Question

Two true-breeding pea plants were crossed. One parent is round, terminal, violet, constricted, while the other expresses the respective 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 \(\mathrm{F}_{1}\) only round, axial, violet, and full were expressed. In the \(\mathrm{F}_{2},\) all possible combinations of these traits were expressed in ratios consistent with Mendelian inheritance. (a) What conclusion about the inheritance of the traits can be drawn based on the \(\mathrm{F}_{1}\) results? (b) In the \(\mathrm{F}_{2}\) results, which phenotype appeared most frequently? Write a mathematical expression that predicts the probability of occurrence of this phenotype. (c) Which \(\mathrm{F}_{2}\) phenotype is expected to occur least frequently? Write a mathematical expression that predicts this probability. (d) In the \(F_{2}\) generation, how often is either of the \(P_{1}\) phenotypes likely to occur? (e) If the \(F_{1}\) plants were testcrossed, how many different phenotypes would be produced? How does this number compare with the number of different phenotypes in the \(\mathrm{F}_{2}\) generation just discussed?

Short answer

Answer: In the F2 generation, the most frequent phenotype (round, axial, violet, and full) has a probability of 81/256, while the least frequent phenotype (wrinkled, terminal, white, and constricted) has a probability of 1/256. In the F1 testcross offspring, there are 16 different phenotypes present.

Step-by-step solution

a) Conclusion based on F1 results

The F1 generation expresses only the round, axial, violet, and full traits, suggesting that these traits dominate their respective contrasting phenotypes (wrinkled, terminal, white, and constricted). This observation supports the idea of Mendelian dominant and recessive inheritance of traits.

b) Most frequent F2 phenotype

The most frequent F2 phenotype will be the one where the dominant traits are all expressed, which is the round, axial, violet, and full. To predict the probability of occurrence, we can consider each trait's independent inheritance. With a dominant-to-recessive ratio of 3:1, the probability of each dominant trait appearing for each locus is \(\frac{3}{4}\). For all four traits being dominant, the probability is: \(\frac{3}{4} \times \frac{3}{4} \times \frac{3}{4} \times \frac{3}{4} = \frac{81}{256}\)

c) Least frequent F2 phenotype

The least frequent F2 phenotype is the one expressing all recessive traits: wrinkled, terminal, white, and constricted. For each trait, the probability of being recessive is \(\frac{1}{4}\). For all four traits being recessive, the probability is: \(\frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} = \frac{1}{256}\)

d) Frequency of P1 phenotypes in F2 generation

There are two original P1 phenotypes: round, terminal, violet, constricted (parent 1) and wrinkled, axial, white, full (parent 2). To find the probability of each phenotype occurring in the F2 generation, we use the product of the probabilities for each trait. Parent 1 phenotype probability: \(\frac{3}{4} \times \frac{1}{4} \times \frac{3}{4} \times \frac{1}{4} = \frac{9}{256}\) Parent 2 phenotype probability: \(\frac{1}{4} \times \frac{3}{4} \times \frac{1}{4} \times \frac{3}{4} = \frac{9}{256}\) Therefore, either of the P1 phenotypes will be expected to occur \(\frac{9}{256} + \frac{9}{256} = \frac{18}{256}\) times in the F2 generation.

e) Number of different phenotypes in F1 testcross

When F1 plants are testcrossed (crossed with plants homozygous recessive for all traits), each gene will segregate independently, creating all possible combinations of traits. In this case, there are four genes (trait pairs) with two possible phenotypes for each, resulting in 2^4 = 16 different phenotypes in the F1 testcross offspring. Comparing this to the F2 generation previously discussed, there would be the same number of different phenotypes present, as the segregation of traits is similar in both cases.

Key concepts

True-Breeding Plants

In genetics, true-breeding plants are those that, when self-fertilized, only produce offspring with the same phenotypic traits as the parent. This concept is pivotal because it indicates that the parent plants are homozygous for the genes controlling those traits. In other words, they possess two identical alleles for each gene of interest, either both dominant or both recessive.

A classic example is seen in the work of Gregor Mendel, the father of modern genetics, who studied true-breeding pea plants to discern patterns of inheritance. Mendel’s experiments with true-breeding plants laid the foundation for understanding how traits are passed from one generation to the next—observations that are just as relevant in today's genetics education.

Dominant and Recessive Traits

Dominant and recessive traits are fundamental to Mendelian inheritance. Dominant traits are those that are expressed or visible when at least one dominant allele is present in an organism. Conversely, a recessive trait only manifests when an organism has two copies of the recessive allele — in other words, it is homozygous recessive.

Understanding this is crucial because it helps explain the resulting phenotypes of genetic crosses, such as the one where F1 generation pea plants expressed round, axial, violet, and full traits, even though the true-breeding parents had contrasting characteristics. This dominance inherently masks the presence of recessive alleles unless they are in a homozygous state, shaping the patterns of inheritance observed in offspring.

Phenotypic Ratios

Phenotypic ratios refer to the relative number of offspring manifesting different traits in a genetic cross and are an important prediction tool in genetics. After analyzing many genetic crosses, Mendel deduced that for each gene, the phenotypic ratio of dominant to recessive traits in the F2 generation typically follows a 3:1 pattern, assuming the genes are on separate chromosomes and not linked.

This ratio arises from the segregation and independent assortment of alleles during gamete formation. For example, when true-breeding plants with contrasting phenotypes are crossed, the F1 generation exhibits only the dominant traits; however, in the F2 generation, the phenotypic ratio illustrates both dominant and recessive traits according to the principles Mendelian inheritance.

Testcross

A testcross is a genetic cross between an organism with an unknown genotype and one that is homozygous recessive for the trait in question. The purpose of a testcross is to determine the genotype of the unknown parent by analyzing the phenotypes of the offspring. Because the recessive parent can only contribute recessive alleles, any offspring displaying the dominant phenotype must have received a dominant allele from the unknown parent.

This type of cross was instrumental in establishing an organism’s genotype in Mendel’s experiments, and it continues to be a valuable tool in genetic analysis. For instance, when an F1 hybrid with the dominant phenotype is testcrossed, the variety of resulting phenotypes can inform us about the hybrid's genotype and whether traits are indeed segregating in a Mendelian fashion.