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 genotypes that are possible with these three genes.

Verified step by step guidance

1. Step 1: Understand the problem. The question asks for the number of different genotypes possible with three pairs of genes (A, B, and C), each having two alleles (A₁/A₂, B₁/B₂, C₁/C₂). Each gene pair is independent, and we need to calculate the total number of genotype combinations.
2. Step 2: Recall the formula for calculating the number of genotypes for a single gene pair. For a gene with two alleles, the possible genotypes are: homozygous dominant (e.g., A₁A₁), heterozygous (e.g., A₁A₂), and homozygous recessive (e.g., A₂A₂). This gives 3 genotypes per gene pair.
3. Step 3: Since the three gene pairs (A, B, and C) are independent, the total number of genotypes is the product of the number of genotypes for each gene pair. Use the formula: Total genotypes = (Number of genotypes for gene A) × (Number of genotypes for gene B) × (Number of genotypes for gene C).
4. Step 4: Substitute the values into the formula. Each gene pair has 3 possible genotypes, so the calculation becomes: Total genotypes = 3 × 3 × 3.
5. Step 5: Conclude that the total number of different genotypes is the result of the multiplication in Step 4. This represents all possible combinations of genotypes across the three gene pairs.

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). A genotype is the combination of alleles an organism possesses for a particular gene, which can be homozygous (two identical alleles) or heterozygous (two different alleles). Understanding how these combinations form is crucial for determining the total number of genotypes.

Additive Genetic Effects

Additive genetic effects occur when the contributions of different alleles to a trait are summed together. In this case, each allele contributes a specific height increment to the plant. This concept is essential for understanding how multiple genes can influence a single phenotype, such as plant height, by adding their effects together based on the alleles present.

Combinatorial Genetics

Combinatorial genetics involves calculating the total number of possible genotypes based on the combinations of alleles from multiple genes. For three genes, each with two alleles, the total number of genotypes can be determined using the formula 2^n, where n is the number of genes. This principle helps in predicting genetic variation and understanding inheritance patterns in organisms.