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.