- Use the allele frequencies \(p=0.1\) and \(q=0.9\) to calculate genotype frequencies using the Hardy-Weinberg formula \(p^2 + 2pq + q^2 = 1\).
- The frequency of \(CC\) is \(p^2 = (0.1)^2 = 0.01\).
- The frequency of \(Cc\) is \(2pq = 2(0.1)(0.9) = 0.18\).
- The frequency of \(cc\) is \(q^2 = (0.9)^2 = 0.81\).
- Final genotype frequencies: \(CC: \boxed{0.01}\), \(Cc: \boxed{0.18}\), \(cc: \boxed{0.81}\).
Explanation
- Understanding Hardy-Weinberg Equilibrium
The Hardy-Weinberg principle provides a way to calculate genotype frequencies in a population based on allele frequencies, assuming the population is in equilibrium. The frequencies of the alleles in the population are given as \(p = 0.1\) for the dominant allele \(C\) and \(q = 0.9\) for the recessive allele \(c\). The relationship between genotype frequencies and allele frequencies is given by the equation \(p^2 + 2pq + q^2 = 1\), where:
- \(p^2\) represents the frequency of the homozygous dominant genotype, \(CC\).
- \(2pq\) represents the frequency of the heterozygous genotype, \(Cc\).
- \(q^2\) represents the frequency of the homozygous recessive genotype, \(cc\).
- Calculating the Frequency of the CC Genotype
To find the expected frequency of the homozygous dominant genotype \(CC\), we calculate the value of \(p^2\):
\[p^2 = (0.1)^2 = 0.01\]
Thus, the expected frequency of the \(CC\) genotype is \(0.01\).
- Calculating the Frequency of the Cc Genotype
To find the expected frequency of the heterozygous genotype \(Cc\), we calculate the value of \(2pq\):
\[2pq = 2 \times 0.1 \times 0.9 = 0.18\]
Thus, the expected frequency of the \(Cc\) genotype is \(0.18\).
- Calculating the Frequency of the cc Genotype and Verification
To find the expected frequency of the homozygous recessive genotype \(cc\), we calculate the value of \(q^2\):
\[q^2 = (0.9)^2 = 0.81\]
Thus, the expected frequency of the \(cc\) genotype is \(0.81\). Finally, we can verify that these frequencies sum to 1:
\[0.01 + 0.18 + 0.81 = 1.00\]
This confirms our calculations are correct.
Examples
In population genetics, the Hardy-Weinberg principle is essential for predicting the genetic structure of a population over generations. For example, if a conservationist is monitoring a specific breed of animal with a known recessive mutation, they can use the current frequency of the mutation (allele frequency) to estimate the proportion of carriers (heterozygotes) in the population, even if those carriers do not display the recessive trait. This helps in managing breeding programs to preserve genetic diversity and health within the population.