- Identify the population size \(N = 110\) and the given frequencies for the three genotypes.
- Apply the formula for expected frequency: \(N_{genotype} = N \times f(genotype)\).
- Multiply the total population by each genotype frequency to find the counts for \(CC\), \(Cc\), and \(cc\).
- Verify the total count sums to 110.
- The expected counts are: \(CC = \boxed{1.1}\), \(Cc = \boxed{19.8}\), and \(cc = \boxed{89.1}\).
Explanation
- Analysis of the Population and Frequencies
The population consists of \(N = 110\) dogs, with the following genotype frequencies: \(f(CC) = 0.01\), \(f(Cc) = 0.18\), and \(f(cc) = 0.81\). The total sum of frequencies is \(0.01 + 0.18 + 0.81 = 1.00\), which confirms that these frequencies represent the entire population. Our objective is to determine the expected number of dogs for each of these three genotypes.
- Methodology for Calculating Expected Numbers
To find the expected number of individuals with a specific genotype in a population, we multiply the total number of individuals by the frequency of that genotype. Specifically:
- The expected number of dogs with genotype \(CC\) is \(N_{CC} = N \times f(CC) = 110 \times 0.01\).
- The expected number of dogs with genotype \(Cc\) is \(N_{Cc} = N \times f(Cc) = 110 \times 0.18\).
- The expected number of dogs with genotype \(cc\) is \(N_{cc} = N \times f(cc) = 110 \times 0.81\).
- Calculation and Verification
Performing the multiplications:
- For \(CC\): \(110 \times 0.01 = 1.1\).
- For \(Cc\): \(110 \times 0.18 = 19.8\).
- For \(cc\): \(110 \times 0.81 = 89.1\).
To verify the accuracy of these calculations, we sum the expected counts: \(1.1 + 19.8 + 89.1 = 110.0\). The sum matches the original population size of 110, confirming our calculations are correct.
- Final Results
Based on the calculations above, the expected number of dogs for each genotype in a population of 110 is:
- Dogs with genotype \(CC\) = \(\boxed{1.1}\)
- Dogs with genotype \(Cc\) = \(\boxed{19.8}\)
- Dogs with genotype \(cc\) = \(\boxed{89.1}\)
Examples
Understanding expected frequencies is fundamental in population genetics, as it helps researchers predict the prevalence of specific traits or genetic diseases within a group. For example, if a specific genotype is associated with a manageable health condition, a breeder can estimate how many puppies in a litter or an entire population might require special veterinary care. This predictive modeling allows for better resource management and responsible breeding practices.