How many total ancestors do you have?
Genealogists identify ancestors by following paper trails preserved in archivesâtraditional and digital. Although the goals of genealogists vary, a large pedigree chart is one measure of success. Yet even the most fruitful family trees are unlikely to yield more than a few thousand ancestors. One royal genealogy database shows only ~42,000 for the Queen of Canada herself. Yet, as the mathematically-inclined will be quick to point out, one can never find the names of more than a tiny fraction.
So, is an answer possible? I think the beginning of an answer is possible, within certain limits. This is a question for what might be called theoretical genealogy. Like any question of this magnitude, no matter what the discipline, it requires some agreement on definitions. An ancestor is someone who could theoretically been the source of some of your DNA. I say "theoretically," because most of your ancestors could not actually have passed DNA on to you. The probability is too low, since your number of ancestors greatly exceeds your number of genes. So we are counting parents, plus grandparents, plus great-grandparents, etc., until we reach an arbitrary beginning. 10,000 BCE should do nicely, as it puts us at the very beginning of the Anthropocene, the planet's first geologic era caused by us.
My video is an attempt to answer the question, using a theoretical model, some speculation, and a little calculus. A full DK version of the answer, for those who would rather read and engage here, is below the Orange Squiggle of Wonder, and see how closely we are all connectedâto each other and to billions of shared ancestors. It's based on the video script, but different because the format is different.
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.
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.