Question

In the mouse, gene \(A\) allows pigmentation to be deposited in the individual coat hairs; its allele \(a\) prevents such deposition of pigment, resulting in an albino. Gene \(B\) gives agouti (wildtype fur); its allele \(b\) gives black fur. (a) Diagram the cross between a doubly heterozygous agouti mouse mated with a doubly homozygous recessive white mouse. (b) What would be the expected phenotypic ratio in the progeny?

Short answer

Answer: The expected phenotypic ratio in the progeny of this cross is 1 agouti: 1 black: 2 albino.

Step-by-step solution

Determine the genotypes of the parent mice

Before we can diagram the cross, we need to determine the genotypes of the parent mice. For the doubly heterozygous agouti mouse, it has one allele from each gene (gene A: A, a; gene B: B, b) resulting in a genotype of AaBb. The doubly homozygous recessive white mouse has two recessive alleles for each gene (gene A: a, a; gene B: b, b) resulting in a genotype of aabb.

Set up a Punnett square for the cross

Now that we know the genotypes of the parent mice, we can set up a Punnett square to predict the genotypes of the progeny. Firstly, we need to determine the possible gametes each parent can produce: - The AaBb mouse can produce AB, Ab, aB, and ab gametes. - The aabb mouse can only produce ab gametes. Creating a 4x1 Punnett square, with the AaBb gametes on the top and the aabb gamete on the side: ``` AB | Ab | aB | ab ab ```

Fill in the Punnett square

Now, we combine the gametes in each cell of the Punnett square: ``` AB | Ab | aB | ab ab AaBb | Aabb | aaBb | aabb ```

Determine the phenotypes of the progeny

We can now use the genotypes in the Punnett square to determine the phenotypes of the offspring: - AaBb: Agouti (A allows pigmentation deposition, B gives agouti fur) - Aabb: Black (A allows pigmentation deposition, bb gives black fur) - aaBb: Albino (aa prevents pigmentation deposition, B gives agouti fur, but it doesn't matter due to albinism) - aabb: Albino (aa prevents pigmentation deposition, bb gives black fur, but it doesn't matter due to albinism)

Determine the expected phenotypic ratio

Now that we know the phenotypes of the offspring, we can determine the expected phenotypic ratio. Out of the 4 offspring in the Punnett square: - 1 is agouti: AaBb - 1 is black: Aabb - 2 are albino: aaBb and aabb Thus, the expected phenotypic ratio in the progeny is 1 agouti: 1 black: 2 albino.

Key concepts

Punnett square

The Punnett Square is a useful tool for predicting the genetic outcomes of a cross between two organisms. Imagine it as a simple grid that allows us to visualize and organize the possible gene combinations coming from each parent.

For example, when dealing with two traits, like in the mouse example, we use a 4x1 Punnett square:

• One parent, the doubly heterozygous agouti mouse, can produce four types of gametes: AB, Ab, aB, and ab.
• The other parent, the doubly homozygous recessive white mouse, can only produce one type of gamete: ab.

Using the square, we place the gametes from one parent along the top and those from the other down the side. The intersections within the square represent possible offspring genotypes. The simplicity of the Punnett square belies its power, as it elegantly reveals which combinations of alleles are possible in the offspring.

genetic cross

A genetic cross involves breeding two organisms to examine how certain traits or genes are passed to their offspring. In our mouse example, the cross happens between a doubly heterozygous mouse (AaBb) and a doubly homozygous recessive mouse (aabb).

This cross aims to observe how different combinations of alleles from each parent contribute to the traits of their progeny. Each parental genotype comes into play, and through crossing, they segregate into various gametes:

• The AaBb mouse contributes gametes that have combinations of both dominant and recessive alleles, resulting in AB, Ab, aB, and ab.
• The aabb mouse contributes only ab gametes due to its homozygosity.

Genetic crosses like these are fundamental in understanding the principles of inheritance, such as segregation and independent assortment, which dictate how alleles are distributed during gamete formation.

phenotypic ratio

The phenotypic ratio is a representation of the various physical characteristics or traits that appear in the offspring of a genetic cross. In our example, after filling out the Punnett Square, the genetic possibilities translate into observable traits or phenotypes.

Here, the possible phenotypes are:

• 1 agouti mouse (AaBb) - possesses pigmentation and the agouti fur color.
• 1 black mouse (Aabb) - has pigmentation but displays black fur.
• 2 albino mice (aaBb and aabb) - due to the lack of pigmentation in both cases, regardless of the B alleles.

These results yield a phenotypic ratio of 1 agouti: 1 black: 2 albino. This ratio helps in predicting the frequency of each phenotype appearing in any given set of offspring, thereby providing valuable insight into the patterns of genetic inheritance.