Question

Pigment in mouse fur is only produced when the \(C\) allele is present. Individuals of the \(c c\) genotype are white. If color is present, it may be determined by the \(A, a\) alleles. AA or \(A a\) results in agouti color, while aa results in black coats. (a) What \(F_{1}\) and \(F_{2}\) genotypic and phenotypic ratios are obtained from a cross between \(A A C C\) and aacc mice? (b) In three crosses between agouti females whose genotypes were unknown and males of the aacc genotype, the following phenotypic ratios were obtained:

Short answer

Answer: The genotypic ratio for the F1 generation is entirely AaCc. The phenotypic ratio for the F1 generation is 100% agouti. For the F2 generation, the genotypic ratio is 2:4:4:12:4, and the phenotypic ratio is 11:2 (11 agouti and 2 black).

Step-by-step solution

Determine Gametes of each parent

The parent genotypes given are \(A A C C\) and aacc. We'll find the possible gametes for each parent. The \(A A C C\) parent can only produce AC gametes. The aacc parent will only produce ac gametes. Therefore, any offspring will inherit one AC gamete from the \(A A C C\) parent and one ac gamete from the aacc parent.

Perform Punnett square for F1 generation

Since we know the gametes from each parent (AC and ac), we will create a Punnett square to find the genotypes of the F1 generation. The Punnett square will be: | AC -------------- ac| AaCc The only genotype possible for the F1 generation is AaCc.

Determine F1 generation phenotype

According to the given information, since the F1 generation offspring have the C allele, which produces pigment, and they also have the Aa genotype, they will have agouti color. Hence, the phenotypic ratio for the F1 generation is 100% agouti. Now, let's find the \(F_{2}\) genotypic and phenotypic ratios.

Determine F2 generation gametes

For the F2 generation, we must evaluate a cross between two individuals from the F1 generation. Since all F1 offspring have the AaCc genotype, we will use this genotype for both parents. The possible gametes from an AaCc parent are AC, Ac, aC, and ac.

Perform Punnett square for F2 generation

Now that we have determined the possible gametes of AaCc, we will create a Punnett square for the F2 generation. | AC | Ac |aC | ac -------------------- AC |AACc|AACC|AaCc|AaCC Ac |AaCc|AaCC|Aacc|AaCc aC |AACc|AACC|AaCc|AaCc ac |AaCc|AaCc|Aacc|Aacc

Determine F2 generation genotypic and phenotypic ratios

Let's summarize the genotypes resulting from the Punnett square: 1. \(A A C C\): 2 offspring 2. \(A A C c\): 4 offspring 3. \(A a C C\): 4 offspring 4. \(A a C c\): 12 offspring 5. \(A a c c\): 4 offspring So, the genotypic ratio for the F2 generation is 2:4:4:12:4. To find the phenotypic ratios, we need to associate each genotype with its corresponding phenotype: 1. \(A A C C\), \(A A C c\), \(A a C C\), \(A a C c\): Agouti (22 offspring) 2. \(A a c c\): Black (4 offspring) The phenotypic ratio for the F2 generation is 22:4, or simplified to 11:2, where 11 represents agouti colored offspring and 2 represents black colored offspring.

Key concepts

Genotypic Ratio

Understanding the genotypic ratio is crucial when predicting the outcome of genetic crosses, such as those using a Punnett square. It refers to the numerical ratio of different genotypes that result from a genetic cross.

For example, in the step-by-step solution for the mouse fur color cross, the F2 generation had a genotypic ratio of 2:4:4:12:4. This ratio tells us how many times each genotype occurs when compared to the others. It's important to note that these numbers only give us a proportion and don't represent exact counts. The genotypic ratio helps us visualize the genetic diversity that can result from a single pair of breeding mice, assuming that all possible gametes have an equal chance of combining.

The concept of genotypic ratio is applicable to various inheritance patterns, and understanding it lays the foundation for exploring more complex genetic topics. To ensure comprehension, consider this like a recipe; just as you might combine ingredients in certain proportions to bake a cake, the genotypic ratio mixes genetic information to produce an array of offspring with diverse traits.

Phenotypic Ratio

In contrast to the genotypic ratio, the phenotypic ratio refers to the observable characteristics or traits of the offspring, such as fur color in mice. After performing a genetic cross, the phenotypic ratio helps us determine what the offspring will look like.

Continuing from our problem's solution, we found the F2 generation had a phenotypic ratio of 11:2. This break down means, for every 11 agouti mice, we can expect approximately 2 black mice, assuming a large enough sample size. Phenotypic ratios are crucial because they connect the genetic information (genotype) to the actual, visible outcome (phenotype). It's the bridge between the encoded genetic instructions and their final expression. In educational terms, think of the phenotypic ratio as the summary of an essay—it conveys the main outcomes succinctly, without diving into the genetic details.

Inheritance Patterns

The study of inheritance patterns helps us map out how traits are transmitted from parents to offspring, dictated by the genetic makeup of the organisms involved. Patterns can range from simple mendelian to more complex non-mendelian types, which might involve multiple genes or varying levels of dominance.

In our mouse example, we delve into a simple mendelian scenario where each gene has a dominant and recessive allele. The inheritance pattern is determined by how these alleles interact—which brings us to the next concept. Understanding inheritance patterns is akin to learning the rules of a language, it provides a framework for predicting and explaining the genetic outcomes seen in offspring.

Allele Interactions

The nuances of genetic expression often come down to allele interactions. These interactions determine the inheritance pattern of a particular trait. Alleles can be dominant, such as the 'C' allele for color production in our mouse example, or recessive, like the 'c' allele that results in a lack of pigment. Additionally, some genes, such as the agouti 'A' or the non-agouti 'a', showcase incomplete dominance or co-dominance.

In the case of the mice, the 'C' allele is necessary for any fur color, while 'A' or 'a' alleles determine the specific fur color. The step-by-step solution illustrates how these interactions shape the F1 and F2 generations' phenotypes. Simplified, allele interactions are like a team project, where the contribution of each team member (allele) can affect the project's (phenotype's) outcome. Therefore, understanding these interactions is akin to assessing individual team dynamics and their overall performance in achieving a collective goal.