4 Months: It's All Relative

Mathematically, you're inbred, and not as far back as you think.

Take me, Mary, and August for example; and all other European-descended white folk in America and elsewhere.

The population of all of Europe around the year 1350 is estimated to have been around 70-100 million. Estimates of the population lost to the famines and plagues of the mid 14th century run from 25 million to as high as 50 million, most say a third to more than half the population. Almost every estimate has the population dropping to around 50-70 million or less by around 1400.

1350 A.D. was 350 years ago. If a generation takes about 25 years on average, then we are separated from our post-plague European ancestors by roughly 26 generations.

The math is that you have 2^[generations] ancestors (2 parents, 4 grandparents, 8 great grandparents, etc.).

Only, you can't.

2^26 is more than 67 million people. That's probably more ancestors than there were people in Europe at the time, or getting close to it. And if you take into account the fact that not everyone reproduced, and that those who did sometimes had their entire line disappear, and the effect of standard deviation in family size, then you know the true number of Europeans who could have had a part in your family tree had to be something much less than say 40%, or 30%, or maybe even much lower (10%!? lower!?!?) of the population at the time. So if you're white, you know you're inbred at least as recently as 24-26 generations ago. Probably much more recently as well, all the way down your line.

I thought some similar math might be in play for slave-descended African Americans. If you assume you have a similarly homogenized group that starts with a small pool, and work your way back, might we find the mathematical evidence of much interbreeding?

The answer is no. The numbers only get dramatic when you go back a certain distance. My 67 million number doubles to 134 million if you go back just another 25 years from 1350 to 1325, and that's more than the peak population estimate for the middle ages. But even if you say that black Americans' ancestors were mostly already here by 1700 (and they weren't, the slave trade continued for a long time afterwards) there was only time for about 12 generations between then and now. Twelve generations back, one has about 4,000 ancestors... that's a tiny number compared to the numbers of people in that population at that time. Even if you really get aggressive with the "levers" of our little equation, and tweak the length of a generation to 20 years, you still have fewer than 33,000 ancestors between now and the beginning of the 18th century.

But in the long run the same principal applies to all people, no matter where your ancestors were. For our species to work, mathematically, there must be many "multi-purposed" ancestors in your line. You've only got 25 or 26 generations before it gets unreasonable to assume that you aren't inbred! That's only 500 to 650 years, max.