Let's go through the problem step-by-step to calculate various frequencies and understand how they change over the generations in a clean forest environment.
### 1. Initial Phenotype Frequencies
- Initial Typica (light-colored) Moths: 490
- Initial Carbonaria (dark-colored) Moths: 510
- Total Initial Moths: 490 + 510 = 1000
The initial phenotype frequencies are as follows:
- Typica: [tex]\( \frac{490}{1000} = 0.49 \)[/tex]
- Carbonaria: [tex]\( \frac{510}{1000} = 0.51 \)[/tex]
### 2. Phenotype Frequencies in G5
From the final generation (G5) data:
- Typica in G5: 878
- Carbonaria in G5: 54
- Total Moths in G5: 878 + 54 = 932
The phenotype frequencies for G5 are:
- Typica: [tex]\( \frac{878}{932} = 0.94 \)[/tex]
- Carbonaria: [tex]\( \frac{54}{932} = 0.06 \)[/tex]
### 3. Initial Allele Frequencies
We determine the initial allele frequencies under the assumption that the population is in Hardy-Weinberg equilibrium.
Given initial frequency for the recessive allele (q or 'd'):
- [tex]\( q = 0.70 \)[/tex]
Then the frequency of the dominant allele (P):
- [tex]\( p = 1 - q = 1 - 0.70 = 0.30 \)[/tex]
### 4. Allele Frequencies in G5
We use the Hardy-Weinberg equilibrium to calculate the recessive allele frequency (q) from G5.
The frequency of homozygous recessive individuals (carbonaria) in G5 is:
- [tex]\( q^2 \)[/tex] = Frequency of carbonaria in G5 = 0.06
To find q:
- [tex]\( q = \sqrt{0.06} \approx 0.24 \)[/tex]
Then, the frequency of the dominant allele (p) in G5:
- [tex]\( p = 1 - q = 1 - 0.24 = 0.76 \)[/tex]
### Summary Tables:
#### Phenotype Frequency
[tex]\[
\begin{array}{cccc}
& Color & \textbf{Initial Frequency} & \textbf{Frequency G_5 (Round to 2 decimal places)} \\
Typica & Light & 0.49 & 0.94 \\
Carbonaria & Dark & 0.51 & 0.06 \\
\end{array}
\][/tex]
#### Allele Frequency
[tex]\[
\begin{array}{cccc}
& Allele & \textbf{Initial Allele Frequency} & \textbf{G_5 Allele Frequency (Round to 2 decimal places)} \\
q & d & 0.70 & 0.24 \\
p & & 0.30 & 0.76 \\
\end{array}
\][/tex]
Through this detailed step-by-step solution, we see how the environment has influenced the moth population, causing a change in both phenotype and allele frequencies over generations.
