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\begin{tabular}{|c|c|c|c|c|c|c|}
\hline & Moths Released & [tex]$G _1$[/tex] & [tex]$G _2$[/tex] & [tex]$G _3$[/tex] & [tex]$G _4$[/tex] & [tex]$G_5$[/tex] \\
\hline Typica & 490 & 301 & 387 & 456 & 556 & 878 \\
\hline Carbonaria & 510 & 210 & 190 & 186 & 166 & 54 \\
\hline Total & 1000 & 511 & 577 & 642 & 722 & 932 \\
\hline
\end{tabular}

Phenotype Frequency

\begin{tabular}{cccc}
& Color & Initial Frequency & \begin{tabular}{c}
Frequency [tex]$G _5$[/tex] \\
(Round to 2 decimal places)
\end{tabular} \\
Typica & Light & 0.49 & 0.94 \\
Carbonaria & Dark & 0.51 & 0.06
\end{tabular}

Allele Frequency

\begin{tabular}{cccc|}
& Allele & Initial Allele Frequency & \begin{tabular}{c}
[tex]$G _5$[/tex] Allele Frequency \\
(Round to 2 decimal places)
\end{tabular} \\
\hline q & d & 0.70 & [tex]$d$[/tex] \\
\hline D & 0.30 & 0 \\
\hline
\end{tabular}

Genotype Frequency

\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline & Moths & Genotype & Color & \begin{tabular}{l}
Moths \\
Released
\end{tabular} & \begin{tabular}{l}
Initial \\
Frequency
\end{tabular} & Frequency [tex]$G _5$[/tex] & \begin{tabular}{l}
Number of \\
Moths [tex]$G _5$[/tex]
\end{tabular} \\
\hline[tex]$q^2$[/tex] & Typica & dd & Light & 490 & 0.49 & & \\
\hline 2 pq & Carbonaria & Dd & Dark & 420 & 0.42 & & \\
\hline[tex]$p^2$[/tex] & Carbonaria & DD & Dark & 90 & 0.09 & & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Let's work through the genotype frequencies, the number of moths released, and the changes observed over time in generations up to [tex]\(G_5\)[/tex]. The following steps outline the process of understanding these changes.

### 1. Initial Phenotype Frequencies

- Typica (Light) at the initial frequency: [tex]\(0.49\)[/tex]
- Carbonaria (Dark) at the initial frequency: [tex]\(0.51\)[/tex]

### 2. Frequencies at [tex]\(G_5\)[/tex]

- Typica (Light) at [tex]\(G_5\)[/tex] frequency: [tex]\(0.94\)[/tex]
- Carbonaria (Dark) at [tex]\(G_5\)[/tex] frequency: [tex]\(0.06\)[/tex]

### 3. Initial Allele Frequencies

- Allele [tex]\(q\)[/tex] (d) initial frequency: [tex]\(0.70\)[/tex]
- Allele [tex]\(p\)[/tex] (D) initial frequency: [tex]\(0.30\)[/tex]

### 4. Genotype Frequencies and Numbers

### Initial Genotype Frequencies and Numbers:

#### Typica (Light), Genotype [tex]\(dd\)[/tex], [tex]\(q^2\)[/tex]:

- Initial Frequency: [tex]\(0.49\)[/tex]
- Moths Released: 490
- [tex]\(dd\)[/tex] Moths at Initial Generation: [tex]\(490.0\)[/tex]

#### Carbonaria (Dark), Genotype [tex]\(Dd\)[/tex], [tex]\(2pq\)[/tex]:

- Initial Frequency: [tex]\(0.42\)[/tex]
- Moths Released: 420
- [tex]\(Dd\)[/tex] Moths at Initial Generation: [tex]\(420.0\)[/tex]

#### Carbonaria (Dark), Genotype [tex]\(DD\)[/tex], [tex]\(p^2\)[/tex]:

- Initial Frequency: [tex]\(0.09\)[/tex]
- Moths Released: 90
- [tex]\(DD\)[/tex] Moths at Initial Generation: [tex]\(90.0\)[/tex]

### Frequencies and Number of Moths at Generation [tex]\(G_5\)[/tex]:

#### Typica (Light), Genotype [tex]\(dd\)[/tex]:

- Frequency at [tex]\(G_5\)[/tex]: [tex]\(0.94\)[/tex]
- Number of Moths at [tex]\(G_5\)[/tex]: [tex]\(876.08\)[/tex]

#### Carbonaria (Dark), Genotype [tex]\(Dd\)[/tex]:

- Frequency at [tex]\(G_5\)[/tex]: [tex]\(0.06\)[/tex]
- Number of Moths at [tex]\(G_5\)[/tex]: [tex]\(55.92\)[/tex]

#### Carbonaria (Dark), Genotype [tex]\(DD\)[/tex]:

- There were no [tex]\(DD\)[/tex] (Dark) moths at [tex]\(G_5\)[/tex], which shows:
- Frequency at [tex]\(G_5\)[/tex]: [tex]\(0.0\)[/tex]
- Initial released moths: [tex]\(90.0\)[/tex] (since no [tex]\(DD\)[/tex] dark moths remained by [tex]\(G_5\)[/tex])

### Final Table Creation:

Finally, we can fill in the required table based on the data we have:

\begin{tabular}{|c|c|c|c|c|c|}
\hline
Genotype & Phenotype & Initial Frequency & Initial Number of Moths & Frequency at [tex]\(G_5\)[/tex] & Number of Moths at [tex]\(G_5\)[/tex] \\
\hline
[tex]$q^2$[/tex] & Light (dd) & 0.49 & 490.0 & 0.94 & 876.08 \\
\hline
[tex]$2pq$[/tex] & Dark (Dd) & 0.42 & 420.0 & 0.06 & 55.92 \\
\hline
[tex]$p^2$[/tex] & Dark (DD) & 0.09 & 90.0 & 0.0 & 90.0 \\
\hline
\end{tabular}

This table summarizes the initial frequencies and number of moths for each genotype and the state at [tex]\(G_5\)[/tex] after several generations.

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