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