Assuming that there were no cousin offspring (even very distantly) a person would have 2046 (1024+512+256…) ancestors from the past 10 generations. How many unique ancestors do most people actually have going back 10 generations?
More specifically, what about an American that the majority of descendents are European and were in America by 1700 when there was a very small population?
By “unique” do you ancestors not shared with anyone else? Because that would require that each generation have only one child on both sides of the family, or else a lot of childless siblings. Pretty unlikely.
No I mean not the same person in your individual family tree. So if your maternal grandfather was also you paternal grandfather you would have 3 unique grandparents instead of 4 unique grandparents like most people. In that case you would have 5 unique ancestors at the second generation (2 parents and only 3 grandparents).
It’s unlikely that all your ancestors in 1700 were already in the Americas. But I’m not sure if there is a meaningful “average” for such a number which must have a very high degree of variation, especially at that point in time. As you go very far back, though, it might be more easy to calculate.
If you look for the identical ancestor point, then we all have exactly the same ancestors. That is estimated to have been sometime between 5K and 15K years ago. It would have been longer ago before the Age of Exploration. And we’ve done that discussion at least half a dozen times in this form if you care to do search.
Unfortunately, I’ve never been adept in searching this forum (and am not ashamed to admit I did search first). I don’t believe I’m the only one judging by the number of repeated topics. Care to share a link or search terms to find these discussions?
If I’m understanding your question correctly, it can’t be directly answered unless you know your entire family tree ten generations back. I’m not sure how many people have traced families back that far. And given that we know that a small percentage of children are not actually fathered by the person on the birth certificate, even knowing the supposed names wouldn’t give you a true answer.
There are studies going the other way; i.e. showing that because of immigration and rape and one-night pairings every individual on earth has a common ancestor that is seemingly impossibly recent, around 1000 years ago. That was mentioned in the thread Common Ancestor -- What Are The Odds? - Factual Questions - Straight Dope Message Board.
And that thread cites the Cecil column 2, 4, 8, 16 … how can you always have MORE ancestors as you go back in time? which does seem to give a general answer to your question.
I’d love to see the math on that. Cecil doesn’t do footnotes and all the references I can find in a search just go back to this column.
Anybody know anything about Kenneth Wachtel, demographer?
The general phenomenon, that one has much fewer than (2[sup]k+3[/sup]-2) unique ancestors who are k-great grandparent or closer, is termed “pedigree collapse.” It can be caused by close cousins marrying, due to geographical isolation or, e.g. as among German nobles, requirement to select mates from a small caste.
Pedigree collapse can also be caused by very distant cousins marrying. Such collapse is inevitable if you go back far enough due to saturation; for example you have 4 trillion slots for 40-gt grandparents; comparing that with the entire population of 850 AD it’s clear there must be much duplication! But I don’t think this saturation effect will have great impact over just 10 generations, unless your ancestors were isolated pioneers, or restricted nobles (especially German). Early American enjoyed rapid immigration from the British Isles and other parts of Europe, so extensive intermarriages were unnecessary.
Going back 10 generations as OP asks, there are 2046 ancestor slots. I have names for 601 (29%) of mine. There are 565 unique ancestors (94% of the total).
Counting the ancestors of Britain’s King George VI (father of the present Queen) may be more interesting since high German nobles had to marry within their caste. In one database, names are shown for 1973 (96.4%) of the slots, but only 888 unique ancestors are shown (45% of the total).
