Download Lab 1 Population Genetics: The Hardy

Lab 1 Population Genetics: The Hardy-Weinberg Theorem
Name_________________
Objectives
After completing this lab, you should be able to:
1. Explain Hardy-Weinberg equilibrium.
2. Describe the conditions necessary to maintain Hardy-Weinberg equilibrium.
3. Estimate allele frequencies and use them to calculate genotype frequencies expected under Hardy-Weinberg
equilibrium.
4. Compare observed and expected genotype frequencies.
Introduction
Charles Darwin’s unique contribution to biology was not that he “discovered evolution” but, rather, that he
proposed a mechanism for evolutionary change – natural selection, the differential survival and reproduction
of individuals in a population. In On the Origin of Species, published in 1859, Darwin described natural
selection and provided abundant and convincing evidence in support of evolution, the change in populations
over time. Evolution can be defined as “changes in the genetic constitution of populations over time.” A
population is defined as a group of organisms of the same species that occur in the same area and interbreed or
share a common gene pool, all the alleles at all gene loci of all individuals in the population. The population is
considered the basic unit of evolution. Populations evolve, not individuals.
In 1908, English mathematician G. H. Hardy and German physician W. Weinberg independently developed
models of population genetics that showed that the process of heredity by itself did not affect the genetic
structure (i.e., the allele and genotype frequencies) of a population. The Hardy-Weinberg theorem states that
when certain conditions are met, the frequency of alleles in the population will remain the same from one
generation to the next, regardless of the starting frequencies. Furthermore, the equilibrium genotypic
frequencies will be established after one generation of random mating. The conditions under which this theorem
is valid are:
1. The population is very large.
2. Matings are random.
3. There are no net changes in the gene pool due to mutation; that is, mutation from A to a must be equal to
mutation from a to A.
4. There is no migration of individuals into and out of the population.
5. There is no selection; all genotypes are equal in reproductive success.
Basically, the Hardy-Weinberg theorem provides a baseline model in which gene frequencies do not change and
evolution does not occur. By comparing observed genotype frequencies to those predicted by the HardyWeinberg theorem, biologists can begin to study the extent to which mutation, migration, population size,
nonrandom. mating, and natural selection cause evolutionary change in natural populations. For example, the
Hardy-Weinberg theorem has been used to show that certain alleles in the human population provide a selective
advantage in people infected with HIV, that is, these alleles provide resistance to onset of AIDS symptoms in
people infected with the AIDS virus.
The Hardy-Weinberg Theorem
The Hardy-Weinberg theorem provides a mathematical formula for calculating allele and genotype frequencies
in a nonevolving population. For a population with two alleles at a single gene locus—a dominant allele, A, and
a recessive allele, a—assume that the frequency of the dominant allele is p and the frequency of the recessive
allele is q. Since there are only two alleles, p + q = 1. If the frequency of one allele, p, is known for a
population, the frequency of the other allele, q, can be determined by using the formula q = 1 – p.
In a large population, during sexual reproduction the frequency of each type of gamete produced is equal to the
frequency of the alleles in the population. If the gametes combine at random, then the probability of AA in the
next generation is p2, and the probability of aa is q2. The heterozygote can be obtained in two ways, with either
the sperm or the egg providing a dominant allele, so the probability would be 2pq. The Hardy-Weinberg
theorem can then be written:
p2 + 2pq + q2 = 1,
where p2 is the frequency of AA, 2pq is the frequency of Aa, and q2 is the frequency of aa.
In this lab, you will perform an experiment (using beans) that simulates the “no evolution” case (i.e., the
conditions that result in the Hardy-Weinberg equation—see below) and an experiment (using beans) that
illustrates how natural selection can drive populations away from Hardy-Weinberg equilibrium.
With this material on the Hardy-Weinberg theorem in hand, we are now ready to begin
Experiment 1.
Experiment 1: Testing Hardy-Weinberg Equilibrium Using a Bead Model Materials
paper bag containing 50 red and white beans
Introduction
Working in pairs, you will test Hardy-Weinberg equilibrium by simulating a population using colored beans.
The bag of beans represents the gene pool for the population. Each bean should be regarded as a single gamete,
the two colors representing different alleles of a single gene. Each bag should contain 100 beans of the two
colors in the proportions specified by the instructor. Record in the space provided below the color of the beans
and the initial frequencies for your gene pool.
