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I am trying to find my family of origin.

My dad died several almost 15 years ago before DNA was a common thing. He was adopted and never knew anything about his birth parents and he never wanted to know so he never tried to find out. I have since identified his mother (my grandmother) and established contact with the family although my grandmother indicates that she doesn't know anything about my dad's father. She gave up a baby before my dad was born and put him up for adoption too. Through Ancestry, I have found 2 more 'aunts' who appear to be my dad's half sisters, both of whom were given up for adoption at birth, after he was born. They do not know their parents either. These two aunts and my father were all born within 5 years of each other. After years of research I have been told many times that my great grandfather had incestual relations with all three of his daughters, one of which was my grandmother (Dad's mom) which resulted in several children, all of whom were placed for adoption at birth.

I match to my dad's two siblings at 784 and 933 cM respectively. This would indicate 1/2 aunt which would make sense if they all had the same mother - my grandma - and different fathers but this doesn't seem to fit the story. It would also make sense if they all had the same father but different mothers (one of the three sisters) although I feel like there would still be a higher relationship possibility because they would share the same parent DNA as well as the common great grandmother's DNA (the mom of the three girls)....right?

If the story I've heard is true, how would this affect the DNA relationship I have with these aunts, or would it at all?

Can my DNA results help me figure out who my grandfather is?

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I'm somewhat reluctant to post this as an answer, because it probably won't be. I'm assuming you're familiar with the shared CM tool. You can form multiple hypotheses as to the relationships between you and your presumed half-aunts, and them to each other. It sounds like the two ends of the hypothesis spectrum are: (1) Your great-grandfather is also the biological father of your father and both of these half-aunts; and (2) your father and the two half-aunts all have different biological fathers. Don't rule out the possibility that neither of these is true.

Proving hypothesis (2) is probably easier, and would require access to your aunts' DNA samples (all you'd need would be matches indicating another biological father). Disproving (or a lack of evidence for) hypothesis (2) might go a long way toward proving hypothesis (1).

Regarding the DNA percentages, if hypothesis (1) is correct, then your father and your half-aunts would each have inherited 50% of their DNA from your great-grandfather as their biological father. They would presumably also have inherited on average 25% from him as their maternal grandfather. "On average" is the key there, you'd need to look into the variances on grandparental DNA inheritance.

Also, bear in mind that probably on average half of that 25% will be the same as the 50% inherited directly. The only way to see that would be to discover which of your aunts' segments were identical on both chromosomes. One of the possible reasons why your match numbers aren't higher is that most vendor tools don't distinguish full-IBD vs. half-IBD, so they wouldn't show additional cM from matching on both chromosomes of a pair.

There probably aren't enough documented cases like yours to get a statistically significant estimate of what matching cM ranges to expect. In other forums, such as Facebook's Genetic Genealogy Tips & Techniques, you might find other people who descend from double-cousins (brothers who married sisters), twins, or even other incest scenarios, to give you some idea of how much those situations vary from typical shared cM ranges.

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