Question

Normal-length fur in rabbits is controlled by the dominant allele \(\mathrm{R}\), and a short type of fur, called "rex," is determined by the recessive allele \(\mathrm{r}\). The dominant allele B controls black fur color; the recessive allele b controls brown. (a) Diagram a dihybrid cross between a homozygous rabbit with normal-length black fur and a rex rabbit with brown fur. What are the phenotypic ratios resulting from this cross? (b) What proportion of the normal, black rabbits in the \(\mathrm{F}_{2}\) generation of this cross can be expected to be homozygous for both pairs of genes? (c) What would be the expected phenotypic and genotypic results of a backcross between a member of the \(\mathrm{F}_{1}\) generation and a fully recessive rex, brown parent?

Short answer

(a) In the F1 generation from a dihybrid cross between a homozygous rabbit with normal-length black fur (RRBB) and a rex rabbit with brown fur (rrbb), all offspring have genotype RrBb, resulting in a phenotypic ratio of 100% normal-length, black rabbits. (b) In the F2 generation, the proportion of normal, black rabbits homozygous for both traits (RRBB) is 1/16 or 6.25%. (c) In a backcross between an F1 rabbit (RrBb) and a recessive rex, brown parent (rrbb), the phenotypic ratios are: - 1/4 normal-length, black rabbits (RrBb) - 1/4 normal-length, brown rabbits (Rrbb) - 1/4 rex, black rabbits (rrBb) - 1/4 rex, brown rabbits (rrbb)

Step-by-step solution

Determine the genetic makeup of the parent rabbits

The homozygous rabbit with normal-length black fur has the genotype RRBB, while the rex rabbit with brown fur has the genotype rrbb.

Perform the dihybrid cross for the F1 generation

All offspring in the F1 generation will inherit one allele from each parent for both traits, resulting in a genotype of RrBb. This gives us a phenotypic ratio of 100% normal-length, black rabbits in the F1 generation. (b) Homozygous proportion in F2 generation

Perform a dihybrid cross for the F2 generation

Crossing two F1 rabbits (RrBb x RrBb) will result in 16 possible combinations for the F2 generation, with 9 distinct genotypes. We can use a Punnett square to find these genotypes and the associated phenotypes. The resulting genotypic ratio is 1:2:1:2:4:2:1:2:1 while the phenotypic ratio is 9:3:3:1.

Identify the homozygous, normal black rabbits

Of the 9 distinct genotypes, only the RRBB genotype is homozygous for both traits and has a normal-length, black phenotype. There is only one RRBB individual in the 16 possible combinations, so the proportion of normal black rabbits in the F2 generation that are homozygous for both traits is 1/16 or 6.25%. (c) Results of the backcross

Determine the genotypes for the backcross

A backcross between a member of the F1 generation (RrBb) and a recessive rex, brown parent (rrbb) will produce four distinct genotypes: RrBb, Rrbb, rrBb, and rrbb.

Identify the phenotypes and genotypes of the backcross offspring

The resulting offspring phenotypes and their genotypic ratios are: - 1/4 normal-length, black rabbits with the genotype RrBb - 1/4 normal-length, brown rabbits with the genotype Rrbb - 1/4 rex, black rabbits with the genotype rrBb - 1/4 rex, brown rabbits with the genotype rrbb

Key concepts

Rabbit Genetics

Rabbits, like many other animals, have unique genetic traits that define their physical characteristics. In rabbit genetics, we often study the inheritance of coat color and fur type. For instance, normal-length fur is determined by a dominant allele \(R\), while the "rex" fur type, which is shorter, is controlled by a recessive allele \(r\). This means that a rabbit with either the genotype \(RR\) or \(Rr\) will have normal-length fur, while only \(rr\) will produce the rex type.
Another important genetic trait in rabbits is coat color, which is also determined by alleles. The dominant allele \(B\) will produce black fur, while the recessive allele \(b\) will result in brown fur. Thus, rabbits with \(BB\) or \(Bb\) genotypes will be black, and only \(bb\) rabbits will be brown. Understanding these basic genetic principles is essential to predict offspring characteristics through genetic crosses.

Phenotypic Ratio

In genetics, especially in studies like dihybrid crosses, phenotypic ratios are a critical outcome used to predict the appearance (observable traits) of organisms based on their genotype. When a dihybrid cross between a homozygous normal-length black rabbit (\(RRBB\)) and a rex brown rabbit (\(rrbb\)) is performed, the resulting \(F_1\) generation will all show the dominant phenotypes, resulting in a phenotypic ratio of 100% normal-length, black rabbits.
However, when these \(F_1\) rabbits (\(RrBb\)) are crossed, as in the \(F_2\) generation, a phenotypic ratio of 9:3:3:1 typically emerges. This includes 9 with normal-length black fur, 3 with normal-length brown fur, 3 with rex black fur, and 1 with rex brown fur. This predictable pattern is a classic result of Mendelian inheritance in dihybrid crosses.

Homozygous

The term "homozygous" refers to an individual having two identical alleles for a specific trait. In the context of rabbit genetics, a homozygous rabbit for fur length and color would have genotypes like \(RR\) or \(rr\) for fur length, and \(BB\) or \(bb\) for fur color.
When we observe the \(F_2\) generation from our original cross, the homozygous genotype for both normal-length and black fur (\(RRBB\)) appears in only 1 out of 16 combinations. This means that only 6.25% of the \(F_2\) generation rabbits will be homozygous for both traits. It's important to highlight that being homozygous for dominant traits allows the consistent expression of those traits in offspring.

Genotype vs Phenotype

While genotype refers to the actual genetic makeup of an organism, phenotype describes the visible characteristics. For instance, in the rabbit exercise, the genotypes \(RRBB\), \(RrBb\), \(Rrbb\), and \(rrbb\) translate to different phenotypes based on the combination of alleles.
Understanding the distinction between genotype and phenotype is crucial. Genes might not always visibly express if recessive (\(rr\) or \(bb\)), even if they are present in the genotype. For example, a rabbit with the \(RrBb\) genotype will have a phenotype of normal, black fur, because the dominant alleles \(R\) and \(B\) mask the presence of the recessive \(r\) and \(b\) alleles.
Genotype defines potential, while phenotype shows reality. Recognizing how these concepts interact helps predict breeding outcomes and explore genetic diversity.