Three pairs of genes with two alleles each (A₁ and A₂, B₁ and B₂, and C₁ and C₂) control the height of a plant. The alleles of these genes have an additive relationship: Each copy of alleles A₁, B₁, and C₁ contributes 6 cm to plant height, and each copy of alleles A₂, B₂, and C₂ contributes 3 cm. Identify the number of different phenotypes (expected plant heights) that are possible with these three genes.

Verified step by step guidance

1. Step 1: Understand the problem. The plant's height is determined by three pairs of genes (A, B, and C), each with two alleles. The alleles contribute additively to the height: A₁, B₁, and C₁ contribute 6 cm each, while A₂, B₂, and C₂ contribute 3 cm each. We need to calculate the number of distinct phenotypes (heights) possible.
2. Step 2: Determine the total number of alleles contributing to the phenotype. Each gene pair (A, B, C) has two alleles, and there are three gene pairs. This means there are 6 total alleles (2 alleles per gene × 3 genes).
3. Step 3: Calculate the range of contributions to the phenotype. Each allele contributes either 6 cm (A₁, B₁, C₁) or 3 cm (A₂, B₂, C₂). The maximum contribution occurs when all 6 alleles are of the 6 cm type (6 × 6 = 36 cm), and the minimum contribution occurs when all 6 alleles are of the 3 cm type (6 × 3 = 18 cm).
4. Step 4: Determine the possible combinations of allele contributions. The total contribution to height depends on the number of 6 cm alleles (x) and 3 cm alleles (6 - x). The total height is given by the formula: \( \text{Height} = 6x + 3(6 - x) \). Simplify this to \( \text{Height} = 3x + 18 \), where x ranges from 0 to 6 (the number of 6 cm alleles).
5. Step 5: Calculate the number of distinct phenotypes. Since x can take on integer values from 0 to 6, there are 7 possible values for x. Each value of x corresponds to a unique height, meaning there are 7 distinct phenotypes (heights) possible.

Key Concepts

Alleles and Genotypes

Alleles are different versions of a gene that can exist at a specific locus on a chromosome. In this scenario, each gene (A, B, C) has two alleles (A₁/A₂, B₁/B₂, C₁/C₂). The combination of alleles inherited from both parents forms the genotype, which ultimately influences the phenotype, or observable traits, such as plant height.

Additive Gene Interaction

Additive gene interaction occurs when the effects of different alleles contribute cumulatively to a trait. In this case, each allele contributes a specific height increment to the plant. For example, A₁ contributes 6 cm, while A₂ contributes 3 cm, leading to a total height that is the sum of contributions from all alleles present in the genotype.

Phenotypic Variation

Phenotypic variation refers to the observable differences in traits among individuals, which can arise from genetic differences and environmental influences. In this question, the phenotypes are the different possible heights of the plants, determined by the combinations of alleles from the three genes, leading to a range of potential plant heights based on the additive contributions of each allele.