A =______________________ color_____________________allelic frequency
a =_______________________color_____________________allelic frequency
1. How many diploid individuals are represented in this population?
2. What would be the color of the beans for a:
homozygous dominant individual?
homozygous recessive individual?
heterozygous individual?
Hypothesis
State (in your own words) the Hardy-Weinberg theorem in the space provided. Your working hypothesis will be
that the Hardy-Weinberg theorem holds for the population modeled by the beans.
Procedure
1. Without looking, randomly remove one bean from the bag. Return that bean to the bag, shake the bag for
several seconds, and then remove a second bean from the bag. These two beans represent two gametes (e.g., one
sperm, one egg) that will fuse to
form a diploid individual in the next generation. Record the diploid genotype of the individual formed from
these two gametes.
Diploid
AA=
Aa=
aa=
2. Return the second bean to the bag and shake the bag to replenish the gene pool. By replacing the beans each
time you sample one, the size of the gene pool remains constant and the probability of selecting any allele
remains constant and equal to its frequency in the bag. This procedure is called sampling with replacement.
3. Repeat steps 1 and 2 (select one bean, shake the bag, select another bean, shake the bag, and record the
genotype of the new individual) until you have recorded the genotypes for 50 individuals who will form the
next generation.
Diploids=
Results
1. Before calculating the results of your experiment, determine the expected frequencies of genotypes and
alleles for the population. To do this, use the original allelic frequencies for the population provided by the
instructor; recall that the frequency of A = p, and the frequency of a = q. Calculate the expected genotypic
frequencies using the Hardy- Weinberg equation. The number of individuals expected for each genotype can be
calculated by multiplying 50 (total population size) by the expected frequencies. Record these results in Table
1.1.
Table 1.1
Expected Genotypic and Allelic Frequencies for the Next Generation Produced by the Bead Model
Parent population
Allelic frequency
A
a
New Populations
Genotypic number and (frequency)
AA
Aa
aa
Allelic frequency
A
a
2. Next, using the results of your experiment, calculate the observed frequencies in the new population created
as you removed beads from the bag. Record the number of diploid individuals for each genotype in Table 1.2,
and calculate the observed frequencies for the three genotypes (AA, Aa, aa). In addition, calculate the observed
frequencies for the A and a alleles. Genotypic frequencies and allelic frequencies should each sum to 1.
Table 1.2
Observed Genotypic and Allelic Frequencies for the Next Generation Produced using the Bead Model
Parent population
Allelic frequency
A
a
New Populations
Genotypic number and (frequency)
AA
Aa
aa
Allelic frequency
A
a
Natural Selection
Work with a partner. Pick one background from those provided. Introduce the organisms provided into the
environment. The organisms are blue, orange or white dots. Introduce 10 of each color into the environment.
Then allow your partner to prey on the organisms for 3 seconds. Record your data in the table.
Make sure you record the starting population and the allele frequency of each population after an eating frenzy.
After each eating frenzy mating occurs and organisms are replaced to match the survivors. Base the
replacement organisms on the allele frequency of each surviving population.
Repeat 5 times and then use the Hardy- Weinberg equation to compare the starting population to what remains
after 5 generations.
Blue-AA
White-Aa
Orange-aa
Parent population
Allelic frequency
A
a
XXXXXX XXXXXX
XXXXXX XXXXXX
XXXXXX XXXXXX
XXXXXX XXXXXX
New Populations
Genotypic number and (frequency)
AA
Aa
aa
Allelic frequency
A
a
Hardy Weinberg equation for the starting population
p=
q=
p2=
2pq=
q2=
Hardy Weinberg for the remaining population
p=
q=
p2=
2pq=
q2=
Are the numbers the same??? Why???
NO SELECTION
Repeat with a black background.
Parent population
Allelic frequency
A
a
New Populations
Genotypic number and (frequency)
AA
Aa
aa
XXXXXX XXXXXX
XXXXXX XXXXXX
XXXXXX XXXXXX
XXXXXX XXXXXX
Hardy Weinberg equation for the starting population
p=
q=
Allelic frequency
A
a
p2=
2pq=
q2=
Hardy Weinberg for the remaining population
p=
q=
p2=
2pq=
q2=
Are the numbers the same??? Why???
In what situations do the Hardy Weinberg numbers stay in equilibrium and what situations do they change?