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: Split each offspring's genome by parent.
Every offspring gets half its genes from its mother and half from its father. Since the two offspring here have different, unrelated fathers, none of the paternal genes can match between them. Only the maternal half of each genome can possibly be shared.

Step 2: Work out how much of the maternal share can match.
At any single gene, the mother carries two versions and passes on only one copy to each child, picked at random. So there is a $1/2$ chance that offspring X and offspring Y both happen to receive the same copy from her at that gene.

Step 3: Combine the two fractions.
The genes that could possibly be shared make up $1/2$ of each offspring's genome (the maternal half), and within that half there is a $1/2$ chance of getting the identical copy. Multiply the two:
\[ \frac{1}{2}\times\frac{1}{2}=\frac{1}{4} \]

Step 4: State the result.
So on average, a quarter of the genes in these two half sibs trace back to the identical copy in their mother. This fraction is exactly the coefficient of relatedness.
\[ \boxed{r=0.25} \]