How can 3/4 siblings share mother but not paternal ancestry?

Question

My family is running the DNA test gauntlet and my dad got back some interesting results. He is related to his half sister (1,687 cM across 66 segments) at a level that is to be expected. He is struggling with the connection to his (assumed) half-brother though. (2,085 cM across 70 segments)

Explanations I've seen so far infer that My dad and his brother could be 3/4 siblings, sharing a mother and sibling fathers. However, my dad has no relationship to the father's side of the family. No cousins. No uncles/aunts. His brother does.

The only other explanation we can conjure up is a little bit frightening to consider, so I thought I would see if someone with some book-learning could weigh in on the situation.

Answer 1

According to the Shared cM Project, the match between half siblings can range from 1317-2312 cM.

Your dad is well within the accepted half-sibling range for both his half-sister and his half-brother.

As you know, 2085 cM is too small a match for full siblings (range 2209-3384 cM). 3/4 siblings is certainly possible by the numbers, but you've already disproved it. Your dad's father and your uncle's father do not have matches in common. In fact, you've unknowingly followed the expert's methods for disproving alternate theories of relationship.