Biology
Using a Marble Model
Materials
Box containing 100 marbles of two colors
Introduction
Working in pairs, you will test Hardy‑Weinberg equilibrium by simulating a population using colored marbles. The box of marbles represents the gene pool for the population. Each marble should be regarded as a single gamete, the two colors representing different alleles of a single gene. Each box should contain 100 marbles of the two colors in the proportions specified by the instructor. Record in the space provided below the color of the marbles and the initial frequencies for your gene pool.
A = (color) allelic frequency
a = (color) allelic frequency
(p + q)2 = p2 + 2(pq) + q2 = 1
(0.5 + 0.5)2 = 0.52 + 2(0.5 x 0.5) + 0.52 = 1
1 = 0.25 + 0.50 + 0.25 = 1 (all genes in the population)
1. There are 100 alleles in your box, how many diploid individuals are represented in this population?
2. What would be the color combination of the marbles needed to produce a homozygous dominant individual?
3. What would be the color combination of the marbles needed to produce a homozygous recessive individual?
4. What would be the color combination of the marbles needed to produce a heterozygous individual?
Hypothesis
State the Hardy‑Weinberg theorem in the space provided. This will be your hypothesis (it is sort of a null hypothesis…assuming no selection, etc.)
Predictions
Predict the genotypic frequencies of the population in future generations (if/then). Deductive thinking.
PART I Procedure
1. Without looking, randomly remove two marbles from the box. These two marbles represent one diploid individual in the next generation. In the table to the right, record a tally of the diploid genotype (AA, Aa, or aa) of the individual formed from these two gametes.
2. Return the marbles to the box and shake the box to reinstate the gene pool. By replacing the marbles each time, the size of the gene pool remains constant and the probability of selecting any allele should remain equal to its frequency. This procedure is called sampling with replacement.
3. Repeat steps 1 and 2 (select two marbles, record the genotype of the new individual, and return the marbles to the box) until you have recorded the genotypes for 50 individuals who will form the next generation of the population.
AA individuals  Aa individuals  aa individuals 
PART I 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 p2 + 2pq + q2 = 1 . 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 12.1.
Table 12.1 Expected Genotypic and Allelic Frequencies for the Next Generation Produced by the Marble Model
Parent
Populations 
EXPECTED New
Populations 

Allelic
Frequency 
Genotypic Number (# individuals) and Frequency (proportion)  Allelic
Frequency 

A

a  AA
# = Freq.= 
Aa
# = Freq.= 
aa
# = Freq.= 
A  a 
2. Next, using the results of your experiment , calculate the observed frequencies in the new population created as you removed marbles from the box. Record the number of diploid individuals for each genotype in Table 12.2, and calculate the frequencies for the three genotypes (AA, Aa, aa). Add the numbers of each allele, and calculate the allelic frequencies for A and a. These values are the observed frequencies in the new population. Genotypic frequencies and allelic frequencies should each equal 1.
Table 12.2 Observed Genotypic and Allelic Frequencies for the Next Generation Produced by the Marble Model.
Parent
Populations 
OBSERVED New
Populations 

Allelic
Frequency 
Genotypic Number (# of individuals) and Frequency (proportion)  Allelic
Frequency 

A

a  AA
# = Freq.= 
Aa
# = Freq.= 
aa
# = Freq.= 
A  a 
3. To compare your observed results with those expected, you can use a chisquare test of the genotype frequencies . Table 12.3 will assist in the calculation of the chisquare test. Fill out this table, but then use excel to perform a chisquared test and calculate an actual pvalue.
Table 12.3 ChiSquare of Results from the Marble Model
# of AA individuals  # of Aa individuals  # of aa individuals  
Observed value (o)  
Expected value (e)  
Deviation (o – e) = d  
d2  
d2/e  
Calculated Chisquare value (X2) = Σd2/e 
Degrees of freedom (# of possible genotypes – 1) = __________, Pvalue from excel chisquare test = ____________
Are your observed genotypic frequencies the same, or significantly different, than what is expected according to HW Equilibrium? Why?
PART II Procedures
1. Follow the same procedures as in PART I, except this time keep your eyes open as you select the marbles. Decide on one of the two colors to have a “selective advantage”, then make your selections favoring choosing that color. (You don’t need to choose them every time, but don’t choose the marbles randomly.)
2. Record your tallies for the new population below, then calculate your “observed frequencies” and record them in Table 12.4, below.
AA individuals  Aa individuals  Aa individuals 
3. Disregard the fact that you did not select the marbles randomly, and use your original “expected frequencies” from Table 12.1 (according to HW Equilibrium) to run a chisquare test on the genotype frequencies, using excel .
PART II Results
Table 12.4 Observed Genotypic and Allelic Frequencies for the Next Generation Produced by the (nonrandom) Marble Model.
Parent
Populations 
OBSERVED New
Populations 

Allelic
Frequency 
Genotypic Number (# of individuals) and Frequency (proportion)  Allelic
Frequency 

A

a  AA
# = Freq.= 
Aa
# = Freq.= 
aa
# = Freq.= 
A  a 
Chisquare test pvalue:
Are your observed genotypic frequencies the same, or significantly different, than what is expected according to HW Equilibrium? Why?
Postlab 5 Questions
(detach and turn in next week along with your abstract)
1. In your PART I newly produced generation, what proportion of your population was…
a. Homozygous dominant?
b. Homozygous recessive?
c. Heterozygous?
2. Do your results in PART I match your predictions for a population at HardyWeinberg equilibrium?
3. If you continued the PART I simulation for 25 generations…
a. What would you expect to happen to the frequencies of each allele?
b. Would that population be evolving? Explain your response.
4. Consider each of the conditions for the Hardy‑Weinberg model. Does your model meet each of those conditions?
Consider what you did in PART II:
5. How did the simulation in PART II differ from your methods in PART I?
6. Which condition necessary for HW Equilibrium was violated?
7. What did your chisquare test allow you to identify about the genotype frequencies in the new population in PART II?
8. Is the population in PART II evolving? Explain your response.
9. How could this method be useful when studying population genetics of real organisms?
10. What might be some of the difficulties you would encounter while using this in a real population genetics study?
For example, if the “A” allele has a frequency of 0.75 in a gene pool, then p = 0.75, and the frequency of “a” can be calculated as q = 0.25.
If “A” has a frequency of p = 0.75 the probability of getting an “AA” genotype is:
p2 = 0.752 = 0.5625
Likewise for “a”, with q = 0.25, probability of “aa” is:
q2 = 0.252 = 0.0625
Prob. of “Aa” or “aA” is:
2pq = 2(0.75 x 0.25) = 0.375
NOTE:
p2 + 2pq + q2 = 1
0.5625+0.375+0.0625 =1
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Bio 112 Bignami & Olave Spring 2016