# What proportion of the people who lived 1000 years ago have genetic descendants alive today?

For context, I've been wondering about this for a paper I'm writing (in philosophy). Really, I want to figure out the chances that someone alive today will end up still having descendants 1000 years in the future. But people from 1000 years ago should be a good approximation.

This is not a full answer, but I post it as one because the reasoning is too long to post it as a comment.

You can make a rough estimation using a few assumptions.

1) Let's say 1 generation = 25 years, so 1000 years are 40 generations.

2) Let's say that half of the population is able to leave offspring, so the probability of one individual having descendants = 0.5

3) Supposing that the average number of siblings is 3.

• The probability of not having descendants in the 2nd generation = 0.5

• The probability of not having descendants in the 3rd generation is 0.5*(1-0.5^3) = 0.4375

After the 3rd generation, it becomes a combinatorial problem that is too hard for me. I can tell that the probability of not having offsprings, giving that it already has, is going to 0 because of the number of offspring > 2

If this approach appears useful, I suggest you ask for a more complete solution on https://math.stackexchange.com/

• Thanks, this is great! – HW. May 23 '19 at 17:53