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How Many Ancestors Do We Have?

If we double the number of ancestors in each generation, 2 parents, 4 grandparents, and so on, we can see that by the time we are back 10 generations, we have the potential for 1024 ancestors. If we were to go back to the time of Charlemagne, we would find we had the potential for 281 trillion ancestors all living at that one moment in history. But this is statistically impossible! The world’s population at that time does not support these numbers. So where did our ancestors go?

It is estimated that 80% of the marriages in history were between second cousins. Why? Because the population base was smaller, people lived in small communities and migrated within those same small communities. The theory in genealogical research is that our family trees are actually shaped like a diamond, not an inverted pyramid. Tracing back a few generations gives a wider shape. Keep going and you find the shape narrowing, eventually, the theory holds, converging to only a few ancestors.

This may sound mind-boggling but I've seen the truth of it. I am back a total of 14 generations which takes me to the last half of the 1500s. I've found that in two cases so far, I am descended from more than one child of one specific couple. Need an example? Pieter Uziele and his wife Cornelia Damen were my 8th great grandparents. I descend from two of their children: Sophia Uziele and her sister Maria Uziele. Remember, they are my 7th great-grandmothers and are in my 10th generation. I also descend from two children of Jochem Lambertse Van Valkenburg and his wife Eva Hendrickse Vrooman, who were my 8th great-grandparents. Their son Isaac and his sister Jannetie are my 7th great-grandparents and are in my 10th generation. So we see the gene pool narrowing in my 11th generation!

How is this possible? In the pyramid theory of doubling ancestors each generation, these four 7th great-grandparents would give me eight distinct individuals as ancestors for my 8th great-grandparents - but they don't. Because they are sets of siblings, I have only four new distinct individuals as ancestors for my 8th great-grandparents - half the number I should have if the doubling theory held true.

Assuming I have double sets of siblings at least three times on that 10th generation, I've lost six individuals from my 11th generation. That carries over to my 12th generation, but doubles the number I lose for a total of 12 ancestors. If I had three more double sets of siblings in my 11th generation, I've lost another six individuals in my 12th - for a total of 18 fewer individuals. Keep doing this for a few more generations and you'll see the shape your ancestral tree is taking. It’s not an inverted pyramid, it’s a diamond.

Luckily for the human race, this tendency to marry cousins reversed itself in more recent years, due to larger population bases and easier access to possible mates. Otherwise, our search for the missing link might prove to be just that !

One very interesting probability model created by a demographer for genealogists, is that a child born in 1947 in Englad tracing back to 1492 would have 60,000 ancestors. Going back further to 1215, this child would find that 80% of the entire population of England at that time would be on his or her family tree! So anyone living in present-day England who traces his or her lineage back through English history would theoretically be related. This is why genealogists find so many people searching for the same families in the 1600s and earlier, and why we find so many "cousins" out there in our search. I've found hundreds of cousins in the last year while searching via the Internet.

Genealogy is fascinating, and becomes even more so when we make those human contacts in present-day times with folks as far away as Norway who are descended from the same immigrant ancestor of 1624. I've become almost blasé about new cousins - I expect to find them, and I do!

Inverted Pyramid Theory of Doubling Ancestors

Screenshot 2016-07-22 13.33.31

Inverted Pyramid Theory

In this theory the number of ancestors double each generation. I can't represent the rest of the generations on this page, so following is the number of theoretical ancestors in each generation, starting at Generation 12 where the figure above leaves off.


Gen. 12: 2048
Gen. 13: 4096
Gen. 14: 8192
Gen. 15: 16384
Gen. 16: 32768

Diamond Theory of Ancestors

In this theory the pyramid begins to narrow beyond the 10th generation. I can't represent this with numbers as they would be unknown, so I am representing the basic shape with x representing the number of individuals in each generation. I will, however make some assumptions about the number of parents and grandparents back to the 10th generation.

LFT DIamond Theory

Diamond Theory of Ancestors


Basically the Diamond Theory explains that we can't keep going back through the generations and doubling the number of ancestors in each generation. (That's the inverted pyramid theory). Why not? Because eventually the world's population will not be large enough to support the numbers! 

In the Diamond Theory we see that as you keep going back through the generations you will eventually find cousins marrying cousins which narrows the number of unique ancestors and results in a diamond shape rather than a pyramid. 

