How Many Genetic Ancestors Do You Have?

Bob Jenkins has published an interesting article concerning the origins of your DNA. As he writes:

“The number of genealogical ancestors you have n generations is 2n: 2 parents, 4 grandparents, 8 great-grandparents, and so forth. The only way to have fewer is if some of them are the same person. (For example, I have two great-great-great-great grandparents who are also my great-great-great-great-great grandparents by another line.)

“The difference between genealogical ancestors and genetic ancestors is that genetic ancestors are the ones that you actually got some DNA from. They’re a subset of your genealogical ancestors. Humans have about 3 billion base-pairs of DNA, so that limits the number of genetic ancestors to about 3 billion no matter how far back you go. There are also around 46,000 hotspots (reference Genetic Crossovers Are Predicted Accurately by the Computed Human Recombination Map, figure 6). Hotspots are the places where crossovers usually happen. Each of the 46,000 segments bounded by neighboring hotspots usually has a single line of descent, so you’re limited to about 46,000 ancestors.

“But I’m interested in something that happens much sooner than that: after about eight generations back, the number of genetic ancestors only increases linearly with the number of generations, while the number of genealogical ancestors keeps increasing exponentially. Once you go back 20 generations, you have only 1300 or so genetic ancestors despite having over a million genealogical ancestors.”

He also writes:

“One practical upshot of this is that those ancestors you do inherit something from, you inherit a lot from. And large stretches of DNA are passed down from generation to generation, those stretches usually aren’t finely divided.”

The article includes tables showing the “crossovers.” You can read Bob Jenkins’ article in his personal web site at: http://burtleburtle.net/bob/future/ancestors.html.

11 Comments

Legacy Tree Genealogists December 30, 2014 at 11:53 pm

Wow those charts are amazing!

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Although the concept is generally correct, Bob included some incorrect statements. He states there is a recombination for each chromosome every generation. In fact some of the smaller chromosomes are usually passed in tact (without recombination) in each generation. On average, a recombination event occurs about every 100 cM, so larger chromosomes get more crossovers than smaller ones. The crossovers tend to be near hot spots, so the distribution is not completely random.

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Looking at those charts makes my head hurt.
Quoted from Ancestry:
In general we think of a generation being about 25 years – from the birth of a parent to the birth of a child. We also generally accept that the length of a generation in earlier periods of history was closer to 20 years when humans mated younger and life expectancies were shorter.

SO, 100 generations ago would be, for simplicity, 2,000 years [ plus a bit ]. The charts ignore the pinchoff in genealogical ancestors. I don’t believe that 2,000 years ago there were a nonillion [1,000,000,000,000,000,000,000,000,000,000] people alive on the planet. The current population is only around 8 billion [8,000,000,000] today. Kind of makes me a bit skeptical of his article.

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    Billie, maybe because your head was hurting, I don’t think you grasped the difference between genealogical and genetic ancestors. Genealogically, 100 generations ago you would have had a nonillion positions on your pedigree chart, but because the same individual will occur many times in many positions on that chart, the number of actual ancestors will be much less than a nonillion. Then if you try to factor in all the various ways that genetic material is passed along to succeeding generations and how much of it is actually passed along, you end up with far fewer genetic ancestors than genealogical ones.

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I guess this is an interesting exercise when thinking about the concepts of genealogical and genetic ancestors. But, in my opinion, it leaves out the biggest factor that effects a person when considering the issue. And that is the geographical, and political, areas of dispersal or isolation around the world. America is a bubbling pot that is mixing pedigrees from all around the world, and will continue to do so for quite awhile into the future. While, a given native population in the Congo, or in Scandinavia, etc, etc, will be marrying today partners with whom they share hundreds, if not thousands of years of inbreeding. The difference between the number of genetic and genealogical ancestors for each of these groups of “isolated” people will be different than a country with a host of recent immigrants, like the US, maybe some Latin American populations, or even Australia.

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In this case, I wonder how the “rules” get adjusted.

http://www.iflscience.com/health-and-medicine/meet-girl-dna-three-parents

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Unfortunately the superscript was dropped in the first sentence. The formula is “2 raised to the nth power” or 2, 2×2, 2x2x2, 2x2x2x2, and so on.

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mathematical correction:
He says “The number of genealogical ancestors you have n generations is 2n: 2 parents, 4 grandparents, 8 great-grandparents, and so forth.

It is 2 to the nth power not 2n!!

If n=3 2n would be only 6 ancestors
2 to nth power is 8 ancestors!!!!

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It was commented above, “We also generally accept that the length of a generation in earlier periods of history was closer to 20 years when humans mated younger and life expectancies were shorter.” But if in those days a woman had 10 kids, then on average you would be the 5th kid so the average (not the minimal) generation would be 20 + (5 x 1.5) = 28 (1.5 being my estimate for a woman having a child a year but one dying every so often). I have never heard of this being taken into consideration before; am I daft?

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    I ignore the “length of a generation” nonsense. Like any other statistical average, it is generally worthless and without meaning. A woman may have 0 to 16 children (I have a great grandmother had 16 children all of whom lived to adulthood) and a man may have more than one wife. Meanwhile, a healthy man or woman who managed to escape death by epidemic, war, childbirth, accident, etc. might easily live well into his/her 90’s and have children over a period of 30-35 years. So using a “life expectancy” average to estimate the length of a generation means using one statistical average that tells you little to calculate another average and the end result is useless..

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Length of time between generations? Any rule for estimating these things was recently put to the test in my family. A cousin died at the age of 102. In her family, she was the youngest child, b. in 1912. Her brother, b. in 1898, died as a toddler in 1900. My cousin had a brother who died 114 years before she did.

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