on class information (i.e., number of tasters and nontasters in the class, percentage of tasters and non-tasters in the class, and allele frequency in the class
and in the North American Population).
2. Calculate the percentage of heterozygous tasters (2pq) in your class.
a. What is it?
3. Calculate the number of individuals in the North American population that is heterozygous for the taster
allele.
a. What is it?
Part II: Case Studies (Fondly Referred to as “Grebe, Grebe”)
You as a class will become a population of randomly mating grebes. Each of you will receive your initial grebe
genotype cards (AA, Aa or aa) at the beginning of the simulation. Grebes are aquatic birds similar to ducks.
You will play the role of a grebe for the remainder of today’s activity, so we will begin with the information you
need for successful “grebing”. In order to insure random mating, you must be completely promiscuous.
Choose any of the students in the class and confidently approach them: they will not refuse. You will indicate
your intentions using the classic line, “Grebe, Grebe”, to which your future (albeit brief) mate will reply,
“Grebe, Grebe”. You will then grebe by placing your two allele cards behind your back and randomly shuffling
them. Each parent contributes a haploid set of chromosomes to the next generation. Each couple must have
two offspring. The first two cards displayed will become the genotype of one student. Repeat by shuffling the
cards behind the back again and display two more cards. These will represent the genotype of the second
student.
To maintain a constant population size, after each grebing session, the parent genotype dies, and you
assume the genotype of one of the offspring, and your partner assumes the other offspring’s genotype. To do
this, you may need to visit the central allele supply and pick up a new card. After each grebing session,
be sure to record your new genotype in the appropriate slot on the data table. Thank your partner and
proceed to a new individual. Follow the exact same procedures, being sure to record your new genotype after
each generation. After five generations, the class total for AA, Aa and aa will be recorded.
Case I: Hardy-Weinberg Equilibrium
The starting class population will have genotype frequencies of 0.25 AA, 0.5 Aa and 0.25 aa (in other words,
25% of the class will receive two “A” cards, 50% of the class will receive one “A” and one “a” card, and 25%
will receive two “a” cards). Record your initial genotype on the data page.
Answer questions 1-3 in the data section before moving on to Case III
Questions
Case 2: Selection
In this case you will modify the simulation to make it more realistic. In the natural environment, not all
genotypes have the same rate of survival; that is, the environment might favor some genotypes while
selecting against others. An example is the human condition sickle-celled anemia. It is a condition caused by
a mutation on one allele, in which a homozygous recessive does not survive to reproduce. For this simulation
you will assume that the homozygous recessive individuals never survive. Heterozygous and homozygous
dominant individuals always survive.
The procedure is similar to that for Case 1. Start again with your initial genotype, and produce your "offspring"
as in Case 1. This time, however, there is one important difference. Every time your offspring is aa it does
not reproduce. Since we want to maintain a constant population size, the same two parents must try again
until they produce two surviving offspring. You may need to get new allele cards from the pool. Proceed
through five generations, selecting against the homozygous offspring 100% of the time. Then add up the
genotype frequencies that exist in the population and calculate the new p and q frequencies in the same way
as it was done in Case 1.
Answer questions 4-5 in the data section before moving on to Case III
Case III: Heterozygote Advantage
Data from many human populations show an unexpectedly high rate of people
that are heterozygous for the sickle cell trait. These people are protected from
malaria to a certain extent due to the presence of some abnormal red blood
cells. We will incorporate this fact into our simulation. In this round, keep
everything the same as in Case II where aa dies all the time. However, in this
case, if your offspring is AA, flip a coin. Heads the offspring lives, tails the
offspring dies of malaria and the same parents must mate again until they
have a viable offspring (Aa). After five generations, total the genotypes for the
class and record AA, Aa and aa. Now, keep your most recent genotype and
through five more generations, recording the results. Finally, again start with
most recent genotype for another five generations. Record all class totals for
Aa and aa.
Questions
1. What does the Hardy-Weinberg equation predict for the new p and q you found at the end of five
generations?
2. Do the results you obtained in this simulation agree?
a.
If not, why not?
3. What major assumption(s) were not strictly followed in this simulation?
4. How do the new frequencies of p and q compare to the initial frequencies?
a. How has the allelic frequency of the population changed?
5. Predict what would happen to the frequencies of p and q if you simulated another 5 generations.
a. Explain your prediction.
