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 \(F_{1}\) generation, only round, axial, violet, and full are expressed. In the \(\mathrm{F}_{2}\) generation, all possible combinations of these traits are expressed in ratios consistent with Mendelian inheritance. (a) What conclusion can you draw about the inheritance of these traits based on the \(\mathrm{F}_{1}\) results? (b) Which phenotype appears most frequently in the \(\mathrm{F}_{2}\) results? Write a mathematical expression that predicts the frequency of occurrence of this phenotype. (c) Which \(\mathrm{F}_{2}\) phenotype is expected to occur least frequently? Write a mathematical expression that predicts this frequency. (d) How often is either \(P_{1}\) phenotype likely to occur in the \(F_{2}\) generation? (e) If the \(F_{1}\) plant is testcrossed, how many different phenotypes will be produced?

Short answer

Answer: The phenotype expected to appear most frequently in the F2 generation is round, terminal, violet, and constricted. The probability of its occurrence is 81/256.

Step-by-step solution

Determine the Genotype of F1 generation

We need to determine the genotypes of the F1 plants in order to understand how the traits are inherited. Since Parent 1 is true-breeding, they are homozygous dominant for each gene. Parent 2 is homozygous recessive for each gene. Cross them to get the F1 generation's genotype: Parent 1: RRTTVVCC Parent 2: rrttvvcc F1: RrTtVvCc (All round, axial, violet, full) (a) The conclusion we can draw based on the F1 results is that the inheritance of these traits is consistent with Mendel's law of dominance; the dominant phenotypes are expressed in the F1 generation.

Calculate the frequencies of each phenotype in the F2 generation

Analyze the self-crossing of F1 offspring to generate F2: F1: RrTtVvCc x RrTtVvCc To find the phenotypes that appear most frequently and least frequently in the F2 results, we need to determine the probability of each phenotype combination based on the independent inheritance of these traits from their parents. Phenotype probabilities: - Round (3/4), Wrinkled (1/4) - Terminal (3/4), Axial (1/4) - Violet (3/4), White (1/4) - Constricted (3/4), Full (1/4) (b) The phenotype that appears most frequently in the F2 results is round, terminal, violet, and constricted. The mathematical expression predicting the frequency of occurrence is: (3/4)^4 = 81/256 (c) The F2 phenotype expected to occur least frequently is wrinkled, axial, white, and full. The mathematical expression predicting this frequency is: (1/4)^4 = 1/256

Calculate the frequency of P1 phenotype in the F2 generation

(d) To find how often either P1 phenotype likely occurs in the F2 generation, we need to determine the probability of each P1 phenotype occurring. For Parent 1 phenotype (Round, Terminal, Violet, Constricted): Probability = (3/4) * (3/4) * (3/4) * (3/4) = 81/256 For Parent 2 phenotype (Wrinkled, Axial, White, Full): Probability = (1/4) * (1/4) * (1/4) * (1/4) = 1/256 The combined frequency of either P1 phenotype occurring in the F2 generation is: 81/256 + 1/256 = 82/256

Determine the number of different phenotypes produced in a testcross

(e) For a testcross, the F1 plant is crossed with a homozygous recessive plant (rrttvvcc). To find the number of different phenotypes produced in the testcross, analyze all possible combinations that can be produced. Testcross: RrTtVvCc x rrttvvcc The possible combinations are as follows: - Round, Terminal, Violet, Constricted - Round, Terminal, Violet, Full - Round, Terminal, White, Constricted - Round, Terminal, White, Full - Round, Axial, Violet, Constricted - Round, Axial, Violet, Full - Round, Axial, White, Constricted - Round, Axial, White, Full - Wrinkled, Terminal, Violet, Constricted - Wrinkled, Terminal, Violet, Full - Wrinkled, Terminal, White, Constricted - Wrinkled, Terminal, White, Full - Wrinkled, Axial, Violet, Constricted - Wrinkled, Axial, Violet, Full - Wrinkled, Axial, White, Constricted - Wrinkled, Axial, White, Full There are 16 different phenotypes that can be produced in a testcross.