Question

In goats, development of the beard is due to a recessive gene. The following cross involving true-breeding eoats was made and carried to the \(\mathrm{F}_{2}\) generation: \(\mathrm{P}_{1}=\) bearded female \(\times\) beardless male \(\mathrm{F}_{1}:\) all bearded males and beardless females \\[ \mathbf{F}_{1} \times \mathbf{F}_{1} \rightarrow\left\\{\begin{array}{l} 1 / 8 \text { beardless males } \\ 3 / 8 \text { bearded males } \\ 3 / 8 \text { beardless females } \\ 1 / 8 \text { bearded females } \end{array}\right. \\] 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

Answer: The inheritance pattern of the beard gene in goats is a sex-limited trait, where beard development is due to a recessive gene (b). To test this hypothesis further, we could perform a test cross between a bearded male from the \(\mathrm{F}_{2}\) generation (Bb) and a true-breeding bearded female from the \(\mathrm{P}_{1}\) generation (bb). We would expect a 1:1 bearded to beardless ratio in male offspring and a 1:1 true-breeding to non-true breeding ratio in female offspring.

Step-by-step solution

Rewrite the cross

The cross given in the exercise is: \(\mathrm{P}_{1}=\) bearded female \(\times\) beardless male \(\mathrm{F}_{1}:\) all bearded males and beardless females \(\mathrm{F}_{2}:\) $\left\{\begin{array}{l} 1 / 8 \text { beardless males } \\\ 3 / 8 \text { bearded males } \\\ 3 / 8 \text { beardless females } \\\ 1 / 8 \text { bearded females } \end{array}\right.$

Identifying the inheritance pattern

Development of a beard in goats is due to a recessive gene. In this problem, bearded female goats are true-breeding, which means they have two copies of the recessive allele (let’s use the symbol b for beard). The beardless male has the dominant allele, denoted as B. So their genotypes are: Bearded female (bb) \(\times\) Beardless male (BB).

Creating a Punnett Square for the \(\mathrm{P}_{1}\) cross

To determine the outcome of their offspring, create a Punnett Square for the \(\mathrm{P}_{1}\) cross: $\begin{array}{c|c|c|} \multicolumn{1}{r}{} & \multicolumn{1}{c}{B} & \multicolumn{1}{c}{B} \\ \cline{2-3} b & Bb & Bb \\ \cline{2-3} b & Bb & Bb \\ \cline{2-3} \end{array}$

Analyzing the \(\mathrm{F}_{1}\) generation

All offspring in the \(\mathrm{F}_{1}\) generation will have the genotype Bb. As beard development is a sex-limited trait, it only manifests in males. Therefore, in the \(\mathrm{F}_{1}\) generation, we have the following phenotypes: all bearded males (Bb) and beardless non-true breeding female goats (Bb).

\(\mathrm{F}_{1} \times \mathbf{F}_{1}\) cross

The next step is to cross the \(\mathrm{F}_{1}\) generation to obtain the \(\mathrm{F}_{2}\) generation. We can cross a bearded male (Bb) with a beardless female (Bb). So the Punnett square will look like this: $\begin{array}{c|c|c|} \multicolumn{1}{r}{} & \multicolumn{1}{c}{B} & \multicolumn{1}{c}{b} \\ \cline{2-3} B & BB & Bb \\ \cline{2-3} b & Bb & bb \\ \cline{2-3} \end{array}$

Analyzing the \(\mathrm{F}_{2}\) generation

The resulting genotypes of the \(\mathrm{F}_{2}\) generation are as follows: 1/4 BB: Beardless males and females (not shown separately) 1/2 Bb: Bearded males and beardless females (sex-limited trait) 1/4 bb: Bearded males and bearded females (beard is only expressed in males, but females can be carriers) This results in the ratios provided in the exercise: $\left\{\begin{array}{l} 1 / 8 \text { beardless males } \\\ 3 / 8 \text { bearded males } \\\ 3 / 8 \text { beardless females } \\\ 1 / 8 \text { bearded females } \end{array}\right.$

Proposing a test cross

To test this hypothesis further, we could perform a test cross. Cross a bearded male from the \(\mathrm{F}_{2}\) generation (Bb) with a true-breeding bearded female from the \(\mathrm{P}_{1}\) generation (bb). If the inheritance pattern is consistent, we will expect a 1:1 bearded to beardless ratio in male offspring and a 1:1 true-breeding to non-true breeding ratio in female offspring.

Key concepts

Punnett square

A Punnett square is a diagram used to predict the genetic outcomes of a particular cross or breeding experiment. It's like a genetic calculator that helps us visualize how each parent's alleles can combine and possibly manifest in their offspring. In our goat example, the Punnett square illustrates how beard development might be inherited.
Imagine we have two parents with known genotypes: a bearded female with genotype "bb" and a beardless male with "BB". When these parents are crossed, the Punnett square shows the potential combinations of alleles that the offspring may inherit:
- Top row represents the male gametes (each carrying a "B" allele).- Side row represents the female gametes (each carrying a "b" allele).
The resulting squares show that all offspring from this cross (\( ext{Bb} \)) will carry one dominant and one recessive allele. This demonstrates why all \( ext{F}_1 \) generation males are bearded while the females are beardless, due to the expression of the sex-limited trait.

recessive gene

A recessive gene is an allele that must be present in two copies (homozygous) for its associated trait to be expressed in the individual's phenotype. Only when both parents pass on the recessive allele will the trait appear. In genetics, dominant genes are often given capital letters, while recessive genes are given lowercase letters.
In this goat scenario, the gene responsible for beard development is recessive. We symbolize this gene as "b" for a bearded trait. For a goat to express this trait, they need two copies of this allele ("bb").
- Bearded female goats are "bb", since both of their alleles are recessive. - Beardless individuals can either be "BB" (homozygous dominant) or "Bb" (heterozygous), where the dominant "B" allele masks the presence of the "b" allele.
Because beard development in goats is a recessive trait, it requires specific conditions for expression, particularly in the case of producing a bearded female, which occurs at a lower frequency due to a combination of both genetics and the sex-limited aspect of the trait.

sex-limited traits

Sex-limited traits are traits whose expression is restricted solely to one sex, even if both sexes carry the genetic potential for the trait. These traits can be influenced by hormonal differences between the sexes that affect gene expression.
In goats, beard development is a sex-limited trait, meaning it only appears in males even though both males and females may carry the beard gene. This can be explained by the influence of hormones like testosterone that typically only affect males and can turn on the expression of the beard gene.
- In the \( ext{F}_1 \) generation, although both males and females have the "Bb" genotype, only the males express a beard. - In the \( ext{F}_2 \) generation, the appearance of 3/8 bearded males arises because this trait's expression is activated in the presence of male-specific hormones.Consequently, understanding sex-limited traits is crucial, especially in the context of hereditary studies and breeding programs, because it helps explain why certain traits only emerge in one sex and not the other.