Eram Haider
Chandresh Nandani
The Hardy-Weinberg Theorem Regarding Genetic Inheritance
Background
Purpose
The purpose of this lab is to demonstrate the Hardy-Weinberg Theorem regarding two alleles as a
simulated population breeds.
Materials
1 Opaque plastic cup
100 Beads of relatively same sizes (65 of one color and 35 of another)
Paper and Pencil
Calculator
Chi-square Chart
Procedure
As instructed by the lab manual
Data
Expected Genotypic and Allelic Frequencies for the Next Generation Produced by the Bead Model
Parent Populations
Allelic Frequency
A
a
0.65
0.35
New Populations
Genotypic Number (and
Allelic Frequency
Frequency)
AA
Aa
aa
A
a
0.28 0.62
0.1
0.68
0.32
Observed Genotypic and Allelic Frequencies for the Next Generation Produced by the Bead Model
Parent Populations
Allelic Frequency
A
a
0.68
0.32
New Populations
Genotypic Number (and
Allelic Frequency
Frequency)
AA
Aa
aa
A
a
0.40
0.5
0.1
0.68
0.32
Chi-Square Results from the Bead Model
AA
0.40
0.28
0.12
0.0144
0.0514
Aa
Aa
Observed Value (o)
0.50
.10
Expected Value (e)
0.62
.1
Deviation (o-e)=d
-0.12
0.00
d2
0.0144
0.00
2
d /e
0.0232
0.00
Chi-square (χ2)=Σd2/e
0.0746
The calculated χ2 value is less than the given χ2 value at degrees of freedom=2 and p < 0.05;
therefore, the data is significant
Calculations
See calculations (attached)
Data Analysis
1. The proportion of the population that was homozygous dominant was 0.40, or 40 %. The
proportions for homozygous recessive and heterozygous were 0.10 or 10 % and 0.25 or 25%,
respectively.
2. The observed results were very consistent with the expected results in terms of the allelic
frequency. The observed genotypic frequency of the homozygous recessive was exactly the same
as the expected frequency. The homozygous dominant and heterozygous observed frequencies
were a little different from the expected frequencies, but they were set each other off so that the
differences in the two observed did not have an impact on the allelic frequency.
3. COMPARE
4. The results do match our predictions with the Hardy-Weinberg Theorem since the expected
frequencies—which were calculated using the theorem—were very similar to the observed
frequencies in both the allelic and genotypic sense.
If the simulation were to continue for 25 generations, I would expect the allelic and genotypic
frequencies to hover around the same frequencies as the original population—with a little bit of
variation.
This would mean that the population is not evolving; since the genotypic frequencies are
relatively similar each generation, the population cannot be evolving. This makes sense since
evolution requires genetic drift, natural selection, etc. in order to change the population genetics.
In this type of “Hardy-Weinberg Equilibrium,” those factors are not addressed, and evolution
may not occur.
5. The model follows the Hardy-Weinberg Model as closely as it can. The population is relatively
large—50 individuals is a fairly decent sample size, with 100 alleles in total; The “matings” were
indeed random, since we used sampling with replacement, and we didn’t look to see which alleles
we were picking. There were no net changes to the gene pool—there were no alleles added or
changed in any way to the gene pool. There was no selection either—each allele had an equal
chance of being picked relative to the allelic frequency; so, the each of the dominant alleles had a
65% chance of being picked, and each of the recessive alleles had a 45% chance of being picked.
Conclusion
In this lab, the purpose was to simulate the Hardy-Weinberg Model using the Hardy-Weinberg
Theorem and beads of different colors. 100 beads, which represented alleles, made up the original
population. An allelic frequency of 65 and 45 beads were assigned by our instructor. In our case, the
dominant (65 beads) was white in color and the recessive (45 beads) were blue in color. We made sure the
sizes of the beads were relatively similar so that there was no advantage of one bead being picked over
another due to size, and we randomly chose two beads, or alleles, to contribute to the next generation.
