Question

In a cross between a black and a white guinea pig, all members of the \(\mathrm{F}_{1}\) generation are black. The \(\mathrm{F}_{2}\) generation is made up of approximately \(3 / 4\) black and \(1 / 4\) white guinea pigs. (a) Diagram this cross, showing the genotypes and phenotypes. (b) What will the offspring be like if two \(\mathrm{F}_{2}\) white guinea pigs are mated? (c) Two different matings were made between black members of the \(\mathrm{F}_{2}\) generation, with the following results. Cross Cross 1 Cross 2 Offspring All black \(3 / 4\) black, \(1 / 4\) white Diagram each of the crosses.

Short answer

Answer: In Cross 2, when two black guinea pigs with heterozygous genotypes (Bb) are mated, the ratio of black and white offspring will be 3:1, with 3/4 of the offspring being black and 1/4 being white.

Step-by-step solution

Analyze F1 generation cross

First, note that the black guinea pig is dominant over the white guinea pig, as all members of F1 generation are black. Represent the black guinea pig allele with 'B' and white guinea pig allele with 'b'. Therefore, the initial cross is between a black guinea pig (BB) and a white guinea pig (bb).

Create a Punnett square for the F1 cross

A Punnett square can be used to visualize and predict offspring genotypes by pairing alleles from each parent. \[ \begin{array}{c|c c} \times & B & B \\ \hline b & Bb & Bb \\ b & Bb & Bb \\ \end{array} \] All members of F1 generation are black (Bb). #b) What will the offspring be like if two 𝐅2 white guinea pigs are mated?#

Analyze the F2 generation

Since there are white guinea pigs present in the F2 generation, their genotype must be (bb). When two F2 white guinea pigs (bb) are mated, we should determine the offspring's genotypes and phenotypes.

Create a Punnett square for the white F2 cross

Create a Punnett square, similar to Step 2, to visualize the offsprings' genotypes and phenotypes. \[ \begin{array}{c|c c} \times & b & b \\ \hline b & bb & bb \\ b & bb & bb \\ \end{array} \] All offspring from this cross will be white (bb). #c) Two different matings were made between black members of the 𝐅2 generation, with the following results.#

Analyze the different matings in F2 generation

Two different crosses between black members of the F2 generation are given: - Cross 1: All black offspring - Cross 2: \(\frac{3}{4}\) black, \(\frac{1}{4}\) white offspring

Diagram Cross 1

Considering dominant nature of black guinea pig, "All black offspring" in the F2 generation suggests that at least one parent must have been homozygous dominant (BB). \[ \begin{array}{c|c c} \times & B & B \\ \hline B & BB & BB \\ b & Bb & Bb \\ \end{array} \] In Cross 1, one parent is homozygous dominant (BB) and the other parent is heterozygous (Bb). All offspring are black: 1/2 (BB) and 1/2 (Bb).

Diagram Cross 2

This cross resulted in offspring with the following phenotypes: \(\frac{3}{4}\) black and \(\frac{1}{4}\) white. This indicates that both parents in this cross are heterozygous (Bb). \[ \begin{array}{c|c c} \times & B & b \\ \hline B & BB & Bb \\ b & Bb & bb \\ \end{array} \] In Cross 2, both parents are heterozygous (Bb). The offspring are: 1/4 (BB), 1/2 (Bb), and 1/4 (bb). The phenotypes are \(\frac{3}{4}\) black and \(\frac{1}{4}\) white.

Key concepts

Punnett Square

The Punnett square is an essential tool used in genetics to predict the possible genotypes of offspring from two parents. It provides a simple graphical way of illustrating the cross between the alleles of the parents' genes.

For instance, in our guinea pig exercise, the Punnett square allowed us to visualize how the black and white traits were inherited. By organizing the two possible alleles from each parent along the axes of a grid, we mapped out the potential combinations in the offspring. It's almost like making a chart to see every possible outcome of a genetic pairing.

When interpreting a Punnett square, remember that each cell represents a potential genotype of an offspring. So, it provides a structured and easy way to calculate the probability of each genotype and, by extension, the related phenotype—whether guinea pigs turn out black or white in this case.

Genotype and Phenotype

Every organism has a set of genetic instructions used to build and maintain its cells, known as its genotype. The physical expression of this genetic information is known as the phenotype. In other words, the genotype can be thought of as the genetic 'blueprint', while the phenotype is like the completed 'construction'.

The exercise showcases how two guinea pigs with different genotypes can have the same phenotype. A black guinea pig might have the genotype 'BB' (homozygous dominant) or 'Bb' (heterozygous), yet in both cases, the phenotype is a black coat color. Thus, the genotype refers to the actual alleles inherited, while the phenotype is the observed trait, such as fur color, in our furry friends.

F1 and F2 Generations

In Mendelian genetics, the terms 'F1' and 'F2' refer to the first and second filial generations, respectively. The F1 generation results from the crossing of two parent (P) organisms, while the F2 generation is produced by crossing two members of the F1 generation.

As seen in the exercise, all the F1 offspring exhibited the dominant phenotype—black fur. The F2 generation, born from the F1 individuals, shows the reemergence of the recessive white fur trait. Through careful analysis of these generational patterns, we can determine how traits are transmitted from parents to offspring and predict future occurrences of these traits with remarkable accuracy.

Dominant and Recessive Traits

Traits in Mendelian genetics are determined by alleles which are either dominant or recessive. Dominant traits mask the expression of recessive traits when they are together in a heterozygous genotype. To express a recessive trait, like the white fur in guinea pigs, an organism must inherit two copies of the recessive allele (bb).

It is fascinating how the combination of alleles, BB, Bb, or bb, determines the fur color of guinea pigs. In the exercise, we discovered that two black F2 guinea pigs could produce white offspring because they carried the recessive allele. This exemplifies why it's vital to look beyond the phenotype and consider the underlying genotype for a full understanding of inheritance patterns.