To solve this genetics problem, we'll use a Punnett square to determine the different combinations of traits in the offspring when two fruit flies that are heterozygous for body color and eye color are crossed.
Here, we have:
- Body color: Brown (B) is dominant to black (b). So, possible genotypes are BB (brown), Bb (brown), and bb (black).
- Eye color: Red (R) is dominant to brown (r). So, possible genotypes are RR (red), Rr (red), and rr (brown).
Since both flies are heterozygous for both traits, their genotypes are BbRr. We will set up a Punnett square for a dihybrid cross (two traits).
Here is the step-by-step process to determine the progeny ratios:
1. Determine the gametes: Each parent can produce four types of gametes: BR, Br, bR, and br.
2. Set up the Punnett square: The Punnett square will be a 4x4 grid because each parent can produce four types of gametes.
3. Fill in the Punnett square with all possible combinations:
[tex]\[
\begin{array}{cc|c|c|c|c|}
& & \text{BR} & \text{Br} & \text{bR} & \text{br} \\
\hline
\text{BR} & & \text{BBRR} & \text{BBRr} & \text{BbRR} & \text{BbRr} \\
\hline
\text{Br} & & \text{BBRr} & \text{BBrr} & \text{BbRr} & \text{Bbrr} \\
\hline
\text{bR} & & \text{BbRR} & \text{BbRr} & \text{bbRR} & \text{bbRr} \\
\hline
\text{br} & & \text{BbRr} & \text{Bbrr} & \text{bbRr} & \text{bbrr} \\
\hline
\end{array}
\][/tex]
4. Count the phenotypes:
- Brown body and red eyes (BBRR, BBRr, BbRR, BbRr): These combinations are BB(RR or Rr), Bb(RR or Rr), leading to 9 out of the 16 cells.
- Brown body and brown eyes (BBrr, Bbrr): These combinations are BBrr, Bbrr, leading to 3 out of the 16 cells.
- Black body and red eyes (bbRR, bbRr): These combinations are bb(RR or Rr), leading to 3 out of the 16 cells.
- Black body and brown eyes (bbrr): This combination is just bbrr, leading to 1 out of the 16 cells.
The phenotypic ratio is as follows:
- Brown body and red eyes: 9/16
- Brown body and brown eyes: 3/16
- Black body and red eyes: 3/16
- Black body and brown eyes: 1/16
Thus, the answer to the question is:
- Brown body and red eyes: [tex]\( \frac{9}{16} \)[/tex] or 9 out of 16
- Brown body and brown eyes: [tex]\( \frac{3}{16} \)[/tex] or 3 out of 16
- Black body and red eyes: [tex]\( \frac{3}{16} \)[/tex] or 3 out of 16
- Black body and brown eyes: [tex]\( \frac{1}{16} \)[/tex] or 1 out of 16
