Question

Two true-breeding pea plants are crossed. One parent is round, terminal, violet, constricted, while the other expresses the contrasting phenotypes of wrinkled, axial, white, full. The four pairs of contrasting traits are controlled by four genes, each located on a separate chromosome. In the F₁ generation, only round, axial, violet, and full are expressed. In the F₂ generation, all possible combinations of these traits are expressed in ratios consistent with Mendelian inheritance.
Which F₂ phenotype is expected to occur least frequently? Write a mathematical expression that predicts this frequency.

Accepted Answer

Identify the dominant and recessive alleles for each trait based on the F1 phenotype. Since the F1 generation shows round, axial, violet, and full phenotypes, these are the dominant traits, and wrinkled, terminal, white, and constricted are recessive. Assign symbols for each gene, for example: R (round) dominant over r (wrinkled), A (axial) dominant over a (terminal), V (violet) dominant over v (white), and F (full) dominant over f (constricted). Determine the genotype of the F1 plants. Since the parents are true-breeding and contrasting, the F1 will be heterozygous for all four genes: Rr Aa Vv Ff. Recall that in the F2 generation, the genes assort independently, and the phenotypic ratio for each gene follows Mendelian inheritance: 3 dominant : 1 recessive. The least frequent phenotype will be the one that is recessive for all four traits. Write the mathematical expression for the frequency of the least frequent phenotype (all recessive traits) as the product of the probabilities of each recessive phenotype: $\left(\frac{1}{4}\right)^4$.

Key Concepts

Mendelian Inheritance and Independent Assortment

Genotype and Phenotype Ratios in Dihybrid and Multihybrid Crosses

Calculating Phenotype Frequencies Using Probability Multiplication