Question

Inbreeding coefficient in the first generation when half sibs are bred is

• A. 0
• B. 0.062
• C. 0.125
• D. 0.25

Hint:

Standard inbreeding coefficients to remember:
- Selfing: \( F = 0.500 \)
- Full-sib mating: \( F = 0.250 \)
- Half-sib mating: \( F = 0.125 \)
- First-cousin mating: \( F = 0.0625 \)

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The inbreeding coefficient (\( F \)) measures the probability that two alleles at any given locus in an individual are identical by descent (IBD).
It is determined by the degree of genetic relationship between the parents.
Half sibs share exactly one parent in common.
Key Formula or Approach:
The inbreeding coefficient of an offspring \( X \) is calculated using path analysis:
\[ F_X = \sum \left( \frac{1}{2} \right)^{n_1 + n_2 + 1} (1 + F_A) \]
where:
\( n_1 \) and \( n_2 \) are the number of generation steps from each parent to the common ancestor \( A \),
\( F_A \) is the inbreeding coefficient of the common ancestor (assumed to be 0 for non-inbred ancestors).

Step 2: Detailed Explanation:
Let us trace the genetic path for half-sib mating.
The parents \( P_1 \) and \( P_2 \) share a single common ancestor \( A \).
The path of inheritance is:
\[ P_1 \leftarrow A \rightarrow P_2 \]
Here, the number of generation steps from \( P_1 \) to \( A \) is \( n_1 = 1 \).
The number of generation steps from \( P_2 \) to \( A \) is \( n_2 = 1 \).
Substituting these values into the path formula:
\[ F_X = \left( \frac{1}{2} \right)^{1 + 1 + 1} (1 + F_A) \]
Assuming the common ancestor is not inbred (\( F_A = 0 \)):
\[ F_X = \left( \frac{1}{2} \right)^3 = \frac{1}{8} = 0.125 \]
This indicates that the offspring of a half-sib mating has a \( 12.5\% \) probability of being homozygous by descent at any locus.

Step 3: Final Answer:
The inbreeding coefficient of the offspring of half sibs is 0.125.