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 height is expected in the F₁ progeny of a cross between A₁A₁B₁B₁C₁C₁ and A₂A₂B₂B₂C₂C₂?

Verified step by step guidance

1. Determine the genotype of the F₁ progeny resulting from the cross. The parents are homozygous for each gene: A₁A₁B₁B₁C₁C₁ (parent 1) and A₂A₂B₂B₂C₂C₂ (parent 2). The F₁ progeny will inherit one allele from each parent for each gene, resulting in the heterozygous genotype A₁A₂B₁B₂C₁C₂.
2. Understand the additive relationship of the alleles. Each A₁, B₁, and C₁ allele contributes 6 cm to the plant height, while each A₂, B₂, and C₂ allele contributes 3 cm.
3. Count the number of each allele in the F₁ genotype. The F₁ progeny has one A₁ allele, one A₂ allele, one B₁ allele, one B₂ allele, one C₁ allele, and one C₂ allele.
4. Calculate the total contribution to height from each allele. Multiply the number of A₁, B₁, and C₁ alleles by 6 cm, and the number of A₂, B₂, and C₂ alleles by 3 cm. Add these contributions together to determine the total height.
5. Combine the contributions from all alleles to find the expected height of the F₁ progeny. This will give the final height of the plant in centimeters.

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 height of the plant is influenced by three pairs of alleles, where each allele contributes a defined amount to the overall height. This means that the total height can be calculated by summing the contributions from each allele present in the genotype.

Genotype and Phenotype

The genotype refers to the genetic makeup of an organism, while the phenotype is the observable physical or biochemical characteristics resulting from the genotype. In the given question, the genotypes A₁A₁B₁B₁C₁C₁ and A₂A₂B₂B₂C₂ represent the genetic combinations of the parent plants, which will determine the height of the F₁ progeny based on the additive contributions of the alleles.

F₁ Generation

The F₁ generation is the first filial generation resulting from a cross between two parental genotypes. In this scenario, the F₁ progeny will inherit one allele from each parent for each gene, leading to a unique combination of alleles. The expected height of the F₁ plants can be calculated by determining the alleles they inherit and applying the additive contributions of each allele to find the total height.