Question

In shorthorn cattle, hair color is governed by co-dominant alleles. Red alleles are co-dominant with white alleles, and heterozygotes have red and white hairs. They are called roans. Cross a roan cow and red bull. What is the probability of having a heterozygous calf?

Answer 1

To determine the probability of having a heterozygous calf from the cross of a roan cow and a red bull in Shorthorn cattle, we first need to understand the genotypes involved.

1. Let's denote the alleles:
- R = red allele
- W = white allele

2. The genotypes:
- A red bull would have the genotype RR (homozygous for red).
- A roan cow would have the genotype RW (heterozygous, possessing both alleles).

Now, we set up the possible offspring from crossing a roan cow (RW) with a red bull (RR):

| Parent Genotypes | Possible Gametes from the Cow (RW) | Possible Gametes from the Bull (RR) |
|-------------------|-------------------------------------|----------------------------------------|
| Roan Cow (RW) | R, W | R, R |

Now we can use a Punnett square to find the potential genotypes of the calves:

\[
\begin{array}{c|c|c}
& R & R \\
\hline
R & RR & RR \\
\hline
W & RW & RW \\
\end{array}
\]

From this Punnett square, the possible genotypes of the calves are:
- 2 RR (red)
- 2 RW (roan)

This shows that:
- 2 out of 4 total offspring will be RW (heterozygous).
- 2 out of 4 total offspring will be RR (homozygous red).

Thus, the probability of having a heterozygous calf (RW) is:

\[
\text{Probability of RW} = \frac{\text{Number of RW offspring}}{\text{Total number of offspring}} = \frac{2}{4} = \frac{1}{2} = 0.5
\]

So the probability of having a heterozygous calf from this cross is **50%**.