DNA sequencing is revolutionizing the study of human origins and prehistory, but also genealogy.
The number of ancestors you have at each preceding generation is given by 2n, where n = 1, 2, 3, and so on (parents, grandparents, great-grandparents, etc.). The total number of ancestors you have back to any preceding generation is given by 2n+1 – 2. The number of ancestors for the first seven generations is shown in the following table.
| Generation | n | Generation Ancestors | Cumulative Ancestors |
| Parents | 1 | 2 | 2 |
| Grandparents | 2 | 4 | 6 |
| Great-Grandparents | 3 | 8 | 14 |
| 2G-Grandparents | 4 | 16 | 30 |
| 3G-Grandparents | 5 | 32 | 62 |
| 4G-Grandparents | 6 | 64 | 126 |
| 5G-Grandparents | 7 | 128 | 254 |
It is natural to wonder, is there a point at which you don’t receive any distinguishable1 DNA from an ancestor? As an example, looking at your 128 great-great-great-great-great-grandparents, what are the chances that any one of them contributed no DNA to you? The answer is about 0.5%. You would expect, on average, that 128×0.005 = 0.64 ancestors at this generation has contributed nothing to your DNA. In other words, either 127 or 128 of your 5G-grandparents contributed to your DNA. As we go even further back in time, the number of ancestors at each preceding generation that did not contribute to your DNA rapidly increases, as shown in the following table.
| Generation | n | Generation Ancestors | Likelihood of inherited DNA |
| Parents | 1 | 2 | 100% |
| Grandparents | 2 | 4 | 100% |
| G-Grandparents | 3 | 8 | 100% |
| 2G-Grandparents | 4 | 16 | 100% |
| 3G-Grandparents | 5 | 32 | 100% |
| 4G-Grandparents | 6 | 64 | 99.99% |
| 5G-Grandparents | 7 | 128 | 99.5% |
| 6G-Grandparents | 8 | 256 | 96% |
| 7G-Grandparents | 9 | 512 | 84% |
| 8G-Grandparents | 10 | 1024 | 64% |
So you can see that of your 1,024 G-G-G-G-G-G-G-G-grandparents, you will not have received any DNA from about 1024×0.36 = 369 of them.
Another question you might have relates to cousins. What is the probability that you and a cousin share DNA? That is shown in the following table.
| Relationship | Likelihood of a DNA Match |
| Sibling | 100% |
| 1st Cousin | 100% |
| 2nd Cousin | 100% |
| 3rd Cousin | 98% |
| 4th Cousin | 71% |
| 5th Cousin | 32% |
| 6th Cousin | 11% |
| 7th Cousin | 3.2% |
As you can see, beyond your 3rd cousins, there’s a reasonably good chance you have no distinguishable DNA in common.
DNA Tests
The usual DNA test that most folks get is an autosomal DNA test. It is that test that we are referring to in the sections above.
There are two other DNA tests you might want to consider. The Y-DNA test and the mtDNA test, which allow you to trace your patrilineal (father) and matrilineal (mother) lines, respectively.
Y-DNA Tests
A Y-DNA test looks at the Y-chromosome, which only men have. The Y-chromosome is passed down from father to son generation after generation virtually unchanged. So if you are male and took the Y-DNA test, and another male also took the Y-DNA test, if they matched you would know that you are both descended from the same common ancestor along male lines, whether it could be proved by records or not. I’ll use myself as an example.
I have been able to trace my male line ancestors back to my 7G-grandfather.
| Ancestor | Relationship |
| Andreas Oesper (?-1721) | 7G-Grandfather |
| Andreas Oesper (1709-1776) | 6G-Grandfather |
| Zacharias Oesper (1744-1792) | 5G-Grandfather |
| Johann Georg Oesper (1780-?) | 4G-Grandfather |
| Johann Peter Oesper (1817-1890) | 3G-Grandfather |
| Ernst William Oesper I (1846-1918) | 2G-Grandfather |
| Ernst William Oesper II (1874-1951) | Great-Grandfather |
| Ernst William Oesper III (1904-1976) | Grandfather |
| Ernst William Oesper IV (1928-1997) | Father |
| David Oesper (1956-) | Self |
Any male that descended along the male line from any of these ancestors (or unknown earlier generations) would have a Y-DNA match with me. They probably also have the surname Oesper, but not necessarily for a variety of reasons.
Though we haven’t both taken a Y-DNA test, my 2nd cousin once removed Pete Oesper and I would have matching Y-chromosomes. Pete is descended along the male line from my great-great-grandfather Ernst William Oesper I.
mtDNA Tests
A mitochondrial DNA (mtDNA) test looks at the mitochondria, which both males and females have. Mitochondrial DNA is passed down from a mother to her children generation after generation virtually unchanged. So if you and another person took a mtDNA test, if they matched you would know that you are both descended from the same female ancestor along mother-lines, whether it could be proved by records or not. I’ll again use myself as an example.
I have been able to trace my female line ancestors only back to my great-grandmother, or perhaps my great-great-grandmother, but all we have for her is a first name and perhaps not even that.
| Ancestor | Relationship |
| Mary? (?-?) | 2G-Grandmother |
| Katherine Curtin (1855-1931) | Great-Grandmother |
| Sarah Geneva Smith (1896-1992) | Grandmother |
| Carla Mary Pieroni (1929-1985) | Mother |
| David Oesper (1956-) | Self |
My great-grandmother Katherine Curtin and her brother and sister were orphaned at a young age in New York City. We know that her parents immigrated from Ireland, but nothing more for certain. If I were to take a mtDNA test and could find someone in Ireland who is a mtDNA match, they would likely have descended along the female line from the same female ancestor as me, presumably my great-great-great grandmother, or her mother, grandmother, etc. See how it works?
1 All humans have about 99.5% identical DNA. The half percent that differs between us is what we might call traceable or distinguishable DNA. When you see the term DNA in this article, we are always referring to the portion of the human genome that is distinguishable between individuals, present and past.
References
What is genetic inheritance?
https://www.ancestry.com/cs/dna-help/matches/inheritance
Accessed: November 17, 2021
Y-DNA, mtDNA, and Autosomal DNA Tests
https://support.ancestry.com/s/article/Y-DNA-mtDNA-and-Autosomal-DNA-Tests?language=en_US
Accessed: November 17, 2021
Acknowledgements
I’d like to thank Paul Martsching for emails he sent to me that I utilized in the writing of this article. I alone am responsible for any errors or inaccuracies herein, so please let me know if you find anything in need of correction.