Because Sam shares a parent with each of them, Matthew and Daisy are both his half siblings. However, Matthew and Daisy are not siblings in any way, for they do not share any parents nor do they share stepparents.
Assuming that neither one of Matthew's parents are blood relatives of either of Daisy's parents, then they do not share a blood relation that would forbid their marriage under any law or standard of incest of which I have heard.
(As for describing the relationship of Matthew and Daisy: The best English term is step-siblings, even though the order of parental relationships that produced them may not be the most common sequence that produces step-siblings.)
This is definitely NOT considered incest if Sam's half-brother and half-sister grew up in separate households. The problem arises that when Sam's half-siblings marry and have children, and one day they discover that their uncle is the brother of each of their parents. He's literally on "both sides" of his nieces & nephews' family tree. Which side of the aisle does uncle Sam sit on when his nieces and nephews get married? The bride's side or the groom's side?
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?
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.
"We went to my grandmother's for Christmas dinner, and my uncle drank too much. He kind of hinted that he had an affair with my mother. A couple of months and two DNA tests later, we found out my sister is actually his daughter. My dad never spoke to his brother again. And of course, my parents got divorced. And I needed a lot of therapy...and chocolate."
"I started having problems with my teeth. Spontaneous abscess that resulted in multiple root canals. My dentist did some looking into what the cause might be and found some really odd abnormalities with my incisor roots and nerves. When my next appointment came up, he was really quiet for a bit before verbally stumbling about. It turns out that what was happening with my teeth was a classic sign of inbreeding. I brought it up to my mom and she was like, 'Oh well, yeah, didn't you know?' Of course I didn't know! Turns out that not very far back in the family tree, several of my relatives decided that it was a good idea to get married to one another and no one bothered to mention it."
"My uncle served in Vietnam. While over there, his troop found a baby that had been orphaned or abandoned. My uncle was shipping back to Australia soon and wanted to adopt him, but my aunt said no. My uncle's troop found a family to raise the baby, and that's the story the whole family knows. The secret is that my uncle and some other guys from his troop stayed in contact with the family and the kid, sending them money every month to help raise him and then to help him go to university. Eventually they helped him and his adoptive family move to Australia in the late '90s."
"My mother is kid number 7 of 10. My aunt, the fourth kid, was born in 1945. She looked at her ancestry and found out that she has a different father from everyone else. She was devastated. There was always a rumor that there was an affair, but nobody talked about it. She has so many questions, but nobody's alive to answer her."
"My grandma didn't drive. I thought she couldn't, but it was just never discussed. One day, no one would take me to the store. Finally I said I'd just ask Grandma, and my cousin chimed in with, 'Grandma can't drive.' But Grandma said, 'Oh, you bet your sweet ass I can drive. They just don't let me!'
"Years later, my mom explained that during Prohibition, Grandma bootlegged alcohol for moonshiners. She was so successful at it that when the moonshiners were finally busted, her license was suspended by the state. Later in life, she was told she could petition for it back, but it came with an admission of guilt or some such. She told 'em to go to hell."
"My parents 'had' to get married. They always told us they got married in 1961, but it was 1962, three months before my sister was born. What's amusing is that my father was an accountant who was insanely fast with math. Whenever he was asked how many years they'd been married, he'd be off by one. My mother would correct him through clenched teeth, and then my father would nod and agree."
"My father died when I was 17. During the viewing, a young lady and her boyfriend showed up. She was probably two or three years older than me. Nobody recognized her, so she was asked why she was there; she stated she was there to see her father. My siblings and I were naturally confused; our mom just stood there shaking her head, and my uncles asked her to leave. She left crying in her boyfriend's arms. Our mother explained that our father had an affair years ago and that was our stepsister. I never heard any more about her, never learned her name, and have never met her. I would like to meet her and apologize for my family. Seeing her rejected and crying because she couldn't even attend a viewing for her dead father bothers me to this day."
"My aunt wasn't my grandfather's child. He met my granny when my aunt was a very sick infant; she had polio and wasn't expected to survive. My granddad married my granny so she could get on his insurance and move to an area that had proper medical support. My granddad loved my aunt as if she was his own, and I never knew until she went to her bio dad's funeral when I was a teenager."
"Last week, I discovered that my dad died two years ago and no one bothered to tell me. I'd been looking for him. He was a drifter and I'm his only child. I stumbled across his headstone on findagrave.com while digging through Ancestry. His marker was labeled 'Beloved brother.' My aunts and uncles are pieces of shit...I'm not hard to find. I don't even know how he died."
"After my mom died, I found out the real story behind my parents' marriage. She came to my father's country to visit some of her relatives. She met my father, and after just one week, she asked him to marry her so she could stay in the country. My father accepted because he had no one else and his parents were pressing him to get married already. But the highlight of the story is that over some time, the two of them fell in love."
"About a month ago, my mother-in-law's 88-year-old sister revealed on her death bed that her husband's best friend was actually the father of all four of her children. Her husband was an abusive jerk, by all accounts. While everyone was shocked, no one was saddened by this news."
"My grandfather was an atomic soldier. Instead of sending him to fight in the Korean War, they sent him to Nevada, where he witnessed the mushroom cloud. After that was over, he was ordered to march to the detonation point, where he was unwittingly exposed to high amounts of radiation. Luckily for my family, my grandpa is now in his nineties and the rest of us are cancer-free and fairly healthy, but this is medical information that we really should have known earlier!"
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