In Drosophila, a cross was made between females—all expressing the three X-linked recessive traits scute bristles (sc), sable body (s), and vermilion eyes (v)—and wild-type males. In the F₁, all females were wild type, while all males expressed all three mutant traits. The cross was carried to the F₂ generation, and 1000 offspring were counted, with the results shown in the following table.

No determination of sex was made in the data.
Using proper nomenclature, determine the genotypes of the P₁ and F₁ parents.

Verified step by step guidance

1. Step 1: Understand the genetic background and notation. The traits sc (scute bristles), s (sable body), and v (vermilion eyes) are all X-linked recessive. The P₁ females express all three recessive traits, so their genotype must be homozygous recessive for all three loci on their two X chromosomes, written as X\textsuperscript{sc s v}/X\textsuperscript{sc s v}. The P₁ males are wild type, so their single X chromosome carries the wild-type alleles: X\textsuperscript{+ + +}Y.
2. Step 2: Analyze the F₁ generation. Since all F₁ females are wild type and all F₁ males show all three mutant traits, this indicates that the F₁ females are heterozygous carriers (X\textsuperscript{+ + +}/X\textsuperscript{sc s v}) and the F₁ males inherited the mutant X chromosome from their mother (X\textsuperscript{sc s v}Y).
3. Step 3: Consider the F₂ generation data. The F₁ females (X\textsuperscript{+ + +}/X\textsuperscript{sc s v}) were crossed with F₁ males (X\textsuperscript{sc s v}Y). Since no sex determination was made, the offspring phenotypes represent a mixture of male and female progeny.
4. Step 4: Use the phenotypic classes and their counts to deduce the arrangement of alleles on the X chromosomes in the F₁ females. The largest classes correspond to parental (non-recombinant) types, while smaller classes correspond to recombinant types. This helps determine if the three loci are linked and the order of the genes on the X chromosome.
5. Step 5: Write the genotypes of the P₁ and F₁ parents using proper nomenclature. For P₁: females are X\textsuperscript{sc s v}/X\textsuperscript{sc s v} and males are X\textsuperscript{+ + +}Y. For F₁: females are X\textsuperscript{+ + +}/X\textsuperscript{sc s v} (heterozygous) and males are X\textsuperscript{sc s v}Y.

Key Concepts

X-linked Recessive Inheritance

X-linked recessive traits are carried on the X chromosome and typically manifest in males who have only one X chromosome. Females, having two X chromosomes, are usually carriers if heterozygous and show the trait only if homozygous recessive. This pattern explains why all F1 males show mutant traits when crossed with mutant females and wild-type males.

Genetic Nomenclature and Genotype Determination

Proper genetic nomenclature uses symbols to represent alleles, with '+' indicating wild-type and lowercase letters for recessive mutants. Determining genotypes involves analyzing phenotypes and inheritance patterns, especially in crosses involving multiple linked genes, to infer parental and offspring genotypes.

Linkage and Recombination in Multi-Gene Crosses

Genes located close together on the same chromosome tend to be inherited together due to linkage, reducing independent assortment. Recombination during meiosis can produce new allele combinations, affecting offspring ratios. Analyzing offspring phenotypes and frequencies helps map gene order and calculate recombination frequencies.