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 is the expected height of a plant with the genotype A₁A₂B₂B₂C₁C₂?

Verified step by step guidance

1. Identify the contribution of each allele to the plant's height. Alleles A₁, B₁, and C₁ contribute 6 cm each, while alleles A₂, B₂, and C₂ contribute 3 cm each.
2. Break down the genotype A₁A₂B₂B₂C₁C₂ into individual alleles: A₁, A₂, B₂, B₂, C₁, and C₂.
3. Calculate the contribution of each allele to the plant's height. For example, A₁ contributes 6 cm, A₂ contributes 3 cm, each B₂ contributes 3 cm, C₁ contributes 6 cm, and C₂ contributes 3 cm.
4. Add the contributions of all alleles together to determine the total height of the plant. Use the formula: Total height = (contribution of A₁) + (contribution of A₂) + (contribution of B₂) + (contribution of B₂) + (contribution of C₁) + (contribution of C₂).
5. Simplify the expression to find the expected height of the plant.

Key Concepts

Alleles and Genotypes

Alleles are different versions of a gene that can exist at a specific locus on a chromosome. In this context, A₁, A₂, B₁, B₂, C₁, and C₂ represent the alleles for three different genes controlling plant height. The genotype of an organism is the combination of alleles it possesses, which determines its traits, such as height in this case.

Additive Genetic Effects

Additive genetic effects occur when the contributions of different alleles to a trait are summed together. In this scenario, each allele contributes a specific amount to the plant's height: A₁, B₁, and C₁ add 6 cm each, while A₂, B₂, and C₂ add 3 cm each. This means the total height can be calculated by adding the contributions of all alleles present in the genotype.

Calculating Expected Phenotype

The expected phenotype, or observable trait, can be calculated by determining the total contribution of all alleles in a given genotype. For the genotype A₁A₂B₂B₂C₁C₂, we identify the alleles present and apply the additive contributions to find the expected height. This involves counting the number of each type of allele and multiplying by their respective height contributions.