The following chart details 19 lines of descent from the Duke of Brunswick who was namesake of the Kings George to King George VI:
1. Georg GUELPH (Duke) of BRUNSWICK (1583 - 1641)
2. Ernest Augustus I (1st Elector) of HANOVER (1629 - 1698)
3. George I Louis HANOVER (King) of ENGLAND (1660 - 1727)
+ Sophia Dorothea von BRUNSWICK-CELLE (1666 - 1726)
3. Sophia Charlotte von BRUNSWICK-LUNEBURG (1668 - 1705)
4. Friedrich Wilhelm I (King) of PRUSSIA (1688 - 1740)
+ Sophia Dorothea von HANOVER (1687 - 1757)
5. Sophia D. M. BRANDENBURG of PRUSSIA (1719 - 1765)
6. Friederike S. D. of BRANDENBURG-SCHWEDT (1736 - 1798)
7. Ludwig Fried. Alex. (Duke) of WUERTTEMBERG (1756 - 1817)
+ Henriette (Princess) of NASSAU-WEILBURG (1780 - 1857)
8. Alexander P. L. C. (Duke) of WUERTTEMBERG (1804 - 1885)
9. Franz (1st Duke) of TECK (1837 - 1900)
+ Mary Adelaide (Princess) of CAMBRIDGE (1833 - 1897)
10. Mary (Princess) of TECK (1867 - 1953)
+ George V WINDSOR (King) of ENGLAND (1865 - 1936)
2. Sofie Amalie GUELPH von BRUNSWICK-LUNEBURG (1628 - 1685)
3. Christian V OLDENBURG (King) of DENMARK (1646 - 1699)
4. Frederick IV OLDENBURG (King) of DENMARK (1671 - 1730)
5. Christian VI OLDENBURG (King) of DENMARK (1699 - 1746)
6. Frederick V OLDENBURG (King) of DENMARK (1723 - 1766)
7. Frederik (Hereditary Prince) of DENMARK (1753 - 1805)
8. Luise Charlotte (Princess) of DENMARK (1789 - 1864)
+ Wilhelm X (Landgrave) of HESSE-CASSEL (1787 - 1867)
+ Louisa von HANOVER (1724 - 1751)
7. Louise OLDENBURG (Princess) of DENMARK (1750 - 1831)
+ Karl (Landgraf) von HESSE-CASSEL (1744 - 1836)
2. George William (Duke) von BRUNSWICK-LUNEBURG (1624 - 1705)
3. Sophia Dorothea von BRUNSWICK-CELLE (1666 - 1726)
+ George I Louis HANOVER (King) of ENGLAND (1660 - 1727)
4. Sophia Dorothea von HANOVER (1687 - 1757)
+ Friedrich Wilhelm I (King) of PRUSSIA (1688 - 1740)
4. George II Augustus (King) of ENGLAND (1683 - 1760)
5. Frederick Louis (Prince) of ENGLAND (1707 - 1751)
6. George III (King) of ENGLAND (1738 - 1820)
7. Edward Augustus (Prince) of GREAT BRITAIN (1767 - 1820)
8. Victoria of HANOVER (Queen) of ENGLAND (1819 - 1901)
9. Edward VII (King) of ENGLAND (1841 - 1910)
+ Alexandra C. M. (Princess) of DENMARK (1844 - 1892?)
7. Adolphus Fred. (Prince) of GREAT BRITAIN (1774 - 1850)
+ Augusta W. L. of HESSE-CASSEL (1797 - 1889)
8. Mary Adelaide (Princess) of CAMBRIDGE (1833 - 1897)
+ Franz (1st Duke) of TECK (1837 - 1900)
5. Louisa von HANOVER (1724 - 1751)
+ Frederick V OLDENBURG (King) of DENMARK (1723 - 1766)
5. Anne HANOVER (Princess Royal) of ENGLAND (1709 - 1759)
6. Wilhelmine (Princess) of NASSAU-ORANGE (1743 - 1787)
7. Henriette (Princess) of NASSAU-WEILBURG (1780 - 1857)
+ Ludwig F. A. (Duke) of WUERTTEMBERG (1756 - 1817)
5. Mary HANOVER (Princess) of ENGLAND (1723 - 1772)
6. Friedrich III (Landgrave) of HESSE-CASSEL (1747 - 1837)
7. Wilhelm X (Landgrave) of HESSE-CASSEL (1787 - 1867)
+ Luise Charlotte (Princess) of DENMARK (1789 - 1864)
8. Louise W. F. C. A. J. of HESSE-CASSEL (1817 - 1898)
+ Christian IX OLDENBURG (King) of DENMARK (1818 - 1906)
7. Augusta W. L. of HESSE-CASSEL (1797 - 1889)
+ Adolphus Fred.(Prince) of GREAT BRITAIN (1774 - 1850)
6. Karl (Landgraf) von HESSE-CASSEL (1744 - 1836)
+ Louise OLDENBURG (Princess) of DENMARK (1750 - 1831)
7. Luise C. C. (Landgravine) von HESSE-CASSEL (1789 - 1867)
8. Christian IX OLDENBURG (King) of DENMARK (1818 - 1906)
+ Louise W. F. C. A. J. of HESSE-CASSEL (1817 - 1898)
9. Alexandra C. M. (Princess) of DENMARK (1844 - 1892?)
+ Edward VII of (King) of ENGLAND (1841 - 1910)
10. George V WINDSOR (King) of ENGLAND (1865 - 1936)
+ Mary (Princess) of TECK (1867 - 1953)
11. George VI (King) of ENGLAND (1895 - 1952)
Going back three more generations in George VI’s pedigree, the database has names for 14475 of 16384 slots (88%), but only 2574 unique names are shown (18%). Philip “the Magnanimous” of Hesse, who among other connections was the great grandfather of George Guelph’s wife, appears 186 times in George VI’s pedigree.