In Your Family Past, Present and Future the author, Tim Urban of Wait But Why has some very informative and interesting ideas on this topic. At the end he comes up with four conclusions including this, my favorite one:

Writing this post has really hammered home the point that humans are mainly a temporary container for their genes. In 150 years, all 7,100,000,000 people alive today will be dead, but all of our genes will be doing just fine, living in other people. (Tim Urban. https://waitbutwhy.com/2014/01/your-family-past-present-and-future.html)

Tim's article has illustrations and sources and is well worth the read. 

 

Lorine McGinnis Schulze is a Canadian genealogist who has been involved with genealogy and history for more than thirty years. In 1996 Lorine created the Olive Tree Genealogy website and its companion blog. Lorine is the author of many published genealogical and historical articles and books.

Comments

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This is why I don't get excited about being descended from royalty. It seems that most people of European ancestry would be at some point or another. I've concentrated on breadth of information in my tree rather than depth. I figure once I get back about 10 to 12 generations, I will have so little to no DNA from those ancestors and certainly no culture to make much difference to me. And interestingly for me, a vast majority of my pedigree were in the US/Colonies by then. I only have a few German ancestors who came to the US after 1800 and none after 1865. As a result, I've been able to find almost all of my 3gggrandparents and later generations in the 1850 and on US censuses.

I have traced my father's ancestry back to the mid-1500s, with a few branches going back to the early 1400s. The vast majority of his family came from the same rural parish in Trentino (now part of northern Italy). I cannot even COUNT the number of "collapse" points on my tree where two lines have intersected. My oldest known ancestor (born about 1400) is related to me by blood no fewer than 12 different ways!! I find it absolutely fascinating.

I have discovered that both of my father's parents descend form Mayflower Stephen Hopkins. Grandmother through his son from the first marriage and Grandfather through his daughter from his second marriage. My grandparents are eighth cousins, once removed to each other.

Another reason for the diamond theory relates to the fact that children and grandchildren a few centuries ago frequently remained in the same town/area as their elders. My father's family lived in the same town in Quebec Province for over 350 years. Thus, when I go back 10 generations, I am frequently descended from the same couple multiple times. This also decreases the number of individual ancestors.

Actually, there is a hitch in the math.

The claim "... by the time we are back 10 generations, we have the potential for 1024 ancestors" is not quite correct.

Yes, at the 10th generation you have 1,024 ancestors:

    2^10 = 1.024 (said in English, 2 raised to the 10th power = 1,024)

But, you forgot to count ancestors in the intervening generations.
    2 parents + 4 grandparents + 8 great grandparents and so on.

The correct statement is that, at the 10th generation, you have "1,024 ancestor LINES", one for each 10th generation ancestor. (It could be less if some of the 10th generation are the same person because cousins married cousins.)

You have almost twice as many "total ancestors" as you do ancestor LINES at any generation level.

If you count all of the people between you and the 10th generation you have:

    (2^(n+1) - 2) = 2,046 ancestors, or
    (2 to the 11th power) minus 2 = 2.048 - 2 = 2,046

Check it out at the 2nd generation level (grandparents):

    (2^(2+1)) = (2 raised to the 3rd power) = 2 cubed = 8
    8 - 2 = 6 = 2 parents plus 4 grandparents

In my grandparent level there is the case where two sisters married two brothers. In each family all of the children have the same four grandparents. Legally they are cousins but genetically they are essentially siblings. Comparing these two groups, they have essentially lost a whole DNA generation level between the cousins all of the way back.
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There is also a peculiarity in the size of you generation gene pools. Some generations may have reproduced in 20 years; others may have taken 50 years. In one ancestor case, the father is 22 years older than the wife. My wife's aunt is a year younger than she is. The 10th generation gene pool -- from the youngest to the oldest -- is smeared out over some period of time.

In any case, go far enough back and the gene pool is too small for us to have unique ancestors.

Isn't inheritance amazing!

