Suppose that r, red, and sc, scarlet, are two recessive eye-color mutations that lie 20 map units apart on the Drosophila X chromosome, and that each causes a red eye color in place of the wild type purple color.

A. If a female from pure-breeding rr stock is mated with a red-eyed (sc) male, what phenotypes will the F1 sons and daughters display?

B. If these F1 flies are interbred, what will be that phenotypic ratios among the F2 granddaughters and grandsons?

A. In this case, the female is homozygous recessive for the red-eye mutation (rr) and the male is heterozygous for the red-eye mutation (sc). Since both mutations are recessive, the F1 sons and daughters will display the wild type purple eye color. Their genotype would be Rr for the eye color gene.

B. When the F1 flies are interbred, the possible genotypes of the F2 flies can be determined using a Punnett square. Since the mutations are 20 map units apart, there is a possibility of recombination occurring between the two genes during meiosis.

The four possible gametes produced by the F1 flies are: R and r from the female, and s and c from the male.

Using these possible gametes, the F2 phenotypic ratios can be determined:
- 1/4 of the F2 flies will have the wild type purple eye color (RR)
- 1/4 of the F2 flies will have the red eye color due to the rr genotype
- 1/4 of the F2 flies will have the red eye color due to the sc genotype
- 1/4 of the F2 flies will have the scarlet eye color due to the rrsc genotype

So the phenotypic ratios among the F2 granddaughters and grandsons will be:
- 1/4 will have the wild type purple eye color
- 1/4 will have the red eye color
- 1/4 will have the red eye color
- 1/4 will have the scarlet eye color.

To answer these questions, we need to understand the principles of Mendelian genetics and inheritance patterns. Let's break it down step by step.

A. To determine the phenotypes of the F1 offspring, we need to consider the genotype of the parents in the cross: a pure-breeding rr female and a red-eyed (sc) male.

1. Pure-breeding rr female: This means the female has two copies of the recessive red-eye mutation (rr) and no wild-type (purple) allele. Therefore, all her gametes will contain the red-eye mutation (r), because she can only pass on what she has.

2. Red-eyed (sc) male: This male has the red-eye mutation (r) and the wild-type (purple) allele. Consequently, he can produce two types of gametes, one with the red-eye mutation (r) and another with the wild-type (purple) allele (sc).

During fertilization, the possible combinations between the female's gametes (r) and the male's gametes (r or sc) will determine the phenotypes of the F1 offspring:

- Male offspring: They will receive the Y chromosome from the male parent, which is irrelevant for eye color. Since they inherit a single X chromosome from their mother, which carries the red-eye mutation (r) allele, all F1 male offspring will have red eyes.

- Female offspring: They receive an X chromosome from each parent, meaning they can inherit either the red-eye mutation (r) or the wild-type (purple) allele (sc). Thus, the F1 female offspring will display a combination of red and purple eyes, exhibiting a variegated phenotype (mosaic).

B. To determine the phenotypic ratios among the F2 granddaughters and grandsons when the F1 flies are interbred, we need to consider their genotypes. Let's recap the possible genotypes of the F1 flies:

- Red-eyed male offspring (all have rr genotype)
- Variegated female offspring (carrying both r and sc alleles)

Now, let's consider the F1 offspring's possible genotypes that will be involved in the F2 generation:

- Red-eyed male offspring: They can only produce one type of gamete (r) because they have a homozygous genotype (rr).

- Variegated female offspring: They can produce two types of gametes, one with the red-eye mutation (r) and another with the wild-type (purple) allele (sc).

When these F1 flies are interbred, the possible combinations during fertilization between the male's gamete (r) and the female's gametes (r or sc) will determine the phenotypic ratios among the F2 generation:

- Grandsons (male offspring of the F1 females): Since they inherit a single X chromosome from their mother, which carries either the red-eye mutation (r) or the wild-type (purple) allele (sc), the grandsons will display both red and purple eye colors, resulting in a variegated phenotype (mosaic).

- Granddaughters (female offspring of the F1 females): They receive an X chromosome from each parent, which means they can inherit four possible genotypes: rr, rsc, scsc, and r. The phenotypic ratio among the granddaughters will depend on the combination of these genotypes.

To determine the exact phenotypic ratios among the F2 granddaughters, you can use a Punnett square or the principles of probability to calculate the expected outcomes based on the possible genotypes.