Question

In goats, the development of the beard is due to a recessive gene. The following cross involving true-breeding goats was made and carried to the ${\mathrm{F}}_2$ generation: Offer an explanation for the inheritance and expression of this trait, diagramming the cross. Propose one or more crosses to test your hypothesis.

Short answer

Question: Explain the inheritance and expression of beard development in goats, diagram the cross, and suggest possible crosses to test the hypothesis. Answer: Beard development in goats is determined by a recessive gene, meaning an individual must have two copies of the same allele (bb) for the trait to be expressed. A Punnett square can be used to diagram the cross, resulting in an F2 generation with a genotypic ratio of 1:2:1 (BB: Bb: bb) and a phenotypic ratio of 3:1 (no beard: beard). To test the hypothesis, we suggest two crosses: (1) Cross an F2 goat with a beard (bb) with a true-breeding goat with a beard (bb), resulting in a 100% probability of offspring with beards. (2) Cross an F2 goat without a beard (Bb) with a true-breeding goat without a beard (BB), resulting in genotypes of 50% BB and 50% Bb and supporting our hypothesis of recessive inheritance since none of the offspring will have beards.

Step-by-step solution

Understand the concept of recessive gene

In this case, the development of the beard in goats is determined by a recessive gene. A recessive gene is one that is expressed only when an individual has two copies of the same allele, both carrying the trait. In a breeding process, if only one copy of the allele is present, the dominant allele will prevail, and the trait will not be expressed.

Use Punnett Square to diagram the cross

A Punnett square is a graphical representation of a cross between two individuals, showing the possible genotypes their offspring could inherit. In this case, let's use "B" for the dominant allele (no beard) and "b" for the recessive allele (beard). Since these are true-breeding goats, it means that they have homozygous genotypes, either "BB" or "bb". The initial cross (P generation) can be represented as: P generation: BB x bb To create the F1 generation, we will cross the P generation: F1 generation (genotype): Bb Considering that beard development requires the presence of two recessive alleles, all F1 generation goats will not have beards because they only have one recessive allele. Next, cross two F1 generation goats to create the F2 generation: F1 generation: Bb x Bb The Punnett square for this cross will show the following possible genotypes for the F2 generation: $$$\left[\begin{array}{cc}BB& Bb\\ Bb& bb\end{array}\right]$$$ F2 generation: 1 BB, 2 Bb, 1 bb (genotypic ratio = 1:2:1)

Analyze the phenotypes of the F2 generation

The F2 generation will exhibit two possible phenotypes: goats with beards (bb) and goats without beards (BB and Bb). Based on the genotypic ratio of the F2 generation, we will have a phenotypic ratio of 3:1, where 75% of goats will not have beards, and 25% will have beards. This phenotypic ratio confirms the inheritance and expression of the trait.

Propose one or more crosses to test the hypothesis

To test the hypothesis, we can carry out two different crosses: 1. Cross an F2 goat with a beard (bb) with a true-breeding goat with a beard (bb). This cross will produce offspring with a genotype of bb, resulting in a 100% probability that all offspring will have beards. This will support the recessive inheritance hypothesis. 2. Cross an F2 goat without a beard (Bb) with a true-breeding goat without a beard (BB). The resulting Punnett square will show the following genotypic outcomes: $$$\left[\begin{array}{cc}BB& Bb\\ BB& Bb\end{array}\right]$$$ The resulting offspring will have genotypes of 50% BB and 50% Bb, which also supports the hypothesis of the recessive inheritance of the trait, as none of the offspring will have beards.

Key concepts

Recessive Gene

When studying traits, like the development of a beard in goats, the concept of a recessive gene is pivotal. A recessive gene requires two copies, one from each parent, to be expressed in an organism's physical appearance, which is known as its phenotype. Unlike its counterpart, dominant genes, which express their traits even with just one allele, recessive traits surface only when both alleles are of the recessive form.

For example, in goats, the allele for a beard is represented as 'b', and it is recessive. This means that a goat will only showcase a beard if it has two 'b' alleles (bb). If a goat has at least one dominant allele for no beard (B), such as 'Bb' or 'BB', the trait for a beard will not be visible. Because of this, recessive traits may sometimes skip generations before appearing and can be unpredictable without genetic analysis.

Punnett Square

Understanding how traits are passed on calls for a tool like the Punnett square, a simple graphical method of displaying all possible genotypes from the pairing of parental genes. By setting up a Punnett square, students can visualize how alleles from each parent may combine and what the likelihood is for each potential genotype.

In our example with goats, the Punnett square aids in predicting the possible offspring from true-breeding parents. True-breeding individuals have two copies of either the dominant or recessive allele, such as 'BB' for dominant and 'bb' for recessive traits. By mating a 'BB' individual with a 'bb' individual and then mapping their F1 generation ('Bb' goats) in a Punnett square, we determine potential F2 offspring outcomes.

Genotypic Ratio

The result of a cross, depicted in a Punnett square, leads to the genotypic ratio, which is the proportion of different genotypes obtained. This ratio is essential for geneticists and students to understand what to expect from breeding experiments.

In the case of bearded goats, when true-breeding parents ('BB' and 'bb') are crossed, the genotypic ratio among F1 offspring is uniform, all being heterozygous ('Bb'). However, crossing two 'Bb' goats from this F1 generation yields an F2 with a genotypic ratio of 1:2:1 (BB:Bb:bb), meaning there is one chance of a 'BB' outcome, two chances of a 'Bb' outcome, and one chance of a 'bb' outcome. This genotypic ratio is a powerful prediction tool for understanding future generations.

Phenotypic Ratio

The phenotypic ratio relates directly to what can be observed, the physical expression of the genes. Unlike the genotypic ratio, which considers genetic makeup, the phenotypic ratio reflects how traits manifest and can be tallied.

From the earlier goat example, the genotypic ratio of the F2 generation is 1:2:1, however, since 'B' is dominant over 'b', the phenotypic ratio simplifies to 3:1 for non-bearded to bearded goats. This is because both 'BB' and 'Bb' goats lack beards, thus they are grouped together in the phenotypic ratio. Knowing the phenotypic ratio is crucial as it predicts the likelihood of a trait's appearance in a population, which is invaluable in the fields of agriculture, breeding, and genetic counseling.