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.
What are the expected heights of plants with each of the homozygous genotypes A₁A₁B₁B₁C₁C₁ and A₂A₂B₂B₂C₂C₂? 

Verified step by step guidance

1. Identify the alleles and their contributions to plant height. A₁, B₁, and C₁ each contribute 6 cm per allele, while A₂, B₂, and C₂ each contribute 3 cm per allele.
2. Determine the total number of alleles for each genotype. For A₁A₁B₁B₁C₁C₁, there are 2 copies of A₁, 2 copies of B₁, and 2 copies of C₁. For A₂A₂B₂B₂C₂C₂, there are 2 copies of A₂, 2 copies of B₂, and 2 copies of C₂.
3. Calculate the total contribution to height for the A₁A₁B₁B₁C₁C₁ genotype. Multiply the number of A₁ alleles (2) by their contribution (6 cm), the number of B₁ alleles (2) by their contribution (6 cm), and the number of C₁ alleles (2) by their contribution (6 cm). Add these values together.
4. Calculate the total contribution to height for the A₂A₂B₂B₂C₂C₂ genotype. Multiply the number of A₂ alleles (2) by their contribution (3 cm), the number of B₂ alleles (2) by their contribution (3 cm), and the number of C₂ alleles (2) by their contribution (3 cm). Add these values together.
5. Compare the expected heights of the two genotypes based on the total contributions calculated in the previous steps.

Key Concepts

Additive Gene Interaction

Additive gene interaction occurs when multiple genes contribute to a single trait, with each allele having a specific effect on the phenotype. In this case, the alleles A₁, B₁, and C₁ each add 6 cm to the plant's height, while A₂, B₂, and C₂ add 3 cm. This means that the total height of the plant is the sum of the contributions from all alleles present.

Homozygous Genotypes

A homozygous genotype consists of two identical alleles for a particular gene. In the question, A₁A₁, B₁B₁, and C₁C₁ represent homozygous dominant genotypes, while A₂A₂, B₂B₂, and C₂C₂ represent homozygous recessive genotypes. Understanding these genotypes is crucial for calculating the expected plant heights based on the additive contributions of the alleles.

Phenotypic Expression

Phenotypic expression refers to the observable traits or characteristics of an organism, which result from the interaction of its genotype with the environment. In this scenario, the height of the plants is the phenotypic expression influenced by the specific combinations of alleles present in the homozygous genotypes, allowing for a straightforward calculation of expected heights.