Question

Suppose that the inbreeding coefficient of I in the following pedigree is 0.25:
What is the inbreeding coefficient of I's common ancestor, C
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• A. 0.25
• B. 0.50
• C. 0.75
• D. 1.00

Hint:

For half-sib mating, the inbreeding coefficient is \( F = 0.125(1 + F_C) \).
If \( F = 0.25 \), then \( 0.25 / 0.125 = 2 \), which means \( 1 + F_C = 2 \implies F_C = 1 \).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The inbreeding coefficient (\( F \)) measures the probability that two alleles at a given locus in an individual are identical by descent from a common ancestor.
Sewell Wright's path coefficient method is used to calculate this coefficient from a pedigree.
Key Formula or Approach:
The formula for the inbreeding coefficient of an individual \( I \) is:
\[ F_I = \sum \left(\frac{1}{2}\right)^{n_1 + n_2 + 1} (1 + F_A) \] where:
\( n_1 \) is the number of generations from parent 1 to the common ancestor \( A \).
\( n_2 \) is the number of generations from parent 2 to the common ancestor \( A \).
\( F_A \) is the inbreeding coefficient of the common ancestor.

Step 2: Detailed Explanation:
Let us analyze the pedigree diagram:
Individual \( I \) is the offspring of maternal half-sibs who share a single common ancestor \( C \).
The path of gene transmission is through \( C \), from one parent of \( I \) to \( C \), and then to the other parent of \( I \).
Thus, the number of steps in the pathway is:
\[ n_1 = 1, \quad n_2 = 1 \] The total exponent is:
\[ n_1 + n_2 + 1 = 1 + 1 + 1 = 3 \] Using the inbreeding formula:
\[ F_I = \left(\frac{1}{2}\right)^3 (1 + F_C) = \frac{1}{8} (1 + F_C) \] We are given that the inbreeding coefficient of \( I \) is \( 0.25 \):
\[ 0.25 = \frac{1}{8} (1 + F_C) \] Multiply both sides by 8:
\[ 2.00 = 1 + F_C \implies F_C = 1.00 \] This indicates that the common ancestor \( C \) is completely inbred (\( F_C = 1.00 \)), meaning it is entirely homozygous.

Step 3: Final Answer:
The inbreeding coefficient of individual I's common ancestor, C, is 1.00.