Question

In chickens, the Leghorn variety has white feathers due to an autosomal dominant allele. Silkies have white feathers due to a recessive allele in a second (different) gene. If a true-breeding white Leghorn is crossed to a true-breeding white Silkie, what is the expected phenotype of the \(F_{1}\) generation? If members of the \(F_{1}\) generation are mated to each other, what is the expected phenotypic ratio of the \(\mathrm{F}_{2}\) generation? Assume the chickens in the parental generation are homozygous for the white allele at one gene and homozygous for the brown allele at the other gene. In subsequent generations, nonwhite birds will be brown.

Short answer

The \(F_{1}\) generation is expected to be all white. In the \(F_{2}\) generation, the expected phenotypic ratio is 9:3:3:1, with 15 of the chickens being white due to either the dominant or the recessive white allele and 1 of the chickens being brown.

Step-by-step solution

Define Genotypes

Firstly, define the genotypes of the parental generation. The white Leghorn can be denoted as \(WW'bb\) and the white Silkie as \(wwBB\), where \(W'\) represents the white dominant allele in Leghorns, \(w\) the white recessive allele in Silkies, \(B\) represents the brown dominant allele that isn't expressed in Silkies due to the white recessive allele and \(b\) the brown recessive allele that isn't expressed in Leghorns due to the white dominant allele.

Find F1 Generation

The \(F_{1}\) generation results from a cross between two parental chickens. Since each parent can only pass one allele from each gene to the offspring, all \(F_{1}\) chickens will receive \(W'\) and \(b\) from the white Leghorn, and \(w\) and \(B\) from the white Silkie. So, the genotype of the \(F_{1}\) generation chickens will be \(W'wBb\), and they will all have white feathers since the allele for white feathers from Leghorn is dominant.

Find F2 Generation

Next, find the phenotypes of the \(F_{2}\) generation, which is a result of a cross between \(F_{1}\) generation chickens. To find all the genotype combinations, a Punnett square can be utilized. There are four possible combinations of these two genes, \(W'B\), \(W'b\), \(wB\), and \(wb\). Using Punnett square, the phenotypic ratio in the \(F_{2}\) generation can be calculated which is expected to be 9:3:3:1 (9 white, 3 white, 3 white, 1 brown). Here, nonwhite birds are considered brown.

Key concepts

Autosomal Dominant Allele

An autosomal dominant allele is one that appears in a pair of chromosomes referred to as autosomes and expresses itself in the presence of a recessive allele. In genetics, the term 'dominant' indicates that a single copy of this allele is enough for its associated trait to appear.

In the exercise regarding chickens, the white feather trait in Leghorns is due to this type of allele. It's labeled as \(W'\). Since it's dominant, a Leghorn needs only one \(W'\) allele to express the white feather trait, whether the second allele in the pair is dominant as in \(W'W'\) or recessive like in \(W'w\).

This dominance affects the offspring significantly in breeding, as seen with the cross between Leghorn and Silkie. Despite Labradors carrying a brown allele, the dominance of \(W'\) ensures that the offspring in \(F_1\) generation also exhibit white feathers.

Recessive Allele

A recessive allele can be overshadowed by a dominant allele, requiring two copies for the trait to manifest. In the given chicken problem, the Silkie's white feathers come from two recessive alleles, represented by \(ww\). This means a chick must have two recessive alleles to appear with white feathers if the dominant allele from Leghorn is absent.

When the true-breeding Silkie with \(ww\) alleles for white feathers is bred with a Leghorn, the recessive alleles alone aren't seen in the \(F_1\) generation. The presence of the dominant \(W'\) allele in Leghorns conceals the recessive white trait due to Silkies, causing \(F_1\) chicks to show the dominant trait. As you move to \(F_2\), the interaction of these alleles becomes more evident, leading to a more diverse set of chick colors.

Punnett Square

The Punnett square is a simple diagram used in genetics to predict the genotype and phenotype composition of offspring from a particular cross. It helps visualize how alleles from two parents can combine and aids in forecasting the results of genetic crosses.

Using the exercise's parental chickens, the Punnett square becomes a reliable tool for calculating the offspring's phenotypes and understanding their genetic mix. The white Leghorn with alleles \(W'b\) and the Silkies with alleles \(wB\) combine as shown in this grid. The resulting configurations denote potential genetic outcomes in offspring.

The Punnett square for the \(F_1\) generation is relatively simple, yielding complete dominance of the white feather trait. However, for the \(F_2\) generation, the square showcases four types of potential genetic combinations: \(W'B\), \(W'b\), \(wB\), and \(wb\). This results in a more varied phenotype which supports the 9:3:3:1 phenotypic ratio of white and brown feathers.

Phenotypic Ratio

The term phenotypic ratio refers to the relative numbers of various phenotypes manifesting in offspring from a genetic cross. It's a summary of how often we expect different traits to be visible in the resulting generation.

In the chicken example, after examining the \(F_2\) generation, we find a classic 9:3:3:1 phenotypic ratio. This result is typical in dihybrid crosses resulting from two separate genes influencing the characteristics of the offspring.

Specifically, 9 chicks are expected to display dominant white feathers due to the evident autosomal dominance of \(W'\). Another 3 progeny will show the alternative white phenotype from the Silkie, and 1 - the only one with both sets of recessive alleles - will turn out brown, visibly different in color from the others. This demonstrates the principles of dominance, recessive traits, and independent assortment at play.