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 \(F_{1}\) and \(F_{2}\) generations in a cross between a true-breeding medium-red plant and a white plant.

Short answer

Answer: In this case, there are two genes involved in the production of color. For each phenotype, the number of additive alleles needed are as follows: 4 for darkred, 3 for medium-dark-red, 2 for medium-red, 1 for light-red, and 0 for white. The possible genotypes for the medium-red phenotype are AABB, AAbb, and aaBB, while the possible genotypes for the light-red phenotype are AABb, AaBB, and aaBb.

Step-by-step solution

a) Determining the Number of Involved Genes

Based on the F2 population ratio, we see the ratio is 1 darkred : 4 medium-dark-red : 6 medium-red : 4 light-red : 1 white. Since we have 5 categories this indicates a polygenic inheritance with two genes. This is because 3 categories would be present if only one gene was involved (e.g. 1:2:1 ratio). The given ratio (1:4:6:4:1) indicates a two-gene inheritance.

b) Number of Additive Alleles per Phenotype

In a two-gene inheritance, we have a total of four additive alleles (two from each gene). We can now assign the number of additive alleles to produce each phenotype: 1. Darkred: 4 additive alleles 2. Medium-dark-red: 3 additive alleles 3. Medium-red: 2 additive alleles 4. Light-red: 1 additive allele 5. White: 0 additive alleles

c) Assigning Symbols and Listing Genotypes

Let's use 'A' and 'B' as the two genes, with their respective capital and lowercase letters representing dominant and recessive alleles. Dominant alleles (A, B) are additive, while recessive alleles (a, b) are not. We will now list possible genotypes for medium-red and light-red phenotypes. 1. Medium-red (2 additive alleles): AABB, AAbb, aaBB 2. Light-red (1 additive allele): AABb, AaBB, aaBb

d) Predicting F1 and F2 Generations in a Specific Cross

We will now predict the outcome of the F1 and F2 generations in a cross between a true-breeding medium-red plant (AABB) and a white plant (aabb). F1 generation: All offspring will be heterozygous (AaBb) in this cross, resulting in a medium-red phenotype. For the F2 generation, we will need to perform a dihybrid cross of AaBb x AaBb: 1. Darkred (AABB): 1/16 2. Medium-dark-red (AABb, AaBB, AAbb, aaBB): 4/16 3. Medium-red (AaBb, AABB, AAbb, aaBB, aaBb): 6/16 4. Light-red (AAbB, AaBb, aaBb): 4/16 5. White (aabb): 1/16 The F2 generation will have a phenotypic ratio of 1 darkred : 4 medium-dark-red : 6 medium-red : 4 light-red : 1 white.

Key concepts

Additive Alleles

In genetics, the concept of additive alleles plays a key role in understanding inheritance patterns, especially in polygenic traits. An allele is a variant of a gene, and when alleles are additive, each one contributes to the overall effect on a trait. In the context of the wheat color problem, we have two genes involved in determining the color of wheat grains. These genes have alleles that can either be additive or non-additive.

Additive alleles mean that each dominant allele (e.g., 'A' or 'B') contributes to an increase in a particular trait - in this case, the intensity of the red color. Each additive allele has a cumulative effect which sums up to produce various intensities of red.

• For a dark-red phenotype, all four alleles are additive.
• A medium-dark-red phenotype has three additive alleles.
• The medium-red phenotype has two additive alleles.
• A light-red phenotype has one additive allele.
• A white phenotype has no additive alleles.

In the wheat example, understanding the distribution of additive alleles helps us predict the outcomes of various genetic crosses. It highlights how multiple genes can interact to produce a continuum of phenotypic traits.

Genotype-Phenotype Relationship

In genetics, the genotype refers to the genetic constitution of an organism, whereas the phenotype is the observable trait or characteristic, such as plant color. The relationship between genotype and phenotype is often influenced by multiple genes, especially for traits that show continuous variation, such as the red color in wheat.

For instance, in our wheat color problem:

• The genotype with all dominant alleles (AABB) results in a dark-red phenotype, showing a full expression trait.
• Genotypes with a mix of dominant and recessive alleles, like AaBB or AAbb, result in intermediate colors, such as medium-red.
• If all alleles are recessive (aabb), the phenotype will show no color, resulting in white grains.

The genotype determines the number of additive alleles present, which in turn influences the intensity of the color phenotype. Different combinations of alleles can produce the same phenotype, demonstrating that the genotype-phenotype relationship can be complex and multifaceted, particularly in polygenic inheritance.

Dihybrid Cross

A dihybrid cross is a breeding experiment between organisms that are heterozygous for two traits. It helps to determine how different gene combinations can result in various phenotypic ratios. For the wheat color problem, a dihybrid cross involves plants with two sets of gene pairs, each influencing the color trait.

To perform a dihybrid cross:

• We begin with the F1 generation, which consists of heterozygous plants (AaBb) bred from true-breeding lines (like AABB and aabb).
• The F2 generation results from crossing these F1 plants (AaBb x AaBb).
• This process produces offspring with a phenotypic ratio of 1 darkred : 4 medium-dark-red : 6 medium-red : 4 light-red : 1 white.

The dihybrid cross illustrates how two sets of heterozygous pairs interact to create a variety of phenotypes. It demonstrates the principle of independent assortment, as each pair of alleles segregates independently of the other during gamete formation. By understanding dihybrid crosses, students can predict the distribution of phenotypes in progeny, illustrating the underlying genetic mechanisms of polygenic traits.