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.