Whose baby is it?

Scenario:

Girl "G" has a brother "Br" who is married to a pregnant girl "PG". G's boyfriend "BF" hypothesizes that G's baby "Ba" was not produced by communion with Br, but rather with an unknown 3rd party, "P". To prove Ba's origin, BF would like to compare Ba's DNA with G's. What can we deduce?

 

Assumptions  **:

1. PG is not related to G, meaning they are no nearer than 6th cousins and can therefore be expected to share less DNA than, say, 4th cousins (chosen because there's a range of sharing published). Thus, PG and G have at most 0.5% common DNA

2. Br is related to G as full sibling and is therefore expected to share 50% DNA. The exact amount may vary significantly, but he should certainly be no further in sharing than a 1st cousin, whose low end of sharing is 7%.

** - reference: 23andme.com's table. Also pasted at the end of the entry.

 

So, what's in the baby?

If the baby is a product of Br and PG, we'd expect to see half each of 50% and less than 0.5%, which should yield something around 25% (also called out in the niece/nephew section). A lower bound can be established by using the 1st cousin range, from that we should see half each of 7% and 0.5%, for a total of ~4% shared DNA. Using the 1st cousin as a crosscheck (because they also have half a family tree that is totally unrelated) we should see no lower than 7% aggregate. The latter is the more correct number, really, because it's already tested for realistic distributions of gene passing.

 

If the baby is a product of P and PG, we'd expect to see half each of less than 0.5% each, for a total of less than 0.5% DNA sharing.

Interpreting the results:

If the sharing is:

1. Greater than 7%, it is highly probable that Br is the father. I think in practice this number would be quite a bit higher (we'd expect it to be around 25%, typically). The edge-case is if P is significantly related to Br, such as Br's parent, uncle, or even grandparent.

2. Less than 0.5%, it is highly probably that Br is not the father.

3. Between 0.5% and 7%, we have a curious case on our hands. Either P or PG are more related to Br than expected. Choice of options depends highly on state of residence.