I liked Lynn's reference to "collapses" in her tree. I've always thought of it more as a tapestry than a pyramid, which implies a solid structure (as does "diamond". I am a weaver, and it is easy for me to visualize the many smaller population groups whose DNA "collapsed" and then expanded again when they came into contact with other groups. There is even a kind of weaving that is called "collapsed weave", as threads wrap around one another in some areas, and left open in others. The connecting areas hold the all together, and when washed the weaving reveals a lovely lace. I like this way of thinking of my ancestors, and of my mashup of a family. I have found quite a number of cousin marriages, especially in early New England, followed by an amazing convergence in one part of the western US in the mid-1800s. Now we are again spreading and interlinking with other groups. It is so interesting to see it happen.

The reality is, however, that you don't have to go back 10 generations to see this effect happening. In my wife's family from Tasmania I have already seen this effect inside of 4 generations. Van Diemen's Land (as it was known in the early 1800's) was primarily a convict based settlement with free settlers thrown in for good measure. After around 50 years, the population had spread throughout the island and it was becoming quite common (from my research at least) to find that cousins were marrying cousins - in many cases, unknowingly because the families had been spreading out to new areas and then intermarrying when they returned to common lands again.

It is even more interesting when you consider descendants. IF each of the 1024, (512) families had 4 children per generation then in 10 generations of descendants you have 524,288 children for each line. Times 512 family lines, = 268,435,456 descendants in the 10th generation, Many had more children per generation. Of course many of those 512 families the children intermarried cousins in the community. Still a lot of relatives. In one of my lines, my 3rd great grandparents had 13 children, 81 grandchildren, 432 great grandchildren. My grandfather was one of the 432.

Additionally, In my case, I'm descended from 4 children of Tristram Coffin (Nantucket, MA), 2 children from Thomas Macy, and 4 children of Richard Gardner. This was in the 1650 era, My brother and his wife were related 16 different ways.
My grandfather and his wife were 8th cousins.

Very interesting article. I have several pairs of Cornish & Scottish cousins marrying in the 1600s-1700s, both countries having small populations at that time. And as Stephen Rowe pointed out, in early Australia in some areas the population was so small cousins married. My daughter-in-law's Western Australian family has quite a lot, her parents are 3rd cousins and in recent time her sister married a 4th cousin and her mother and his father are 3rd cousins. One of their ancestors had 18 children to 2 wives. Because of an extremely small population, quite a few of the WA families intermarried, brothers to sisters or cousins so like others, many share the same set of grandparents or great-grandparents which all reduces their number of ancestors. I have carefully recorded all those relationships so my grandchildren will know if they end up marrying a distant relative, if they remain in that part of Australia.

NOTE: when I wrote brothers to sisters, I didn't mean incest but brothers of one family marrying sisters of another family.

This happens also, when a husband died young and left a wife and small children.Is there was an unmarried brother to the dead husband, he would marry the widow, so her children would still care the surname they were born with. This happened in my family late 1800's. The brother married his brother's widow, then a few years later, she died and he married one of her unmarried sisters! Talk about keeping it in the family! This actually almost happened with my husband's grandmother. Her husband died in an accident, and one of his brother's asked for the widow's hand in marriage, but she refused. I never found out the reason, for the refusal, this happened in about 1946.
Something additional to this post. Could this be one of the many factors in Infant mortality. The biggest reason why we have "rules" about cousins marrying, today. My last time I know of 1st cousins, marrying, they had to get special permission from the church (Catholic), and they never had children. This was in the late 1800's, I believe. Great subject, thanks for all the comments.

The calculations don't take into account the mixing of populations from different parts of the globe. Thus the numbers are probably larger for people with both non-European and European ancestry.

Carole,
My Uncle Gus, who was not a genealogist, surprised my dad and I on a genealogy road trip as we went through another small Northeastern Montana town near we were all raised, when he told us that we had "double cousins" in that community. What he was referring to was that two brothers married two sisters. I had never heard the term "double cousins" before that. When you sit down and figure out the cousins from both marriages, it is a good term to define them.

That was @ 1996. In @ 2003 one of those double cousins found me on the old RootsWeb and contacted me and we began working together. I live in the same community, now, that both my family and hers moved to from the small Montana towns. So, I am working on both lines, now as she passed before we could meet. I would never had known our connection before she contacted me had it not been for my Uncle Gus', term "Double Cousins.

Dani Lee

This is good. If I could only find and understand my last seven generations I would be satisfied. DNA may help find what region of the world one of your blood lines come from, but it doesn't find their documented narratives.

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