Question

Two independently assorting loci, \(\mathrm{c}\) and \(\mathrm{a}\), control coat color in mice. Mice which are homozygous for recessive c cannot synthesize pigment, and thus have white hair (albino). Mice which are homozygous for a have completely black hair. It is thought that the a locus is involved in pigment placement, because in the case of aa, melanin is distributed throughout the hair; but, when the dominant allele \(\mathrm{A}\) is present, the melanin only goes to parts of the hair, resulting in a grayish coat called "agouti" Of course, this color cannot occur when the mice have the albino alleles, cc, no matter what a alleles are present. Consider a cross between black with CCaa genotypes and white mice carrying ccAA genes. What are the phenotypic ratios for the \(\mathrm{F}_{1}\) and \(\mathrm{F}_{2}\) generations?

Short answer

The phenotypic ratios for the F1 generation will be 100% agouti mice, as all offspring will have the CcAa genotype. In the F2 generation, the phenotypic ratio will be 1:9:6 for black:agouti:white mice, following a cross between F1 generation mice with genotypes of CcAa x CcAa.

Step-by-step solution

Determine the genotype of the parent mice

It is given that the parental generation includes: 1. A black mouse with genotype CCaa 2. A white mouse with genotype ccAA

Perform the F1 cross (CCaa x ccAA) using a Punnett square

Since each locus is independently assorting, we can focus on each locus separately. At locus C: | | C | C | |---|---|---| |c | Cc | Cc | |c | Cc | Cc | All offspring in the F1 generation are heterozygous (Cc) at locus C. At locus A: | | a | a | |---|---|---| |A | Aa | Aa | |A | Aa | Aa | All offspring in the F1 generation are heterozygous (Aa) at locus A. The F1 generation genotype is CcAa for every individual.

Determine the phenotype for the F1 generation

All mice in the F1 generation have the genotype CcAa. As per the information given, all F1 mice will produce melanin (due to C allele presence) and show agouti coloration (due to A allele presence). Thus, the complete F1 generation mice will display the agouti phenotype.

Perform the F2 cross (CcAa x CcAa) using a Punnett square

To generate the F2 generation, we cross the F1 mice with each other. Breaking down our F1 cross by loci: Locus C: | | C | c | |---|---|---| |C | CC | Cc | |c | Cc | cc | Locus A: | | A | a | |---|---|---| |A | AA | Aa | |a | Aa | aa |

Combine results of Locus C and Locus A to determine F2 genotypes and phenotypes

We will now combine the results of Locus C and Locus A to get our F2 genotypic ratios, from which we can determine phenotypic ratios. Combining the genotype ratios: - CCyy: \( \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \) - CCYy: \( \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} \) - CCYY: \( \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \) - Ccyy: \( \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \) - CcYy: \( \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \) - CcYY: \( \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \) - ccyy: \( \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \) - ccYy: \( \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} \) - ccYY: \( \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \) Phenotypic ratios (using the rules described in the problem statement and the genotypes above): - Black (CCaa): \(\frac{1}{16}\) - Agouti (CcAa, CcAA, CCAA, CCaa, ccAA): \(\frac{9}{16}\) - White (ccAA, ccAa, CCcc, CcCc): \(\frac{6}{16}\) The F2 phenotypic ratio is 1:9:6 for black:agouti:white mice.

Key concepts

Phenotypic Ratio

In genetics, the phenotypic ratio is a calculation that describes the relative number of offspring exhibiting different traits or phenotypes from a particular genetic cross. It helps in predicting and understanding how different traits are expressed based on parent genotypes.
In this exercise, the phenotypic ratio for the F1 generation is straightforward. All mice display the "agouti" phenotype due to the presence of both Cc (allowing pigment production) and Aa (resulting in agouti color) genotypes. So, the ratio is 1:0:0 for agouti:black:white.
For the F2 generation, things become more interesting. We observe a variety of phenotypes resulting from the genetic variations. The phenotypic ratio becomes 1:9:6 for black:agouti:white mice:

• Black mice result from specific genetic combinations that permit black fur only.
• Agouti mice result from having one or more AA or Aa along with Cc or CC genotypes.
• White mice result from the cc genotype when no pigment can be produced regardless of the other gene.

This complex ratio showcases genetic diversity attributed to genetic inheritance and the variety that independent assortment can produce.

Independent Assortment

Independent assortment refers to the way genes are inherited independently of each other during gamete formation. This means genes on different chromosomes or far apart on the same chromosome separate and recombine randomly.
In the context of our exercise, independent assortment plays a critical role. The c and a genes are on different loci, which means their segregation into gametes is independent. This leads to a variety of possible combinations in offspring genes.
During the F1 cross, each pair of alleles sorts independently, leading to all F1 mice being CcAa. In the subsequent F2 generation, the principle of independent assortment allows us to draw the large Punnett square needed to determine all genetic outcomes, culminating in the observed phenotypic ratio of 1:9:6.
This principle is a cornerstone of Mendelian genetics, highlighting the randomness and variety of genetic inheritance.

Punnett Square

The Punnett square is a diagrammatic tool used in genetics to predict the probability of different genotypes from a genetic cross. It helps in visualizing how alleles from parent organisms combine to form offspring.
In our exercise, we used Punnett squares in two main steps:

• To determine all offspring in the F1 generation as CcAa because of their equally mixed parental alleles (Cc from one parent, Aa from another).
• To evaluate the F2 generation, involving four simultaneous combinations of loci (two for C and two for A), to reveal all possible genotypes, and by extension, the phenotypes.

The Punnett square simplifies complex genetic crosses into manageable visual formats, making it easier to track how independent assortment results in different phenotypic expressions. It effectively demonstrates how diverse combinations of traits can emerge from a set of parents.