In Drosophila, the two mutations Stubble bristles (Sb) and curled wings ( $c u$ ) are linked on chromosome III. Sb is a dominant gene that is lethal in a homozygous state, and \(c u\) is a recessive gene. If a female of the genotype \\[ \frac{S b}{+} \\] is to be mated to detect recombinants among her offspring, what male genotype would you choose as her mate?

We are given a female genotype that has Stubble bristles (Sb) and the wild type (+) paired on her chromosome III. The Stubble bristles gene is dominant, but lethal when homozygous. The curly wings gene (\(cu\)) is recessive. The female's genotype is given as: \\[ \frac{Sb}{+} \\]

Since the Sb gene is dominant and lethal in a homozygous state, as well as the \(cu\) gene being recessive, there are 3 possible genotypes for a male that could be the mate: 1. Homozygous recessive for both traits: \(sb\ sb\ \ cu\ cu\) 2. Heterozygous for Stubble bristles and homozygous recessive for curled wings: \(Sb\ sb\ \ cu\ cu\) 3. Homozygous recessive for Stubble bristles and heterozygous for curled wings: \(sb\ sb\ \ Cu\ cu\)

We want a male genotype that, when mated with a female, will help us detect recombinants among the offspring. Let's examine the potential offspring genotypes for each male option: 1. Homozygous recessive for both traits: \(sb\ sb\ \ cu\ cu\) Offspring genotypes would include: *Sb sb Cu cu (wild type with no curly wings) *sb sb Cu cu (recessive phenotype with no Stubble bristles) 2. Heterozygous for Stubble bristles and homozygous recessive for curled wings: \(Sb\ sb\ \ cu\ cu\) Offspring genotypes would include: *Sb sb Cu cu (recessive phenotype) *Sb sb cu cu (recessive phenotype for both traits) 3. Homozygous recessive for Stubble bristles and heterozygous for curled wings: \(sb\ sb\ \ Cu\ cu\) Offspring genotypes would include: *Sb sb Cu Cu (wild type) *Sb sb Cu cu (recessive phenotype for Stubble bristles)

Considering the possible offspring genotypes from each potential male genotype, the best male genotype to detect recombinants would be the one that results in the most variety of phenotypes in the offspring. In this case, option 2 (Heterozygous for Stubble bristles and homozygous recessive for curled wings: \(Sb\ sb\ \ cu\ cu\)) would give the most variety of phenotypes. Therefore, the male genotype that should be chosen as the mate for the female is \(Sb\ sb\ \ cu\ cu\).