Two pure-breeding wheat strains, one producing dark red kernels and the other producing white kernels, are crossed to produce F₁ with pink kernel color. When an F₁ plant is self-fertilized and its seed collected and planted, the resulting F₂ consists of 160 plants with kernel colors as shown in the following table.

Based on the F₂ progeny, how many genes are involved in kernel color determination?

Verified step by step guidance

1. Step 1: Understand the problem. The kernel color in wheat is determined by genetic factors, and the F₁ generation shows intermediate phenotypes (pink kernels), suggesting incomplete dominance or additive effects. The F₂ generation displays a range of phenotypes, which indicates polygenic inheritance.
2. Step 2: Analyze the phenotypic ratios in the F₂ generation. The table shows five distinct phenotypes: white, light pink, pink, red, and dark red. This suggests that multiple genes contribute to kernel color, with each gene having additive effects on the phenotype.
3. Step 3: Use the formula for polygenic inheritance to determine the number of genes involved. The number of phenotypic classes in the F₂ generation is given as 2n + 1, where n is the number of genes. Here, there are 5 phenotypic classes (white, light pink, pink, red, dark red). Solve for n using the equation: \( 2n + 1 = 5 \).
4. Step 4: Rearrange the equation to isolate n. Subtract 1 from both sides: \( 2n = 4 \). Then divide both sides by 2: \( n = 2 \). This indicates that two genes are involved in kernel color determination.
5. Step 5: Verify the result by considering the genetic mechanism. Each gene likely has two alleles, and the additive effects of these alleles result in the observed phenotypic variation. The F₂ generation ratios align with the expected distribution for two genes with additive effects.

Key Concepts

Mendelian Inheritance

Mendelian inheritance refers to the principles of heredity established by Gregor Mendel, which include the concepts of dominant and recessive traits. In this scenario, the dark red and white kernel colors represent two alleles, where one may be dominant over the other. Understanding these principles helps in predicting the phenotypic ratios in offspring based on parental genotypes.

Phenotypic Ratios

Phenotypic ratios describe the relative frequencies of different phenotypes in the offspring of a genetic cross. In this case, the F₂ generation shows a variety of kernel colors, which can be analyzed to determine the underlying genetic mechanisms. By examining the observed ratios of the different colors, one can infer the number of genes and their interactions involved in kernel color determination.

Polygenic Inheritance

Polygenic inheritance occurs when multiple genes influence a single trait, resulting in a continuous range of phenotypes. The variation in kernel colors in the F₂ generation suggests that more than one gene is involved in determining the final color. By analyzing the distribution of the phenotypes, one can estimate the number of genes contributing to the trait, which is essential for understanding complex traits in genetics.