The answer seems easy at first. Your two parents each have two parents, making four grandparents, eight great-grandparents, sixteen great-great-grandparents, thirty-two great-great-great-grandparents... Just keep doubling and adding right? Not for long. While your 10th generation could just
have 1,024 unique ancestors, bringing your total to 2,046, it probably doesn't. I've never come across anyone who had this complete of a pedigree, all with unique ancestors.
In any case, doubling is guaranteed to fail. While everyone's ancestral lines increase in this way, many of the slots are filled by repeats.
Here's why this is inevitable. Even if we had no living examples and no records, the existence of cousin marriage could be proved by math alone.
28-year generations mean that we should expect our average 31st generation ancestors to have been born around the year 1117, when the population of Earth was less than 600 million. But the 31st generation requires more than 2 billion ancestral lines.
Scholars who lived in the 12th century were fascinated by impossible doublings like these. In one legend, an Indian king is so impressed by the game of chess that he offers its inventor a reward of his choosing. The inventor's request--1 grain of wheat on the first square of the chessboard, 2 on the second, 4 on the third, the doubling continuing until the 64th square--amounts to more than 10 to the 19th grains. The king could never have paid this amount, over 9 times the value of the global economy in 2014, or enough grains of wheat to completely fill Lake Superior. That same number is your number of ancestral lines in the 64th generation, less than 2,000 years ago. If they were all unique individuals, they couldn't fit on the surface of Earth, plus 12 Jupiters.
So, we need to refine the question. How many unique ancestors do you have? For this we need a real world example, and for counting ancestors the most complete family trees available are those of European royalty. The ancestors of the current queen of Denmark double for a few generations, but in the 5th generation, she has 28 instead of the expected 32. Because her parents were double 3rd cousins, these ancestors (and all of their ancestors) repeat. Continued cousin marriage makes her ancestry look more like a family spinning top than a family tree. Instead of over a million 20th generation ancestors, she has only about 6,000, mostly of the tiny ruling class of Renaissance Europeâ16 millionths of the world population.
It's well known that European royals often married close cousins, although they've mostly stopped. While the Queen and Duke of Edinburgh are second cousins (and related in countless other ways), the closest relation of the Duke and Duchess of Cambridge is 12th cousin once removed, and European royals are even starting to marry non-Europeans like the Queen of the Netherlands, from Argentina, and Princess Angela of Liechtenstein, who is Afro-Panamanian, and thus probably even more distantly related to her husband.
But your ancestors married close cousins too, guaranteed. One anthropologist, Robin Fox, has estimated that the average marriage has been between second cousins and closer. In any case, the cause of children is sex, not marriage, and real genealogies are real life. On the more tragic end of this spectrum, children, just as today, were born of rape within families. Some of them are your ancestors too.
Small populations mean that nearly every possible mate is closer than a 4th cousin. Your ancestors grow much like the queen's if they lived in small villages or isolated islands, or if they maintained traditions that encouraged close cousin marriage, such as tribal, religious, or caste endogamy.
Ethnic diversity and other forms of exogamy in your background will tend to make your number of 20th generation ancestors higher than the queen's 3,000. People with geographically diverse ancestry have more small in-marrying groups in their ancestry. At the other extreme are groups like the Sentinelese, who some believe are the most isolated community in the world. If they have truly remained uncontacted, and have rejected migrants to their Andaman Sea island for centuries, their number of 20th generation ancestors could be just a few hundred. Sustained first cousin marriage could make someone's number even less... as low as 6. 6 great-great-grandparents, 6 great-great-great-grandparents, etc.
We know that your number of ancestors at any given point is less than the world population. Some people never become ancestors. Others have lines that go extinct. However, our number of ancestors does approach the world population, and in historical time. If we assume that the queen's ancestors continue to accumulate at about the same rate, they converge toward the total population of Earth about 150 generations ago in the third millennium BC.
This fits well with one model of the timing of the identical ancestors point--the point in time before which every living human today shares the same set of ancestors. Anyone who was alive at or before this identical ancestors point either became the ancestor of everyone living today or the ancestor of no one living today. In a series of papers, Chang, Rohde, and Olson have run an increasingly complex series of simulations of human population history that attempt to calculate the date of this point. Their most recent paper identifies a mean identical ancestry date of 2158 BC, assuming relatively high migration. This is especially relevant for Eurasia and Africa, core regions of humanity that have been connected by trade and migration routes for thousands of years. A recent identical ancestors point for these regions of the world is starting to become supported by genetic data. In 2013, Ralph and Coop studied long genomic segments in Europeans' DNA that reflect these shared ancestors. Their distribution shows that ancestry can spread very quickly, with "individuals from opposite ends of Europe... expected to share millions of common genealogical ancestors over the last 1,000 years." The same applies to densely populated parts of Asia, which have held the majority of humanity for all of recorded history.
If we integrate the area under the curve we get by following this model, we get the number of years that our ancestors lived over the past 150 generations. Dividing by a life expectancy of 40 gives the figure of about 400 million ancestors since the 22nd century BC. By the same logic, there are another 1.5 billion people from the 150th generation to the 250th generation--Chang, Rohde, and Olson's more conservative IAP--then 4 billion more people back to 10,000 BC.
Using this model, a first estimate, the queen has about 6 billion ancestors since the domestication of wheat, a bit less than the current population of Earth, plus billions more in the Paleolithic past. a more complete answer than this requires a definition for the beginning of humanity or a decision to count pre-human ancestors, not only Neanderthals and Denisovans, but the ancestors that we share with chimpanzees, bonobos, all the other primates, all the other euarchontoglires, all the other mammals, all the other eukaryotes, etc. changing our numbers radically. So for this answer, let's stick to the relatively recent human past.
So, you have 6 billion ancestors in the past 12,000 years, plus or minus a few billion. Ancestry in endogamous groups will reduce this number, but not so low that you never catch up. You still have billions of Paleolithic ancestors you share with everyone. Indigenous peoples of the Americas and Australia, as well as smaller islands, might have the lowest, and people with diverse ancestry from various parts of Afroeurasia and the Americas, and long traditions of exogamy, will have the most ancestors. A lot of people in the United States, particularly African Americans and white Americans who have ancestry going back a few hundred years in North America will have the most, because of having ancestry from so many places. Just as a very, very rough estimate, I'd say that the range since 10,000 BCE is between 3 billion and 15 billion. A better mathematician should work on this.
We do not all share the exact same number of ancestors, but it is clear that we all share the majority. 5,000 years ago, you could find your ancestors in any village on the planet. Today, their descendants, your cousins, are everyone you know.
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