These two alleles made up the individual regarding its genotype with the gene. Each time two beads were
chosen, those beads were returned to the cup and the cup was shaken before another two beads were
picked. We repeated the procedure fifty times and recorded to genotype of each of the fifty individuals
that made up the next generation. After the expected frequencies were recorded for the next generation,
we repeated the procedure again, with fifty more individuals as the generation after the last generation.
We then compared the observed frequencies to the expected frequencies.
The original population yielded a generation that was very close to the allelic frequency as the
original population: the allelic frequencies of this new population were off by only ±3% from the original
population. The generation after that was also very similar in both the allelic frequencies (it was the exact
same as its parental generation) and the genotypic frequencies were also very close. The homozygous
recessive was exactly what the expected frequencies were with the parental generation and the while the
homozygous dominant and the heterozygous frequencies were off by 12% (a gain of 12% in the
homozygous dominant, and a loss of 12% in the heterozygous genotypic frequencies), the offset each
other so the resulting allelic frequencies were the same. This verifies the Hardy-Weinberg Model because
the Model states that the population in which the population is very large, the matings are random, there is
no net change in the gene pool due to mutation, there is no migration of individuals into and out of the
gene pool, and there is no selection will have the same allelic frequency every generation. The procedure
followed Hardy-Weinberg’s model and kept the gene pool as stable as possible. Since the population was
large but not very large (for example, 1,000 individuals), there was a little bit of variation; however, in a
larger population, it can be expected that the allelic frequency would be nearly the same. The Chi-square
test shows, also, that there the results are significant and that the null hypothesis—that there is no
significant difference between the expected and the observed result—has a less than 5% chance of being
true.
These results mean that in a stable gene pool, the population would essentially stay the same
generation after generation. In the real world, however, the population is never stable. There are
environmental factors that cause natural selection, as well as the five factors that the Hardy-Weinberg
Theorem lays out does not occur in the real world. Phenomena such as sexual selection or mutations do
occur, which means that the gene pool will favor one trait or another, depending on all the factors. This is
a good thing because if the population were always the same, and something were to happen—such as a
natural disaster—that affected the population, the entire population would be extinct because there was no
genetic variation that allowed individuals to survive. It is the lack of stability in the gene pool that makes
the life on Earth so diverse, and it allows for life to adapt to the changing world.
Data Analysis—Non AP Lab
Experiment A. Simulation of Genetic Drift
Results
Generation
0
1
2
3
4
5
Genotypic Frequency
Observed
AA
Aa
aa
------------0.40
0.60
0
0.60
0.40
0
0.60
0.40
0
0.80
0.20
0
1.00
0
0
Allelic Frequency
Observed
A (p)
A (q)
0.5
0.50
0.70
0.30
0.80
0.20
0.80
0.20
0.90
0.10
1.00
0.00
Genotypic Frequency
Expected
p2
2pq
q2
0.25
0.50
0.25
0.49
0.42
0.09
0.64
0.32
0.04
0.64
0.32
0.04
0.81
0.18
0.01
1.00
0.00
0.00
1. We generated five generations.
2. See graph attached
3. The dominant allele fixated, and it never seemed as if the recessive allele would have ever
fixated.
4. None of the genotypic frequencies fixated because the A was required for Aa, and there was a
greater chance of the homozygous dominant and the heterozygous genotypes to be picked as well,
compared to the homozygous recessive.
5. COMPARE
Discussion
1. COMPARE
2. OBSERVE/COMPARE I would expect the dominant allele to become fixated nearly every time
if the bottleneck effect was simulated 100 times.
3. The results would have been different if the allelic frequencies were different in the sense that the
greater quantity allele (q=0.8), which is still recessive, would become fixated.
4. No because evolution is on a larger scale and has to include things such as sexual selection,
natural selection, mutations, etc. The chance events only allow the population to survive
randomly, which is not evolution.
Experiment B: Simulation of Migration: Gene Flow
1.