A fruit fly with a gray body and red eyes (genotype BbPp) is mated with a fly having a black body and purple eyes (genotype bbpp). What ratio of offspring would you expect if the body-color and eye-color genes are on different chromosomes (unlinked)? When this mating is actually carried out, most of the offspring look like the parents, but 3% have a gray body and purple eyes, and 3% have a black body and red eyes. Are these genes linked or unlinked? What is the recombination frequency?

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1. Identify the genotypes of the parent fruit flies. The first parent has a genotype of BbPp, which means it has one dominant allele for gray body (B) and one recessive allele for black body (b), and one dominant allele for red eyes (P) and one recessive allele for purple eyes (p). The second parent has a genotype of bbpp, indicating homozygous recessive alleles for both traits: black body and purple eyes.
2. Determine the gametes produced by each parent. Since the genes are on different chromosomes and are unlinked, each allele pair will assort independently. The first parent (BbPp) can produce gametes BP, Bp, bP, and bp. The second parent (bbpp) can only produce gametes bp.
3. Perform a Punnett square using the gametes from each parent to predict the genotypes of the offspring. The gametes from the first parent (BP, Bp, bP, bp) will combine with the gametes from the second parent (bp), resulting in the genotypes BbPp, Bbpp, bbPp, and bbpp.
4. Analyze the phenotypes of the offspring based on their genotypes. BbPp results in gray body and red eyes, Bbpp results in gray body and purple eyes, bbPp results in black body and red eyes, and bbpp results in black body and purple eyes. Normally, if the genes are unlinked, each phenotype would occur with equal frequency (25%).
5. Calculate the recombination frequency to determine if the genes are linked. Since 3% of the offspring have a gray body and purple eyes (Bbpp) and 3% have a black body and red eyes (bbPp), the recombination frequency is 3% + 3% = 6%. A recombination frequency less than 50% suggests that the genes are linked.