Biology: Relatedness Between Nephew & Uncle

[nobahar]

Hello.
This has been bugging me for a while. If I use an example to demonstrate:
A nephew and his uncle and the average relatedness between them.
If for some trait, say eye colour, the grandmother of the nephew carries one for Blue (B), and one for Green (G), and the grandfather of the nephew carries one for Orange (O) and one for Azure (A). No one gene is more likely than any other, so each has a 1/4 probability. The probability of the uncle inheriting B, G, O or A is 1/2. And thus the probability that they both have the same gene is 4(1/4 x 1/2)= 4/8 = 19/2. But this will make up 1/2 of the complete set of genes for the nephew. 1/2 of 1/2 (i.e. 1/4) of the complete set that the nephew has will be shared with the uncle, on average.

I know that the relatedness is in fact 1/4. But is my reasoning correct? I'm assuming the 'filtering process' that occurs from the nephew's mother to the nephew - there are four possibilities, but B and G compete for a place in the nephew's mother and O and A do - has no influence on the probabilities, is this correct. It must be, but it almost seems as if it should be considered...

Thanks in advance.
Nobahar.

 

[Ygggdrasil]

Your reasoning is basically correct. Here's how I think of it. The relatedness is the probability that the two individuals will share a gene. Now, let's assume that the uncle inherited the blue allele. What is the problem that the nephew also has the blue allele? For this to occur, the uncle's sibling/nephew's parent must have inherited the blue allele, which occurs with probability of 1/2. The nephew must also have inherited the blue allele from the parent, also occurring with a probability of 1/2. Thus the overall probability that the two individuals share this allele is 1/4. This occurs no matter what allele you look at (e.g. if you assume the uncle inherited the green allele, the math is exactly the same).

 

[nobahar]

Thanks yggdrasil. You reasoning is certainly a lot more compact and efficient than mine! But I am glad to know that my reasoning is sound nonetheless.