In pea plants, purple flower color, $C$, is dominant to white flower color, $c$. The table shows the frequencies of the dominant and recessive alleles in three generations of peas in a garden. Generation 1 has 200 flowers, generation 2 has 400, and generation 3 has 400.

\begin{table}

\captionsetup{labelformat=empty}

\caption{Allele Frequency for Flower Color in Peas}

Generation $p$ $q$

1 0.5 0.5

2 0.6 0.4

3 0.7 0.3

\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.

Question

taschneider2015 taschneider2015

06-11-2026
Biology

Answered

In pea plants, purple flower color, $C$, is dominant to white flower color, $c$. The table shows the frequencies of the dominant and recessive alleles in three generations of peas in a garden. Generation 1 has 200 flowers, generation 2 has 400, and generation 3 has 400.

\begin{table}

\captionsetup{labelformat=empty}

\caption{Allele Frequency for Flower Color in Peas}

Generation $p$ $q$

1 0.5 0.5

2 0.6 0.4

3 0.7 0.3

\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 :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-06T20:43:31-05:00

Calculate white flowers: $W_1 = 50$, $W_2 = 64$, $W_3 = 36$.
Calculate purple flowers: $P_1 = 150$, $P_2 = 336$, $P_3 = 364$.
Compare the calculated values against the provided options.
The correct statement is: $\boxed{\text{Generation 1 has fewer purple flowers than generation 3.}}$

Explanation

Analyze the population and allele frequencies

To analyze the population of pea plants, we use the Hardy-Weinberg equilibrium principle. The frequency of the dominant allele ($p$) and the recessive allele ($q$) allows us to determine the distribution of phenotypes. White flowers, which have the recessive genotype ($cc$), appear with a frequency of $q^2$. Purple flowers, having either the dominant homozygous ($CC$) or heterozygous ($Cc$) genotypes, appear with a frequency of $1 - q^2$ (or $p^2 + 2pq$). We multiply these frequencies by the total population ($N$) for each generation to find the absolute number of each flower color.

Calculate number of white and purple flowers per generation

We calculate the number of white ($W$) and purple ($P$) flowers for each generation:

Generation 1 ($N_1 = 200, q_1 = 0.5$):
$f(W)_1 = (0.5)^2 = 0.25$
$W_1 = 200 \times 0.25 = 50$
$P_1 = 200 - 50 = 150$
Generation 2 ($N_2 = 400, q_2 = 0.4$):
$f(W)_2 = (0.4)^2 = 0.16$
$W_2 = 400 \times 0.16 = 64$
$P_2 = 400 - 64 = 336$
Generation 3 ($N_3 = 400, q_3 = 0.3$):
$f(W)_3 = (0.3)^2 = 0.09$
$W_3 = 400 \times 0.09 = 36$
$P_3 = 400 - 36 = 364$

Evaluate the statements and conclude

Now we evaluate the four given statements:

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

Therefore, the statement "Generation 1 has fewer purple flowers than generation 3" is the correct description of the population.

Examples

This method of calculating genotype distributions is fundamental in population genetics. For example, researchers use these calculations to track how environmental changes or selective pressures affect the prevalence of specific traits in wild populations over time, allowing for the prediction of future population health and diversity. For instance, if $p$ and $q$ represent alleles for drought resistance, calculating $q^2$ helps predict how many plants in a field might struggle during a dry season.