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Transcript
Population Genetics and Hardy-Weinberg Populations Lab
General Biology 2
Learning Objectives
1. You will determine if a sample random population meets the definition of an Ideal Population for a
non-apparent trait.
2. You will simulate a randomly mating population to see if this maintains an Ideal Population and
discuss reasons that may result in it moving away from an Ideal Population.
3. You will model a large, randomly mating population and investigate the effects of mutation, selection
and population size.
4. You will formulate a hypothesis about the effect of various environments on a model population and
then design an experiment to test this hypothesis.
Introduction
Mendel’s work on mechanisms of inheritance was not sufficient to determine the effect that genetics
had on evolution. Later work by various scientists undertook the question of how genes and alleles
interacted on a population-level scale and how the changes in this distribution led to observable
evolution of species. The study of genes as a function of the entire population, rather than in
individuals, is referred to as population genetics, and it is easiest to explain using the work of G.H. Hardy
(a mathematician) and Wilhelm Weinberg (a physician who independently developed the concept
contemporary to Hardy).
Hardy-Weinberg Genetic Equilibrium
The concept of genetic equilibrium is that the allele and genotype frequencies of a population will
remain constant (in equilibrium) unless a disturbing force is introduced into the population. A
population in genetic equilibrium is considered an Ideal Population and has a number of distinct
characteristics.
1. The population is very large.
2. The population randomly mates
3. The alleles of the population have identical chances of success
4. There is no immigration out of or emigration into the population
5. There is no mutation
Obviously, very few populations meet these criteria and therefore very few populations are in genetic
equilibrium. This is a good thing, since genetic equilibrium implies an unchanging genetic population
(remember though this will be a dynamic, not static, equilibrium) and evolution is by definition a change
in the population gene allele frequencies.
Genetic equilibrium can be mathematically described in the following manner. For a gene with two
alleles, their frequencies (q and p, expressed as decimals) would be mathematically related by the
following equation.
q2 + 2pq + p2 = 1
Equation 1
For a gene with simple dominant/recessive inheritance, where q is the dominant allele you get the
following.
q2 + 2pq = frequency of dominant phenotype
p2 = frequency of recessive phenotype
Equation 2
Equation 3
It should be apparent from these equations that 2pq represents the frequency of the heterozygote
while q2 and p2 represent the homozygotes. The equations can be drawn out to include even more
alleles, but quickly become mathematically tedious.
Testing a Random Population
We can learn to work with the basic mathematics of Hardy-Weinberg and analyze some real data with a
very simple experiment on the class. We will test whether the class population is in agreement with the
population average distribution for a specific genetic trait. For this to work we need a trait that easily
measured, demonstrates simple dominant/recessive inheritance, and is non-apparent in the overall
population (so as to limit bias). The trait will use is the ability to test the chemical phenylthiocarbamide
(PTC). Being able to taste the compound is a dominant trait in humans and allows you to detect a very
bitter taste from this compound (don’t ask me to describe it any better, since I cannot taste it).
Nontasters possess the recessive phenotype.
Question 1
If you use “A” and “a” to designate the alleles for tasting and nontasting, what would the genotype(s) of
a taster and nontaster be?
Procedure
1. Take a piece of the PTC test paper and place it on your tongue.
2. Record whether you are a taster or nontaster on the lab data sheet.
3. Determine the percentage of the population that are tasters and nontasters from pooled lab
numbers.
4. Since nontasters are homozygote recessives, the allele frequency for the recessive gene can be
determined by taking the square root of the decimal percentage for nontasters (p2 in equation
3).
5. The total distribution of alleles is p+q = 1, therefore the allele frequency for q (dominant allele)
can be calculated.
6. Determining the frequency of homozygous dominant individuals is determined by squaring q.
7. The frequency of heterozygotes is determined by 2pq.
8. Record your results in provided table on the lab data sheet.
9. Compare to the provided values for North American populations.
Question 2
What factors could play into our sample being different from the North American average.
An Ideal Population
In this experiment the entire class will represent an entire breeding population. In order to ensure
random mating, choose another student at random. The class will simulate a population of randomly
mating heterozygous individuals with an initial gene frequency of .5 for the dominant allele A and the
recessive allele a and genotype frequencies of .25AA, .50 Aa and .25 aa. Your initial genotype is Aa.
Record this in your notebook. Each member of the class will receive four cards. Two cards have a and
two cards have A. The four cards represent the products of meiosis. Each “parent” contributes a haploid
set of chromosomes to the next generation.
Procedure
1. Begin the experiment by turning over the four cards so the letters are not showing, shuffle
them, and take the card on top to contribute to the production of the first offspring. Your
partner should do the same.
2. Put the two cards together. The two cards represent the alleles of the first offspring. One of you
should record the genotype of this offspring in your notebook.
