Question

Pigment in the mouse is produced only when the \(C\) allele is pres- ent. Individuals of the ce genotype have no color, If color is present, it may be determined by the \(A\) and \(a\) alleles. AA or Aa results in agouti color, whereas aa results in black coats. (a) What \(\mathrm{F}_{1}\) and \(\mathrm{F}_{2}\) genotypic and phenotypic ratios are obtained from a cross between \(A A C C\) and aace mice? (b) In the three crosses shown here between agouti females whose genotypes were unknown and males of the aacc genotype, what are the genotypes of the female parents for each of the following phenotypic ratios? (1) 8 agouti (2) 9 agouti (3) 4 agouti 8 colorless 10 black \(\quad 5\) black 10 colorless

Short answer

(a) F1 genotype is AaCe, and F1 phenotype is agouti. (b) F2 genotypic ratio is 1AACC:4AACe:6AaCC:4AaCe:2aaCC:4aaCe:1aaee, and the phenotypic ratio is 15 agouti:6 black:1 colorless. (c) The genotypes of the female parents for different phenotypic ratios are: (1) AaCc for 8 agouti (2) AaCe for 9 agouti (3) Aace for 4 agouti: 8 colorless: 10 black.

Step-by-step solution

Cross the parent generation to obtain F1

Cross the parent genotypes \(A A C C\) and aace to obtain the F1 generation. It's easier to deal with the two alleles separately: \(A A \times aa\) results in all offspring carrying the Aa genotype for the first gene. \(C C \times ce\) results in all offspring carrying the Ce genotype for the second gene. Thus, the F1 genotype for their offspring will be AaCe.

Cross the F1 generation to obtain F2

Cross AaCe x AaCe to obtain F2 genotypic ratios: For the first gene (A, a): Aa x Aa produces: 1 AA, 2 Aa, 1 aa (1:2:1 ratio) For the second gene (C, e): Ce x Ce produces: 1 CC, 2 Ce, 1 ee (1:2:1 ratio) Now, we will combine the results from these crosses: 1:2:1 × 1:2:1 = 1:4:6:4:2:4:1:2:1 The genotypic ratio for the F2 offspring is 1AACC:4AACe:6AaCC:4AaCe:2aaCC:4aaCe:1aaee.

Determine the F2 phenotypes based on the genotypic ratios

According to the problem: 1. Color is determined by A and a alleles only if the C allele is present. 2. AA or Aa results in agouti color, whereas aa results in black coats. Therefore, we can list the phenotypes using the given information: 1 AACC: Agouti 4 AACe: Agouti 6 AaCC: Agouti 4 AaCe: Agouti 2 aaCC: Black 4 aaCe: Black 1 aaee (Colorless): Colorless The phenotypic ratio for the F2 offspring is 15 agouti:6 black:1 colorless. (a) F1 genotype: AaCe F1 phenotype: Agouti (b) In all the crosses, the male parent has aacc genotype, and we know that the female parents are agouti. Thus, the female parent must have one A allele and at least one C allele.

Determine Female Parent Genotypes for the Phenotypic Ratios

(1) 8 agouti: Male genotype: aacc Possible female genotype: AaCc (2) 9 agouti: Male genotype: aacc Possible female genotype: AaCe (Self-cross AaCe x AaCe to verify that this combination can produce the 9 phenotypic ratios) (3) 4 agouti: 8 colorless 10 black: Male genotype: aacc Possible female genotype: Aace (Self-cross AaCe x AaCe to verify that this genotype combination can produce the 4 agouti: 8 colorless: 10 black phenotypic ratio) Therefore, the genotypes of the female parents are: (1) AaCc (2) AaCe (3) Aace

Key concepts

Mendelian Inheritance

Mendelian inheritance refers to the fundamental principles of heredity first described by Gregor Mendel, an Austrian monk, in the 19th century. These principles form the basis of genetic inheritance and are critical for understanding how traits are passed from parents to offspring.
Mendel studied pea plants and determined that traits are controlled by discrete units, which we now know as genes. Each gene has variations called alleles, which can be dominant or recessive. During reproduction, organisms receive two alleles for each gene, one from each parent.
This concept explains patterns in genetic crosses, also called genetic experiments or breeding experiments. In a typical genetic cross, Mendel's laws of segregation and independent assortment govern the transmission of alleles.

• Law of Segregation: Each organism contains two alleles for each trait, and these alleles separate or "segregate" during the formation of gametes, ensuring that offspring receive one allele from each parent.
• Law of Independent Assortment: Alleles of different traits are passed to offspring independently of one another. This means that the inheritance of one trait generally does not affect the inheritance of another.

Mendelian inheritance is fundamental in predicting the courses of alleles through generations, forming the backbone of studying genetics.

Phenotypic Ratio

The phenotypic ratio is a comparison of different physical appearances in the offspring, resulting from a particular genetic cross. It reveals the expected distribution of observable traits, like flower color or coat type in animals, based on the inheritance patterns of alleles.
In a typical monohybrid cross, where only one trait is studied, the phenotypic ratio is often simpler to observe. For example, crossing two heterozygous plants with a dominant and recessive allele might result in a 3:1 phenotypic ratio—three plants displaying the dominant trait to one displaying the recessive trait.
In the context of dihybrid or more complex crosses, where multiple genes are involved, the phenotypic ratio can be more complicated. For instance, in the mouse exercise mentioned, the phenotypic ratio found was 15 agouti:6 black:1 colorless in the F2 generation, derived from more than one gene controlling the coat color:

• Agouti: Visible if the A allele occurs alongside a C allele.
• Black: Observed when aa combination appears with at least one C allele.
• Colorless: Occurs only if the ee genotype is present, regardless of the A gene.

By analyzing phenotypic ratios, we can predict how likely certain traits are to occur in offspring, providing a valuable tool for geneticists and breeders.

Genotypic Ratio

A genotypic ratio represents the proportion of different genetic makeups, or genotypes, in offspring resulting from a genetic cross. Unlike the phenotypic ratio, it focuses on the arrangement of alleles rather than the observable traits.
For a simple monohybrid cross, the genotypic ratio for heterozygous parents might be 1:2:1, where:

• 1 represents offspring with two dominant alleles (e.g., AA).
• 2 represents offspring with one dominant and one recessive allele (e.g., Aa).
• 1 represents offspring with two recessive alleles (e.g., aa).

In the given mouse exercise, the genotypic ratio in the F2 generation was 1AACC:4AACe:6AaCC:4AaCe:2aaCC:4aaCe:1aaee. Each group in this ratio symbolizes a different combination of alleles for the genes considered. This detailed ratio enables geneticists to assess genetic variety within a group of organisms more comprehensively.
The genotypic ratio is crucial for understanding the underlying genetics of potential phenotypes and provides a more complete picture of genetic variation within offspring.

Alleles

Alleles are various forms or variants of a gene that occur on the same position, or locus, on a chromosome. Every organism inherited one allele from each parent for any given gene. These combinations of alleles that organisms inherit determine their traits.
An allele can be dominant or recessive. A dominant allele only needs one copy present to express its associated phenotype. In contrast, a recessive allele requires two copies to display its specific trait, otherwise, it's overshadowed by a dominant allele.
In the case study of mouse coat color, the alleles involved were:

• A allele: Leads to agouti coloration when present.
• a allele: Results in black coloration in a homozygous recessive state (aa).
• C allele: Necessary for any pigmentation to be expressed – without which, mice do not show any color.
• e allele: Lack of color when homozygous (ee), regardless of the A allele.

Understanding alleles and their interactions is a cornerstone for grasping genetic crosses and predicting how organisms may appear or behave based on their genetic information.