Lab: Population Genetics I: Hardy-Weinberg Theorem
Procedure
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.
Table 1
| AA individuals |
Aa individuals |
aa individuals |
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PART II Procedures-
1. Follow the same procedures as in PART 1, 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 2 below.
Table 2
| AA individuals |
Aa individuals |
aa individuals |
|
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3. Disregard the fact that you did not select the marbles randomly, and use your original "expected frequencies" from Table 3 (according to H-W Equilibrium) to run a chi-square test on the genotype frequencies, using excel.
Table 3
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Parent
Populations
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EXPECTED New
Populations
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Allelic
Frequency
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Genotypic Number (# individuals) and Frequency (proportion)
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Allelic
Frequency
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A
|
a
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AA
# =
Freq.=
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Aa
# =
Freq.=
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aa
# =
Freq.=
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A
|
a
|
Read the Lab procedures and watch the online Hardy-Weinberg video (https://youtu.be/xPkOAnK20kw and posted on BlackBoard), then complete this assignment prior to lab.
1. The Hardy-Weinberg Theorem states...
2. What are the five key assumptions that are necessary for the H-W Theorem to be valid?
3. Write the Hardy-Weinberg equation:
4. Dominant allele "R" has a frequency (p) of 0.45 in a particular gene pool. Calculate the following showing all your work and using the proper variables for each value (e.g. p, q, p2, q2, 2pg).
a. The frequency of allele "r" in that same gene pool?
b. The proportion of the population that has the genotype RR.
c. The proportion of the population that has the genotype Rr.
d. The proportion of the population that has the genotype rr.
5. If 17% of a population displays the recessive trait for Disease B, what are the frequencies of the recessive allele "b" and the dominant allele "B" in the gene pool?
6. You perform an experiment where you allow a large population of fruit flies to mate randomly. The parental generation had 30% homozygous recessive genotypes. The F1 generation consisted of 100 flies, 40 of which displayed the recessive trait. Calculate the expected values for each phenotype assuming Hardy-Weinberg equilibrium, then fill in the table below and use the Chi-Square test instructions document (posted online) to compare your calculated X2 value with the tabulated X2 value for a P-value of 0.05.
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# of dominant phenotypeindividuals
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# of recessive phenotype individuals
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Observed value (o)
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Expected value (e)
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Deviation (o - e) = d
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d2
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d2/e
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Calculated Chi-square (X2) = Σd2/e
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Degrees of Freedom
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Tabulated X2 value at P=0.05 (from X2 instructions document)
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a. According to your analysis above, are the observed proportion of genotypes in the F1 generation the same, or significantly different, than those expected according to the H-W theorem?
b. If you allowed your F1 generation to mate, what would you expect the frequency of the recessive allele (q) to be in the F2 generation, assuming the H-W theorem applies?