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Diana, Goddess of the Hunt for Ancestors!
 
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Number of Ancestors in a Given Generation
 
The formula for the number of ancestors in a given generation is:
2n = x
where n is the number of generations back
and x equals the number of individuals in that generation.
Based on the table below, if you go back 40 generations, you have over two trillion ancestors!  Of course, this number doesn't mean you have that many unique ancestors in 40 generations.  What is happening is repetition of ancestors, that is, the same ancestors appearing over and over again in a pedigree.  Repetition seldom appears within the first ten generations, but the further back you go, the more repetition you are likely to find.

As an example of repetition of ancestors, there is a famous pedigree that begins having significant repetition within the first few generations:  that of outlaw, Jesse JAMES.  There is even more pronounced repetition in his wife's pedigree, so the repetition is further compounded for their children:

Pedigrees of Jesse Woodson JAMES & Zerelda Cole MIMS

When repetition happens in the near generations, we call it "inbreeding."  It happens so often among southerners, like Jesse & Zerelda, that it's become a cultural cliché, as in the movie,  Deliverance.

For those of you being autosomal-DNA tested (e.g., FTDNA's FamilyFinder test, 23andMe, and the Ancestry-DNA test), an examination of this table makes it very clear why At-DNA is most useful within five generations, with it's use diminishing rapidly with each additional generation.  Even at five generations, you are likely to have only 3.125% of each ancestor's genes, and by seven generation, you are likely to have less than one percent.  This is the reason my genealogical goal is not to go deeply into my ancestry though I inadvertently have on some lines my goal is to get all lines back eight generations.  I'll know more about myself that way, than I do by the fact that I've bumped into a connection to Charlemagne (la de dah).

The greatly diminishing percentage of one ancestor's genes in your personal genome as you go back in your pedigree is just one reason why it's so biologically insignificant to have distant illustrious ancestors.  Socially, culturally, and historically it may be very significant to you, personally, but not because you are any kind of genetic "image" of your ancestor.  It's also a cautionary as to why it's foolish to think you live on in your children.  Your genetic contribution to your descendants diminishes so rapidly, the idea that bearing children gives you "continuence" is absurd.  You do share 99.9% of your genetic endowment with other human beings; the variable part we study amounts to less than one percent of our genetic endowment.  Be more concerned that the human genome has continuence.

The table below is based on an average generation time of 30 years and uses a person born in 1950 as an example.

 
GENERATIONS BACK NUMBER OF INDIVIDUALS Single Ancestor's
DNA Contribution
BIRTH
Each Generation (x) Cumulative
Name of Generation n Decimal Binary Decimal Percent Year
self 0 1 1 1 1950
parents 1 2 2 3 50.00 1920
grandparents 2 4 4 7 25.00 1890
great-grandparents 3 8 8 15 12.50 1860
2nd great-grandparents 4 16 16 31  6.25 1830
3rd great-grandparents 5 32 32 63  3.125 1800
4th great-grandparents 6 64 64 127  1.5625 1770
5th great-grandparents 7 128 128 255  0.78125 1740
6th great-grandparents 8 256 256 511  0.390625 1710
7th great-grandparents 9 512 512 1023  0.1953125 1680
8th great-grandparents 10 1024 1K 2047  0.09765625 1650
9th great-grandparents 11 2048 2K 4095 Need I go on? 1620
10th great-grandparents 12 4096 4K 8191   1590
11th great-grandparents 13 8192 8K 16,383   1560
12th great-grandparents 14 16,384 16K 32,767   1530
13th great-grandparents 15 32,768 32K 65,535   1500
14th great-grandparents 16 65,536 64K 131,071   1470
15th great-grandparents 17 131,072 128K 262,143   1440
16th great-grandparents 18 262,144 256K 524,287   1410
17th great-grandparents 19 524,288 512K 1,048,575   1380
18th great-grandparents 20 1,048,576 1M 2,097,151   1350
19th great-grandparents 21 2,097,152 2M 4,194,303   1320
20th great-grandparents 22 4,194,304 4M 8,388,607   1290
21st great-grandparents 23 8,388,608 8M 16,777,215   1260
22nd great-grandparents 24 16,777,216 16M 33,554,431   1230
23rd great-grandparents 25 33,554,432 32M 67,108,863   1200
24th great-grandparents 26 67,108,864 64M 134,217,727   1170
25th great-grandparents 27 134,217,728 128M 268,435,455   1140
26th great-grandparents 28 268,435,456 256M 536,870,911   1110
27th great-grandparents 29 536,870,912 512M 1,073,741,823   1080
28th great-grandparents 30 1,073,741,824 1G 2,147,483,647   1050
29th great-grandparents 31 2,147,483,648 2G 4,294,967,295   1020
30th great-grandparents 32 4,294,967,296 4G 8,589,934,591    990
31st great-grandparents 33 8,589,934,592 8G 17,179,869,183    960
32nd great-grandparents 34 17,179,869,184 16G 34,359,738,367    930
33rd great-grandparents 35 34,359,738,368 32G 68,719,476,735    900
34th great-grandparents 36 68,719,476,736 64G 137,438,953,471    870
35th great-grandparents 37 137,438,953,472 128G 274,877,906,943    840
36th great-grandparents 38 274,877,906,944 256G 549,755,813,887    810
37th great-grandparents 39 549,755,813,888 512G 1,099,511,627,775    780
38th great-grandparents 40 1,099,511,627,776 1T 2,199,023,255,551    750

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