Submitted by vesuvisian t3_zwg75b in askscience
lookmeat t1_j1vds4s wrote
In theory it's around the area that the generation side spreads to larger than the population, in practice this won't matter much since the size of disconnected populations that su but reach a branch is tiny compared to the greater world, unless you happen to be a member of that specific branch. The other factor is that incest probably covers a good chunk of that tree, which child reduce how quickly your tree widens (that is there could be multiple people in your tree that only have two grandparents) so technically our generation exponentiation is not 2, but some slightly smaller number (the average). It probably is very close to 2 though, so it should be a good enough estimate. Another factor that we're not considering is that not everyone reproduced, and that we really want the population that reproduced, but that's hard to measure and the number is probably pretty close to the total population.
So you find the average gap between generations, lets say 17 years (consider that for the greatest amount of time people got married at 13 and it was common to have had most of your children before 20). So it's mapping the population in year *x* vs *((YOB-x)/17)^2* where *YOB* is the year you where born. The
x` is almost certainly with an error of 10 years, though it could easily be a century before you even hit the millennia. I am sure you won't go to BCE, and I'd be surprised if the year was any time before 500CE.
A more interesting question is: assuming modern family conventions, and generally full population mix, how long would it take until someone is probably a descendants of everyone that reproduced?
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