Answered

In pea plants, purple flower color, $C$, is dominant to white flower color, $c$. The table shows the frequencies of the alleles.



\begin{table}

\captionsetup{labelformat=empty}

\caption{Allele Frequency for Flower Color in Peas}


Generation		$p$$q$

1		0.600.40

2		0.640.36

3		0.750.25

4		0.800.20




\end{table}



Which generation showed the greatest frequency of having one of each allele?


Ageneration 1
Bgeneration 2
Cgeneration 3
Dgeneration 4

Verified Answer :

  • Identify the heterozygous genotype frequency formula as \(2pq\).
  • Calculate the values for each generation: Gen 1 (\(0.48\)), Gen 2 (\(0.4608\)), Gen 3 (\(0.375\)), and Gen 4 (\(0.32\)).
  • Compare the results to determine the maximum frequency.
  • The highest value is \(\boxed{\text{Generation 1}}\).

Explanation

  1. Analysis of Genotype Frequencies

The problem asks us to determine which generation has the highest frequency of heterozygous individuals. According to the Hardy-Weinberg principle, for a gene with two alleles, where \(p\) is the frequency of the dominant allele \(C\) and \(q\) is the frequency of the recessive allele \(c\), the frequency of heterozygous individuals (genotype \(Cc\)) is given by the expression \(2pq\). We are given the values for \(p\) and \(q\) for four consecutive generations and need to calculate this value for each to find the maximum.

  1. Calculation of Heterozygous Frequencies

We calculate the frequency of heterozygotes (\(2pq\)) for each generation:

  • Generation 1: \(2 \times 0.60 \times 0.40 = 0.48\)
  • Generation 2: \(2 \times 0.64 \times 0.36 = 0.4608\)
  • Generation 3: \(2 \times 0.75 \times 0.25 = 0.375\)
  • Generation 4: \(2 \times 0.80 \times 0.20 = 0.32\)
  1. Comparison and Conclusion

Comparing the calculated values:

  • Generation 1: \(0.48\)
  • Generation 2: \(0.4608\)
  • Generation 3: \(0.375\)
  • Generation 4: \(0.32\)

The highest frequency of \(0.48\) corresponds to Generation 1. Therefore, Generation 1 shows the greatest frequency of having one of each allele. The final answer is \(\boxed{\text{Generation 1}}\).

Examples

Understanding allele frequencies is crucial in fields like conservation biology and medical genetics. For example, if a rare genetic disease is recessive, scientists can calculate the proportion of "carriers" (heterozygous individuals) in a population using the \(2pq\) formula. This helps them assess the risk of the disease appearing in future generations and develop public health strategies to manage or prevent the trait if necessary. Applying this simple algebraic formula allows researchers to track how genetic diversity changes over time within a group.

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