- Identify the initial frequency of the recessive genotype as \(q^2 = 0.169\).
- Calculate the recessive allele frequency \(q = \sqrt{0.169} \approx 0.411\).
- Apply the Hardy-Weinberg principle where \(p + q = 1\), leading to \(p = 1 - 0.411\).
- Determine the final value for the dominant allele frequency, which is \(\boxed{0.589}\).
Explanation
- Analyze the provided data and problem statement
The problem asks us to determine the expected allele frequency \(p\) (the dominant allele frequency) for a population of four o'clock plants in the next generation. We are given the population size, which is \(1,000\) plants, and the expected counts for each phenotype in the next generation: Red (AA) = \(105\), Pink (Aa) = \(484\), and White (aa) = \(411\). Additionally, we are given the condition for the current population as \(q^2 = 0.169\), where \(q\) represents the recessive allele frequency.
- Calculate the expected p value using allele frequencies
In a population governed by Hardy-Weinberg equilibrium, the allele frequencies \(p\) and \(q\) remain constant from one generation to the next, provided the evolutionary forces such as mutation, selection, genetic drift, and gene flow are not acting upon the population. The initial condition provides the frequency of the recessive phenotype (aa), which is \(q^2 = 0.169\). From this, we can calculate the frequency of the recessive allele \(q\) by taking the square root:
\[q = \sqrt{0.169} \approx 0.411\]
Since the sum of the allele frequencies in the population must equal \(1\) (i.e., \(p + q = 1\)), we can find the frequency of the dominant allele \(p\) by subtracting \(q\) from \(1\):
\[p = 1 - q = 1 - 0.411 = 0.589\]
This represents the expected value of \(p\) in the next generation under the assumptions of Hardy-Weinberg equilibrium.
- Conclusion and comparison with options
We have calculated the expected value of \(p\) using the provided equilibrium condition, yielding \(0.589\). Comparing this result with the given choices:
- \(0.105\)
- \(0.411\)
- \(0.516\)
- \(0.589\)
The calculated value of \(0.589\) matches the final option provided in the problem. Therefore, the expected \(p\) value in the next generation is \(0.589\).
Examples
This calculation is essential in population genetics, where researchers predict how genetic traits will be passed on across generations. For example, by knowing the frequency of a recessive trait (like white flower color in four o'clock plants), one can determine the frequency of the dominant allele in the population, which helps in understanding the genetic structure and potential evolution of the species. Using the formula \(p = 1 - \sqrt{q^2}\), scientists can effectively model and predict future phenotypic distributions.