- The calculated Chi-squared value is \(\approx 5.11\), which is greater than the critical value of \(3.84\), indicating the population is not in Hardy-Weinberg equilibrium.
- Allele frequency for C increased from \(0.1\) to \(0.145\).
- Allele frequency for c decreased from \(0.9\) to \(0.855\).
- The C allele is increasing.
- Final Answer: \(\text{Equilibrium: No, Increasing allele: C}\)
Explanation
- Assess Hardy-Weinberg equilibrium using the Chi-squared test
To determine if the population is in Hardy-Weinberg equilibrium, we compare the actual genotype counts to the expected genotype counts using the Chi-squared (\(\chi^2\)) test. The \(\chi^2\) statistic is calculated as \(\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}\), where \(O_i\) is the actual count and \(E_i\) is the expected count.
For the given data:
- CC: \(O=2, E=1 \implies \frac{(2-1)^2}{1} = 1\)
- Cc: \(O=28, E=20 \implies \frac{(28-20)^2}{20} = \frac{64}{20} = 3.2\)
- cc: \(O=80, E=89 \implies \frac{(80-89)^2}{89} = \frac{81}{89} \approx 0.910\)
Adding these values, we get \(\chi^2 = 1 + 3.2 + 0.910 = 5.11\).
For 1 degree of freedom (3 genotypes - 2 alleles), the critical value at the 0.05 significance level is 3.84. Since 5.11 > 3.84, we reject the null hypothesis of Hardy-Weinberg equilibrium. The population is not in equilibrium.
- Calculate and compare allele frequencies
To identify which allele is increasing, we compare the allele frequencies calculated from the observed counts to the frequencies in the expected (baseline) counts.
The total number of individuals is \(N = 110\), so there are \(220\) total alleles.
- Expected frequencies:
- Frequency of C (\(p_{exp}\)): \(\frac{2(1) + 20}{220} = \frac{22}{220} = 0.1\)
- Frequency of c (\(q_{exp}\)): \(\frac{2(89) + 20}{220} = \frac{198}{220} = 0.9\)
- Observed frequencies:
- Frequency of C (\(p_{obs}\)): \(\frac{2(2) + 28}{220} = \frac{32}{220} \approx 0.145\)
- Frequency of c (\(q_{obs}\)): \(\frac{2(80) + 28}{220} = \frac{188}{220} \approx 0.855\)
Comparing these values, the frequency of the C allele has increased from \(0.1\) to \(0.145\), while the frequency of the c allele has decreased from \(0.9\) to \(0.855\). Therefore, the C allele is increasing in frequency.
Examples
Biologists use the Hardy-Weinberg principle as a "null model" to detect evolutionary changes in wild populations. By comparing observed genotype frequencies with expected ones, they can determine if a population is undergoing natural selection, genetic drift, or migration. For example, if a specific gene variant that provides resistance to disease becomes more common than expected in a population, scientists can identify which allele is under positive selection pressure.