How Many Ancestors Do You Have?

NOTE: This is a repeat of an article I published 2 years ago. The subject popped up again recently so I decided to republish this article again for the benefit of those new readers of this newsletter who did not see the original article. I also made a couple of minor updates to  the original article.

A newsletter reader asked a simple question this week that generates a longer answer:

How many individuals does it take to make up 42 generations? Is there a website or other source that would help me calculate the answer?

I am sure there are such web sites, but you can also calculate the same numbers within a few seconds by using Excel or any other spreadsheet. I used a spreadsheet to generate the following:

# of generations

Total ancestors

1

0

2

2

2 parents

3

6

2 parents + 4 grandparents

4

14

2 parents + 4 grandparents + 8 great-grandparents

5

30

2 parents + 4 grandparents + 8 great-grandparents + 16 great-great-grandparents

6

62

2 parents + 4 grandparents + 8 great-grandparents + 16 great-great-grandparents + 32 great-great-great-grandparents

7

126

and so on and on…

8

254

9

510

10

1,022

11

2,046

12

4,094

13

8,190

14

16,382

15

32,766

16

65,534

17

131,070

18

262,142

19

524,286

20

1,048,574

21

2,097,150

22

4,194,302

23

8,388,606

24

16,777,214

25

33,554,430

26

67,108,862

27

134,217,726

28

268,435,454

29

536,870,910

30

1,073,741,822

31

2,147,483,646

32

4,294,967,294

33

8,589,934,590

34

17,179,869,182

35

34,359,738,366

36

68,719,476,734

37

137,438,953,470

38

274,877,906,942

39

549,755,813,886

40

1,099,511,627,774

41

2,199,023,255,550

42

4,398,046,511,102

43

8,796,093,022,206

44

17,592,186,044,414

45

35,184,372,088,830

46

70,368,744,177,662

47

140,737,488,355,326

48

281,474,976,710,654

49

562,949,953,421,310

50

1,125,899,906,842,620

In 42 generations you have more than 4 trillion ancestors!

Of course, that is far more than the total of all the people who ever lived on the face of the earth. The fact is that there are not 4 billion unique ancestors. We all have multiple lines of descent from many individuals. That is, if we were able to create a complete pedigree chart for 42 generations or more, we would see the same individuals appearing at multiple locations on the same chart.

This is often called “pedigree collapse.” See Wikipedia at https://en.wikipedia.org/wiki/Pedigree_collapse for more information about “pedigree collapse.”

 

7 Comments

Thanks, Dick. For those of us who are math challenged, what is the formula you used?

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    The formula for the NUMBER OF ANCESTORS in any one generation is:
    2n = x
    where n is the number of generations back
    and x equals the number of individuals in that generation.

    However, I prefer to count the TOTAL NUMBER of ancestors up to and including that generation, not limiting it to only one generation. To do that, have the spreadsheet simply add all the cells above it in the “Total ancestors” column.

    In other words, the 6th generation shows as 32 great-great-great-grandparents in that generation but adding together ALL GENERATIONS from generation #1 through generation #6 equals a TOTAL of 62 ancestors.

    Like

And when would that be? If we figure 4 generations per 100 years….would 42 generations be at 970 AD/ or?

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    —> And when would that be? If we figure 4 generations per 100 years….would 42 generations be at 970 AD/ or?

    Yes, although that would be a VERY approximate number. In some ethnic groups, the average age of parents can be considerably higher or lower than 25 years. For instance, in French-Canadian ancestors, the mothers tend to be between 15 to 30 years of age when children are born, while the fathers tend to be about 10 years older (25 to 40 years of age). All numbers are rough approximations and vary over time, over geography, over religion, and perhaps by other factors as well.

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Interesting. A few years ago for fun, I traced (sure I did) my ancestry back to Adam and Eve. According to my genealogy program, they are my 124th great-grandparents and that is sure a lot more than 42 generations. Of course, some of that research does not have good evidence to support it. (vbg)

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So, ultimately, we’re all related to one another?

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William DeW. Horrocks February 9, 2020 at 9:39 am

You might be interested in my method for calculating the number of ancestors one has. It is described in my article “THE UNLIKELIHOOD OF ONE’S EXISTENCE” published in the Journal of the Cape Cod Genealogical Society, 8, 183-189, 2018 (Vol 8, Number 2, Fall 2018).

To address the Pedigree Collapse problem, I introduced a method which I call quantitative pruning of the binary tree. This method eliminates duplicate entries (proxy ancestors) and all ancestors of those proxies from the ever-expanding binary tree. Using this method, along with some reasonable assumptions, it is easy to show how one’s number of real ancestors in a particular earlier generation can be equal to or even less than the number of real ancestors in a more recent generation. As an example I used parameters which cause an ancestry line to remain constant at 818,341 individuals per generation beyond 28 generations, (at this point the (unpruned) binary tree has 268,435,456 nodes and the time-frame would be around 1100 CE when the population of Great Britain is estimated to have been between 1.25 and 2 million) I go on to calculate the total number of real ancestors of the subject person back 10,000 generations to when species Sapiens appeared, about 300,000 years ago. This number is 8.2 x 109 distinct individuals. This result depends, of course, on some unknown and unknowable parameters, but it gives a possibly realistic analysis of the situation. Your comments are welcome.

William DeW. Horrocks, Ph.D.

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