Sure! Let's walk through the problem of determining the phenotypic ratios from the cross of two fruit flies that are heterozygous for both body color (B/b) and eye color (E/e). The traits are defined as follows:
- Brown body color (B) is dominant over black body color (b).
- Red eye color (E) is dominant over brown eye color (e).
Both parents have the genotype [tex]\( BbEe \)[/tex]. To determine the phenotypic ratios of their offspring, we need to fill in a Punnett square for these dihybrid crosses.
### Setting Up the Punnett Square
Each cell in the Punnett square will show the genotype combination from one [tex]\( BbEe \)[/tex] parent with the other. The potential gametes from each [tex]\( BbEe \)[/tex] parent are BE, Be, bE, and be. Let's create the Punnett square:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
& BE & Be & bE & be \\
\hline
BE & BBEE & BBEe & BbEE & BbEe \\
\hline
Be & BBEe & BBee & BbEe & Bbee \\
\hline
bE & BbEE & BbEe & bbEE & bbEe \\
\hline
be & BbEe & Bbee & bbEe & bbee \\
\hline
\end{array}
\][/tex]
Each cell represents a different genotype for the offspring. Now let's categorize these genotypes according to their phenotypes:
### Counting the Phenotypes
1. Brown body and red eyes (B_E_):
- BBEE
- BBEe
- BbEE
- BbEe
There are 9 instances of this phenotype:
- Cells: 1 (BBEE), 2 (BBEe), 5 (BBEe), 6 (BbEe), 9 (BbEE), 10 (BbEe), 13 (BbEe), 14 (BbEe), 17 (BbEe).
2. Brown body and brown eyes (B_ee):
- BBee
- Bbee
There are 3 instances of this phenotype:
- Cells: 7 (BBee), 11 (Bbee), 15 (Bbee).
3. Black body and red eyes (bbE_):
- bbEE
- bbEe
There are 3 instances of this phenotype:
- Cells: 3 (bbEE), 8 (bbEe), 12 (bbEe).
4. Black body and brown eyes (bbee):
- bbee
There is 1 instance of this phenotype:
- Cell: 16
### Calculating Ratios
We have a total of 16 offspring (all cells in the Punnett square).
- Brown body and red eyes: 9 out of 16, or a ratio of [tex]\( \frac{9}{16} = 0.5625 \)[/tex].
- Brown body and brown eyes: 3 out of 16, or a ratio of [tex]\( \frac{3}{16} = 0.1875 \)[/tex].
- Black body and red eyes: 3 out of 16, or a ratio of [tex]\( \frac{3}{16} = 0.1875 \)[/tex].
- Black body and brown eyes: 1 out of 16, or a ratio of [tex]\( \frac{1}{16} = 0.0625 \)[/tex].
### Summary
- Brown body and red eyes: 9 offspring, ratio 0.5625
- Brown body and brown eyes: 3 offspring, ratio 0.1875
- Black body and red eyes: 3 offspring, ratio 0.1875
- Black body and brown eyes: 1 offspring, ratio 0.0625
- Total offspring: 16
This detailed step-by-step breakdown explains how we derive the ratios for each phenotype using a Punnett square and the dihybrid cross principles.
