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.