To determine whether a population is at Hardy-Weinberg equilibrium, we need to compare the observed genotype frequencies to the expected genotype frequencies based on the allele frequencies in the population. The expected genotype frequencies can be calculated using the Hardy-Weinberg equilibrium equation:
p^2 + 2pq + q^2 = 1
where p is the frequency of the B allele and q is the frequency of the b allele.
To calculate the allele frequencies, we can use the observed genotype frequencies as follows:
- The frequency of the B allele (p) is calculated as the sum of the frequencies of the BB and Bb genotypes, divided by the total number of alleles:
p = (2 x 405 + 90) / (2 x 500) = 0.81
- The frequency of the b allele (q) is calculated as the sum of the frequencies of the bb and Bb genotypes, divided by the total number of alleles:
q = (2 x 5 + 90) / (2 x 500) = 0.19
Now we can use these allele frequencies to calculate the expected genotype frequencies:
p^2 = (0.81)^2 = 0.6561
2pq = 2 x 0.81 x 0.19 = 0.3082
q^2 = (0.19)^2 = 0.0361
So the expected genotype frequencies are approximately:
BB: 0.6561 x 500 = 328
Bb: 0.3082 x 500 = 154
bb: 0.0361 x 500 = 18
Comparing the observed and expected genotype frequencies:
BB: Observed = 405, Expected = 328
Bb: Observed = 90, Expected = 154
bb: Observed = 5, Expected = 18
We can see that the observed and expected genotype frequencies differ quite substantially. Therefore, the population is not at Hardy-Weinberg equilibrium for this gene. The correct answer is D. No.