Question

A dark-red strain and a white strain of wheat are crossed and produce an intermediate, medium-red ${\mathrm{F}}_1$. When the ${\mathrm{F}}_1$ plants are interbred, an ${\mathrm{F}}_2$ generation is produced in a ratio of 1 darkred: 4 medium-dark-red: 6 medium-red: 4 light-red: 1 white. Further crosses reveal that the dark-red and white ${\mathrm{F}}_2$ plants are true breeding. (a) Based on the ratios in the ${\mathrm{F}}_2$ population, how many genes are involved in the production of color? (b) How many additive alleles are needed to produce each possible phenotype? (c) Assign symbols to these alleles and list possible genotypes that give rise to the medium-red and light-red phenotypes. (d) Predict the outcome of the ${\mathrm{F}}_1$ and ${\mathrm{F}}_2$ generations in a cross between a true-breeding medium-red plant and a white plant.

Short answer

Answer: The predicted phenotype ratio of the F2 generation in a cross between a true-breeding medium-red wheat plant and a white wheat plant is 1 dark-red : 4 medium-dark-red : 6 medium-red : 4 light-red : 1 white.

Step-by-step solution

Determine the number of genes involved in color production

To determine the number of genes involved, observe the ratio of the phenotypes in the F2 generation: 1 dark-red : 4 medium-dark-red : 6 medium-red : 4 light-red : 1 white. This looks like a modified Mendelian ratio that occurs when traits are not determined by a single gene but are decided by multiple genes. In this case, 2 genes are involved (A and B). Considering the F2 generation ratio, we can assume that each gene has two additive alleles, i.e., one dark allele and one white allele.

Determine the number of additive alleles required for each phenotype

The phenotypes and their ratios suggest that the alleles contribute to the color in an additive fashion. We can now assign the number of additive alleles in each phenotype as follow: - Dark-red: 4 additive alleles - Medium-dark-red: 3 additive alleles - Medium-red: 2 additive alleles - Light-red: 1 additive allele - White: 0 additive alleles

Assign symbols to the alleles and list the genotypes for medium-red and light-red phenotypes

Let's denote the dark-red alleles as A and B and the white alleles as a and b. The possible genotypes for medium-red and light-red phenotypes will be: - Medium-red (2 additive alleles): AABB, AaBB, aaBB, AABb, AAbb - Light-red (1 additive allele): AaBb, aaBb, Aabb

Predict the outcome of the F1 and F2 generations in a cross between a true-breeding medium-red plant and a white plant

Let's first define the genotypes of the true-breeding medium-red and white plants: - Medium-red: AABB - White: aabb Now, let's predict the outcome of the F1 and F2 generations: F1 generation cross: AABB x aabb All F1 offspring: AaBb (medium-red phenotype) F2 generation cross: Assuming self-fertilization of the F1 plants, we can make a Punnett Square for this cross (AaBb x AaBb): | | AB | Ab | aB | ab | |----|----|----|----|----| | AB | AABB | AABb | AaBB | AaBb | | Ab | AABb | AAbb | AaBb | Aabb | | aB | AaBB | AaBb | aaBB | aaBb | | ab | AaBb | Aabb | aaBb | aabb | F2 Phenotypes: - 1/16 Dark-red (AABB) - 4/16 Medium-dark-red (AABb, AaBB, AAbb, AaBb) - 6/16 Medium-red (AaBb, AaBb, AaBb, AAbb, AAbb, aaBB) - 4/16 Light-red (AAab, Aaab, aABB, aaBb) - 1/16 White (aabb) The predicted outcome of the F1 generation in a cross between a true-breeding medium-red plant and a white plant would be all medium-red plants. The predicted outcome of the F2 generation would have the following phenotype ratio: 1 dark-red : 4 medium-dark-red : 6 medium-red : 4 light-red : 1 white.

Key concepts

Additive alleles

Additive alleles are a key component of polygenic inheritance, where multiple genes influence a trait. In the case of additive alleles, each allele contributes a certain amount to the phenotype. This is different from having one dominant and one recessive allele, where one allele completely masks the effect of the other. Instead, additive alleles have a cumulative effect.
The concept of additive alleles helps explain the range of phenotypes seen in traits that are controlled by multiple genes, such as skin color or height in humans. Each allele "adds" something to the trait, resulting in a wide range of possible phenotypes rather than a few discrete categories.
In the wheat color problem, two genes with additive alleles are involved. Each genotype can have a different combination of alleles, leading to different intensities of color in the F2 generation. More additive alleles result in more intense color, according to the calculated contributions.

• Dark-red: 4 additive alleles
• Medium-dark-red: 3 additive alleles
• Medium-red: 2 additive alleles
• Light-red: 1 additive allele
• White: 0 additive alleles

Genotype

Genotype refers to the genetic makeup of an organism, specifically the combination of alleles that are present. It is the genotype that largely determines the phenotype, or the physical expression of a trait in an organism. In polygenic inheritance, like our wheat color example, the genotype involves multiple genes, each having multiple alleles.
In this scenario, each gene contributing to the wheat color can have two possible alleles: a dark-red allele and a white allele, represented as A/a and B/b. The different combinations of these alleles make up the genotype and influence the resulting phenotype.
For example, the medium-red wheat can have genotypes AABB, AaBB, or AABb among others, with each one having two additive alleles. Each genotype combination here contributes a specific number of additive alleles to achieve the phenotypic color seen.

• Dark-red: AABB
• Medium-dark-red: AaBB, AABb
• Medium-red: AaBb, AAbb
• Light-red: Aabb, AaBb
• White: aabb

Phenotypic ratio

Phenotypic ratio describes the relative number of offspring showing each particular trait combination, or phenotype. In genetics, it serves as an important tool for understanding the outcome of genetic crosses. The phenotypic ratio reflects the visible traits of organisms, often revealing how alleles interact to influence expression.
In our example with wheat color, the F2 generation yields a phenotypic ratio of 1:4:6:4:1, corresponding to dark-red, medium-dark-red, medium-red, light-red, and white wheat. This distinct ratio is a hallmark of polygenic inheritance and suggests the presence of two genes with additive effects.
By analyzing this phenotypic ratio, we can infer the number of genes involved, their allelic variations and predict future generations. Such a predictive power of phenotypic ratios allows breeders and scientists to anticipate and manipulate desirable traits in plants and animals.