Grain colour in wheat is determined by 3 pairs of polygenes. A cross between AABBCC x aabbcc will produce progeny in `F_(2)` in what proportion that is likely to resemble either parent.

Options

A. None
B. One third
C. Less than 5%
D. Half

Answer

To solve the problem of determining the proportion of progeny in the F2 generation that resembles either parent in a cross involving three pairs of polygenes (AABBCC x aabbcc), we can follow these steps:

### Step 1: Understand the Genetic Cross
We start with two parents:
- Parent 1: AABBCC (homozygous dominant)
- Parent 2: aabbcc (homozygous recessive)

### Step 2: Determine the F1 Generation
When we cross these two parents, all offspring (F1 generation) will be heterozygous for all traits:
- F1 Genotype: AaBbCc

### Step 3: Gamete Formation
Each F1 individual can produce gametes with different combinations of alleles. Since there are three pairs of alleles, the number of different gametes produced by the F1 individual can be calculated using the formula \(2^n\), where \(n\) is the number of gene pairs:
- Number of gametes = \(2^3 = 8\)

### Step 4: Selfing the F1 Generation
When we self the F1 generation (AaBbCc x AaBbCc), we can use a Punnett square to determine the genotypic ratios in the F2 generation. The total number of genotypes produced from this selfing is:
- Total genotypes = \(8 \times 8 = 64\)

### Step 5: Identify Parental Types
In the F2 generation, we are interested in the genotypes that resemble the parental types:
- Parental types: AABBCC and aabbcc
- There is 1 way to get AABBCC (all dominant) and 1 way to get aabbcc (all recessive).

### Step 6: Calculate the Proportion of Parental Types
The total number of parental types is 2 (one for each parent). Therefore, the proportion of progeny resembling either parent is:
- Proportion = \(\frac{2}{64} = \frac{1}{32}\)

### Step 7: Convert Proportion to Percentage
To express this proportion as a percentage:
- Percentage = \(\frac{1}{32} \times 100 \approx 3.125\%\)

### Conclusion
Thus, the proportion of progeny in the F2 generation that resembles either parent is less than 5%.

### Final Answer
The correct answer is: **Less than 5%**.

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