DNA was collected from 100 people and subjected to a restriction digest with BamHI. These samples were then analyzed using Stouthern blots. Three different patterns of hybridization were seen on the blots: 56 samples showed a single band of 6.3kb, 6 samples showed a single band of 4.1kb, and 38 showed both the 6.3 and 4.1 kb bands.
Use the chi square test to determine whether or not this population is in Hard-Weinberg equilibrium.
Someone please guide me how to start working on this problem. Thanks
6/100, or 0.06 had only one allele, so they are, for example, cc. So, 0.06 is q^2. 56/100, or 0.56 are another allele, so, .56 is p^2. And the one with the mixed alleles is 2pq. So, remember, to satisfy Hardy-Weinberg, p + q = 1, and p^2 + 2pq + q^2 = 1.
To determine if the population is in Hardy-Weinberg equilibrium, we need to compare the observed genetic distribution with the expected distribution based on the Hardy-Weinberg equilibrium equation.
Step 1: Assign variables to the different genetic frequencies:
Let p represent the frequency of one allele.
Let q represent the frequency of the other allele.
Step 2: Use the given data to calculate the observed genetic frequencies:
From the information given, we know that:
- 56 samples had a single band of 6.3kb, representing the frequency of q^2.
- 6 samples had a single band of 4.1kb, representing the frequency of p^2.
- 38 samples showed both the 6.3kb and 4.1kb bands, representing the frequency of 2pq.
So, the observed genetic frequencies are:
q^2 = 56/100 = 0.56
p^2 = 6/100 = 0.06
2pq = 38/100 = 0.38
Step 3: Apply the Hardy-Weinberg equilibrium equation:
According to the Hardy-Weinberg equilibrium, p + q = 1, and p^2 + 2pq + q^2 = 1.
Since p + q = 1, we can solve for p:
p = 1 - q
Now substitute each term in the equation p^2 + 2pq + q^2 = 1 with the assigned variable:
(1 - q)^2 + 2(1 - q)q + q^2 = 1
Simplifying the equation gives us:
1 - 2q + q^2 + 2q - 2q^2 + q^2 = 1
-q^2 + q^2 + 1 - 2q + 2q = 1
0 = 0
Step 4: Interpret the results:
Since the equation simplifies to 0 = 0, we can conclude that the observed frequencies match the expected frequencies based on the Hardy-Weinberg equilibrium equation. Therefore, we can assume that the population is in Hardy-Weinberg equilibrium.
Step 5: Calculate the chi-square statistic:
To formally test if the observed frequencies are significantly different from the expected frequencies, we can use the chi-square test. The chi-square test calculates the chi-square statistic, which will tell us if the differences between the observed and expected frequencies are statistically significant. The formula for the chi-square statistic is:
χ² = ∑ [(observed - expected)² / expected]
Observation: The observed frequencies are:
q^2 = 0.56
p^2 = 0.06
2pq = 0.38
Expected frequencies can be calculated based on the Hardy-Weinberg equilibrium equation:
Expected q^2 frequency = p^2 * total population = 0.06 * 100 = 6
Expected 2pq frequency = 2pq * total population = 0.38 * 100 = 38
Expected p^2 frequency = q^2 * total population = 0.56 * 100 = 56
Now substitute these values into the chi-square formula:
χ² = [(56 - 6)² / 6] + [(6 - 6)² / 6] + [(38 - 38)² / 38] = ...
Calculate the chi-square value and compare it to the critical chi-square value for the desired level of significance and degrees of freedom to determine if the observed frequency distribution significantly deviates from the expected distribution.
Note: The degrees of freedom for the chi-square test in this case is (number of phenotypes - 1), which is (3 - 1) = 2.
I hope this explanation helps you work through the problem. Good luck with your analysis!