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: The genotype ratio of the offspring in the $F_2$ generation is 1 BB (homozygous dominant), 2 Bb (heterozygous dominant), and 1 bb (homozygous recessive). The phenotype ratio is 3 black to 1 white. The Punnett square for this cross is as follows: ``` B b -------- B | BB | Bb | -------- b | Bb | bb | -------- ```

Step-by-step solution

Determine the Parental Genotypes

Since all the offspring in the $F_1$ generation are black, we can assume that black is the dominant trait and white is the recessive trait. We will let "B" represent the dominant allele for black and "b" represent the recessive allele for white. The parental genotypes are therefore BB (black) x bb (white).

Determine the Genotypes of the $F_1$ Generation

Create a Punnett square for the cross: ``` B B -------- b | Bb | Bb | -------- b | Bb | Bb | -------- ``` All guinea pigs in the $F_1$ generation have the Bb genotype, which phenotypically produces black fur.

Perform a Cross for the $F_2$ Generation

The offspring in the $F_1$ generation will cross with each other. So, it will be Bb (black) x Bb (black). Create another Punnett square for this cross: ``` B b -------- B | BB | Bb | -------- b | Bb | bb | -------- ```

Determine the Genotypes and Phenotypes of the $F_2$ Generation

From the Punnett square, the genotypes in the $F_2$ generation are: - 1 BB: Homozygous dominant (black) - 2 Bb: Heterozygous dominant (black) - 1 bb: Homozygous recessive (white) Phenotypically, there are 3 black guinea pigs and 1 white guinea pig, giving a ratio of 3:1 black to white as stated in the problem.

Key concepts

Mendelian Inheritance

Mendelian inheritance, named after Gregor Mendel, who is often called the father of modern genetics, refers to the patterns of inheritance for traits controlled by genes. Mendel observed that certain traits exhibit a predictable mode of inheritance from one generation to the next, following basic principles of dominant and recessive alleles. These fundamental principles are known as Mendel's laws, which include the law of segregation and the law of independent assortment.

Mendel's first law, the law of segregation, states that during the formation of gametes, the two alleles for a gene separate, so that each gamete carries only one allele for each gene. The second law, the law of independent assortment, asserts that the alleles of different genes segregate independently of each other during the formation of gametes. This means the inheritance of one trait generally does not influence the inheritance of another trait.

The exercise involving the guinea pigs demonstrates Mendelian inheritance by showing that the trait for black fur is dominant and follows the typical 3:1 dominant to recessive pattern seen in the offspring of a monohybrid cross.

Phenotype and Genotype

Understanding the distinction between phenotype and genotype is crucial in genetics. The genotype refers to the genetic makeup of an organism in terms of the alleles that it carries. For example, in our guinea pig exercise, genotypes are depicted as BB, Bb, or bb, where 'B' represents the allele for black fur and 'b' represents the allele for white fur.

The phenotype, on the other hand, is the observable physical or physiological trait that an organism displays, which results from both its genotype and environmental influences. In the case of the guinea pigs, the phenotypes are black fur or white fur. A genotype containing at least one dominant 'B' allele (BB or Bb) results in a black fur phenotype, while a genotype with two recessive 'b' alleles (bb) is required to produce a white fur phenotype.

By analyzing both phenotype and genotype, one can understand the genetic mechanism behind the manifestation of traits and predict the potential outcome of genetic crosses.

Dominant and Recessive Alleles

Alleles are different versions of a gene that determine specific traits. Dominant alleles, such as the allele for black fur in guinea pigs represented by 'B', are expressed in the phenotype even if there is only one copy present in the genotype. This means that individuals with a BB or Bb genotype will have black fur because the dominant allele 'masks' the presence of a recessive allele.

Recessive alleles, like the allele for white fur represented by 'b', only manifest in the phenotype when two copies are present (homozygous recessive genotype, 'bb'), because there is no dominant allele to mask their effect. This is why white fur is only observed in guinea pigs with a bb genotype.

It is important to understand the behavior of dominant and recessive alleles when predicting the outcome of genetic crosses. In the guinea pig exercise, we can clearly see how the dominant allele for black fur influences the phenotypes of the offspring in both the F1 and F2 generations.

Monohybrid Cross

A monohybrid cross involves a single pair of contrasting traits, such as the cross between black and white guinea pigs focusing solely on the color trait. This type of cross examines the inheritance of one characteristic, controlled by one gene with two alleles - one dominant and one recessive.

A Punnett square is a useful tool for visualizing a monohybrid cross and predicting the genotypic and phenotypic ratios of the offspring. It is a grid that allows us to combine the gametes from each parent to visualize the possible genotypes of their offspring. In our guinea pig example, the F1 generation resulted from a cross between BB and bb genotypes producing Bb offspring. When these Bb offspring were crossed for the F2 generation, the Punnett square helped us determine the expected genotypes (1 BB, 2 Bb, 1 bb) and phenotypes (approximately 3 black and 1 white out of 4 guinea pigs).

This approach not only predicts the ratios of traits in the offspring but also demonstrates the reassortment of alleles due to Mendelian inheritance patterns.