3. Each student pair must produce two offspring, so all four cards must be reshuffled and the
process repeated to produce a second offspring. Then, the other partner should record the
genotype. The very short reproductive career of this generation is over.
4. Now you and your partner need to assume the genotypes of the two new offspring.
5. Next, the students should obtain the cards requires to assume their new genotype.
6. Each person should then randomly pick out another person to mate with in order to produce
the offspring of the next generation. Follow the same mating methods used to produce
offspring of the first generation.
7. Record your data. Remember to assume your new genotype after each generation.
8. We will collect class data after each generation.
Analysis
1. Determine the allele frequencies of each allele in each of the generations.
2. Compare these to the initial values for the alleles.
Question 3
Is this population in genetic equilibrium, if not, why not?
Return of the Dotties
You guys remember the Dotties from last semester in BIO161. For those that have blocked that memory
out, they are the hypothetical little creatures that we use to mimic populations. In BIO161 we simply
black boxed the equations for how these populations bred, but now we will elaborate a little on their
genetics.
Dotties come in six colors and this is governed by three alleles for a single locus. The phenotypes and
genotypes are as follows:
Color
Blue
Purple
Red
Orange
Yellow
Green
Genotype
BB
BR
RR
RY
YY
BY
Question 4
From the preceding information, what type of inheritance pattern is most likely for the Dotties with
regards to color?
We will be starting with initial populations in equilibrium (even distributed frequencies of alleles) and
looking at the effects of various changes on the equilibrium. For the work I have provided a spreadsheet
to calculate the allele frequencies and successive generations. Each population should start with sixty
(60) total Dotties.
Initial Population Behavior
We are going to look at an initial population of Dotties in a neutral background to note their behavior.
This population will be fairly large (60 total), not subject to mutation or emigration/immigration and
randomly mate (all Dotties randomly mate by definition). This means that we are only limited by the
success of the alleles. We will provide a random selection and see if the resultant population is in
equilibrium.
Procedure
1. Count out ten (10) of each color Dotty and place them in the small beaker.
2. Shake the Dotties in the beaker and then pour the across the neutral grey fabric background.
3. Starting at the upper left corner of the background scan across the fabric from left to right, top
to bottom removing every third Dotty you come across.
4. Recover the remaining forty (40) Dotties and record their phenotype distribution in your
notebook.
Analysis
1. Determine the allele frequencies for the three alleles.
2. Determine the expected phenotype distributions given an Ideal Population.
3. Construct a table with three columns (Genotype, Observed Frequency, Expected Frequency) and
seven rows (one for each genotype and titles) to organize your data.
4. To determine if the observed population matches the expected data we will look at a ChiSquared Analysis of the data. Determine the following for each data row, where O = observed
and E = Expected.
(
)
5. Sum the values determined in Step 4.
6. Since there are six values, we have five degrees of freedom (df=5) and for a confidence interval
of 0.05 the Chi-Square Tables give a value of 11.07. We can only reject our null hypothesis (that
the populations are the same) if our value in Step 5 exceeds this value.
Question 5
Is your final population in equilibrium? (be sure to have the work in your notebook)
The Effect of Mutation
Now we will go back to primitive prehistoric Dotty lore, where there were only three colors of Dotties in
existence, red, yellow and orange. The Dotties had legends of weird “colored” Dotties appearing in their
myths but there has never been conclusive proof of this in prehistoric Dotty populations. Let us see
what would have happened in the population as these unusual alleles appeared.
Methodology
1. Start with an initial population of sixty Dotties, 19 each for Yellow, Orange and Red and then one
each of the Green and Purple (yes, I know it is 59, go with it).
2. Have one individual be the predator for your population and remove themselves from the bench
while the remaining students place the Dotties onto the environment.
3. When all Dotties are place the “Predator” must, as quickly as possible, remove twenty (20)
Dotties with the provided tweezers.
4. Recover the remaining thirty-nine Dotties and categorize them by phenotype.
5. Using the provided Spreadsheet, calculate and record the allele frequencies for each allele and
the predicted population distribution for the next generation.
6. Using the population calculated in Step 5, repeat Steps 2-5 with the new population (same
predator) for three successive generations.
7. Record the results of the final population and determine if the final population is in equilibrium.
8. Repeat the procedure with a second, different environment.
Lab Write-Up
1. The lab write-up should contain the following.
2. The lab handout with answered questions
3. Your lab notebook sheets with all data and calculations
4. Formal Lab Report Containing
a. Introduction
b. Procedure write-up (paragraph form) for the final Effect of Mutations
c. Analysis write-up (tables) of the two successive environments
d. Graphs of the Allele Frequency vs. Generation for each environment
e. Discussion of whether the populations are in equilibrium and what factors play into
them either being or not being in equilibrium. Compare this to how a species might
develop in a real environment.