We received an interesting email from Bailey Edsall-Parr,
an anthropology student, customer and
genealogy enthusiast from Michigan. We present it here as a guest blog post.
I am currently researching the inter-relatedness of most, if not all, humans alive today. Anyways, I have a personal interest in genetics, mathematics, statistics and probability theory and have incorporated it into my studies. Any information if my theory is in any way "valid" is what I am seeking. Before I elaborate my theory, here is some background information: According to the Law of Truly Large Numbers... "that with a sample size large enough, any outrageous thing is likely to happen. In a sample of 1000 independent trials, the probability that the event does not happen in any of them is
or 36.8%. The probability that the event happens at least once in 1000 trials is then 1 − 0.368 = 0.632 or 63.2%. The probability that it happens at least once in 10,000 trials is .
This means that this 'unlikely event' has a probability of 63.2% of happening if 1000 chances are given, or over 99.9% for 10,000 chances. In other words, a highly unlikely event, given enough tries, is even more unlikely to not occur.
That was the Law of Truly Large Numbers. What I have below is from a computer scientist:
If there were random intermixing, then we would each have ~1 million ancestors living in 1500 AD, out of a world population of ~500 million. So the fractional overlap between two people would be about 1/500th.
But the probability that two people share at least one common ancestor would be essentially 100%. Basically, you are choosing a random number between 1 and 500 a million times and you're asking whether you ever choose number 500. In a million trials, we expect this to happen 2000 times. So that it happens at least once is guaranteed.
If we get rid of the random intermixing, the fractional overlap will drop to much less than 1/500th. But I suspect that the probability of at least one overlap will remain very high.
Calculations and Premises
If the population in 1500 was 500 million, and it is 6 billion today (12x larger).
If the average generation length is 30 years, there are 17 generations in 500 years.
So the average number of surviving children per mother is exp((log 12)/17) = 1.157
Since a child has two parents, the average number of surviving children per person is 2 * 1.157 = 2.315
So this is the average growth rate per generation for the descendants of a person in 1500.
2.315^17 = 1.575 million. So an average person in 1500 has about 1.5 million offspring alive today. Sampling from the whole world, the probability that a random person from 1500 is an ancestor of a random person in 2000 would be 1.5 million / 6 billion = 0.025%. If you were only considering people in a region like Europe, it would probably be something like 1.4 million / 700 million = 0.2%.
Would this theory likely be true given enough time?
Comment? Contact the author at baileyedsallparr (a) yahoo.com.