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.

Key concepts

Genotype

In the context of Mendelian inheritance, a genotype refers to the genetic makeup of an organism, specifically the alleles that an organism possesses for a particular trait. Genotypes are typically represented by letters, where capital letters denote dominant alleles and lowercase letters represent recessive alleles.
For example, in the given exercise, the genotypes of the parent plants are homozygous, meaning each plant has two identical alleles for each trait. Parent 1 is homozygous dominant, represented as RRTTVVCC, indicating that it has dominant alleles for all four traits. In contrast, Parent 2 is homozygous recessive (rrttvvcc), possessing recessive alleles for each trait.
This combination of alleles forms the basis for predicting the traits of their offspring using a Punnett square or other genetic tools. The F1 generation, resulting from a cross of these two parents, has the genotype RrTtVvCc, showcasing an example of heterozygosity where two different alleles for each trait are present.

Phenotype

The phenotype of an organism encompasses all its observable characteristics, which result from the interaction of its genotype with the environment. Unlike the genotype, which remains constant, phenotype can vary based on environmental factors or due to mutations.
In the context of the exercise, the phenotype descriptions such as round, axial, violet, and full are observable traits. These traits manifest when dominant alleles in the F1 generation overshadow the recessive alleles originating from Parent 2. Consequently, despite the heterozygous genotype RrTtVvCc, the phenotype of the F1 generation will reflect those dominant characteristics.
This concept highlights how phenotypic expression often involves dominant traits masking recessive ones, creating a uniform appearance in the F1 generation, as seen with the pea plant's traits in this exercise.

Law of Dominance

Gregor Mendel's law of dominance is a fundamental principle of Mendelian genetics. It states that when two different alleles are present, one may mask the expression of the other, resulting in the dominant phenotype being expressed, while the recessive phenotype remains hidden.
In the exercise, the F1 generation consistently displays the round, axial, violet, and full phenotypes. This outcome illustrates the law of dominance, as the dominant alleles from Parent 1 (RRTTVVCC) override the recessive alleles present in Parent 2 (rrttvvcc).
The uniformity in the phenotype of hybrid offspring highlights how dominant alleles dictate the observable traits, making this law crucial for predicting patterns in genetics, breeding, and inheritance.

Testcross

A testcross is a genetic tool used to determine the genotype of an organism showing a dominant phenotype but possessing an unknown genotype. In a testcross, the organism in question is crossed with another organism that is homozygous recessive for the trait of interest.
In the example provided, the F1 plant with a genotype of RrTtVvCc is testcrossed with a plant exhibiting the recessive genotype rrttvvcc. This allows the determination of how the alleles segregate and combine during reproduction, predicting the variety of phenotypes produced, which, for this case, amounts to 16 different combinations.
The outcomes of testcrosses are pivotal in revealing the genetic structure behind phenotypes, providing a deeper understanding of inheritance patterns, and confirming the presence of hidden recessive alleles in heterozygous individuals.