Answered

The table below shows the frequencies of dominant and recessive alleles in three generations of peas in a garden. Generation 1 has 200 flowers, generation 2 has 400 flowers, and generation 3 has 400 flowers.



\begin{table}

\captionsetup{labelformat=empty}

\caption{Allele Frequency for Flower Color in Peas}


Generation		$p$$q$

1		0.50.5

2		0.60.4

3		0.70.3




\end{table}



Which best describes the number of flowers?

AGeneration 1 has more white flowers than generation 2.
BGeneration 3 has more white flowers than generation 2.
CGeneration 2 has fewer purple flowers than generation 1.
DGeneration 1 has fewer purple flowers than generation 3.

Verified Answer :

  • We determine the number of white flowers using the formula \(N \times q^2\) and purple flowers using \(N \times (1 - q^2)\).
  • Calculated counts are:
  • Generation 1: 50 white, 150 purple.
  • Generation 2: 64 white, 336 purple.
  • Generation 3: 36 white, 364 purple.
  • Comparing these, we find that \(150 < 364\).
  • Final Answer: \(\boxed{\text{Generation 1 has fewer purple flowers than generation 3}}\)

Explanation

  1. Analysis of Hardy-Weinberg principles and data setup

To solve this problem, we use the Hardy-Weinberg equilibrium principles, which state that in a stable population, the genotype frequencies are related to allele frequencies as follows: the frequency of homozygous recessive individuals (white flowers) is \(q^2\), and the frequency of individuals with at least one dominant allele (purple flowers) is \(1 - q^2\). We calculate these values for each generation, using the provided total population sizes (\(N_1=200, N_2=400, N_3=400\)) and allele frequencies (\(p\) for purple, \(q\) for white).

  1. Calculations for generation 1

For generation 1: \(N_1 = 200\), \(q_1 = 0.5\).

  • Frequency of white flowers: \(q_1^2 = (0.5)^2 = 0.25\).
  • Number of white flowers: \(200 \times 0.25 = 50\).
  • Frequency of purple flowers: \(1 - 0.25 = 0.75\).
  • Number of purple flowers: \(200 \times 0.75 = 150\).
  1. Calculations for generation 2

For generation 2: \(N_2 = 400\), \(q_2 = 0.4\).

  • Frequency of white flowers: \(q_2^2 = (0.4)^2 = 0.16\).
  • Number of white flowers: \(400 \times 0.16 = 64\).
  • Frequency of purple flowers: \(1 - 0.16 = 0.84\).
  • Number of purple flowers: \(400 \times 0.84 = 336\).
  1. Calculations for generation 3

For generation 3: \(N_3 = 400\), \(q_3 = 0.3\).

  • Frequency of white flowers: \(q_3^2 = (0.3)^2 = 0.09\).
  • Number of white flowers: \(400 \times 0.09 = 36\).
  • Frequency of purple flowers: \(1 - 0.09 = 0.91\).
  • Number of purple flowers: \(400 \times 0.91 = 364\).
  1. Comparison and conclusion

Now we compare the results across the generations:

  • White flowers: Gen 1 (50), Gen 2 (64), Gen 3 (36).
  • Purple flowers: Gen 1 (150), Gen 2 (336), Gen 3 (364).

Evaluating the options:

  • "Generation 1 has more white flowers than generation 2" is \(50 > 64\) (False).
  • "Generation 3 has more white flowers than generation 2" is \(36 > 64\) (False).
  • "Generation 2 has fewer purple flowers than generation 1" is \(336 < 150\) (False).
  • "Generation 1 has fewer purple flowers than generation 3" is \(150 < 364\) (True).

Therefore, the last statement is correct. The final answer is "Generation 1 has fewer purple flowers than generation 3".

Examples

Hardy-Weinberg equilibrium is essential in conservation biology and population genetics to predict how genetic traits change over time. By calculating the number of individuals with specific phenotypes, scientists can track whether a population is evolving or adapting to new environmental pressures. For example, if you observe the distribution of flower colors in a greenhouse, this method allows you to verify if the population follows predicted genetic patterns or if external factors are influencing survival rates.

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