Question

The coefficient of relatedness \(r\) is the probability that a gene in one individual is identical by descent with a gene in another individual. In a large, diploid, sexually reproducing population with outbreeding, the value of \(r\) for two offspring with the same mother but different fathers is __________ (round off to two decimal places).

Hint:

Half sibs share only one parent, so relatedness is half that of full sibs: use \(r=(1/2)^L\) with \(L\) equal to the number of links through the shared parent.

Answer 1

Correct Answer: 0.25

Step 1: Set up the family tree.
Two offspring share the same mother but have different, unrelated fathers. Call the offspring X and Y, and the shared mother M. Since the fathers are unrelated to each other and to M, the only path connecting X and Y runs through M.

Step 2: Use the path counting rule for relatedness.
The coefficient of relatedness between two relatives through a common ancestor is found with
\[ r = \left(\frac{1}{2}\right)^{L} \] where \(L\) is the number of parent to offspring links (meioses) in the path joining the two relatives through that ancestor.

Step 3: Count the links for half sibs.
The path is X to M to Y. That is one link from M down to X and one link from M down to Y, so \(L = 2\).

Step 4: Apply the formula.
\[ r = \left(\frac{1}{2}\right)^{2} = \frac{1}{4} = 0.25 \]
This matches the standard textbook value for half siblings: full sibs share both parents and get \(r = 0.5\), while half sibs share only one parent and get half that value, \(r = 0.25\).

Final Answer:
The coefficient of relatedness for the two half sib offspring is
\[ \boxed{r = 0.25} \]