While vermilion is X-linked in Drosophila and causes eye color to be bright red, brown is an autosomal recessive mutation that causes the eye to be brown. Flies carrying both mutations lose all pigmentation and are white-eyed. Predict the \(F_{1}\) and \(F_{2}\) results of the following crosses: (a) vermilion females \(\times\) brown males (b) brown females \(\times\) vermilion males (c) white females \(\times\) wild males

To analyze this cross, assign the following symbols: V (vermilion mutation), B (brown mutation), and + (wild-type or normal allele). Since vermilion is X-linked, vermilion females are represented as XX\(_{V}\), and wild-type males are represented as XY. The brown mutation is autosomal recessive, so brown males are represented as bb. The parental cross is XX\(_{V}\) (vermilion females) \(\times\) XY;bb (brown males). The \(F_{1}\) generation will include females with one vermilion allele and one wild-type allele, and males with one brown allele (but no vermilion allele, since it is X-linked): X\(_{V}\)X (vermilion females) and X\(_{V}\)Y;bb (brown males).

This cross includes females with the brown mutation (bb) and males with the vermilion mutation (X\(_{V}\)Y). The offspring in the \(F_{1}\) generation will inherit one X chromosome from each parent: X\(_{V}\)X;bb (white females due to both mutations) and XY;Bb (wild-type males with one brown allele).

In this case, the white females have both the vermilion and brown mutations (XX\(_{V}\);bb) and are crossed with wild-type males (XY;BB). The offspring in the \(F_{1}\) generation will inherit one X chromosome and one brown allele: X\(_{V}\)X;Bb (vermilion females with one brown allele) and X\(_{V}\)Y;Bb (brown males with one vermilion allele). Now, let's analyze the \(F_{2}\) generations for each cross: 1. Cross \(F_{1}\) vermilion females (X\(_{V}\)X) with \(F_{1}\) brown males (X\(_{V}\)Y;bb) from scenario (a). The expected \(F_{2}\) phenotypes would be: - Vermilion females (X\(_{V}\)X;BB) - Brown females (XX;Bb) - Vermilion males (X\(_{V}\)Y;BB) - White males (X\(_{V}\)Y;bb) 2. Cross \(F_{1}\) white females (X\(_{V}\)X;bb) with \(F_{1}\) wild-type males (XY;Bb) from scenario (b). The expected \(F_{2}\) phenotypes would be: - White females (X\(_{V}\)X;bb) - Vermilion females (X\(_{V}\)X;Bb) - Wild-type males (XY;Bb) - Brown males (XY;bb) 3. Cross \(F_{1}\) vermilion females (X\(_{V}\)X;Bb) with \(F_{1}\) brown males (X\(_{V}\)Y;Bb) from scenario (c). The expected \(F_{2}\) phenotypes would be: - White females (X\(_{V}\)X;bb) - Vermilion females (X\(_{V}\)X;Bb) - Vermilion females (X\(_{V}\)X;BB) - Brown males (XY;bb) - Vermilion males (X\(_{V}\)Y;Bb) - Vermilion males (X\(_{V}\)Y;BB).