6. In a large population, would it be possible to completely eliminate a deleterious recessive allele?
a. Explain:
7. How do the new frequencies of p and q compare to the initial frequencies in Case 1?
8. How has the allelic frequency of the population changed?
9. What were some general trends you saw throughout this activity?
go
the
AA,
Data Tables
Case 1 (Hardy-Weinberg Equilibrium)
Initial Class Frequencies:
AA ________ Aa________ aa_________
My initial genotype: _______________
F1 Genotype ______
F2 Genotype ______
F3 Genotype ______
F4 Genotype ______
F5 Genotype ______
Final Class Genotypes:
AA ________ Aa________ aa_________ Final Class Frequencies
Case 2 (Selection)
Initial Class Genotypes:
AA ________ Aa________ aa_________
p ________ q ________
My initial genotype: _______________
F1 Genotype ______
F2 Genotype ______
F3 Genotype ______
F4 Genotype ______
F5 Genotype ______
Final Class Genotypes:
AA ________ Aa________ aa_________
Final Class Frequencies
p ________ q ________
Case 3 (Heterozygote Advantage)
Initial Class Genotypes:
AA ________ Aa________ aa_________
My initial genotype: _______________
Genotypes by generation:
F1 Genotype ______
F6 ___________
F11______________
F2 Genotype ______
F7 _______
F12 _____________
F3 Genotype ______
F8 _______
F13 _____________
F4 Genotype ______
F9 _______
F14 _____________
F5 Genotype ______
F10 _______
F15 _____________
Final Class Genotypes (after 5, 10 and 15 generations):
AA ________ Aa________ aa_________
Final Class Frequencies (after 5, 10 and 15 generations)
p _________ q __________
Hardy-Weinberg Problems (you must show all work for all problems to get credit)
1. You have sampled a population in which you know that the percentage of the homozygous recessive
genotype (aa) is 36%. Using that 36%, calculate the following:
a. The frequency of the "aa" genotype.
b. The frequency of the "a" allele.
c. The frequency of the "A" allele.
d. The frequencies of the genotypes "AA" and "Aa."
e. The frequencies of the two possible phenotypes if "A" is completely dominant over "a."
2. There are 100 students in a class. Ninety-six did well in the course whereas four blew it totally and received
a grade of F. Sorry. In the highly unlikely event that these traits are genetic rather than environmental, if
these traits involve dominant and recessive alleles, and if the four (4%) represent the frequency of the
homozygous recessive condition, please calculate the following:
a. The frequency of the recessive allele.
b. The frequency of the dominant allele.
c. The frequency of heterozygous individuals.
3. Within a population of butterflies, the color brown (B) is dominant over the color white (b). And, 40% of all
butterflies are white. Given this simple information, which is something that is very likely to be on an exam,
calculate the following:
a. The percentage of butterflies in the population that are heterozygous.
b. The frequency of homozygous dominant individuals.
4. A very large population of randomly-mating laboratory mice contains 35% white mice. White coloring is
caused by the double recessive genotype, "aa". Calculate allelic and genotypic frequencies for this
population
5. Cystic fibrosis is a recessive condition that affects about 1 in 2,500 babies in the Caucasian population of
the United States. Please calculate the following.
a. The frequency of the recessive allele in the population.
b. The frequency of the dominant allele in the population.
c. The percentage of heterozygous individuals (carriers) in the population.
6. The ability to taste PTC is due to a single dominate allele "T". You sampled 215 individuals in biology, and
determined that 150 could detect the bitter taste of PTC and 65 could not. Calculate all of the potential
frequencies.
7. In Drosophila, the allele for normal length wings is dominant over the allele for vestigial wings. In a
population of 1,000 individuals, 360 show the recessive phenotype. How many individuals would you
expect to be homozygous dominant and heterozygous for this trait?
8. The allele for the hair pattern called "widow's peak" is dominant over the allele for no peak. In a population
of 1,000 individuals, 510 show the dominant phenotype. How many individuals would you expect of each of
the possible three genotypes for this trait?
9. In the U.S. albinism is quite rare, occurring in 1 of every 10,000 persons. It is a recessive trait. The
population in Iowa is almost 4 million. How many people in Iowa would you expect for each of the three
possible genotypes for this trait?
10. After graduation, you and 19 of your closest friends (lets say 10 males and 10 females) charter a plane to
go on a round-the-world tour. Unfortunately, you all crash land (safely) on a deserted island. No one finds
you and you start a new population totally isolated from the rest of the world. Two of your friends carry (i.e.
are heterozygous for) the recessive cystic fibrosis allele (c). Assuming that the frequency of this allele does
not change as the population grows, what will be the incidence of cystic fibrosis on your island?