Question

In a cross between a black and a white guinea pig, all members of the \(F_{1}\) generation are black. The \(F_{2}\) generation is made up of approximately $3 / 4\( black and \)1 / 4$ white guinea pigs. Diagram this cross, and show the genotypes and phenotypes.

Short answer

Answer: In the F1 generation, all guinea pigs have a heterozygous genotype (Bb) and black fur phenotype. In the F2 generation, the genotypic ratio is 1 BB (homozygous dominant; black fur), 2 Bb (heterozygous; black fur), and 1 bb (homozygous recessive; white fur). The phenotypic ratio is approximately 3 black fur to 1 white fur guinea pigs.

Step-by-step solution

Identifying the Parental Genotypes

Consider black fur as the dominant trait (B) and white fur as the recessive trait (b). Since we know that one parent exhibits the dominant phenotype, it must have at least one B allele. Therefore, the black guinea pig’s genotype can be represented as BB (homozygous dominant) or Bb (heterozygous). The white guinea pig has the recessive phenotype so it must have two b alleles, making their genotype bb (homozygous recessive).

Estimating the F1 Generation Genotypes

As all the offspring in the F1 generation are black, the genotypes of the offspring must contain at least one B allele. This implies that the black parent is heterozygous (Bb). The parents' genotypes are: Black guinea pig: Bb (heterozygous) White guinea pig: bb (homozygous recessive) Create a Punnett square using the given genotypes of the parents to determine the genotypes of the F1 generation.

Constructing Punnett Square for F1 Generation

A Punnett square represents all possible combinations of parental alleles in the offspring. Fill the Punnett square with the possible allele combinations using the parent genotypes. ``` | | B | b | | - | - | - | | b | Bb| bb| | b | Bb| bb| ```

Determining the F1 Generation Phenotypes

Now that we have the genotypes of the F1 generation from the Punnett square, we can determine their phenotypes. All F1 guinea pigs have Bb genotype, and as B (black) is dominant, all these offspring will have black fur.

Calculating the F2 Generation Genotypes

To determine the genotypes of the F2 generation, choose two representatives of the F1 generation (both Bb) and cross them together. Create a Punnett square with F1 individuals' genotypes.

Constructing Punnett Square for F2 Generation

Create the Punnett square for the F2 generation using the following genotypes: ``` | | B | b | | - | - | - | | B | BB| Bb| | b | Bb| bb| ```

Determining the F2 Generation Phenotypes

Given the genotypes of the F2 generation from the Punnett square, we can now determine their phenotypes. Since the dominant trait is black fur, any guinea pig with either the BB or Bb genotype will have black fur. Only those with the bb genotype will have white fur. The phenotypic ratio in the F2 generation: BB: 1 (black) Bb: 2 (black) bb: 1 (white) Therefore, approximately 3/4 are black and 1/4 are white guinea pigs in the F2 generation, as stated in the problem.