A 15 : 1 `F_(2)` ratio of a cross between a wheat variety with red kernels (homozygous for two dominant genes) and another with white kernels shows

Options

A. Polygenic inheritance
B. that the two genes are complementary
C. single factor inheritance
D. that it is a test cross

Answer

To solve the problem regarding the 15:1 F2 ratio from a cross between a wheat variety with red kernels (homozygous for two dominant genes) and another with white kernels, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Cross**:
- We have two varieties of wheat: one with red kernels (homozygous for two dominant genes, let's denote them as AABB) and another with white kernels (homozygous for two recessive genes, aabb).

2. **Determine the F1 Generation**:
- When these two varieties are crossed (AABB x aabb), all offspring in the F1 generation will be heterozygous (AaBb) and will exhibit the dominant phenotype, which is red kernels.

3. **Self-Cross the F1 Generation**:
- The F1 generation (AaBb) is then self-crossed to produce the F2 generation. The cross can be represented as AaBb x AaBb.

4. **Use a Punnett Square**:
- To find the phenotypic ratio in the F2 generation, we can use a Punnett square for a dihybrid cross (two traits). The possible gametes from each parent (AaBb) are AB, Ab, aB, and ab.

5. **Calculate the Phenotypic Ratios**:
- The phenotypic ratio from a dihybrid cross (AaBb x AaBb) will yield:
- 9 red kernels (A_B_)
- 3 red kernels (A_bb)
- 3 white kernels (aaB_)
- 1 white kernel (aabb)
- However, since the question specifies a 15:1 ratio, we need to consider that the presence of one dominant allele from either gene A or gene B results in red kernels.

6. **Interpret the 15:1 Ratio**:
- The 15:1 ratio indicates that there are 15 instances of red kernels (A_B_ + A_bb + aaB_) and 1 instance of white kernels (aabb). This suggests that the red kernel trait is controlled by two complementary genes, which together influence the color.

7. **Conclusion**:
- The observed 15:1 ratio is characteristic of polygenic inheritance, where multiple genes contribute to a single trait. Therefore, the answer to the question is that this cross exhibits polygenic inheritance.

### Final Answer:
The 15:1 F2 ratio from the cross between a wheat variety with red kernels (homozygous for two dominant genes) and another with white kernels indicates **polygenic inheritance**.

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