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.

Key Concepts

Alleles and Phenotypes

Alleles are different versions of a gene that can exist at a specific locus on a chromosome. In this scenario, each gene has two alleles, which can combine in various ways to produce different phenotypes, or observable traits, such as plant height. The phenotype is influenced by the combination of alleles inherited from the parents.

Additive Gene Action

Additive gene action occurs when the effects of multiple alleles contribute cumulatively to a trait. In this case, 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. This means that the total height can be calculated by summing the contributions of the alleles present.

Combinatorial Genetics

Combinatorial genetics involves calculating the different combinations of alleles that can result from multiple genes. With three genes, each having two alleles, the total number of combinations can be determined using the formula 2^n, where n is the number of genes. This concept is essential for predicting the variety of phenotypes that can arise from the genetic makeup of the plants.