Some people eat, sleep and chew gum, I do genealogy and write...

Sunday, October 29, 2017

Pedigree Collapse, Binary Progression, and DNA: Part One

If you recognize this image, you will realize that it constitutes a theoretical limit of time and a physical limitation of possibility. If we considered this chart to represent your possible ancestors, we can see that by the time we go back 12 generations we have the potential of 4096 grandparents. By going back 24 generations, we accumulate 16,777,216 grandparents. Estimates of the total number of people that have lived on the earth run around 108 billion. That number is exceeded by the 27th generation.

A generation, according to the International Society of Genetic Genealogy Wiki, in an article by Donn Devine, CG, FNGS entitled, "How long is a generation? Science provides an answer" the common estimates used by genealogists are questioned. Quoting different studies, the answer to the question about the length of a generation is about 33 years for male lines and about 29 years for female lines. However, depending on the study, the numbers range from 31 years for male lines to 38 years and from about 25 years to 29 years. The intervals were calculated on the average age of the mothers from the birth of their first child to the age at last birth.

Given these figures and using the 25-year interval, as the article observes, 20 generations in the past would put an ancestor in about the year 1500 at the outer limits of genealogically useful records in European countries and most of the rest of the world. Nonetheless, you would still have a potential of 1,048,576 direct line ancestors at that point in time. Personally, I do not know anyone who has approached a documented 20 generation pedigree of more than one or two lines at the most. So for all practical purposes, there is no real way to determine who we are related to back even 20 generations and from my own experience, any pedigree going back more than 20 generations is highly suspect.

I would also suspect that these same limits apply to the accuracy of DNA testing results because of the absolute certainty of pedigree collapse, i.e. where people sharing a common ancestor produce offspring. For example, because of the new family tree technology, it is fairly certain that I am related to both my wife's father and her mother, although many generations in the past.

Now, if you try to think this through, you will begin to see that DNA testing has some interesting limits. We know that the actual world population in the past is no longer even realistically represented by the required number of direct line ancestors and ultimately, as is reported by a number of researchers, we are all descended from a couple of proto-ancestors. Here is a summary of the issue from the Wikipedia article on "Human evolutionary genetics."
By estimating the rate at which mutations occur in mtDNA, the age of the common ancestral mtDNA type can be estimated: "the common ancestral mtDNA (type a) links mtDNA types that have diverged by an average of nearly 0.57%. Assuming a rate of 2%-4% per million years, this implies that the common ancestor of all surviving mtDNA types existed 140,000-290,000 years ago."[26] 
Most, but not all (see fr. Multiregional origin of modern humans), scientists in the relevant fields consider this observation robust. This common direct ancestor in the line of mother to daughter (or mitochondrial most recent common ancestor (mtMRCA)) of all extant humans has become known as Mitochondrial Eve. (Mitochondria are inherited from the mother only.) The observation that the mtMRCA is the direct matrilineal ancestor of all living humans does not mean either that she was the first anatomically modern woman, nor that no other women lived concurrently with her, nor even excluding the existence of other women being ancestors of today's people. Other women would have lived at the same time and passed nuclear genes down to living humans, but their mitochondrial lineages were lost over time. This could be due to events such as producing only male children. [I left in the links for reference.]
By the way, dividing those estimates of years by 25 gives us 5,600 generations to 11,600 generations. What this implies is that over time genes are lost from the "gene pool." So, if we go back far enough, the geneticists agree that there is pedigree collapse to the point that we all share a common ancestor, but on the other hand just going back a mere 39 generations or about 975 years implies that we have over 549 billion direct line ancestors.

Stay tuned for futher discussion and observations.


  1. I must be missing something. You wrote that ". . .by the time we go back 12 generations we have the potential of 4096 grandparents." Why isn't that number 9188 which is the cumulative number of grandparents possible (assuming no cross-marriages)? The 4096 number is just the number of "new" grandparents added without regard for the number of grandparents preceding them. Wouldn't the total grandparents after n generations be the sum of 2^n+2^(n-1)?

    1. No, you aren't missing anything at all. The idea is even more complicate than that since there is no way to know how many descendants each of those ancestors had and how many had and how many of those descendants had children. The binary progression is merely a starting point.