Question

In goats, 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: \(P_{1}:\) bearded female \(\times\) beardless male \(\mathrm{F}_{1}:\) all bearded males and beardless females \\[ \mathrm{P}_{1} \times \mathrm{F}_{1} \longrightarrow\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

To summarize, in this problem involving inheritance patterns of the beard gene in goats, we analyzed given information and used Punnett squares to predict genotypes and phenotypes in the F1 and F2 generations. Based on the results, the phenotypic ratio revealed that beard development in males is due to a recessive gene. To test this hypothesis, we proposed a cross between a beardless male (BB) and a bearded female (bb) in the F2 generation, which is expected to yield all bearded males and beardless females in a 1:1 ratio, thereby confirming the recessive nature of the gene responsible for beard development in goats.

Step-by-step solution

Analysis of Cross

Given information: - Beard development is due to a recessive gene - The cross: bearded female (bb) x beardless male (BB) - F1 generation: all bearded males (Bb) and beardless females (Bb) Here, we see that the bearded female goat represents the recessive homozygous condition (bb), and the beardless male goat represents the dominant homozygous condition (BB).

Punnett Square for P1 Cross

Create a Punnett square to analyze the P1 cross and predict the genotype and phenotype of F1 generation. | - | B | B | |:--:|:--:|:--:| |**b**| Bb | Bb | |**b**| Bb | Bb | All offspring in the F1 generation will have the heterozygous genotype (Bb), leading to all bearded males and beardless females.

Punnett Square for F1 Cross

Now, we will create a Punnett square to analyze the cross between F1 generation goats (Bb x Bb) to predict the genotype and phenotype of the F2 generation. | - | B | b | |:--:|:--:|:--:| |**B**| BB | Bb | |**b**| Bb | bb | The genotypic ratio for the F2 generation is: 1 BB : 2 Bb : 1 bb The phenotypic ratio for the F2 generation is: 3 bearded males & beardless females : 1 beardless male & bearded female This phenotypic ratio matches the one stated in the problem: 1/8 beardless males, 3/8 bearded males, 3/8 beardless females, and 1/8 bearded females.

Hypothesis Testing Cross

One possible cross to test the hypothesis is to cross two F2 generation goats with known genotypes. For example, cross a beardless male (BB) with a bearded female (bb). Prediction of the offspring genotypes and phenotypes: - All males offspring will develop a beard (Bb). - All female offspring will be beardless (Bb). This cross will indeed confirm that beard development is due to a recessive gene, and that its expression depends on the gender of the offspring. Bearded males and beardless females will be produced in a 1:1 ratio.