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A widespread population of the miniature burrowing pig (Microscrofus troglodytes) is thought to actually consist of smaller local breeding units either side of an ecotone. 120 individuals were sampled across this distribution and genotyped for the AbClocus. The results were as follows: Is this population in HWE? Test using the chi-square test. Show working. If not, how does it deviate from HW expectation? What is the result? Do the data support the original hypothesis? Can you think of any other explanation? How might you test your hypotheses further?

User Mojimi
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Answer:

Step-by-step explanation:

To determine whether the population is in Hardy-Weinberg equilibrium (HWE) for the Ab locus, we need to compare the observed genotype frequencies with the expected frequencies under HWE assumptions. The expected genotype frequencies under HWE can be calculated using the allele frequencies observed in the population.

Let's assume that the Ab locus has two alleles, A and B. We'll denote the allele frequencies as p and q, respectively, and the expected genotype frequencies under HWE as p^2 (AA), 2pq (AB), and q^2 (BB).

Given the genotyping data, we can analyze the observed genotype frequencies and calculate the expected frequencies. Let's say we obtained the following counts:

AA: 45 individuals

AB: 60 individuals

BB: 15 individuals

To determine the allele frequencies, we can calculate the allele counts. Let's denote the frequency of allele A as p and allele B as q.

Count(A) = 2 * AA + AB = 2 * 45 + 60 = 150

Count(B) = 2 * BB + AB = 2 * 15 + 60 = 90

Total count = Count(A) + Count(B) = 150 + 90 = 240

p = Count(A) / Total count = 150 / 240 = 0.625

q = Count(B) / Total count = 90 / 240 = 0.375

Now, we can calculate the expected genotype frequencies under HWE:

p^2 = (0.625)^2 = 0.390625

2pq = 2 * 0.625 * 0.375 = 0.46875

q^2 = (0.375)^2 = 0.140625

To determine whether the population is in HWE, we can perform a chi-square test using the observed and expected genotype frequencies.

Observed:

AA: 45 individuals

AB: 60 individuals

BB: 15 individuals

Expected (calculated above):

AA: (0.390625) * 120 = 46.875

AB: (0.46875) * 120 = 56.25

BB: (0.140625) * 120 = 16.875

To conduct the chi-square test, we compare the observed and expected frequencies for each genotype and calculate the chi-square statistic:

Chi-square = Σ [(Observed - Expected)^2 / Expected]

Calculating for each genotype:

AA: [(45 - 46.875)^2 / 46.875] = 0.07602

AB: [(60 - 56.25)^2 / 56.25] = 0.26765

BB: [(15 - 16.875)^2 / 16.875] = 0.10741

Summing the values:

Chi-square = 0.07602 + 0.26765 + 0.10741 = 0.45108

Degrees of freedom (df) = Number of genotypes - 1 = 3 - 1 = 2

To determine whether the population is in HWE, we compare the chi-square statistic with the critical value from the chi-square distribution table for the given significance level and degrees of freedom. If the calculated chi-square value exceeds the critical value, we reject the null hypothesis of HWE.

Alternatively, we can use statistical software or an online chi-square calculator to obtain the p-value associated with the calculated chi-square value. If the p-value is below the chosen significance level (e.g., 0.05), we reject the null hypothesis.

Further analysis:

If the population is not in HWE, it suggests that there are deviations from the expected genotype frequencies. The deviations could indicate factors such as non-random mating, genetic drift, selection, mutation, or migration.

To explore the deviations further and understand the factors contributing to the population's deviation from HWE, additional investigations can be conducted. These might include:

1. Investigating mating patterns: Assessing whether individuals are preferentially mating with individuals of certain genotypes or from specific breeding units.

2. Genetic drift: Analyzing the population size and potential bottlenecks or founder effects that could contribute to deviations from HWE.

3. Selection: Examining whether natural selection is acting on the Ab locus, leading to deviations from expected genotype frequencies.

4. Mutation and migration: Assessing the potential impact of new mutations or migration from other populations on the observed genotype frequencies.

By conducting these additional investigations, we can gain a better understanding of the factors influencing the population's deviation from HWE and further test the original hypothesis.

User Jason Novak
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